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1. Steering Calibration 40 y 12 043x 80 932 y 10 918x 74 181 R 0 9963 30 R 0 9979 gt F 20 Steering Sensor 1 10 Steering Sensor 2 r Q Linear Steering a 4 2 0 2 10 Sensor 1 g 40 Linear Steering a Sensor 2 3 20 30 40 Steering Sensor Reading V Figure 4 5 Steering Sensor Calibration Figure 4 5 shows that voltage angle relationships are linear with R values of 0 9979 and 0 9963 respectively Therefore the equations for the best fit lines were deemed appropriate for the voltage angle conversion As discussed earlier the steer angles are computed for both steering sensors and their average reading is used for model fits As pointed out in 9 the zero angle voltage of the string potentiometers tends to drift with over time when the system is not in operation To account for this before each data collection session the vehicle was driven along a laser aligned guide rail and the steering sensor voltages were recorded This was then repeated with the vehicle heading the opposite direction The non zero angles calculated from the steering sensor voltage conversion for this straight line data were then subtracted from the angle readings for all data sets recorded during that session This simple calibration routine improves the consistency of the system by eliminating any constant angle offset that may occur 43 4 1 4 Data Acquisition System The DL4plus comes with
2. s Figure 6 12 Lateral Velocity Lag Model and Bicycle Model Comparison Chirp Once again the most drastic improvement is at the higher frequencies of the yawrate data Both frequency and amplitude has improved by the addition of tire lag The phase 89 matched has been improved for lateral velocity however the higher frequency amplitudes are still incorrect as expected from the frequency response plots 6 3 3 Steady State Circles Perhaps the most interesting results come in the steady state circle comparison as shown in Figures 6 13 and 6 14 Yaw Rate Model Comparison Circle Using DC Gains 25 20 M T vi Ling gt A ay 4 Alf a i l OF WF SANA Aa RRI The g 15 Vint gi i R amp gt 10F Measurement Bicycle Model with Tire Lag Bicycle Model no Tire Lag 5 I I I L L L L 5 10 15 20 25 30 35 40 time s Figure 6 13 Yawrate Lag Model and Bicycle Model Comparison SS Circle 90 Lateral Velocity Prediction and Measurement Circle Using DC Gains f al Ay 0 3 Fa Ne Ns ea ad LW WA wh Waal OY 4 wave Pa ve J v YS y n 0 25 AAN a a WH E gt i gt 027 j 4 O xe gt 5 0 157 4 o t ml 0 1 4 0 05 Measurement 4 Bicycle Model with Tire Lag Bicycle Model no Tire Lag 0 I I I L L L 5 10 15 20 25 30 35 40 time s Figure 6 14 Lateral Velocity Lag Model and Bicyc
3. namely the automotive industry and the ability to use a GPS system as a sensor to measure vehicle states One must note that upon inception the Global Positioning System was designed as a two tiered system in which military capability was far superior to commercial and civilian ability The DoD strictly regulated the accuracy of non military users though Selective Availability SA Today the differences between these two sectors have decreased tremendously as the commercial and civilian sector have researched ways around SA to improve accuracy without military grade equipment 2 2 GPS Functionality With the three segments outlined the system can be explained in a straight forward manner First the simple or ideal case can be described to demonstrate how a satellite s position in orbit can translate into precise position on the earth s surface After the ideal case is explained more technical content will be presented 10 2 2 1 Ideal Description Each satellite transmits its own specific binary code which is modulated on a carrier frequency Although the code may appear to be noise it is actually unique to each satellite and completely predicable given the right algorithm Because of this noise like appearance the code is referred to as Pseudo Random Noise PRN Each receiver on earth has the ability to regenerate the carrier frequencies as well as the PRN codes for each satellite When the receiver locks onto a satellite it c
4. Introduction to GPS and INS History Background and Basic Functions This chapter will introduce the fundamentals of two major components of the vehicle sensing system the Global Positioning System GPS and the Inertial Navigation System INS Although it is not necessary to know all theoretical details of these systems in order to understand the use of GPS in passenger vehicle applications a conceptual understanding is necessary for proper implementation and troubleshooting This chapter provides an essential foundation for using these sensors in a vehicle dynamic study 2 1 GPS Background The Global Positioning System is a Department of Defense operated radio based navigation system consisting of 24 satellites orbiting approximately 11 000 miles above the surface of the earth The GPS of today has evolved from early radio navigation systems such as MIT s LORAN Long Range Area Navigation system of the 1940 s 1 Initially developed for military use the system was declared available to civilian use in 1983 and by 1984 the commercial GPS market began to take off though its use in surveying The Global Positioning System can best be described in three main segments Space Segment Control Segment and User Segment Below is a description of each followed by a description of their integration together 2 1 1 Space Segment The space segment consists of a constellation of 24 NAVSTAR NAVigation Satellite Timing and Ranging Satellit
5. KE ue Fe SP ty Fie Fy p U r Figure 9 6 Quarter Car Model Free Body Diagram Using Newtonian mechanics the equations of motion of the quarter car can be written The spring and damper forces are F k z U g A 9 21 F c Zs U Summing forces on the chassis in the vertical direction k z U Z0 Ur m Zs 9 22 Taking the Laplace transform of equation 9 22 k z s k U s s c z s s c U s s m z s 9 23 Equation 9 23 can be rearranged to solve for the transfer function relating the vertical displacement of the sprung mass to the road disturbance Z 5 _ c S k U s m s s k 9 24 130 Equation 9 24 can be combined with the results of the Kinematic model to relate the pitch angle to the rear road disturbance for the Identical Suspension model 0 s eS s Z 8 2 i n S cS k U s Z s U 8 a b ns ms n m s c 5 k 2 2 n c S 2 nyk s 9 25 a b Cum s ne nm s nk n c nym s nc nyk s nk Again a comparison between models can be made by looking at the frequency response of each system For a vehicle traveling at 25 mph the frequency response is as follows Pitch Model Frequency Response Pitch Angle Rear Disturbance Input 0 1 1 OF 4 g 5 20 pe J gt 40 L a 60 j 1 fp pe eid 1 1 E EE ee A 1 1 i 4 i 10 10 10 10 w rad s 30
6. the front and rear suspensions is in disagreement with this model The simulation of the Identical Suspension Model was similar to that of the Kinematic model The same road input was used in the Kinematic model was used here The 143 Simulink diagram for the generation of the pitch measurement is presented in Figure 9 19 FrontDisturbance cf s kf Zsf Zsr road_input mef s2 cf s kf Suspension cf s kf mef s2 cf s kf Transport Suspension Delay RearDisturbance Figure 9 19 Identical Suspension Model Simulink Diagram Pitch Generation Theta Generation from Road Disturbance RoadInputSim With the suspension blocks in place the simulations performed for the Kinematic Model were repeated Figure 9 20 shows a portion of the simulated vehicle pitch angles Pitch Angle Pitch Angle deg oO L L L 1 L ii ii 60 70 80 90 100 110 120 130 distance m Figure 9 20 Identical Suspension Model Generated Pitch 144 The previous plot shows that the vehicle s pitch angle for a given road profile will vary with speed As the vehicle speed increases the frequency of the input disturbance signal also increases Since the suspension acts as a low pass filter the high frequencies of the road disturbance are filtered out which results in changes in the vehicle s pitch angle In Chapter 8 a low pass spatial filter was applied to the raw p
7. NA 2 5 Rearranging equation 2 5 allows for direct comparison to the Code Pseudorange equation presented earlier R P C NA 2 6 Comparing equation 2 6 to equation 2 3 shows that the Carrier Phase measurement differs from the Code Pseudorange measurement by only an integer number of wavelengths Hofmann Wellenhof 2 points out that the phase of a carrier can be measured to 1 0 01 cycles of its wavelength which corresponds to millimeter precision assuming no other errors are introduced 2 2 2 3 Single and Dual Frequency Receivers The military grade dual frequency receivers have several advantages over the single frequency receivers Their access to the coded messages on the L1 and L2 frequencies give them superior accuracy for various reasons two of which are presented here As discussed above a receiver can calculate its position using Code Pseudoranging or both Code Pseudoranging and Carrier Phase positioning If only C A code is available for a given receiver it may only use the above techniques on the messages transmitted on the L1 frequency However if a receiver has access to both C A and P Y Code it may perform these calculations on both frequencies By having access to the P Y Code on the L2 frequency a receiver can directly remove the code from the L2 frequency and use 17 the underlying Doppler shifted carrier frequency for Carrier Phase positioning Without knowledge of the P Y code one has to use c
8. ac mM b c m n J mM A 56 E J m n A 57 And the F coefficients are F 2ak k n 2bk k n A 58 F 2ac k n 2bc k n 2ac k n 2be k n ak m n bk m n A 59 F 2ac c n 2be c n ak mn bk m n ac m n be m n A 60 F ak m n bk m n ac m n be m n A 61 F ac m n bc m n A 62 When a pole is added to A 50 at p each E coefficient is scaled by p and the denominator is multiplied by s p The resulting equation is of the form U s Pi E s Es Es Es E s Est E O s Fsi Fos Fs ES Fs Fs Where the coefficients are the same as before and the F coefficients are F 2ak k n p 2bk k n p F 2ak k n 2bk k n 2ac k np 2bc k np 2ac k n p 2bc k n p ak m n p bk m n p F 2ac k n 2be k pn 2ac k n 2bc k n ak m n bk m n 2ac c n p 2bc c n p ak m n p bk m n p ac m n p bc m N3P F 2ac c n 2be c n ak m n bk m n ac m n bc m n ak m n p bk m n p ac m n p bc m n p F ak m n bk m n ac m n bc m n ac m n p bc m n P F ac m n bc m n 173 A 63 A 64 A 65 A 66 A 67 A 68 A 69 Appendix B Detailed Interface DSP Operation This appendix gives a detailed example of the Interface DSP operation which was introduced in Section 4 1 4 1 1 This will show how a standard NovAtel data log is decoded processed and sent to the Mater DSP This is
9. users found ways around SA This eventually led to the cancellation of SA in 2000 and users gained access to the full accuracy of the C A message approximately 15 meters in the horizontal direction on a single receiver This system of receiving and processing free C A code on the L1 frequency is known as the Standard Positioning Service SPS The DoD and people authorized by the government can have access to the P code that is modulated on both carrier frequencies When necessary this code can be further encrypted to Y code for added security through a method called anti spoofing The code is much longer than the C A code at 2e14 bits 37 weeks long Each satellite transmits a different 7 day segment of code before the code is reset The pure length of this message makes it nearly impossible for unauthorized users to gain access Advanced dual frequency receivers use the C A code on startup to help track and match the longer P code When demodulated by the receiver the P code message gives accuracy to approximately 5 8 meters This is known as the Precision Positioning Service PPS 2 2 2 2 Calculating Position Each GPS receiver uses its own internal clock usually inexpensive quartz crystal oscillators to replicate the L band carrier frequencies as well as the available PRN codes It then uses bi phase modulation to combine the PRN codes with the carrier signal to generate reference signals for each satellite By aligning and comparin
10. 0 L N oO o me 0 5 F Ak 1 5 L L L L L i I 0 20 40 60 80 100 120 140 time s Figure 8 3 Road Grade Estimation Method Comparison It is obvious that the two methods give similar road grade estimates for the steady state turning maneuver shown above For an initial investigation into using road grade for positioning the low frequency pitch method was used instead of the velocity based method Since the pitch measurement is already computed in real time no extra computation is necessary The oscillation effects of acceleration pointed out by Bae are eliminated from the pitch method by assuming constant longitudinal velocity The IMU mounting offset error is accounted for by utilizing the calibration routine as described previously Utilizing the pitch method above also allows for a GPS free positioning system which can use commercial grade sensors to 105 measure pitch angle If necessary a more accurate solution may be obtained by applying a Kalman filter to blend the two estimation methods This however will not be done here It should also be noted that the disturbances in other states such as roll sideslip and yaw rate can also be analyzed However these states are more dependent on vehicle parameters and road conditions which would make identifying disturbances in these measurements difficult Therefore only the pitch plane disturbances will be considered in this work 8 3 Road Grade Repeatability and Lo
11. 2 m F F 3 18 a F_ b 3 19 In the standard bicycle model derivation the lateral force generated by the tires was assumed to be proportional to each tires cornering stiffness Therefore equations 3 18 and 3 19 can be rearranged and combined with equation 3 2 2 pa ea L R a m 3 20 Paip Cuk b L R Where the cornering stiffness vales are negative quantities To simplify recognize that the weight on the front and rear axle can be written more L 3 21 W BA L Equation 3 20 can then be re written in terms of vehicle axle weights and solved for the front and rear slip angles W U ans oR 3 22 a UF 29 Combining 3 22 with 3 15 gives stal eames 3 23 1 R eR Co Cy ar Again the cornering stiffness values are negative quantities Equation 3 23 is used extensively in literature for its ability to correlate parameters which are easy to measure steer angle velocity turn radius vehicle length and axle weights to quantities which are difficult to measure front and rear cornering stiffnesses From equation 3 23 the understeer gradient K s is defined Ww W K g 3 24 C Cy Once again it must be noted that the cornering stiffness values used in equation 3 24 are negative values The understeer gradient derived in this section is important in characterizing the steering characteristics of a vehicle A vehicle with a positive understeer gradient will be
12. 5 1 Pepe H A p 2 OF Parc S t Pa R 5 4 7 Increasing Lag 0 L L n ni L L L L 1 10 10 w rad s 0 E po th g 50 2c J a iB Q 4 me a 100 a Bicycle Model Lag k Bicycle Model No Lag ik E L ni n L 10 10 w rad s Figure 6 10 Lateral Velocity Lag Model and Bicycle Model Comparison Freq Resp The Lag Model is considerably more accurate in the frequency domain than the standard bicycle model This is especially true at high frequencies most notably in the phase plots By modeling the tire force generation as an exponential rise to the steady state value the models accuracy has greatly improved 6 3 2 Chirp Response Figures 6 11 and 6 12 show the comparison in the time domain for the chirp response 88 Yaw Rate deg s 20 6 Yaw Rate Prediction and Measurement Chirp Using DC Gains Measurement Bicycle Model with Tire Lag Bicycle Model no Tire Lag I I I I I 8 10 12 14 16 time s Figure 6 11 Yawrate Lag Model and Bicycle Model Comparison Chirp Lateral Velocity m s Lateral Velocity Prediction and Measurement Chirp Using DC Gains 3 0 2 0 1 F 02L 0 34 0 4 6 Measurement Bicycle Model with Tire Lag Bicycle Model no Tire Lag A if I if if 8 10 12 14 16 time
13. F cos a F b F a F b dt l Referring back to chapter 3 equation 3 11 can be combined with equation 6 1 79 dt m m d b 6 2 Ol 2 ale ge dt TA i The lateral tire forces Ff and F must be modeled differently in this derivation to incorporate tire lag The force generated by the tire can be modeled as a first order differential equation increase to its steady state value Therefore the force as a function of time can be written as Ut F t F l e ae Where Fss is the force the tire will generate at steady state and is the tire s relaxation length Karnopp 6 describes the differential equation relating the force generated by the tires F and the steady state force Fss based on the time behavior in equation 6 3 as o dF fai pe 6 4 acai Also the steady state force Fss has been described previously as V a r Fis Cap pss Cu U 5 6 5 Fis C SS C SF pss s U Combining equations 6 4 with 6 5 and rearranging for the time rate of change of the force generated 6 6 80 Where the front and rear tire relaxation lengths have been assumed to be the same and there is no rear steering input Equation 6 6 can be further rearranged dF C C C U Z eraf E r a A g dt o o oO oO dF S v Set L r dt o o o The model can be written in state space representation with the states being lateral 6 7 velocity yaw rate and the forces gen
14. Figure 8 10 Single Lane Experiment To increase the spatial resolution for this experiment the pitch and velocity samples are taken at a 100Hz rate An estimate of the path distance covered by the vehicle is 114 calculated by integrating the velocity measurements with respect to time The most accurate highest resolution map is desired for the template generation and this can be obtained by driving the target lane at very low velocities For this experiment the map was generated at the near idle speed of Smph Several samples were then collected to investigate the effect of velocity on the positioning routine To do this the vehicle was driven over the same path at various speeds ranging from 5 65 mph while the vehicle states were recorded The unfiltered pitch measurements recorded at various speeds have been aligned and plotted for comparison in Figure 8 11 Measured Pitch Angle Unfiltered 0 5 5 mph 0 4 40 mph 65 mph 0 3 0 21 Pitch Angle deg oO 0 1 L iE Yi AM WN Big 0 2L 0 4 i 20 40 60 80 100 120 140 160 180 Distance m Figure 8 11 Road Grade Velocity Dependence Figure 8 11 shows the measured pitch angle varies with speed As the vehicle s speed increases the frequency at which the position dependent road disturbances will occur increases Since the suspension acts as a low pass filter the vehicle s pitch measurements are filtered at hi
15. This is a built in capability of Wincon which allows the users to monitor and record data in real time from outside the vehicle or anywhere internet is available In the future this allows controller gains and other system inputs to be modified remotely An unfortunate downfall of the Wincon package is its inability to transmit variables of type double This issue with the software prevents the user from monitoring latitude and longitude data collected from the GPS In order to collect and save this data it is transmitted as 4 16 bit sections and reassembled in post processing Since this data is almost always transformed into local planar coordinates during post processing the DSP has been programmed to directly do this transformation in Real Time This eliminates the need to transfer data of double precision as the local X Y data is calculated in meters can be captured with a float precision variable This code however has not been tested at this time 4 2 System Setup Pictures 10 49 Modem Antenna GPS Antenna NovAtel SPAN Technology System Characteristics and Performance 2005 Alberta Canada NovAtel NovAtel DL 4plus Specification Sheet version 2 0 2004 Alberta Canada Honeywell HG1700 AG17 Datasheet 2005 Minneapolis MN Ford T et al OEM4 Inertial A Tightly Integrated Decentralised Inertial GPS Navigation System in Proceedings of ION GPS 01 2001 Salt Lake City Utah The Institute of Navi
16. a 0 02 L fi L f o 2 4 6 8 Time s 80 mph 0 06 m m r 7 l S li j f 4 V i j N iif NY f A X AY WA N Le it g Ye lj iA Wy WE OL yy A Aa y S 20a S j Y W sit Wow 1 w N vig 5 ol j D Q 0 02 l 0 1 2 3 4 5 Time s Figure 9 15 Kinematic Model Disturbance Plots As expected since there is no suspension the road disturbances in the front and rear are identical to the vertical displacement of the sprung mass at the front and rear Figure 9 16 is the plot of the resulting pitch angles as a function of distance traveled where the distance traveled was approximated by integrating the vehicle longitudinal velocity as a function of time 141 Pitch Angle al 5 45 0 8 g0 0 6 E hy fl P o il o S Th ly g 0 24 Al l F ioa Faa UA AH MA at MIL Wan O gel EE f oe ly A ET Aa Ly PHY j I W y C 0 2 n l y y 0 4 L Vo _ 0 6 0 20 40 60 80 1 00 1 20 140 1 60 1 80 200 Distance m Figure 9 16 Kinematic Model Generated Pitch Figure 9 16 shows that the suspension less vehicle will have the same pitch measurements as a function of distance regardless of forward velocity As a proof of concept the inverted kinematic model given in equation 9 25 was simulated to ensure it correctly extracted the known rear input disturbance U The coefficients of the Pad
17. ab C a m U y y l 5 16 CyCa a 2ab m U C a C b f SteadyState The same procedure follows for yawrate 65 c 0 1 5 17 D 0 U C C b a G 1 5 18 CC b a 2ab m U C a C b 5 f SteadyState The lateral velocity and yawrate DC gain equations represent two equations with four unknowns G G Car and Car However by forcing the DC gains to be equal to the measured DC gains the system of equations becomes solvable with only two equations and two unknowns 5 3 2 Alternate DC Gain Derivation Since the DC gain derived above is simply the ratio of lateral velocity or yawrate to steering input at steady state its validity was checked by computing this exact ratio from the bicycle model equations directly The derivation is as follows The steady state steering angle for a vehicle in a turn was shown in equations 3 15 and 3 20 to be L 1 b mU 1 f a mU R CE Re R For a large radius turn the steady state yawrate can be expressed as U fa 5 20 R Therefore the yawrate DC gain should be the ratio of these two steady state equations G o L 1 b mU n 1 a mU 5 21 R C L R C L R 66 A similar expression can be derived for lateral velocity This is most easily done by looking at the sideslip angle As described in equation 5 6 the sideslip angle seen in a steady state turn can be written p 2 a 5 22 R r e By definition this is the angle betwee
18. approximation n n2 and n3 were calculated for each vehicle speed The inversion block diagram is shown in Figure 9 17 Theta E gt gt EE Ur_Extracted den s Inversion Rear Road Disturbance Extraction from Theta Figure 9 17 Kinematic Model Simulink Diagram U Recovery 142 The U values recovered from the inversion are plotted with the original rear input disturbances in Figure 9 18 Input Disturbance and Recovered Ur 0 06 Orignal Rear Input Recovered 5 mph 0 05 Ff A Recovered 45 mph i Recovered 80 mph rar A i l d 0 04 Disturbance m oO wo I Ly Vy oe 0 02 h 0 01 0 20 40 60 80 100 120 140 160 180 Distance m Figure 9 18 Kinematic Model Original Rear Input and Recovered U Figure 9 18 clearly shows the success of the inversion process however this simple kinematic inversion does not represent the true behavior of the vehicle 9 6 2 Model 2 Identical Suspension Model In the second model the suspensions have been included however identical suspension parameters have been assumed for the front and rear As discussed at the end of section 9 5 2 this seems to be a reasonable initial approximation for the suspension current test vehicle However it must be noted that the test vehicle s uneven mass distribution over
19. s a 5 Once again utilizing the expressions in equations 9 12 and 9 13 U s P H H 0 s a b A 13 A 14 A 15 166 Substituting equations A 13 and 9 11 into equation equation A 15 a b 0 s a n N oe OPPE A16 U s ns n stn mys tce stk mS 8 k As with the previous models the frequency response of this transfer function can be viewed for a direct comparison Pitch Model Frequency Response Pitch Angle Rear Disturbance Input 20 Mag dB 60 1 r r a 1 po os srar f en ee oe 1 2 w rad s 300 i 20 Kinematic Model l Identical Suspension Model 200 Different Suspension Model i g 150 J Phase deg 100 7 B cenone N J 50 1 L L a re 1 1 1 E S er oe 1 1 1 TEF S ee 10 10 10 i w rad s Figure A 3 Different Suspension Model Frequency Response As expected the Different Suspension Model exhibits the same low frequency behavior as the previous two models This model only changes slightly in phase and magnitude at high frequencies This is expected since the front and rear suspension parameters of the vehicle are similar As a check it necessary to confirm that the Different Susepension Model reduces to the Identical Suspension Model when the suspension paramters are the same This can be easily confirmed by looking at the frequency response 167 Pitch Model Frequency Respons
20. 17 2 17 15 17 1 17 05 17 X m X m Figure 8 8 Position Match Sample 3 The path error for each Template Sample pair for the third sample is presented in the error histogram below Error Histogram for Sample 3 12 T T T T T T T Number of Samples 1 L L 0 0 05 0 1 O15 02 0 2 03 035 0 4 045 05 Error m Figure 8 9 Error Histogram Sample 3 As reported in Table 8 1 the mean error for Sample 3 was calculated to be 9 cm with a standard deviation of 5 cm 113 It is interesting to note that Sample 1 had both the highest path error and the highest lane keeping error This shows that accuracy of this method of positioning is highly dependent on the vehicle s ability to keep the mapped path Although an improved method of error calculation is needed the results obtained with this elementary method were sufficient enough to prove the validity of the road grade positioning concept 8 5 Longitudinal Positioning The first step in implementing this road grade positioning routine in practice is to accurately position a vehicle driving in a straight line This would best represent a daily drive to work where drivers are often driving on long stretches of interstate at relatively constant velocities In order to emulate this scenario a stretch of the test track was sectioned off with cones to simulate a highway lane An image from the in vehicle video camera system is shown below
21. 25 30 35 40 time s Figure 6 7 Yawrate Steady State Circle Lag Model Lateral Velocity Prediction and Measurement Circle Using DC Gains T T T T T T 0 3 F h 4 o N T 1 Lateral Velocity m s oS a 1 o T 1 0 05 4 Measurement Predicted from Bicycle Model with Tire Lag I I if I L 5 10 15 20 25 30 35 40 time s Figure 6 8 Lateral Velocity Steady State Circle Lag Model 86 6 3 Tire Lag Model Results Discussion 6 3 1 Frequency Response Figures 6 9 and 6 10 show a direct comparison between the Bicycle Model and the Lag Model in the frequency domain As mentioned above both models use the DC gain method to determine front and rear cornering stiffness values The relaxation length which best fit the yawrate data was used for the simulation since lateral velocity is more strongly coupled to the un modeled roll dynamics Steering Angle to Yaw Rate 20 154 T O O e as a Pep iol 4e P a Rk 5F Increasing Lag 7 0 L 3 L ni 1 L L L L L L j 10 10 w rad s R 2 8 50L J 2 2 Eh oO E S a 100 Bicycle Model Lag SN 1 Bicycle Model No Lag Soe I T L ri 1 1 L L L it 10 10 w rad s Figure 6 9 Yawrate Lag Model and Bicycle Model Comparison Freq Resp 87 Steering Angle to Vlat 20 15 7
22. 43 p 31 57 Bae H S J Ryu and J C Gerdes Road Grade and Vehicle Parameter Estimation for Longitudinal Control Using GPS in Proceeings of IEEE Conference on Intelligent Transportation Systems 2001 Sharp R S Wheelbase filtering and Automobiel Suspension Tuning for Minimising Motions in Pitch Journal of Automobiel Engineering 2002 216 6 p 933 946 Chapter 9 Pitch Model Derivations and Implementation In chapter 8 the concept of using road grade measurements for longitudinal positioning was introduced The road grade was estimated by looking at the low frequency portion of the vehicle s pitch measurements These measurements however will be dependent on the vehicle suspension characteristics and the vehicle s velocity In order to extract the true road grade from the pitch measurements a vehicle model must be included If the model accurately represents the dynamics of the vehicle then the calculated road grade measurements should be independent of both the vehicle speed as well as the vehicle recording the pitch measurements In this chapter several pitch plane models are developed The models vary in complexity from a simple kinematic model to a full pitch plane dynamic model In order to test these models vehicle parameters such as the front and rear spring stiffnesses and damping coefficients must be estimated A method to perform this estimation is presented in this chapter The differences between these m
23. 7 3 and 7 4 gives an equivalent expression for the camber angle mh a 7 5 J 5 5 Gillespie 1 demonstrates that the lateral force generated by the tire with camber effects accounted for can be modeled as Fp Cyh Cyd F C a C a 7 6 wr Where Co will be referred to the camber coefficient and the camber angles for the front and rear wheels have been assumed to be different Combining and rearranging equations 7 2 7 5 and 7 6 to solve for the front and rear slip angles gives 95 o1 2m Cymh m Up f 1 Cyll R k R 7 7 1 a mU Cym h U Qr A C IL R k R Since the camber coefficient Ce sprung mass ms roll stiffness 4 CG to roll axis height A and camber transfer constant S are constant for both the front and rear equations these terms can be lumped into new constants and equation 7 7 can be rewritten C ijb mU aU L R f R with 7 8 Equations 7 8 can be combined with the steady state steering angle equation equation 3 15 to generate an expression for the steering input required to negotiate a turn at steady state in terms of cornering stiffnesses and the lumped constants which include the unknown camber transfer constants Lol f mU oo Zh l ome L L R I R C L R R 7 9 R Cy In its present form equation 7 9 has four parameters which are not easily measured the front and rear cornering stiffnesses Cor Car and the lumped
24. 8 L 1 1 L L 1 5 L 1 L fi fi f 0 50 100 150 200 250 300 0 50 100 150 200 250 300 35 Distance m Distance m Road Grade Correlation Sample 3 Road Grade Correlation Sample 4 1 r r r r r r r r 1 r r r r r Max Correlation 0 9893 Max Correlation 0 961 map data 0 5 0 54 4 OL i ro 0 D H va 0 5 Js o B A N i 5 S 3 os l a 5b 4 Ae 4 ak 4 2 5 L f L 1 f f 1 1 1 5 L f L f L 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 Distance m Distance m Road Grade Correlation Sample 5 2 T T T T T T Max Correlation 0 9889 k map 1 5 data H 1L 4 0 54 fc B v vie ke i 3 o NA t a A N hw moa Wy vale W7 aL 4 2 5 1 1 L 1 1 L 50 100 150 200 250 300 350 Distance m Figure 8 7 Road Grade Matches 112 The position match for the third sample is presented in Figure 8 8 35 Position Matching Position Matching Zoomed 0p o cl 80 N Pi Se 250 Peal E 90 SS gt As 200 100b 150 Fa 110 ra a t 160 140 E e a a 100 te E X m j PO a Position Matching Zoomed More he Sof e a a oe 80 3 0 i ei le K 2 o ae 80 4 fae ig abi 50l gerrneeeennnnnte a cae pi ow track data set gt 80 5 1 100 E u og actual Annakin a positioned track 80 6 150 L L L L 1 L f t f f L L fi L I 300 200 100 0 100 200 300 400 17 5 17 45 17 4 17 35 17 3 17 25
25. 800 115 200 Data Parity fe None 1 7 MODBus RTU fo 7 C 230 400 C Other 115200 Turn On Delay fo Turn Off Delay fo Figure C 11 Base Station Modem Baud Rate Settings 5 Under the Call Book tab enter the serial number of the ROVER s modem in the Entry To Call 0 field in the Number Tab This should be the only number listed 195 6 Click the Program Radio button 7 Press the black setup button on the back of the modem and wait for programming to complete C 50 3 2 Rover Station Modem The procedure for programming the Rover Station modem is nearly identical to that of the Base station with only two changes 1 Under the Set Operation Mode tab change the Modem Mode to Point to Point Slave 2 When programming the Call book you have to enter the serial number for the BASE STATION s modem NOTE If you are planning to use the radios short range or to bench test them you may want to lower the Transmit Power on the Transmission Characteristics tab to a number like 1 2 instead of 10 This will stop the radios from screaming at each other C 50 3 3 Modem Loop Testing There is a simple bench test you can do to determine if the radio communication has been successful This method was suggested by the FreeWave customer support With the radio transmission powers set to appropriate levels do the following 1 Connect the Base Station modem to the PC via the serial port 2 Start Hyper
26. City Utah Chapter 3 Two Degree of Freedom Model The planar dynamics of a vehicle is often represented in the form of single track 2 degree of freedom model known as the Bicycle Model This model has been used extensively throughout literature because of its ability to accurately model a vehicle s lateral velocity and yaw dynamics It is defined on a body fixed coordinate system which is centered at the vehicle center of gravity and which rotates and translates with the vehicle In this chapter the derivation of the bicycle model and an important handling characteristic the understeer gradient will be given 3 1 Bicycle Model Derivation Figure 3 1 shows the Bicycle Model layout and Table 3 1 describes the model parameters Note that the tire slip angles are shown to be negative in the figure Figure 3 1 Bicycle Model 23 Table 3 1 Bicycle Model Parameters Z o a Oo TCL ateral velocity O O Side slipangle _ o Frontsteeringangle Oo y Frontslipange _ The coordinate system definition is presented in Figure 3 2 z r direction L of positive yaw rate Figure 3 2 SAE Coordinate System Definition Several assumptions must be made when using the bicycle model formulation First the vehicle mass and tire forces are both assumed to be symmetric about the X Z plane Therefore the vehicle can be modeled as a single tracked vehicle where the two front and two rear wheels can be represen
27. L 1 L L L 1 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 Lateral Acceleration UIR g g s Figure 5 1 Understeer Gradient Calculation 30 5 m Circle Clockwise 53 Each of the best fit lines has the same slope 0 01605 regardless of the radius of the turning circle as expected This corresponds to the average understeer gradient It is important to note that the understeer gradient is no longer linear at accelerations above 0 3 0 4g s again in agreement with what others have noted in the past 3 The exact slopes of each of the data sets in the linear region are presented in the table below Table 5 2 Understeer Gradient Calculation Results Data Set Kus rad g CW 0 0125 CCW 0 0189 36 5mCircle cw 0 0113 cow 0 0215 Average 0 01605 Table Table 5 2 shows the vehicle understeer gradient value to be between 0 013 and 0 0215 rad g For simulation and model matching purposes the average of the four measured understeer gradients was used 0 01605 rad g Another important feature of Figure 5 1 is the non zero Y intercept of each of the best fit lines This steering angle which occurs at zero lateral acceleration during a steady state turn is defined as the Ackerman angle This angle is a function of vehicle length and the turn radius of the circle and is defined in 2 as O nck ack 5 5 by tS Table 5 2 summarizes the calculated and measured Ackerman Angles Table 5 3 Calculated and Best Fit Ackerman A
28. Log Reference OM 20000047 Rev 18 2005 Alberta Canada Ze Novatel SPAN Technology User Manual OM 20000062 Rev 7 2005 Alberta Canada Appendix C GPS INS Setup and Troubleshooting Guide This appendix will present a detailed outline for implementing the DGPS INS and data acquisition systems on a vehicle This is meant to be used by researchers who will follow up this work There are several minor problems with the system which will also be addressed and their temporary solution is given For completeness this guide will assume no prior knowledge of the system that has not been presented elsewhere in this thesis and therefore includes more steps than necessary It will be presented in two sections the first demonstrates what to do with the current state of the system and the second addresses some possible problems C 1 Current Setup Procedure The subsequent three sections describe the setup of the Base station Rover station and the Data Acquisition system It is possible to set up these systems simultaneously if the user chooses to do so The order presented here represents the easiest most logical way to start the system C 1 1 Base Station Setup All of the base station components have been packaged into a locked carrying case for convenience The Receiver s software settings have been saved into memory so no programming should be necessary at this state The modems are also properly programmed at this time so
29. Oy circle Equation 7 13 is particularly useful when it combined in a ratio with equation 7 10 U G a G circle R 7 14 Gen U R By using the expression for the rear slip angle derived in equation 7 8 equation 7 14 can be rewritten and simplified to G circle U HO aN ee og Ge 7 15 G circle Cy L Finally equation 7 15 can be solved for C in terms of measurable parameters C G circle C 5om cef 7 16 r circle 98 Below is a summary of the four equations used to solve for the four unknowns C C C C ar C a m U G on Greine B G ine a b m y sine b m U G ne C r sine C 7 18 a G80 at EEE a C 7 G circle Cage a 7 19 L U S 1 a b LG C m ales 7 20 i a U z Ca L Cy U C Where equations 7 17 and 7 18 are repeated from chapter 5 equations 5 30 and 5 2 respectively and equations 7 19 and 7 20 are repeats of equations 7 15 and 7 11 respectively 7 2 Camber Correction Simulation Results Since the relationship shown in equation 7 4 utilizes the centripetal force seen by a vehicle as it negotiates a steady state turn this derivation is only valid for steady state turns In order to incorporate all maneuvers a full roll model must be derived however such a model is not needed in this work and therefore will not be presented The impact of the roll steer derived above will therefore only be inv
30. Terminal Start Programs Accessories Communications Hyperterminal 3 Create a new connection name called FreeWave and press OK 4 Change the Connect Using pulldown to COM1 and press OK 5 Change the COM1 Properties to the following and press OK a Baud Rate 57600 b Data bits 8 c Partity None d Stop bits 1 e Flow control None 6 7 196 Plug the power into the Rover s radio and connect a serial cable to it as usual Instead of plugging the Slave into the computer short out Pins 2 and 3 on the other end of the serial cable using a jumper wire or a paper clip These are the transmit and receive lines On the PC which is connected to the Base Station start typing in the Hyperterminal program If what you type shows up on the screen the radios are successfully communicating with each other If nothing shows up go back and check your settings If what shows up is gibberish then your baud rates are mis matched C 50 4 Data Acquisition Troubleshooting The majority of the errors regarding the data acquisition system are usually solved by simply reviewing the connections Missing parallel serial or ethernet connections are the primary sources However there has been an instance where these were not the problems On occasion Wincon will display values of infinity for all of the variables being recorded 99 of the time this indicates a missing parallel port connection or a dead Master DSP battery It has been
31. U s art 4 54 A s A s A s A 0 s Bys B s A l Two poles must be added to this transfer function in order to make it causal Both poles will be added at p Therefore the numerator will be scaled by a factor of p and the denominator must be multiplied by s p The resulting transfer function is of the form A s A s 4 8 4 s A US _ apy 2A A 2 0 s B s B s B s B s Where the 4 coefficients are A n k A 3 A n c n k A 4 A nk NAC n m A 5 A nc n m A 6 A nym A 7 And the B coefficients are B 2 k n p B 4 k n p 2 c n p B 2 k n 4 c n p B 2 c n A 3 Model 3 Different Suspensions No Rotational Inertia 165 A 8 AID A 10 A 11 The next level of difficulty is the model which allows the front and rear suspensions and mass distributions to be different In this case the kinematics derived section 9 2 will no longer hold since it treats the rear sprung mass vertical displacement to be a delayed version of the front sprung mass vertical displacement This derivation starts from equation 9 3 Zy Zy 0 a b A 12 The front and rear sprung mass displacements can be written in terms of their respective road input disturbances as in equation 9 24 Z sr s gt k H s U s ms t e st k Z Ss c S k s6 _ ef _ 8 U s MS C S k Which gives U s H s U s H s 6
32. acting on the sprung mass the pitch measurements should not vary as vehicle speed increases To simulate this a signal was used as an example road profile which covered 200 meters with a spacing of 2 5 cm This signal was then added to a time delayed version of itself where the time delay was proportional to the vehicle speed By multiplying the resulting signal by a b a pitch angle measurement was generated for a vehicle with no suspension The block diagram for this can be seen in the figure below FrontDisturbance Zsf Z Uf Z E i 2 ZstZar Ur Ur Zsr Zsr qa Time Delay RoadInputSim Zsr Theta Generation from Road Disturbance Figure 9 14 Kinematic Model Simulink Diagram Pitch Generation The simulated pitch angle can be viewed at different speeds by adjusting the simulation time parameters step size and delay size Figure 9 15 is a plot of the simulated road disturbance and sprung mass displacements for speeds of 5 45 and 80 mph plotted against time 140 5 mph 0 06 g 0 04 ig Q POY nfl A PONI Ni vn ie ee 0 02 aN W A MA Nt f ear Disturbance Q W fo W v __Zef 5 OL a Zsr Q 0 02 l l l r 0 10 20 30 40 50 60 70 80 Time s 45 mph E a Ky hy Fetes PN f A AA 8 AY i f Ay P att J AN j PA D pa Py Ys a id 5 0 02 he nay tf i ann i f y Ly Sy sf hal xe w wyw i 5 ol D
33. advantages and disadvantages of using such a process have been discussed in great detail in 4 5 and will not be discussed here The two filters interact by sharing position and position covariance information The GPS filter assists the inertial filter by supplying it with GPS position measurements to be used to control the error growth in the inertial filter The inertial filter assists the GPS filter by supplying it with inertial position measurements to expedite satellite reacquisition times incase of signal interference or blockage This integration process allows the system to be much more accurate than either GPS or INS 35 alone Further details of the Kalman filtering process including the exact methodology of the propagation and update steps of the filter can be found in 5 4 1 1 2 Rover Station Calibration The Rover Station s GPS INS system required several calibration steps in order to achieve centimeter level accuracy The calibration procedure consists of three main steps which are described below The first step of calibration is performed automatically by the DL 4plus and IMU on startup When it is initially powered the IMU has no information regarding its mounting orientation Although the IMU is labeled with its own body coordinates X Y Z it does not assume that Z is always inline with the gravity vector In order to resolve its orientation a calibration known as frame detection takes place on system startup Th
34. algorithm on several new vehicles If each vehicle measures the same low frequency pitch measurements then it can be assumed that this method is sufficient to determine road grade This would be the ideal case and would make this positioning routine relatively simple to implement since no model inversion would be necessary 160 However it is the belief of the author that each vehicle will show considerably different low frequency pitch measurements In this case accurate models of each of the vehicles would be needed After each of the models were inverted a comparison between the extracted road grade estimates would be needed The model inversion method would be deemed appropriate if each of the vehicles extracted road grade estimates show higher correlation than the low frequency pitch measurements After the proper road grade estimation method is determined a routine for implementing this localization method must be written This must include a recursive real time correlation method which correlates past and current road grade estimations with those of a road grade map The structure of this algorithm would depend on whether this routine was being used to assist a commercial grade GPS system or to replace the GPS system Finally this routine must be tested and debugged In order to achieve additional accuracy in the positioning routine the terrain effects seen in the roll measurements may also be investigated The position obtain
35. at frequencies of 6 rad s and above the bicycle model is not able to accurately predict these states Also the frequency response phases contradict the data for both lateral velocity and yawrate for these frequencies This mismatch is partially the result of tire lag which will be introduced in chapter 6 5 5 Conclusions e The DC gain method should be used to determine front and rear cornering stiffness values e Lateral velocity is more strongly coupled to cornering stiffness values than is yawrate e Time domain yawrate plots are ill suited to show the effects of varying cornering stiffness variation e Model mismatch for steady state circles using DC gain method must be investigated further e High frequency dynamics and phase mismatch as seen in the frequency response plots should be examined in detail Cameron J T Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover 2005 The Pennsylvania State University Gillespie T D Fundamentals of Vehicle Dynamics 1992 Society of Automotive Engineers SAE 495 Mitschke M Dynamik der Kraftfahrzeuge Vol A B C 1995 Berlin Springer Verlag Bevly D M R Sheridan and J C Gerdes Integrating INS Sensors with GPS Velocity Measurements for Continuous Estimation of Vehicle Sideslip and Tire Cornering Stiffness in Proceedings of the 2001 American Control Conference 2001 Arlington Virginia Borner M et al Detection of Lateral Vehicle Driving Con
36. characterized by a parameter known as the understeer gradient In this study the understeer gradient will be used for its ability to relate a vehicles weight distribution to its tires force generating abilities The understeer gradient is a widely used parameter in vehicle dynamics and its full derivation can be 27 found in many text books including 1 and 2 It was also presented in previous work 3 For simplicity only a brief derivation has been included here Figure 3 4 shows a 2 DOF single track vehicle in a high speed steady state turn of radius R The forces are shown in the positive direction however the slip angles are shown as negative in agreement with SAE standards L R Figure 3 4 Bicycle Model Steady State Turn By summing the interior angles of the triangle an equation for the required steering input to negotiate the turn can be solved Sa a 3 15 ITR f r i As in equation 3 1 the sum of forces in the lateral direction the sum of moments about he Z axis gives ma F F dr 3 16 I F a F b dt i 28 In a steady state turn the acceleration in the lateral direction is exactly equal to the centripetal acceleration a 3 17 In order for the vehicle to be at steady state it must be in equilibrium about its center of gravity and therefore the sum of moments about the z axis must be zero By combining equations 3 16 3 17 and setting the sum of moments to zero gives
37. connect to Client incon data reads Aefinity VVincon data Fiat Lines or Reads Zero Possible Causes Not enough satellites in view Receiver needs to be re programmed with current position Receiver not in FIX mode Receiver needs to be re programmed to transmit corrections Not enough satellites in view Calibration not complete Receiver needs to be re programmed to send logs Radio Modem not powered Radio Antenna not connected Base Station not sending corrections Radio Modem s are not connectiong Receiver needs to be re programmed to reveive corrections Ethernet crossover cable not connected Wrong IP Address used Client not powered on Client did not start incon Client Master DSP not connected to Client PC Master DSP battery is dead Master DPS needs to be restarted Signals are noisy Interface DSP is not connected to Reveiver Receiver is not sending logs Interface DSP battery is dying Inteface DSP needs to be restarted View status in GPSolution See Section B 2 1 See Above See Section B 2 1 View Status in GPSolution See Section B 2 2 See Section B 2 3 See Section B 2 2 Connect Parallel Port Check it Replace tt Turn it off and back on See Section B 2 4 Check Serial Cable See Above Check it Replace tt Turn it off and back on 192 C 50 1 Reprogramming the Base Station On occasion the memory of the Base Station receiver will be cleared A common symptom is the receiver s inability to automatically
38. constants C s C In order to quantify the effects of roll steer the bicycle model needs to be modified To fit the camber parameters it is assumed that the effects of camber are negligible with low roll maneuvers such as low frequency sinusoidal inputs used to determine the DC gains for the frequency responses This assumption allows the cornering stiffness values 96 obtained through the DC gains of the frequency response to be used in this derivation The validity of this assumption can be shown by investigating the results from chapter 6 When the DC gains were used to solve for the front and rear cornering stiffnesses and these values were used in the standard bicycle model not accounting for camber the model matches for low frequency portion of the chirp response were excellent However as the frequency of the steering input approaches the natural frequency of the vehicle roll and therefore camber angle increases and the model match quality decreases Also the high roll steady state turn maneuvers also show poor matching By using data collected from low frequency sine waves and the standard bicycle model equations the four unknowns in equation 7 9 can be solved The first two equations to be used in solving for the four unknowns are the standard bicycle model DC gain equations presented in chapter 5 for low frequency sinusoidal inputs As in chapter 5 these equations can be used to solve for the front and rear cornering sti
39. dominated by the n term The resulting expression becomes Os 2 n s U s i a b n 9 16 This shows that that 0 is related to U through a derivative function Intuitively this makes sense because in the limiting case where vehicle s wheel base decreases to zero the pitch angle measured at the center of gravity converges to the angle of the line tangent to the road profile below the center of gravity This is represented pictorially in Figure 9 4 127 Direction of Travel Figure 9 4 Effect of Decreasing Wheelbase The slope of the angle of the tangent line below the CG 77 is simply ratio of the change in profile height over distance covered _U t 7 U _ dU Nee oe a 9 17 Since this angle is simply the derivative of the road disturbance with respect to distance one would expect a similar derivative relationship to appear in the transfer function between the pitch angle and rear road disturbance In order to extract the rear road disturbance input from the vehicle s pitch measurements equation 9 15 can be inverted U s _ a b ns ns m 0 s 7 2 n S 9 18 This transfer function is not causal and therefore its behavior cannot be simulated in standard software such as MATLAB s Simulink In order to correct this a pole can be 128 added to the transfer function The added pole must be considerably faster than the poles of the current system so its dynamics wi
40. fix its position and therefore transmit differential corrections In this situation the Base Station should be reprogrammed by doing the following 1 Connect the COMI serial port to that of the PC which will be used to program the receiver 2 Open the GPSolution4 software on the PC and select Device gt Open gt New and enter a name e g BASE Station 3 Press Settings select COM1 from the PC Port Dropdown 4 Set the Baud Rate to 115200 and uncheck the Use Hardware Handshaking 5 Select OK and then OK and OPEN to open the new device 6 If GPSolution4 connects to the receiver skip to step 8 7 Navigate though the receiver s menus via the onboard LCD to the COM Port settings Make sure that COM1 has been set to a baud rate of 115200 and COM2 has been set to a baud rate of 57600 8 In the command window of GPSolution4 with no other windows open enter the following commands unlogall Interfacemode com2 none rtcm off log com2 rtcm1 ontime 5 log com2 rtcm3 ontime 10 log com2 rtcm22 ontime 10 1 log com2 rtcm1819 ontime 1 fix positon 40 86313783175 77 834902735600 367 3535 saveconfig 9 When the receiver has located four satellites it will display FIX on the LCD and begin to transmit the corrections as seen by the flashing green light above the COM2 port C 50 2 Reprogramming the Rover Station As with the base station the rover station may need to be reprogrammed A symptom of this would be if after 10 minutes
41. for four satellites instead of three The four pseudorange equations will allow the receiver to solve for the four unknowns three position components and the receiver clock bias The equation set can be represented by equation 2 2 XU 402 0 U G 121 234 22 Where U U and U are the receivers coordinates X Y and Z are the position coordinates of satellite n and Cr is the receiver clock bias which is common for all four ranging solutions 1 The clock bias can then be removed from the pseudorange calculations for a more accurate position solution R P Cp 2 3 15 Where R is the true distance from satellite n and P is the corresponding pseudorange and Cr is the receiver clock bias The Code Pseudorange calculation and correction above can result in approximately 3m accuracy on an L1 single frequency receiver and 30cm on an L1 L2 dual phase receiver Users with very stringent accuracy requirements can utilize Carrier Phase or Phase Psedudoranging GPS This method of calculating distance measures the phase of the GPS carrier wave and compares that to the replica carrier 3 Compared to Code Pseudorange algorithms much more accurate position solutions can be achieved carrier based algorithms can achieve accuracies of 1 2 cm 4 This method is typically used in Real Time Kinematic differential positioning solutions In order to perform this measurement the receiver removes the known PRN code from the re
42. format Structs and Unions were used extensively throughout the code to allow access to a variable in memory through both its double integer value or one byte at a time This parsing process is described in this section for the INSSPDSB log After the entire message is received and stored in the UART1MessageArray array the NetReceiveMessageTask is activated This task identifies the message from its message ID which was extracted from the header and sends the message contents to the appropriate sub function for parsing In the case of the INSSPDSB log the message ID and contents are given by NovAtel as 1 2 Table B 2 INSSPDSB Message Structure Structure Message ID 323 Log Type Synch Field Field Type Data Description Binary Binary Bytes Offset INS status see Table 13 on Page 60 32 bit CRC ASCII Binary and Short Binary only CR ILF Sentence terminator ASCII only B a From this log the current system utilizes the Trk gnd velocity direction Horizontal Speed and Vertical speed and disregards the remaining information It is important that only the needed values are extracted from the messages so that the traffic over the CAN bus can be kept to a minimum As indicated in table B 2 the three values to be used are of type double and are 8 bytes long Since the message was read into an array one byte at a time it is necessary to 178 reconstruct these double values from their one byte sections T
43. in all directions Internally velocity and angle changes are sampled at 600 Hz NovAtel s firmware applies non linear corrections to the raw measurements which makes these measurements available in their navigation software at a 100 Hz rate 4 The IMU measurements are taken in its body frame as defined by the sensor axis of the IMU The measurements then require a transformation into the vehicle s body frame to accurately determine vehicle attitude velocity and accelerations 34 Figure 4 3 Honeywell HG1700 IMU NovAtel Enclosure 4 1 1 1 GPS INS Integration The SPAN system integrates the GPS and INS systems through two separate but interacting filters in a decentralized Kalman filtering process A Kalman filter is a procedure that broadly consists of two steps used to optimally estimate a series of parameters that describe the behavior of a system 5 In Real Time operation the SPAN systems decentralized Kalman filter has 15 states Earth Centered Earth Fixed ECEF position velocity attitude Euler angles with respect to the ECEF frame and gyro and accelerometer biases with respect to the IMU body frame 4 The filter system collects IMU s measurements and time tags them with the GPS time It then uses a decentralized approach to generate a blended GPS INS solution The filtering process of the SPAN system has been referred to as decentralized because the GPS and inertial processing occur in two separate filters The
44. in subsections below 5 2 1 Chirp Response A frequency sweeping sinusoidal steering input or chirp input was given to the tracer at various speeds to investigate the bicycle model s accuracy in predicting lateral velocity and yawrate This type of input is helpful in examining model accuracy in the time domain and also gives insight into the frequency domain The frequency of the input was varied from 0 15 Hz to the fastest frequency the driver could input approximately 4 Hz Figure 5 4 shows the predicted and measured yawrate while Figure 5 5 displays the lateral velocity measurements and predictions 58 Yaw Rate Prediction and Measurement Chirp Using Kus Measurement 15L Predicted from Bicycle Model deg s oO 20 L L L L L LA L L L 6 time s Figure 5 4 Yawrate Chirp Response Kus Method Lateral Velocity Prediction and Measurement Chirp Using Kus 0 25 0 2 0 15 an 0 17 0 05 i wn E o 0 05 0 1 F 0 15 0 2 Measurement Predicted from Bicycle Model 0 25 1 i 1 L I I I I I i 6 8 10 12 14 16 18 20 22 24 26 time s Figure 5 5 Lateral Velocity Chirp Response Kus Method Investigation of these plots shows some interesting results With the current model parameters the bicycle model predicts yawrate well for low frequencies however it is unable to match at higher frequencies Figure 5 5 clearly shows a disag
45. is unknown it is not possible to predict the road disturbance at the front with only the pitch measurement The user can however measure and predict the rear road disturbance inputs because the same disturbance has acted on the front tires in an earlier time interval Therefore the goal of this mathematical analysis will be to extract an estimate of the rear displacement using current and past pitch measurements 124 The base assumptions state that the rear input U is a time delayed version of the front disturbance U therefore U t U t 9 5 where z is the time delay between front and rear inputs that can be estimated using the vehicle s length and assumption of constant velocity prc 9 6 U In the Laplace domain equation 9 4 can be expressed as U s U s e 9 7 For simulation purposes it is convenient to replace the e in the above equation with a rational polynomial which estimates the same time delay This can be done through the Pad approximation The n order Pad approximation is shown in 1 as ppp Aaa 9 8 i 7 gt n D s gt c h s k 0 k Where the coefficients are _ 2n k n eiia i Em k i For this work a second order Pad approximation was used The justification for this can be found in Appendix A This approximation is given as t s 6r s 12 P s 9 10 a s t s 6r s 12 To simplify the algebra equation 9 10 will be replaced with 2
46. one decimation length 5 Repeat steps 2 4 until the end of the template has been reached 6 Determine maximum Correlation Coefficient calculated for the entire template 109 7 Find the path along the template corresponding to the location of the maximum Correlation Coefficient To estimate the error associated with this positioning routine the true positions of the vehicle were recorded by the DGPS system during the road grade template construction and during the collection of the test samples This allows the positioning error to be calculated by comparing positions from DGPS to those calculated via correlated road grade If the error were calculated directly from the DGPS readings it would include both the road grade positioning routine s error as well as the lane keeping error associated with the driver s inability to exactly repeat the path traveled for the template generation In order to isolate the error due to the positioning routine only errors in the direction of travel are considered To estimate these errors the path of the sample data must be projected onto the path traveled during template generation This error estimation is computationally intensive and is only used for this proof of concept The method presented pictorially in Figure 8 6 and is explained below Position Matching 76 2 i Matched 76 25 Template Path 76 3 N ae Position from Correlation 76 35 eee a 3 mg ample Pat Lane
47. past two years I believe every all nighter I have ever had was with him His brilliance still amazes me With Haftay I share the unique experience of being both an NSF GK 12 fellow and a student in Dr Brennan s lab He is the only one who truly understands both sides of the story as we have vented many times together Bridget has been through the sometimes painful experience of sharing a test vehicle with me Our days in Blue Steel are not to be forgotten I thank her for her help her patience and her ability to calm me down when nothing seems to be working I would also like to thank all of the great people I have met during my six year stay in State College In particular my undergraduate friends who I still keep in touch with I could not have asked for a better crew to spend my time with You are the only ones who can truly understand and appreciate my college experience And to my girlfriend Kara where would I be without you Four perfect years with you and my love for you grows stronger every day Years ago I would have doubted a relationship like this could have ever existed Thank you for all of your love and support XV And last but not least I would like to thank my parents Over the past six years you have given me more support than I could have ever hoped for In a time of crisis you dropped everything to be by my side You helped me through the most difficult experience in my life and I cannot thank you enough Your l
48. performed when the IMU is remounted 4 1 2 Part 2 Base Station GPS system The base station also utilizes the NovAtel DL4plus receiver Unlike the Rover station this receiver has not been modified to communicate with the IMU As described in previous sections the base station is responsible for calculating and transmitting corrections to the Rover so that Real Time Kinematic differential GPS is possible The base station and rover receivers are capable of communicating both pseudorange and carrier phase corrections for differential mode operation in standard RTCM Radio Technical Commission for Maritime Services format This communication is accomplished using two FreeWave wireless radio modems set in a master slave configuration which have a range of approximately 10 miles The modems communicate with a baud rate of 56 200 bps and transmit RTCM 1 RTCM 3 RTCM 22 and RTCM 18 19 messages Message type 1 contains the differential GPS corrections message types 3 and 22 contain the base station and extended base station parameters respectively 39 to be used in the Real Time Kinematic solution and message types 18 and 19 contain raw carrier phase and pseudorange measurement information 7 8 After the base station is powered on and calibrated it automatically transmits the RTCM corrections to the Rover 4 1 2 1 Base Station Calibration In order for the base station to transmit proper corrections it must compare its calculated posi
49. seen that noise has also played a part in this error An easy way to check for this is to do the following 1 2 3 With the Rover receiver powered calibrated and sending data logs disconnect it from the Interface DSP at the DSP end The serial cable should remain connected to the Rover receiver Since this receiver is only sending messages on the COM1 port only the green light should be lit On occasion when you disconnect the interface DSP the red light will illuminate as well If the red light is illuminated move the serial connector on the receiver side left or right until the red light turns off Reconnect to the Interface DSP and see if issue is resolved
50. suspension dynamics in the front and rear and also considers the rotational inertia of the vehicle After the suspension parameters were determined it was found that the inverted versions of Model 3 and 4 had unstable poles in the denominator Because of this they were not used in simulation and therefore will not be presented in this chapter However the full derivations of each of these models along with discussions of each are given in Appendix A 9 5 Suspension Parameter Estimation In order to test the models presented in the previous sections the vehicle s suspension characteristics must be determined Since the Tracer s spring stiffnesses and damping 132 coefficients are not readily available in literature a method of estimating these parameters is presented here 9 5 1 Spring Stiffness Estimation In order to estimate the spring stiffnesses the following procedure was followed 1 Place a scale under each of the front tires Position a floor jack to the center of the front axle Raise the vehicle until the scales read 100 Ibs less than the current reading Measure and record the distance from the hub center to the fender Repeat Steps 3 4 until a sufficient number of data points have been collected Plot the additional force from the initial value at rest versus the spring displacement from rest 7 The slope of the best fit line of the force versus displacement curve corresponds to the spring stiffness constan
51. the rotational inertia make the actual vehicle considerably different from that used in the inversion Even though more complex vehicle models were derived in this work they were not used due to the presence of unstable poles in the denominators of each of the model inversions These unstable poles will appear with certain combinations of suspension and mass distribution parameters Additional modeling efforts are needed to find a model which accounts for rotational inertia but does not have unstable poles 10 4 Future Work There are several parts of this thesis which require further investigation These are presented below 10 4 1 System Integration During system development many precautions were taken to increase the sytems resistance to the vehicles electrical noise Although care was taken the current system is still susceptible noise On occasion during data collection the Interface DSP needs to be restarted It is believed that this problem is due to noise which interferes with the transmission on the CAN bus One possible solution is to optically isolate the tranmission chips on this board Another easily implemented solution would be to program a simple microprocessor such as the PIC or ATOM to constantly monitor the DSP and to strobe the reset pin when necessary Either solution would greatly improve the reliability of the system 159 The current programming on the both the Master and Interface DSP does not include any er
52. the receiver has not yet begun to transmit logs to the 193 Interface DSP no flashing green light above the COMI port To reprogram the Rover do the following 1 2 3 Perform steps 1 7 of section C 50 1 with the rover receiver Enter the following commands with all other windows closed unlogall interfacemode com2 rtcm none off setimutype IMU_HG1700_AG17 interfacemode aux imu imu OFF interfacemode com2 rtcm none off log insspdsb ontime 0 02 log inspvasb ontime 0 02 saveconfig When the receiver has located four satellites and the IMU has been aligned the receiver will transmit data logs to the Inteface DSP indicated by the flashing green light above the COMI port Also the red light above the COM2 port will be flashing indicating that the receiver is communicating with the base station C 50 3 Reprogramming the Modems Although it has not yet been necessary in the future it may be necessary to reprogram the modems responsible for the receiver receiver communication This procedure will be outlined here C 50 3 1 Base Station Modem 1 2 3 4 Power the Base Station modem and plug it into the computer via the Serial cable DO NOT use a NULL MODEM cable The radio will not be able to communicate with the PC You need a straight RS 232 cable Insert freewave software cd and start EZ setup 2 0 If you do not have the CD download the software from the freewave website under the Software Tools tab
53. to suspension dynamics The roll of the vehicle can affect the forces generated by the tires through an effect known as camber thrust Camber thrust represents the tilt induced on the tire due to the suspension In the standard bicycle model these suspension effects are neglected which may result in poor model fits in high roll situations This chapter will present a camber correction for the bicycle model which is applicable for steady state turns only Simulations results and conclusions will then be presented 7 1 Camber Correction Derivation Camber is the inclination of a wheel outward from the vehicle body 1 The effects of roll and tire camber on a tire s force generating abilities have been supported by the work of others Kim and Park 2 introduce an incremental change in force on the tire model in the form of 0a ap 7 1 This effect is commonly known as roll steer and is usually assumed to be a constant value when the amount of tire slip is small According to 2 the magnitude of the coefficient for the front tires was 0 2 and 0 2 for the rear tires In chapter 3 the equations of motion for a vehicle in a steady state turn were used to derive the understeer gradient The necessary front and rear lateral tire forces necessary to 93 negotiate a turn or radius R at steady state were written in equation 3 20 and are repeated here 2 F 2 mU y Ta poit L R In the standard bicycle model deriv
54. velocity magnitude velocity direction latitude longitude altitude and steering angle in real time at a rate of 50Hz If necessary the system can also output accelerations angular rates and various other measurements at 100Hz This system has significant advantages over systems used in previous studies 4 1 Vehicle System Layout The current vehicle system can most easily be described in four parts the Rover Station the Base Station the Steering Sensors and the Data Acquisition system The Rover Station steering sensors and Data Acquisition system are installed in the vehicle while the Base Station remains outside the vehicle in a fixed location Each of these parts will be descried in the subsequent sections of this chapter Figure 4 1 below shows a general block diagram of the entire setup 32 Rover Station K Base Station RTCM Corrections Steering aa Sensors IE Receiver Receiver Serial Data Acquisition Communication CAN Network Parallel Communication Client PC Wireless TCP IP Wincon Figure 4 1 System Layout 4 1 1 Part 1 Rover Station GPS INS system The Rover GPS INS sensing system being used is the NovAtel SPAN Synchronized Position Attitude Navigation system based off two OEM4 dual frequency GPS receivers and the Honeywell HG1700 military tactical grade IMU This GPS INS combination can provide estimates of position velocity and attitude at rates up to 100Hz In differential carrier
55. yemeseuicra use ienna a a a ar 184 CAD 2 WGP SHINS System narea a a e a e 184 C 49 2 2 Data Acquisition System ccccccsscesecstecesecseceesseecseeeeteeeees 186 C 49 2 3 Data Acquisition Saving Data cccccseceseceseceeeeeeteeenseeees 189 C 2 TrOUDIES MOO GING es ies cactus adects si tesstadindeciascdecetguandadena ude ed aatoGasktuiesuanelanieneds 190 C 50 1 Reprogramming the Base Station ccceceesceeseceteceeeeeeeeeeeeesaeeees 192 C 50 2 Reprogramming the Rover Station ccccecsceessecsteceeeeeeeeeeeeesaeenes 192 C 50 3 Reprogramming the Modems ccescceeceeeseeesceceeceeeeeeeeeeseeesaeenes 193 C5073 Base Station Modem xsacsssussdesviecstangatzasadvtedsbaleczardaantanspinnettoa 193 C 50 3 2 Rover Station Modem yiccscicciccsscetecds cits cetedariecssavtecstestemieteatectres 195 C 50 3 3 Modem Loop Testing oc ces snssenyedeveausssuecsnpanedeaegunsdedseadeaeatasuane 195 C 50 4 Data Acquisition Troubleshooting essssessessseesseseessseserssressessrssees 196 viii LIST OF FIGURES Figure 2 1 Replica and Received Signal Comparison cceccescceseeereeeeeeseceneenneeaee 10 Figure 2 2 Ideal GPS POSION O siirros eanna EEEa EEE Ea EEEa EEEE 11 Figure 2 3 Bi phase Modulation of Carrier Wave ssceesccessceecteeeeeeeeeeeeeaeeneeeaee 12 Figure Jk Bicycle Modelsseeiciarnrnean n E R ERT 22 Figure 3 2 SAE Coordinate System Definition c cscsssssssssssen
56. 0 8 1 1 2 1 4 1 6 1 8 Time s Time s Front Suspension Fit Data Set 2 Rear Suspension Fit Data Set 2 0 04 0 04 Measured Measured Fit with Measured k 56048 and c 3390 Fit with Measured k 55530 and c 2600 0 02 0 02 iad OF a OF e E E 5 E 8 0 02 8 0 02 3 3 S f 0 04 H T 0 041 0 06 0 06 0 08 1 1 1 1 1 1 0 08 1 1 1 1 1 1 r 1 0 0 5 1 1 5 2 2 5 3 0 0 2 0 4 0 6 0 8 1 Ta 1 4 1 6 Time s Time s Front Suspension Fit Data Set 3 Rear Suspension Fit Data Set 3 0 05 0 06 Measured Measured 0 04 L Fit with Measured k 56048 and C 3110 Fit with Measured k 55530 and c 2350 0 04 0 03 _ 0 02 E 0 02 E S 5 8 0 01 H 8 oH 3 a 5 0 fi 0 02 H 0 01 0 04 0 02 0 03 1 1 1 1 i 0 06 1 1 1 1 r 0 5 i 1 5 2 2 5 0 0 5 1 1 5 2 2 5 Time s Time s Figure 9 13 Quarter Car Model Fits 138 The final per axle damping values for the front and rear were determined to be e373 re 9 33 c 2586 m After reviewing the suspension parameters presented in 9 28 and 9 33 it can be seen that the front and rear suspension coefficients are similar but not identical There is also a considerable difference in the sprung mass that rests on each of these suspensions However for a first approximation the Identical Suspension Model presented in Section 9 3 will be used to represent the test vehicle 9 6 Effect of Forward Velocity on Pitch Measu
57. 0 T 20 T Kinematic Model 7 5 Identical Suspension Model S 200 J o 150 4 a N MOO ee ees N El 50 1 1 10 10 10 10 w rad s Figure 9 7 Identical Suspension Model Frequency Response NOTE To generate this frequency response an estimation of the vehicle s suspension parameters was made This is discussed further in section 9 5 By examining Figure 9 7 it can be seen that at very low frequencies the Identical Suspension Model reduces to the Kinematic Model At frequencies higher than 3 rad s the effects of suspension dynamics become apparent As before equation 9 25 can be inverted to extract U from 0 131 U s _ a b nm s ne n m 5 7 T 0 s 2 n S 2 n k s 9 26 a b nk n c nym S nc n k s n k 2 2 nnc 8S 2 n k s Once again the transfer function is not causal In the single suspension model two poles must be added The details of this will not be presented here but can be found in Appendix A 9 4 Additional Suspension Models In addition to Models 1 and 2 presented in the previous two sections two more complex suspension models have also been derived for this work The third model Model 3 is similar to Model 2 in that treats the vehicle as two quarter car models however Model 3 allows each of the front and rear suspensions to have different parameters The fourth model is a Full Pitch Plane model This model accounts for different
58. 15 T iaz tof 4 Z High Amplitude 5p Low Amplitude Increasing Lag 1 Model 0 i T 1 L L 1 L t L 10 10 w rad s 0 eS D B so 4 2 N a 100 4 L L 10 10 w rad s Figure 6 1 Yawrate Frequency Response Varying Relaxation Length It is interesting to note that the value of relaxation length which matches best in the magnitude plot does not correspond to the best match in the phase plot Phase matches at higher values of lag than magnitude does In order to reconcile the differences between the two sigma values the front and rear relaxation lengths were assumed to be independent of each other The parametric variation was repeated with different values of front and rear relaxation lengths After the simulations were complete it was apparent that the rear relaxation length is primarily responsible for the higher order dynamics found in the magnitude plot However by making the two values independent the model matching routine becomes more complex Also the differences between the independent relaxation length model and the model 82 which treats the relaxation length as one parameter were minor Because of this it will be assumed that the relaxation lengths are identical and the model presented in this section will be used in the analysis Steering Angle to Vlat with Tire Lag 20 154 4 a 510 DL 7 g High Amplitude N x 5p Low Amplitude EN 3 Mode
59. 5 18 and 5 21 This will not be presented here 5 3 3 Cornering Stiffness Values from DC Gains In order to accurately model the DC gains and to confirm linearity of the system a frequency response was performed for two different magnitudes of steering input The system magnitude corresponding to the lowest frequency steering input 0 15 Hz was 68 assumed to be the DC gain of the system The frequency response plots for lateral velocity and yawrate are shown below in Figures 5 11 and 5 12 Steering Angle to Vlat T 20 F DC Gain shown in dB o B amp te gt i ae e 5L d o 10 10 w rad s 0 t F pe 5 g 50 6 t 7 aS 8 53 a 100 High Amplitude 7 Low Amplitude F T T L L 1 L 1 i 10 10 w rad s Figure 5 11 Lateral Velocity Frequency Response DC Gain Steering Angle to Yaw Rate 20 4 etl DC Gain shown in dB g P amp 4 Fg jol P g 204 2 5 0 1 10 10 w rad s wepe a S gt d 2 50 4 v amp oO 3 i a 100 High Amplitude 7 i b l Low Amplitude eee ch 10 10 w rad s Figure 5 12 Yawrate Frequency Response DC Gain 69 Since the DC gain varied for the low amplitude and high amplitude frequency responses the values were averaged Table 5 5 below summarizes the measured results Table 5 5 Measured DC Gains 3 599 ra
60. 5 3 Sideslip Measurements Cornering Stiffness Estimation Since there is a timeframe where the sideslip measurements were approximately zero the average velocity during that timeframe was used as the zero sideslip velocity This procedure was repeated for three data collection sets where the same experiment was performed The average zero sideslip velocity was determined to be 14 12 m s The measured zero sideslip velocity vehicle weight on the rear axle and dimension b were used in conjunction with Equation 5 8 to determine the rear cornering stiffness value C ar 3781N z 14122 49258 1 56m 9 81 S s rad 5 10 The understeer gradient from equation 3 24 was used to determine the front cornering stiffness Cu C 68338 5 11 The table below shows a summary of values to be used in the bicycle model simulations 57 Table 5 4 Bicycle Model Parameters m kg 1106 Caf N rad 68338 Car N rad 49258 5 2 Bicycle Model Simulation Results In simulation the parameters presented in table 5 4 were used in the state space representation of the Bicycle Model given in equation 3 14 The model s ability to predict lateral velocity and yawrate was investigated in both the time and frequency domain In the time domain steady state circles and chirp response maneuvers were used The inputs to the state space model were the vehicle velocity and steering angle The results are presented
61. ADC7864_ Start function also consists of only one line of code volatile int 0xA03C0080 0 This line of code is a write command that pulls the CONVST pin low through several pin transitions The ADC portion of the CAN board will not be described here as it is beyond the scope of this work However it is important to note that when the ADC chip has finished converting all of its tracks the ADC sets its BUSY pin to low The BUSY pin is directly connected to the external interrupt pin EXT_INT7 on the DSP so that its value also becomes 0 When the eternal interrupt is triggered the DSP goes into the Interrupt 180 Service Routine that is set for this interrupt pin For this work the hardware interrupt triggers the function ADC_Interrupt_Func which has been copied below void ADC_Interrupt_Func ADC1_CAN_Read amp adcl amp adc2 amp adc3 amp adc4 analog1 data adc analog2 data adc2 analog3 data adc3 analog4 data adc4 This function reads the data from the ADC chip through the function ADC1_CAN_ Read which is also written in the include file ad7864 c Each of the ADC channel values are saved in the variables adcl adc4 The details of this data read will not be discussed here After the analog data has been read it is sent over the CAN bus to the Master DSP by using the SendToCan function just as the DL 4plus data logs were sent l NovAtel OEM4 Family of Receivers User Manual Vol 2 Command and
62. Calculated Leverarm Inertial Frame Coordinate Offset m Uncertainty m 002 003 02 Since the leverarm has been saved to memory the leverarm calibration only needs to be performed if either the IMU or antenna is remounted The final stage of the rover calibration requires aligning the IMU body frame coordinate system with that of the vehicle This routine allows the system to align itself while in motion if necessary and gives the user exact coordinate system rotational offsets to use in data post processing Once again the DL4plus had a built in calibration routine RVBCALIBRATE which computed the coordinate system angular offsets and saved 38 them into system memory The routine consisted of the same circle and figure eight driving maneuvers used in the leverarm calibration At the end of calibration it returns the values for these offsets in the VEHICLEBODYROTATION log as Table 4 3 Vehicle Angular Offsets Inertial Frame Coordinate Offset deg Pitch Roll Yaw The angles in the above table indicate the angles offsets due to the IMU mounting For example while driving in a straight line the velocity direction angle and the yaw angle will have a 0 204 degree disagreement It is important that this is taken into account in data post processing for accurate attitude measurements After this calibration was complete the DL4plus receiver s settings are saved so the process only needs to be
63. Coefficient was calculated for the sample road grade estimates and sections of the road grade template The correlation coefficient is calculated by Cop A r VW 8 2 N 0y Oy Where Y x Y x are the road grade as a function of path distance covered for the template and the sample respectively Y Y are the mean of Y and Y respectively Oy Oy are the standard deviations of Y and Y respectively and E indicates the expected value or mean This correlation coefficient is a measure of the strength of the relationship or association of two independent variables Its value varies from 1 to 1 where 1 indicates variables which are opposites and 1 indicates exact matches A fast MATLAB function to calculate the Pearson correlation prcorr2 is used for this application The steps used to position the vehicle along the template path using the Correlation Coefficient are described below It should be noted that this method is used to position the vehicle offline therefore these steps would have to be modified to work in a real time routine 1 Determine the approximate path distance covered by the sample data by integrating the vehicle s velocity with respect to time 2 Section the track template to cover the same path distance as that covered by the sample data 3 Calculate the correlation coefficient between the road grade measurements of the sample data and the sectioned template 4 Shift the template section by
64. Control Segment The control segment consists of one Master Control Station MCS and five Monitoring Stations MS The main operational tasks for the control segment are to track the satellites for orbit clock determination and prediction to perform time synchronization of the satellites and to upload this information in a data message to the satellites to ensure accurate position solutions 2 One MS is located at the MCS at the Falcon Air Force Base in Colorado Springs Colorado and the remaining four are located on Hawaii Ascension Diego Garcia and Kwajalein islands These stations collect altitude position speed and the health of the orbiting satellites for all satellites in view and send this information to the MCS for real time data processing This whole process is performed twice a day by each of the Monitoring Stations From the data collected the MCS 9 calculates any position or clock errors for each satellite and sends these corrections back to the satellites for more accurate solutions for the end user 2 1 3 User Segment The user segment is the most well known portion of the entire GPS system As one may imagine this segment is made up of all users who receive GPS satellite data This includes military civilian and commercial users The uses for GPS amongst these groups are for the most part common knowledge This work will only investigate the use of GPS in the user segment defined by civilian and commercial users
65. Ds Ds D s y Pi 5 4 3 2 l Which results in AORE Cys Cs C s C s C8 C s C 8 s D s Ds D s oe D s Ds 168 A 18 A 19 A 20 A 21 A 22 A 23 A 24 A 25 A 26 A 27 A 28 A 29 A 30 A 31 Where the D coefficients remain the same as before and the C coefficients are as follows D 2 k k m pi D 2 k k n 2 c k m p 2 c k n p k m n p k m n p D 2 c k n 2 C k n k m n k m n 2 c C n p k m n p kmn p c mpn p c mm n pi D 2 C n k m n k m n C m n c m N k m np k m n p c m n p c M N pi D k m nn k m n c m n c m n C M N p C M N p D c m n c m n A 4 Model 4 Full Pitch Plane Model 169 A 32 A 33 A 34 A 35 A 36 A 37 The most complex model derived in this work will be referred to as the Full Pitch Plane Model This model allows for different suspension dynamics in the front and rear and also accounts for the roational inertia of the vehicle No additional assumptions are made beyond the base assumptions presented in Section 9 1 The derivation will use Newtonian mechanics similar to Models 2 and 3 The front and rear spring and damper forces can be written as in equation 9 21 and the kinematic expressions presented in equation 9 2 can be substituted into each equation Fek 2 U k z 40 U F k z U k z b8 U Fee S4
66. E 9 2 2 V Tdeak DesS ripti oN sinrin ect acetate aed wees 10 2 2 2 Technical Description ss ssesessseesseseesseesesresseesreseessteseseesseesseserssresee 11 2 2 2 ASS ALE IG Signals ien eed tat cea ire e a TAn Salsas te 11 27222 Calculating Position necesn inne iaaa 13 2 2 2 3 Single and Dual Frequency ReceiveFS cccccssceseeseeeeeeeeees 16 2 2 3 Differential GES onnar n ira Ot cra pn a ose a te ot stele 17 2 2 9 NICS ISSAC ma u sl edad ole e ia i a a a a autetigees 18 DS INS Backoro nd sssrin a a a a a a e 18 2AINS Functionality ennan e E O A a TRAA 19 2 5 GPS INS Integrationen n a a n a n tomas 19 Chapter 3 Two Degree of Freedom Model s nsssesssessesessssessesesssressesersseessessessseese 22 3 1 Bicycle Model Dery ation si ss encod tactecascueta wie Tashaite in scesisSihae eae vada 22 3 1 1 Derivation of Understeer Gradient ice2e isch sdueac ciavac cast eccdeosdeenstctoreancnes 26 Chapter 4 Vehicle Systems and Integration cccccccsseceseceeeeeeseeeeseceeeeeeeeenseeesaeees 31 4 1 Vehicle System Layout isieaktssccsiesevatiacteeesnek a a E a aaah 31 4 1 1 Part 1 Rover Station GPS INS system cccessesseceeeeeeseeeteeeeeeees 32 4 1 1 1 GPS INS Inte erations onic ee merece a 34 4 1 1 2 Rover Station Calibration seer gsc cos cosssne at ebecchasegans eneueeeedasdeuaheaonases 35 4 1 2 Part 2 Base Station GPS Systems 2 caslassssecdesesscadeiandddincha laces 38 4 1 2 1 Base Station Calibra
67. I suggest against using the Hyper Terminal method mentioned in the book Select the com port you will be working from should be 1 by default Use the settings displayed in the figures below 194 nox File Radio Model Help Port Settings Main com F Progrem Radio COMI X ry ALL MUUME I High Speed Read Fom Radio ma Serial Number Unknown FW Vers on Unknown Transmission Characteristics MultiPoint Parameters Tools Set Operation Mode Set Baud Rate Call Book Modem Mode 0 Point to Point Master 7 r Ethemet Options ON OFF m Local IP Address And Port Address EthemetMode 205 200 1200 2 200 jna Slave IP Stack Slave UDP Mode o zl Power ON Reply IP Address And Port Number Duplex Half Full 25 25 25 25 jna Figure C 10 Base Station Modem Operation Mode J EZ Config Yersion 2 3 P Fa File Zadio Model Help Fei Port Settings Main Prograrn Radio O Diag COM1 I High Speed Read From Radio SBLLLOGQUWE Serial Number Unknown FW Version Unknown Transmission Characteristics MultiPaint Parameters Tools Set Operation Mode Set Baud Rate Call Book paaa R5232 485 Setup Port C 1 200 R5232 C Main Only c 29 R5485 C Diag Only C 4 800 S 4 z EEA C 9 600 R5422 Both Main amp Diag C 19 200 C 38 400 m Flow Control Fi C 57 600 None C RTs C DIR C 76
68. Keeping Error E 76 4 N gt 76 45 Direction of Travel Path Error i 76 5 76 55 L True Position l 158 4 158 35 158 3 158 25 158 2 158 15 158 1 158 05 158 157 95 X m Figure 8 6 View of Error Calculation 110 First the road grade correlation is performed and the section of the template which best matches that of the sample data is extracted from the template This section is the Matched Template Path in Figure 8 6 and it contains the same number of points as the Sample Path After the correlation each data point along the Sample Path will have a corresponding data point on the Matched Template Path According to the road grade positioning routine the point labeled Z on the Sample Path corresponds to the point labeled 2 on the Matched Template Path Tangent lines are then drawn on both the Sample Path and the Matched Template Path at points Z and 2 respectively A line perpendicular to the Track Tangent is then drawn to intersect the Sample Path The error along the direction of travel is then determined to be the distance from point on the Sample Path and the intersection of the Sample Tangent and Track Perpendicular As mentioned previously this error calculation is elementary and is not fit for real time data processing however it is sufficient as an initial estimate of the path error associated with the road grade positioning ro
69. Relaxation Bens ccs scaccavenssxvssvacsecandecs vas ieccaienncrenetencumennaniet 82 Table 8 1 Average Error Estimates and Correlation Values cceseeseeseeereeeeeeeees 110 Table 9 1 Pitch Model Parameter Definitions ee ceeceseeeeeeneeeeeeeeceseceeeneeeeeeaees 122 Table 9 2 Spring Deflection Measurements cisussscesecvsncsastiovssasiescassavaiissttannduavionsans 132 Table B 1 Short Binary INS Message Header Structure cecccecseceseeeeeeeeeeeteees 175 Table B 2 INSSPDSB Message Structure cssccssscessceseressscsseccssacssetsenseesncesscess 177 Table C 1 Troubleshooting Va Ble ccussiscsssssceasiasanecinsisdevsyishectaatatuassataecantuahecunsisdactens 191 xiv ACKNOWLEDGEMENTS I would first like to thank the National Science Foundation the Department of Mechanical Engineering and the Pennsylvania Transpiration Institute for providing me with the funding and facilities to make my graduate education possible Thanks to my advisor Dr Brennan for his endless support and guidance throughout the course of this work He has taught me a tremendous amount about vehicle dynamics and research in general in particular the importance of a literature review Dr Brennan gave me the opportunity to work on some very interesting projects which made my graduate experience quite unique Also big thanks to my lab group members especially Vishi Haftay and Bridget Vishi spent many hours helping me over the
70. Steady State Circle Response DC Gain Method 5 4 3 Frequency Response 73 Steering Angle to Yaw Rate 20 15 a ay bh Fe Sigh e a Dh 4 D A 3 5 J 0 1 t 1 1 1 1 1 l 1 t 10 10 rad s G es 2 50 v can 8 High Amplitude a 100 Low Amplitude 7 Bicycle Model DC Gain Method ti if ni L L L 1 L al 0 10 10 w rad s Figure 5 17 Yawrate Frequency Response DC Gain Method Steering Angle to Vlat 20 15 J S w oe D Var 3 E Pr F 5p J 0 L L 1 1 1 1 1 L a 1 L 10 10 rad s 0 po E 5 D Ss 50 amp E z mR S High Amplitude d a 100 Low Amplitude Bicycle Model DC Gain Method I T ni ni L L 0 10 10 w rad s Figure 5 18 Lateral Velocity Frequency Response DC Gain Method 74 5 4 4 Bicycle Model Cornering Stiffness Correction Results Discussion A comparison between the results presented in section 5 4 with those in section 5 2 shows a drastic improvement in the model matching for both yawrate and lateral velocity in the time and frequency domains when using the DC gain method to determine cornering stiffness values Comments on each comparison are presented in this section 5 4 4 1 Chirp Response When comparing the chirp response data it is interesting to note that although yawrate matches improved with the DC gain method the chang
71. The Pennsylvania State University The Graduate School Department of Mechanical and Nuclear Engineering GPS INS SENSING COORDINATION FOR VEHICLE STATE IDENTIFICATION AND ROAD GRADE POSITIONING A Thesis in Mechanical Engineering by Ryan David Martini 2006 Ryan David Martini Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2006 I grant The Pennsylvania State University the nonexclusive right to use this work for the University s own purposes and to make single copies of the work available to the public on a not for profit basis if copies are not otherwise available Ryan Martini The thesis of Ryan Martini was reviewed and approved by the following Sean N Brennan Assistant Professor Department of Mechanical and Nuclear Engineering Thesis Advisor H J Sommer III Professor and Interim Head Department of Mechanical and Nuclear Engineering Thesis Reader Stefan Thynell Professor In Charge of Graduate Programs in Mechanical and Nuclear Engineering Signatures are on file in the Graduate School ill ABSTRACT This work demonstrates a methodology of estimating vehicle states through the use of a GPS INS based sensing architecture A sensing system has been developed and implemented in a vehicle for real time data acquisition and model based state prediction The experimental data is then used to modify existing dynamic models to improve their accuracy Modeli
72. a us da a 5 3 y 52 Since the turn radius is assumed to be constant and vehicle length does not change equation 5 3 reduces to d K s Ae 5 4 yX Equation 5 4 shows that the understeer gradient is simply the slope of the plot of steering angle versus lateral acceleration This relationship described by equation 5 4 was used to determine the understeer gradient by measuring steering angle and lateral acceleration around a steady state turn These measurements were recorded while driving around a 30 5 meter radius circle at 6 different speeds in both the clockwise and counterclockwise direction Equation 5 1 was used to determine the lateral acceleration and the steering angles were measured directly from the string potentiometers The exact turning radius for each pass was calculated by averaging GPS data readings for each completed circle The results were complied and a best fit line was added to the linear region of the data The slope of the best fit line corresponds to the calculated understeer gradient using the bicycle model Figure 5 1 shows the results of the 30 5m radius as well as a 36 5m radius turn Figure 5 1 0 12 i i i i i O Small CCW o 0 115H Small CW 4 aay Large CCW Tl Large cw j 0 105 J fa i 4 s Pee ai o weet 0 095 o Oe ll J i a a K 0 016 T 009 aag 70 b r a SO Le 40 3 0 085 H 0 087 m oe en Kys 0 016 0 075 S 0 L
73. a T E F zg U s c ze a0y U ys Then by summing moments about the center of gravity A 38 A 39 A 40 A 41 170 Fy ty la F tFn EJ 0 cre a0 U 2e 08 0 4 A 42 tc b0 U 2 b Oy b J 5 Where J is the rotational inertia in the pitch plane For the Tracer this paramter is given by NHTSA as J 1705 kg m A 43 The forces in the vertical direction can be summed Fy h Fy m Ze kr Fy i ky 2 48 U c ab r ae A 44 Ke b0 U 2 b6 0 m Ze Taking the Laplace transforms of equations A 42 and A 44 z k a k b sz c at c b 0 k a k b sO c a c b kaU c asU k bU c bsU J s 0 a ke k sz c C 0 Ke k b s0 c a c b kU c sU k U c sU m S Z A 45 A 46 Equation A 46 can be rearranged to solve for the vertical displacement at the center of gravity Ze e k U k U U s c U e ak 0 bk 0 ac s0 be_s0 Z A 47 g k k c s c 5 m Equation A 47 is then substituted into equation A 46 This can then be rearranged to solve for the ratio 0 U 171 6 Xe a b Y am s Y a b X bm s U 2abX b Y X s m aX Y s m J s X Y m s with A 48 X k e s Y k s The frequency response of the system is shown in Figure A 5 Pitch Model Frequency Response Pitch Angl
74. ad on system startup or after momentary power outages without having to be returned to a zero or home position As with any standard potentiometer the linear string potentiometer returns a voltage proportional to the applied reference voltage and the position of the sensors wiper with respect to one of the end terminals In the case of the string potentiometer the output voltage is linearly dependent on the wiper position which is linearly dependent on the string s extension length In previous work 9 two of these potentiometers were mounted to the vehicle for redundancy purposes The base of each sensor was mounted to the undercarriage of the vehicle via a custom mounting bracket with one sensor s cable mounted to the driver s side steering arm and the other on the passenger s side steering arm In 9 and at the beginning of this study a constant 5V differential 0 5V reference voltage was applied to 4 each potentiometer After several data sets were collected it was determined that a 5V differential reference was not sufficient to supply angle readings with the necessary accuracy Because of this the reference voltage was increased to a 30V differential 15V to 15V via custom circuit based on the Autodyne SB1R5 515D regulator chip Due to the limited number of analog inputs available previous studies 9 only used one of the two potentiometers for steer angle readings In this study this was determined to be inappropriat
75. an compare the code being received with that it has stored Replica Signal Received Signal gt At Speed of Light X Figure 2 1 Replica and Received Signal Comparison The receiver can then estimate the signal travel time by subtracting the time its internal clock registers from the time indicated by the satellite when it transmitted the relevant pulse phase lag of the received signal from that generated within the receiver 1 The travel time can then be multiplied by the speed of light to tell the receiver how far it is from a given satellite X miles This then implies that the receiver is located somewhere on the surface of a sphere that has a radius of X miles and is centered at the location of the satellite When calculated for three satellites in three dimensional space the three spheres will intersect at 2 points One of which will be on the earth s surface while the other intersection point will be either off in space or well below the earth s surface and therefore can be disregarded Thus the remaining point will be the user s location on the earth s surface This process is represented pictorially in Figure 2 2 11 Disregard Figure 2 2 Ideal GPS Positioning The simple description of GPS operation presented above does not capture all of the intricacies of GPS Although many of these issues fall beyond the scope this work it is necessary to have a greater understanding than the id
76. and J C Gerdes Vehicle Sideslip and Roll Parameter Estimation using GPS in AVEC 2002 6th International Symposium on Advanced Vehicle Control 2002 Hiroshima Japan Yang Y J Farrell and H S Tan GPS aided INS based Control State Calculation for AHS in Proceedings of the 2001 American Control Conference 2001 Arlington Virginia Ryu J and J C Gerdes Estimation Of Vehicle Roll And Road Bank Angle 2004 Boston Massachusetts Bevly D M et al The Use of GPS Based Velocity Measurements for Improved Vehicle State Estimation in Proceedings of the 2000 American Control Conference 2000 Chicago Illinois Bevly D M R Sheridan and J C Gerdes Integrating INS Sensors with GPS Velocity Measurements for Continuous Estimation of Vehicle Sideslip and Tire Cornering Stiffness in Proceedings of the 2001 American Control Conference 2001 Arlington Virginia Bae H S J Ryu and J C Gerdes Road Grade and Vehicle Parameter Estimation for Longitudinal Control Using GPS in Proceeings of IEEE Conference on Intelligent Transportation Systems 2001 Gillespie T D Fundamentals of Vehicle Dynamics 1992 Society of Automotive Engineers SAE 495 Karnopp D Vehicle Stability 2004 New York Marcel Dekker Inc Holzapfel W M Sofsky and U Neuschefer Rube Road Profile Recognition for Autonomous Car Navigation and Navstar GPS Support IEEE Transactions on Aerospace and Electronic Systems 2003 39 1 p 2 12 Chapter 2
77. and roll was left un modeled in the planar model the tire lag value which corresponded to the best yaw rate match was assumed to be the most accurate estimation to the true value Although the addition of tire lag improved the model matches at high frequencies it did not improve the fit of steady state circle data Analysis of the steady state circle data indicated that an additional tire force generation mechanism was present for these maneuvers A hypothesis was made that the additional force generation was due to camber effects By assuming camber effects were only present in high roll maneuvers such as steady state circles an estimation of these effects was made An improvement in 157 the steady state circle lateral velocity model matches was shown by accounting for these effects 10 3 Road Grade Positioning Throughout the analysis of the experimental data it became apparent that the terrain was greatly affecting the integrity of the data An investigation into the nature of these terrain disturbances showed that they were both repeatable and location dependent These two characteristics allow the terrain disturbances to be used in a localization routine Depending on the vehicle it has been shown that the road grade can be estimated by observing the low frequency content of the vehicle s pitch measurements In order for this localization routine to be consistent between vehicles a pitch plane model must be used to remove the
78. and template pitch measurements were transformed to be a function of path length instead of time by integrating the vehicle velocity measurements with respect to time In order to get an approximation of the positioning routine s error the vehicle path and road grade measurements were decimated and interpolated to occur at 25 cm intervals to allow for a direct path dependent comparison between the road grade estimates The 25 cm interval was selected since the highest average velocity of any of the data sets was 12 5 m s and the sampling frequency was 50 Hz This corresponds to 25 cm between samples at the highest speed The data was then passed through a 2 pole low pass Butterworth filter to estimate road grade It is important to note that the cutoff frequency of the filter was constant among each data set in the spatial distance domain as opposed to the time domain This transformation to distance dependent filtering is desirable because the data sets were collected at different speeds With data at different speeds a filter in with a cutoff frequency of fe applied in the time domain will result in different levels of spatial smoothing for each data set when they are taken to the spatial domain Therefore it is important to decimate and interpolate the data 108 at specific and uniform distance increments before applying a constant cutoff frequency filter In order to compare the road grade estimates the Pearson Product Moment Correlation
79. and yaw to measure how a vehicle is moving and rotating in space The system uses these measurements to integrate and solve differential equations to estimate vehicles position velocity and attitude relative to initially known states These estimates can be made available as fast as they system computer can calculate them Although the INS system can offer high speed continuous estimates of position velocity and attitude these estimates are subject to integration error over long periods of time Small errors in acceleration readings grow as they are integrated over time this results in large errors in velocity estimates and even larger errors in position calculations These errors make it necessary to restart or correct stand alone INS systems to ensure accurate operation Since INS calculates change in system orientation and acceleration it needs initial values for these parameters to be input from an external source 2 5 GPS INS Integration The complimentary nature of GPS and inertial navigation has been well known since the inception of GPS In theory the continuity of the inertial system can both fill in 20 positioning gaps left by GPS satellite outages and reduce the effect of high frequency GPS errors while the unbiased nature of the GPS signals can limit the size of the low frequency errors in the inertial system 7 The integration of GPS INS creates an accurate high speed positioning system that can continue to operate w
80. art at the same position common trends became apparent as shown in Figure 8 1 SideSlip Large Circle CCW Roll Large Circle CCW 35mph 30mph 25mph 20mph 15mph SideSlip rad pag QO N Roll deg oo 1 1 1 1 1 i 1 1 1 1 0 10 20 30 40 0 10 20 30 40 50 60 time sec time sec Figure 8 1 Initial Observation of Terrain Disturbance Ideally the roll and sideslip angles for each constant velocity steady state circle would be constant However it is obvious that the measurements have been skewed by the terrain This has also been observed elsewhere in literature where attempts have been made to remove terrain effects from readings in order to improve their accuracy 1 2 This chapter will examine how to quantify and utilize these repetitive location dependent disturbances to obtain accurate position estimations by correlating current disturbances with those of a disturbance map 8 2 Road Grade Estimation For the purposes of this work road grade is defined as the angle of the road with respect to the horizontal plane in the longitudinal direction Road grade estimation has been performed extensively for heavy vehicle applications to ensure safety and to appropriately distribute engine power to overcome steep inclines 3 5 Two simple GPS based methods of road grade estimation presented by Bae et al 5 were investigated in this work A schematic showing the road grad
81. ation the front and rear lateral forces produced by the tires were assumed to be equal to their slip angles multiplied by their cornering stiffnesses In this derivation the lateral forces produced also include camber thrust effect Figure 7 1 shows the rear view of a vehicle in a steady state right hand turn D1 Figure 7 1 Vehicle Exhibiting Camber In Figure 7 1 m represents the sprung mass of the vehicle When negotiating the turn suspension dynamics will cause the mass will roll about its roll axis by an angle of At the same time the wheels will roll from the vertical axis by an angle of This angle is known as the camber angle Although the roll angle of the vehicle is not equal to the camber angle the relationship between them can be assumed to be linear for small amounts of roll angle Under this assumption the wheel angles can be modeled as p S 7 3 94 Where S is a constant to be referred to as the front or rear roll transfer constant It will be assumed that the vehicle suspension stiffness can be modeled as a rotational spring located on the roll axis with stiffness k as shown in Figure 7 2 Figure 7 2 Rotation Spring Suspension Model An expression relating the vehicle roll angle to the centripetal acceleration can be written by taking a force balance in the lateral direction and assuming small angles k a m U i h R 7 4 Combining and rearranging equations
82. cation Dependence In order to use the road grade estimation in a positioning routine it must be highly repeatable as a function of position This repeatability is most easily tested by driving over the same terrain and comparing road grade measurements The results of this experiment are shown below using steady state circle data Figure 8 4 shows the road grade estimate for several passes around the skid pad turning circle Plotted below the road grade is the yaw angle measured in degrees from north to show the vehicle heading Note that the skid pad is one of the flattest portions of the test rack and it is therefore likely that public roads would provide a much better signal to noise ratio 106 Road Grade SS Circle Road Grade deg T T T A 20 40 60 80 time s L 100 1 120 140 ie io is is oS i T T Yaw deg from north S oO oO fo 20 40 60 80 time s Figure 8 4 Road Grade Repeatability 1 100 1 120 140 In order to demonstrate the location dependence of the road grade estimate steady state circle data was collected starting at the same point but traveling at various speeds Figure 8 5 shows two plots for the same data plotted as a function of time left and as a function of path distance right where path distance was calculated by integrating the longitudinal velocity measurements 0 85 0 6 0 44 0 2L Road Gra
83. ceived satellite signal After PRN removal the received signal still contains the navigation message which can be decoded and eliminated by high pass filtering The final result is the Doppler shifted carrier on which phase measurement can be performed 2 The Carrier Phase to be measured is the difference between phase of receiver s replica signal and the signal received plus the number of cycles at the initial start of tracking This number will have an integer and fractional component e g 123456789 871 cycles The fractional component if known can be used to provide additional time resolution which therefore provides additional resolution in the position estimate The derivation of the carrier phase positioning technique is presented in 2 and its details will not be presented here The method is based off of electromagnetic wave propagation and is beyond the scope of this work The resulting equation however has been re written to agree with previous notation and is presented in equation 2 4 D Eon 2 4 Aa 16 Where is the measurable phase 4 is the wavelength Cr is the receiver clock bias c is the speed of light R is the true range and N is the initial number of cycles between the satellite carrier wave and that replicated by the receiver upon initial signal tracking By multiplying the frequency equation equation 2 4 expressed in cycles by the wavelength A of the carrier a range equation is formed P R c Cr
84. correct Model eessssscseeceeeeeceesceseeteeeeeeeseenes 149 Figure 9 28 Aligned Experimental Pitch Measurements cecesceeeeeeeeteeeeeneeeaee 150 Figure 9 29 Road Grade Estimation Method Comparison Experimental Data 151 Figure 9 30 Model Inversion Trend Recovery csccsssesssssceteceeeeneeeeeseeeeeceaeeeeaee 152 Figure A 1 Pad Approximations Rear Road Disturbance eeeeeeeneeereeeeeeeee 162 Figure A 2 Pad Approximations Rear Road Disturbance Zoomed 163 Figure A 3 Different Suspension Model Frequency Response ccsceseeenees 166 Figure A 4 Different Suspension Model Model Check cceecesesceereeeeeeeeeneeees 167 Figure A 5 Full Model Frequency Response srsssciscscssscsssesvscnesensessssesvessavasncdvartooutves 171 Figure C 1 Base Station Mounting lt sas susisessiuenacevnnsaneunea eraeniausteanviansaunentauauaiusassunestias 182 Figure C 2 Radio Antenna Mounting cccciscsscscsscatseesesnesacvacsaaesnstesansnenseaseasancnasvensontes 183 Figure C 3 Receiver with Fixed Position ssesessssssssseseesesseseestsseseessesersessrseesessese 183 Figure C 4 IMU Mounting ss ssesesesseeseseesteseseestssssrssoetrersrcentassnesaressaseentsseseasrssaseane 184 Figure C 5 GPS Antenna Mounting i scca ssssiscendassaseasosssatsdacsdauissenvaevdesasaavsinnantosetsteustas 185 Figure C6 DSP DSP COnnectionS sisis iirinn iaaea e E E E 187 Figure C 7 Steering Sens
85. d s rad 3 804 m s rad The DC gain value for yawrate Gr shows that for one radian of steady state steering input vehicle s yawrate will be 3 599 rad s Similarly Gv shows that for one radian of steady state steering input the vehicles lateral velocity will be 3 804 m s With the DC gains measured equations 5 16 and 5 18 can be rearranged to solve for rear and front cornering stiffness values respectively 2 EE Oa 5 30 G b G a b rad 2 f CU a b G C bY U mG a rad r ar As expected these values are significantly different than those obtained using the understeer gradient method One should note that not only are the magnitudes of each cornering stiffness value different but also that the rear cornering stiffness is now higher in magnitude than the front cornering stiffness Using equation 3 24 with the cornering stiffness values solved for using the DC gain method the understeer gradient can be solved to be rad K 0 0345 5 32 g This value is the same order of magnitude that calculated from the steady state turning maneuvers however it results in very different cornering stiffness values The effect of these new cornering stiffness values on the model matching is investigated in the next section 70 5 4 Bicycle Model Cornering Stiffness Correction Simulation Results The time and frequency domain simulations were completed again with the only change being the corne
86. d their magnitudes were managed by using witness marks on the steering wheel These inputs were given at two different amplitudes at a speed of 25mph 61 Since it is impossible for a drivers input to exactly match the metronome especially at high frequencies a non linear fitting routine was used to extract the input magnitude and phase during post processing As in 1 the routine consisted of minimizing the sum of squares error between the steering input data and a best fit sine wave The same procedure was performed on the output data yawrate and lateral velocity but the frequency of the best fit sine wave was fixed at the input frequency The input and output amplitudes and frequencies were used to determine the frequency responses for both yawrate and lateral velocity It is important to note that the current sensor suite allows the frequency response to be performed on lateral velocity and yawrate which allow for a direct comparison to the bicycle model This is a considerable improvement over the yawrate and lateral acceleration states used in 1 Steering Angle to Yaw Rate 20 j 15 J S E gp P th O FPB 2 10 H 5l J 0 J 1 10 10 w rad s O Z Be F T S D 2 50 P g E 8 High Amplitude Pa a 100 Low Amplitude 7 Bicycle Model Kus Method Lo T T T T T 1 L L 1 F is a 10 10 w rad s Figure 5 8 Yawrate Frequency Response Kus Method 62 Steerin
87. de deg o 0 4L 0 6 b 0 8 b o 2L WR x Road Grade vs Time 0 8 0 6 0 4 0 2 0 24 Road Grade deg o 0 4L 0 6 0 8 1 10 1 15 1 1 1 20 25 30 time s Figure 8 5 Road Grade L 35 Road Grade vs Path Distance 12mph 15mph 18mph 20mph 25mph 30mph r 1 40 45 50 0 L L 1 L T 1 200 250 300 350 400 450 500 Path Distance m Figure 8 5 emphasizes not only the location dependence but also the repeatability 107 These results clearly show that the road grade measurement can be used for longitudinal positioning If a road grade map template is created for a given path a vehicle s position along that path can easily be determined by fitting onboard road grade measurements to those of the mapped template This theory was tested by mapping the inside travel lane of the test track at the Pennsylvania Transportation Institute with results described in the next section 8 4 Road Grade Positioning A road grade template of the entire inside travel lane of the test track at the Pennsylvania Transportation Institute was made by recording the vehicle s pitch velocity and position while it was driven around the path After the template data was recorded the vehicle was driven around the same path and data was recorded over five random sections of track in 10 15 second intervals In post processing the sample
88. de Positioning widest Aches ane teases Sota taas eae es 157 UO eB UUs WWE cen eeni ea e A A AEN te Mh aL 158 10 4 1 System Integration 20s el asaheasio ys ase a a a s 158 10 4 2 Planar Model State Identification 0000000oseeseeeeeeeseeseeeeessssssessssssssse 159 10 4 3 Road Grade Positioninis c ccciui asta eae aisle aut ane 159 Appendix A Pitch Model Derivation Details ceceeceeeceseceecneeeeeeeeeeeeesecnaeeaeeess 162 A l Pad Approximation DiscCussion cccccsccesseceseceeeeeeseeeseeceaecneeeeeeeeeseeeaeens 162 A 2 Model 2 Identical Suspensions No Rotational Inertia 0 0 0 0 eee eeeeeeeee 164 A 3 Model 3 Different Suspensions No Rotational Inertia eeeeeeees 165 A 4 Model 4 Full Pitch Plane Models csissscsscsssdacazavatesnweatasdvtactaved nadsndestevateracseas 169 Appendix B Detailed Interface DSP Operation 0 0 0 cece ccceceteceeeceeeeeeeeeneenteeeeees 174 Bil Data Retrieval from DL 4plus axe alaceccsaeasdceess uadesarscvas cae oiaceseceeousd indeadaaste 174 BZ DLA plus Log Parsing cancel ecco tiated 176 B 3 Data Read from Steering Sensors ccsssccssccssccesessstccssccsscescsesnssseneees 179 Appendix C GPS INS Setup and Troubleshooting Guide cecccecsceseceeeeeeeeeeeee 181 C 1 Current Setiip Procedures ssisyncaaergetsvans Citen asaya E E aeons 181 C 1 1 Base Station Setup tsaccncgor coins paccashoeeted ety lusa anemone dee tasmedtnne Notun teecheneaeces 181 C 49 2 Rover Station SUID
89. ditions Based on the Characteristic Velocity in Proceedings of the 15th Triennial World Congress of the Internation Federation of Automatic Control IFAC 2002 Ann Arbor Michigan Chapter 6 Bicycle Model Tire Lag This chapter further investigates the high frequency mismatch of the bicycle model presented in chapter 5 It is known that there is a time lag between a sudden change in slip angles of a pneumatic tire and the build up of lateral force This has been modeled through the use of the concept of a relaxation length o 1 The relaxation length concept assumes that the force generated by a tire gradually approaches its steady state value as a first order differential equation In the sections to follow the bicycle model is re derived to incorporate tire lag due to the tire s relaxation length The model is then simulated in the time and frequency domain to investigate its validity 6 1 Bicycle Model with Tire Lag Derivation The tire lag model is often represented as a first order system with zero DC gain 2 In previous work 3 a first order tire lag model was introduced only on the front steering input After consultation with the authors of 4 and reviewing 5 6 the following model of tire lag was used which considers tire lag as a function of tire slip on the front and rear tires The fundamental bicycle model equations as written in chapter 3 do not change m a F F cos 6 F F F dr 6 1 I M
90. e Model Check Mag dB w rad s 300 r 20 Kinematic Model Identical Suspension Model 200 Different Suspension Model al Phase deg 150 se 100 L ee ae z J i 7 wi 50 1 po etyl 1 jt p ititrl 1 po ME SEE S SE 2 1 2 w rad s Figure A 4 Different Suspension Model Model Check This expression given in A 16 can be expanded and inverted to obtain the transfer function from U to 0 The result is a lengthy non causal transfer function of power s in the numerator and s in the denominator A single pole must be added for this to be simulated Expanding and inverting equation equation A 16 gives the following U s _ EN C s C s C s s s Cs C 0 s D s D s D s D s Ds A 17 Where the C coefficients are C k k n C Kk k n pn c k n C k km Ck Ny Cpk n c c n k m n k m n C c k pn c k n CCN k m n k m n c m n c m n C c c n k m n k m n c m n c m N m m n C c m n c m n m m n C m m n And the D coefficients are D 2 k k n D 2 c k n 2 c k n k m n k m n D 2 c c n k m n k m n c m n c m n D k m n k m n c m n c m n D c m n c m n Equation A 17 is not causal so as before a pole will be added at p U s 7 a b P Cs Cs Cs Cs Cs Cs a C 0 s s p D s D s
91. e In practice a vehicles steering angle on each side of a vehicle will be different in order to optimize tire wear and performance The exact difference is dictated by the vehicles Ackerman geometry and is a function of the vehicle s physical dimensions Because of this in this study both steering sensors were calibrated and the average angle recorded from both sensors was used as the true steering angle This method is in agreement with the bicycle model which assumes the forces and hence steering angles on either side of a vehicle are symmetric and treats the four tire model as a two tire single track vehicle 4 1 3 1 Steering Sensor Calibration The calibration routine in 9 was repeated in this work for each of the steering sensors The vehicle was first driven in a straight line for 30 seconds and the steering sensor output voltages were recorded The vehicle was then driven in the opposite direction over the same path and once again the output voltage was recorded The average reading for each sensor was taken and this voltage was used as the sensors reading for zero steer angles Slip plates were then used to record the voltages of each steering sensor at 5 degree increments Theses voltage readings were plotted with their corresponding angles and best fit lines applied to each data set Figure 4 5 shows the results of both sensor calibrations and their best fit lines 42
92. e capability of sampling at 100 Hz The constant angle offset due to IMU mounting can then be subtracted out of the measurement in real time since this offset was determined using the IMU calibration techniques outlined in section 4 1 1 2 The resulting measurement can then be low pass filtered as in 5 to estimate the road grade A second method discussed by Bae 5 uses GPS vertical and horizontal velocities to estimate road grade In this work the vertical and horizontal velocities are measured by the IMU at the CG Therefore road grade can be estimated as W A tan 8 1 6 Once again a low pass filter can be applied to the road grade estimation to help remove the higher frequency vehicle dynamics and road irregularities Bae s 5 investigation into the differences between these two methods revealed that the pitch based estimate shows oscillation during periods of rapid acceleration or 104 deceleration while the velocity based estimation is less sensitive to accelerations However outside the periods of acceleration the velocity based measurements show more variability and oscillation For comparison both methods of estimation were compared in their approximation of road grade Both methods were tested on a steady state turn maneuver with a low pass cutoff filter frequency of 1 5 Hz This is shown in Figure 8 3 road grade Ae calculated from Vvert Viong low frequency pitch 0 54
93. e 8 15 Implementation Diagram Model Inversion In the next chapter several pitch plane models are derived These models are then used in conjunction with an inversion technique for a better estimate of the true road grade one which is independent of the vehicle setup and its speed 8 7 Conclusions e The repeatability and location based nature of road grade estimates has been shown e Experimental results have been given to prove the concept of road grade based positioning e For the test vehicle used here the low frequency content of the pitch measurements showed only small variation with large variations of speed e In order to obtain road grade estimates which are independent of vehicle setup and speed investigation an into pitch plane model inversions is needed 119 Ryu J E J Rossetter and J C Gerdes Vehicle Sideslip and Roll Parameter Estimation using GPS in AVEC 2002 6th International Symposium on Advanced Vehicle Control 2002 Hiroshima Japan Ryu J and J C Gerdes Estimation Of Vehicle Roll And Road Bank Angle 2004 Boston Massachusetts Vahidi A A Stefanopoulou and H Peng Experiments for Online Estimation of Heavy Vehicle s Mass and Time Varying Road Grade in Proceeding sof IMECE DSCD 2003 2003 Vahidi A A Stefanopoulou and H Peng Recursive Least Squares with Forgetting for Online Estimatoin of Vehicle Mass and Road Grade Theory and Experiments Journal of Vehicle System Dynamics 2005
94. e Rear Disturbance Input 20 T T T T T T TF T T TT mr O i g i 20 pe gt 40 S 60 L i4 10 10 10 10 w rad s 300 ae Kinematic Model gt Identical Suspension Model P 200 4 a Different Suspension Model D Full Model 100 see 4 oO i L ii 10 10 10 10 w rad s Figure A 5 Full Model Frequency Response This can then be inverted to solve for that ratio U 0 U 2abXY by x s m ax Y s m J s x ae ae ms T 2 A 49 0 Xe a b am s Y a b X bm s y As in the previous derivations the Pad approximation is used to estimate the time delay with a rational function 172 The inverse Pad approximation can be substituted into the above equation for e This algebra was performed in Wolfram s Mathematica and the resulting equation is of the form U s E s Es E s Es Es Es E A 5 0 s Fs Fs Es Fs Es Where the E coefficients are E k k n a by A 51 E k k n a by c k n at b c k n a by A 52 E k kn at by C K pn at by c k m a b c C n a b l A 53 J k n J k n a k m n b k mn E c k n a b c k n at by c c n at by Jk Ny J k n a k m n b k m n C J yn cJn A 54 a c mn b c m n E pl c c n a by Jy k n J k n a k m n b k m n CrJ Nn CSN ac MN b c m n A 55 J m n E CJ yy CJ n
95. e alignment of the inertial system to the vehicle s body frame is derived with a combination of the measured accelerations of the IMU compared to the gravity vector and the angular rate measured by the IMU compared to the earth rate The alignment computation requires that the system does not experience any specific forces except gravity is not physically rotating except from earth rotation and that gyro bias in the unit is small compared to the earth rate 6 The DL 4plus automatically completes this inertial system alignment after it locks onto four satellites and an initial position can be calculated from GPS During this stationary calibration the IMU s roll and pitch alignment is 0 18 degrees while it is only 45 degrees for yaw The yaw is particularly inaccurate because of the system is using the latitude and the earths rotational rate to resolve the yaw angle This calculation is therefore skewed by the high gyro drift to earth rate ratio 5 However over time the stationary system will resolve the yaw heading to within a few degrees approximately 5 degree accuracy after 300 seconds at 40 degree latitude In order to expedite the process the system should be put in motion after the frame detection and coarse alignment and is complete This will make the yaw angle observable and therefore increase its accuracy at 36 a quicker rate As the yaw accuracy improves the INS status message in GPSolution will change from Coarse A
96. e angle is presented in Figure 8 2 ie e Pitch 4 Road Grade Figure 8 2 Pitch and Road Grade Where W is the vehicle s vertical velocity U is its longitudinal velocity 0 is the pitch angle and A is the road grade 103 In 5 a two antenna GPS system mounted to the roof of the vehicle is used to measure the orientation of the vehicle in the X Z plane at a 5 Hz rate The angle measured is the sum of the pitch and road grade angle It is influenced by the vehicle s acceleration as well as high frequency road irregularities and will likely include a constant angle offset due to sensor mounting Bae points out that since the road grade usually changes slower than the pitch motion of the vehicle the low frequency portion of the pitch measurement can be used to estimate the road grade In Bae s work a 0 5 Hz low pass filter is applied to the pitch signal to approximate road grade One must note that in his work the road grade was not used to assist with positioning but to approximate the engine torque required to overcome an uphill climb Therefore the distance resolution of the measurement was not critical and a low sampling frequency was sufficient In order to achieve an accurate position estimate from road grade the road grade estimates must have high spatial resolution In this work the angle corresponding to the sum of the pitch and road grade is directly measured by the IMU at a 50 Hz rate with th
97. e experimental data the effects due to the non uniform terrain became apparent These effects were determined to be highly repeatable and 4 location dependent These two characteristics allow the terrain effects to be used to assist in a positioning solution The terrain influences have been studied previously in works such as 6 where they were removed from the state estimates to improve state accuracy Also the concept of Road Grade positioning was investigated in 12 where the terrain effects were identified with commercial grade sensors however performance was limited in positioning accuracy due to its inferior computing and sensing architecture a pressure sensor to measure changes in vehicle height as well as its lack of vehicle dynamic considerations This work attempts to eliminate these shortcomings This work will also derive and compare multiple Pitch plane models to help achieve higher accuracy in a terrain based positioning method The goal of incorporating vehicle dynamics into the correlation algorithm is to allow the terrain disturbance positioning routine to be used on a wide range of passenger vehicles and speeds 1 2 Outline of Remaining Chapters The remaining chapters of this work will structured as follows Chapter 2 will present the basic concepts behind GPS and INS systems and their integration into a vehicle data acquisition system Although the fine technicalities of each of these sensors will not be pre
98. e following information about this logs header structure 1 2 Table B 1 Short Binary INS Message Header Structure Field Field Type i Description Binary Binary Bytes Offset Sme Char Heroa i sm fow aso Week Number GPS week number Milliseconds Ulong Milliseconds from the beginning of the GPS week 1 y 1 oo 2 s 3 s a feet Te os BA EAMA After the three bytes have been read from the serial port they are compared to the sync bytes OxAA 0x44 and 0x13 integer values 170 68 and 19 respectively If these sync characters do not match they are shifted and a new byte is read else sync bytes do not match Store last 2 sync bytes and read in a new 3rd one to check again syncl sync2 sync2 sync3 checkfornewcharUART1 amp sync3 SYS_FOREVER If the specified bytes do match then the program proceeds to read the remainder of the message First an array is filled with the rest of the short header 9 bytes while UART lheadercollect lt 9 Fill header with 9 bytes short header logs checkfornewcharUART1 amp UART Ireceivechar SYS_FOREVER UART1HeaderArray UART lheadercollect IntValue char UART Ireceivechar amp OxFF UARTIheadercollect 176 After the header array has been filled the message ID can be extracted MessageIDByte1l UART1HeaderArray 1 IntValue MessageIDByte2 UART1HeaderArray 2 IntValue MessageIDByte2 MessageIDByte2 lt lt 8 Shi
99. e is subtle compared that of the lateral velocity matches This is especially apparent in the low frequency steering input portion of the chirp response Below is a direct comparison between the two methods Yaw Rate Prediction and Measurement Chirp Comparison 157 wentttan l 10F w f po ii i a i 7 nil R 4 J FTA TA AS li a i BER OF EIUN riji e 2 i yn k f g Of MS HL a A J a 1 H UEA 51 VAT Ty Y SW REI AAAA MAI 10 10L l j sasaa f Predicted DC Gain Method Predicted Kus Method 15 L f L f T T I i 8 10 12 14 16 18 20 2 24 time s Figure 5 19 Yawrate Chirp Response Method Comparison 75 Lateral Velocity Prediction and Measurement Chirp Comparison ny i i A 0 3 0 24 0 14 m s 0 1 F TESTER y 0 2 o 0 3 Predicted DC Gain Method Predicted Kus Method 0 4 L 1 f L T i I I 6 vf I 8 10 12 14 16 18 20 22 24 26 time s Figure 5 20 Lateral Velocity Chirp Response Method Comparison The circled area of Figure 5 19 suggests that time domain yawrate plots consisting of low frequency steering inputs should not be used to fine tune cornering stiffness values as the results of cornering s
100. eal case in order to implement a GPS system in a vehicle environment Because of this a more descriptive but not a complete description of the details of GPS has been included below 2 2 2 Technical Description 2 2 2 1 Satellite Signals Each NAVSTAR Satellite transmits three codes in the form of Pseudo Random Noise PRN modulated on the two carrier frequencies L1 and L2 There are two ranging codes referred to as the Coarse Acquisition Code C A and Precision code P Code as well as a Navigation message code which contains critical satellite information All three of these codes are modulated on the L1 frequency and only the P code is modulated on the L2 frequency They are modulated on each carrier signal by a rarely used modulation method called Bi Phase Modulation as opposed to the Amplitude Modulation AM and Frequency Modulation FM of common radio signals In Phase Modulation the carrier signals phase reverses when data transmission starts and then re syncs phase at the end of 12 transmission This modulation method is discussed further in 2 and shown in Figure 2 3 Carrier Code Modulated Carrier Figure 2 3 Bi phase Modulation of Carrier Wave The general public has been given free access to the C A code on the L1 carrier frequency Each satellite has its version of the C A code characterized by each satellites PRN number These messages are relatively short in length 1023 bits and are repeat
101. easurement FFT 0 ce eeeeeceeceeeeceecneeeeeeeeeeeeeseenaes 115 Figure 8 13 Unfiltered and Filtered Pitch Measurements c cssseeseeeeeeeceeeeeeeeee 116 Figure 8 14 Implementation Diagram Low Pass Filter ce eeeeseeseeseeereeeeeeeeeeees 117 Figure 8 15 Implementation Diagram Model Inversion cceseeseeseereeeeeeeeeeeee 118 Figure 9 1 Pitch Plane Model Free Body Diagram cceccecsceesseceteeeeeeeeeeenseees 121 Figure 9 2 Kinematic Model Block Diagram cccesscessesseseeceecceseeeseeeeeeneeenes 123 Figure 9 3 Kinematic Model Frequency Response ccccccesceceseceteeeeeeeeeeeeseees 126 Figure 9 4 Effect of Decreasing Wheelbase ccscosssscessrsonsorcerscessesscesetenesones 127 Figure 9 5 Identical Suspension Model Block Diagram cceeeceeeeeeseeereeeteees 128 Figure 9 6 Quarter Car Model Free Body Diagram ccceecceeccecsseceteceeeeeeeeeeeeees 129 Figure 9 7 Identical Suspension Model Frequency Response ceseeseerees 130 Figure 9 8 Spring SUTMESS F Us j ciccieosssantousshccteatsccantalanecsnvetbocensssinctaak tecsavedbecunussnnctas 133 Figure 9 9 Front Oscillation Diagram sessesessesseeessseseesesseseesesseseeseseesesseseesessese 134 Figure 9 10 Measured and Estimated Vertical Displacement at CG eens 135 Figure 9 11 Quarter Car Model Simulink Diagram essssssesssessessesss
102. ed every millisecond A GPS receiver capable of reading C A code on the L1 frequency can use its own internal clock to replicate the L1 carrier frequency signal as well as the PRN signals from each satellite The receiver can then compare these replicated signals sometimes called reference signals with those received to generate ranges as described previously In addition to the C A code on the L1 frequency each satellite also transmits a Navigation message containing its orbital elements clock behavior system time and status messages An almanac is also provided which gives the approximate location for each active satellite so the receiver can track and lock onto additional satellites more efficiently The information in the Navigation message being sent by each satellite is monitored and updated by the MCS and its monitoring stations to ensure accuracy At all times the MCS knows exactly where each satellite is and where it should be next 13 Until the year 2000 non military users operating on the L1 frequency were affected by a service called Selective Availability SA SA is the intentional degradation of GPS messages on the L1 frequency SA was put in place by the DoD to stop users from having dangerously accurate systems During this time when C A messages were decoded on a single receiver one could achieve accuracy on the order of 100 meters in the horizontal direction As the demand for a more accurate non military system increased
103. ed through roll disturbance analysis can then be blended with that of the road grade analysis through a Kalman filter to achieve an optimal solution Cameron J T Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover 2005 The Pennsylvania State University Appendix A Pitch Model Derivation Details This appendix includes the details of the pitch model derivations not presented in Chapter 9 A 1 Pad Approximation Discussion As discussed in Section 9 2 in this work the time delay between the front and rear road inputs has been approximated by a second order Pad approximation To choose the appropriate order of this approximation a simple simulation comparing the error associated with different approximation orders was performed Figure A 1 shows a simulated rear road disturbance and the first four Pad approximations of this disturbance 0 08 0 07 0 06 0 05 0 04 H 0 03 H 0 02 0 01 First order RMS error 0 0057078 Seconds order RMS error 0 002718 Third order RMS error 0 001827 Fourth order RMS error 0 0015703 Original Laval f Hy MA N 7 l AAA Wa Mi Mhag Y Y ii Ri HIN Vy Wy N A KY AN l y1 Vi 20 40 60 80 100 120 140 160 180 200 Figure A 1 Pad Approximations Rear Road Disturbance 163 Figure A 2 shows only portion of the previous figure so the diffe
104. eeeseeeeeeee 59 Figure 5 7 Lateral Velocity Steady State Circle Response Kus Method 60 Figure 5 8 Yawrate Frequency Response Kus Method 0 0 0 0 cesesceeseeeeeeeeeteeneeenee 61 Figure 5 9 Lateral Velocity Frequency Response Kus Method ceseeseeeteees 62 Fig re SM Sideslip Vector vincccaunnesseatsrmurexorstacaassnnesandoniaccad hhundeenpiatsecrininansuanteaasaindaas 66 Figure 5 11 Lateral Velocity Frequency Response DC Gain s ssssessseeseesesseese 68 Figure 5 12 Yawrate Frequency Response DC Gait ceeceseeseeseereeeeeeeeceseeneeeaee 68 Figure 5 13 Yawrate Chirp Response DC Gain Method cccecsccesseeeeeeereeeteees 71 Figure 5 14 Lateral Velocity Chirp Response DC Gain Method eeeeeeeeeeee 71 Figure 5 15 Yawrate Steady State Circle Response DC Gain Method 04 12 Figure 5 16 Lateral Velocity Steady State Circle Response DC Gain Method 72 Figure 5 17 Yawrate Frequency Response DC Gain Method 1 0 0 ce eeeeseereeeeeeees 73 Figure 5 18 Lateral Velocity Frequency Response DC Gain Method 00 73 Figure 5 19 Yawrate Chirp Response Method Comparison ceccssceeseereeeeeeee 74 Figure 5 20 Lateral Velocity Chirp Response Method Comparison 0000 75 Figure 6 1 Yawrate Frequency Response Varying Relaxation Length 0 81 Figure 6 2 Lateral Velocity Frequency Re
105. el DC Gain Derivations s ciscssasscisisssscacsaziacaalacsoaceeareciseas 64 5 3 2 Alternate DC Gain DeriVati Mecsas jisxssseeesaaciecthaastaviians quinn eed a 65 5 3 3 Cornering Stiffness Values from DC Gains 0 ccc eeeceeseeeeeereeeteees 67 5 4 Bicycle Model Cornering Stiffness Correction Simulation Results 70 S41 Chirp R CSP ONS Gi coisa odes ics te a eE RE cide dete eee ada 71 5 4 2 Steady state Arete uiii neieiet sereins i nista tanins ireanii asis 12 54 3 Fregene y IRGES PONS E zerei a E R 73 5 4 4 Bicycle Model Cornering Stiffness Correction Results Discussion 74 5 44 Chirp RESPONSE naisina nana tetas a a i 74 5 4 4 2 Steady state Circles 2216 Gee ine oe onl oes ae etic 75 5 4 4 3 Frequency RESPOMSE gone a asad esas aeccsisseucenss suas vost avense vi anc dseoauceontes 76 Ded Eaa To ADES CO o CA REEE 76 Chapter 6 Bicycle Model Tire Lag osssnsesessesseossesseeseesseesresrressessrssressessessresseeseese 78 6 1 Bicycle Model with Tire Lag Derivation sssesessssssosseesreseessessesrrssressessres 78 6 2 Tire Lag Model Simulation Results cccccesccessceseeeteecseeceseceeeeeeseeeaeees 80 6 2 1 Frequency Response cis s3 csayssedectaessncetgasedecenabeven tedentectensteceesneesnctaessem ees 81 6 22 Chirp Respons eeren niena cae e a a n A aE A ES 84 6 2 3 Steady State Cle Sac fec sua an n a n e a a a R E 85 6 3 Tire Lag Model Results Discussion s seessesessesse
106. erated by the front and rear tires This representation comes directly from equations 6 2 and 6 7 dV 0 U a m m 0 dr 0 0 2 2 4 0 dt l I r C U dF 7 Cy Cya U F t aS 27 68 eres 0 f o dF L f C ar Cab U L dt 0 Oo Oo Oo 6 2 Tire Lag Model Simulation Results The time and frequency domain simulations performed in chapter 3 were repeated here for the new model which includes tire lag Using the results from chapter 5 the cornering stiffness values obtained from the DC gain method were used in these simulations With the cornering stiffness values solved for the A matrix of the state space representation of equation 6 8 still has one unknown o the tire relaxation lengths In order to determine the value of the relaxation lengths parametric variation was performed in the frequency domain This method is similar to that performed in 3 for cornering stiffness variation Because of this parametric variation procedure the frequency response results will be discussed first 81 6 2 1 Frequency Response In order to determine the tire relaxation length the tire lag model was simulated with increasing values of o from 0 4 to 1 6 m in 0 15m increments and the resulting plots were investigated in the frequency domain The figure below shows the effect of tire lag for yawrate Steering Angle to Yaw Rate with Tire Lag 20
107. erefore were not used The I O channels on the DSP used to read the ADC data are limited to 10 to 10V Since in the systems current configuration the string potentiometers only operate in a small portion of their maximum range a 30V differential was applied to each potentiometer to give high resolution readings which still remained in the 10 to 10V range A more detailed description of the DSP programming including sections of the code included in Appendix B 4 1 4 1 2 Master DSP After messages are decoded on the Interface DSP they are transmitted to a second DSP referred to as the Master DSP via custom Controller Area Network CAN daughter cards AT designed by Vishisht Gupta of The Pennsylvania State University The Master DSP has been programmed to run a continuous loop which prepares and sends the data received on the CAN bus over a parallel port to the Server PC It was necessary to include this second DSP in the data acquisition system to ensure enough processing power was available for future vision and control integration Also the parallel port transmission requires continuous processor time which is not available on the Interface DSP due to the interrupts required to run the steering sensor ADC process The master DSP s CAN processing code was developed by Vishisht Gupta and needed not modification for this project It s details will not be presented here 4 1 4 2 PC Operation The data acquisition system s PC plat
108. es which orbit the earth at 11 000 miles above the surface The present constellation consists of 24 operational satellites deployed in six evenly 8 spaced planes A to F with an inclination of 55 degrees and with four satellites per plane 2 This arrangement guarantees 4 8 visible satellites from any given point on the earth assuming open sky visibility These solar powered satellites orbit the earth once every 12 hours at a speed of 3 9 km s Each satellite is equipped with 4 atomic clocks accurate to a billionth of a second The NAVSTAR s accuracy is directly affected by the accuracy of each satellite s onboard atomic clocks These clocks are used to synchronize all system processes and to produce the fundamental L band carrier frequency on which GPS data is modulated The two frequencies used by GPS are denoted L1 1575 42 MHz and L2 1227 60 MHz Civilian GPS receivers use only the L1 frequency on which navigation data and Coarse Acquisition C A code for Standard Positioning Service SPS is transmitted On the other hand the L2 frequency only carries P Code or encrypted P Code called Y code to be used by receivers designed for Precision Positioning Service PPS namely military grade receivers The C A code is purposely omitted from the L2 carrier which allows the Joint Program Office JPO to control the information broadcast by the satellites and allows them to deny full system accuracy to nonmilitary users 2 2 1 2
109. esis will be separated into three sections Systems Integration Planar Model State Identification and Road Grade Positioning Following a discussion of the conclusions the future work will be presented 10 1 System Integration In this study a military grade DGPS INS sensing system was integrated into a DSP based real time data acquisition system for vehicle state identification The system is capabable of collecting centimeter level accurate data at 100 Hz It has a user friendly interface to allow users to capture data directly into MATLAB and to run simulations in teal time for model matching in the field The system can also be expanded to allow for actuation control and future automation requirements When the system used in this work is compared to that used in previous works 1 several conclusions can be made First the measurements of the current military grade system can be considered much more accurate than that of the previous comercial grade system Also the system used in this work give the user the important ability to directly measure vehicle attitude angles This not only allows the user directly analzye things like vehicle roll pitch yaw and sideslip but also allows the user to accurately account for constant angle offsets due to sensor mounting At the end of Cameron s work the signal to noise ratio was brought into question This is a non issue with the current system because of both the sensor quality and the bui
110. esseseesseesseserssressessessees 86 vi 6 2c PREQUETIC VRC SONS Ga G en R a conte R Oat act Uae hae 86 6 3 2 Chirp RESPONSE si eunin Atv ce E etait ane Ane Sarin es 87 6 3 3 Steady Stat Ci Che nsss acy batts caste naiari aa aS oE A otaeditanedatias 89 OA SOT ISOS an i a i a aOR cae oi Tal 90 Chapter 7 Bicycle Model Camber Correction 0 cccccscecsseceteceseeeeeeeeseeesseeeeeees 92 7 1 Camber Correction Derivation jaxissc iccssse tss eeastaotiaseatirvieza davatinotangestavstedactsas 92 7 2 Camber Correction Simulation Results ccccceccceecceeseceeceseeeeeeeeeeenseees 98 7 2 1 Steady state Circles a 5 asses prac cll esata caie cease ane dang CoeadasGacgabaucaneeunlsees 98 Hor ONG LUIS TONS ware raate tate falas ans ht teat ae etna a a aeRO E 100 Chapter 8 Terrain Disturbances for Longitudinal Positioning ccceeeeeeeeetees 101 8 1 Initial Terrain Disturbance Observations ccceccceesseeeseceeeceeeeeeeeeeseeenseenes 101 8 2 Road Grade Bstimationss iia seedy Gentuct sas seacissikteneue anit aau caine 102 8 3 Road Grade Repeatability and Location Dependence ce cceeceesseeeteeees 105 S84 Road Grade Positioning irisscan insni air A E RRA AAE aae 107 8 5 Longitudinal Positioning ssesessseessessesseessessesseesseesesresseessessessressessessressesse 113 8 0 RESUlts DISCUSSION lt x viccal ne nitet a a araa a E E Ea A EAA a 116 xk CONCLUSIONS n na os eae ten eure aR a cous aT 118 Chapter 9 Pi
111. essessrssresseese 136 Figure 9 12 Example Pitch Plane Excitation esseseseseessseseeseeseseeserssrsersessrsersessese 136 Figure 9 13 Quarter Car Model Bite isasssisaisccaciessadexgeantoonsavacteagusnienaesreateasesantoncavaccseees 137 Figure 9 14 Kinematic Model Simulink Diagram Pitch Generation ee 139 Figure 9 15 Kinematic Model Disturbance Plots ce eeeeceseceeeneeeeeeeeeeeeceseeneeeaee 140 Figure 9 16 Kinematic Model Generated Pitch nssnsssssseseesesseseesessersessrsersesseserse 141 Figure 9 17 Kinematic Model Simulink Diagram U Recovery s ssssssssesssssseesee 141 Figure 9 18 Kinematic Model Original Rear Input and Recovered U 00 142 Figure 9 19 Identical Suspension Model Simulink Diagram Pitch Generation 143 Figure 9 20 Identical Suspension Model Generated Pitch ceceeseseeseeeeeeneeenee 143 Figure 9 21 Simulated Pitch Measurements FFT eeeeeeeeeeeseceecneeeeeeeeeeaeeneeeaee 144 Figure 9 22 Identical Suspension Model Low Frequency Pitch eee eeeeeeenee 145 Figure 9 23 Pitch Angle and Extracted Rear Road Disturbance eececeeeeeeeeeees 146 Figure 9 24 Identical Suspension Model Extracted and Actual Rear Disturbance 147 Figure 9 25 Road Grade from Road Disturbance Estimations Diagram Figure 9 26 Road Grade from Road Disturbance Estimations Plot eee 148 Figure 9 27 Model Inversion In
112. estigated in the steady state turning maneuver 7 2 1 Steady state Circles Figures 7 3 and 7 4 show the time domain model matching for steady state circles for the model with and without the roll camber correction 99 Yawrate SS Circle With and Without Camber effects 25 Measurement Predicted from Bicycle Model with Tire Lag amp Roll Predicted from Bicycle Model with Tire Lag Only 20 Hh Nall jl f A o AA kaea ET e Ag D 15H Hane f ne 10 5 i L i i L 1 L 5 10 15 20 25 30 35 40 time s Figure 7 3 Yawrate Camber Model SS Circle Lateral Velocity SS Circle With and Without Camber effects 0 37 0 25 L i 0 2 2 E 0 15 0 1 0 05 Measurement Predicted from Bicycle Model with Tire Lag amp Roll Predicted from Bicycle Model with Tire Lag only 0 ji T T I I I L 5 10 15 20 25 30 35 40 time s Figure 7 4 Lateral Velocity Camber Model SS Circle As seen in Figure 7 3 the yawrate plot has not been significantly changed and the model still accurately predicts this state In Figure 7 4 it is clear that the constant offset value in the lateral velocity plot has been decreased by the addition of a camber model This confirms the theory that vehicle roll is affecting the tire force generation in steady state 100 turns A full roll model can be used to further investigate the roll cambe
113. ffnesses since these values were shown to be valid for these maneuvers In addition to solving for cornering stiffnesses the yawrate DC gain equation can help solve for the remaining two unknowns C and C As discussed above the effect of camber must be accounted for in a steady state circle maneuver The DC gain for the steady state circle maneuver accounting for camber can be written by dividing the steady state yawrate by the required steady state steering input as described in equation 7 10 G ice L 1b mU U 1 a mU U rele 7 10 C C R Cy L R R CIL R R ar f circle Equation 7 10 can be rearranged to solve for C s in terms of C r Pa 1 nm 2 b L G E ei l Gror U EO Cy V C l r circle ar 97 The above equation has only two unknowns C C three measurable parameters U a b m and the two cornering stiffness values which were determined using the DC gain method To get a final equation to solve for the remaining unknowns the behavior of the rear of the vehicle in a steady state turn must be revisited As in equation 5 24 the lateral velocity of a vehicle in a high speed turn can be expressed as v u 2 2 7 12 R Using equation 7 12 and 7 9 the equation for the lateral velocity gain for a steady state circle can be written U f Q y _ R 8 2 U 2 U f circle L 1 b 7 mU C U 1 4 mU C U R Cll R Ry Coll OR R 7 13 Lil G4
114. form is used to monitor and record data in real time after it has been processed by the DPS s It also supplies the user a graphical interface via MATLAB s Simulink from which the user can adjust parameters such as controller gains for real time system modification and tuning The PC platform is divided between a Client PC and a Server PC This division allows the user to monitor data from outside the vehicle The PC platforms functionality is described below After the dual DSPs acquire process and re send the GPS and steering sensor data over the parallel port the data is received by the first half of the PC platform the client PC The client PC has a 400 Mhz Pentium III processor which runs the client portion the Wincon software package Wincon allows Simulink models to be run in real time and ensures that the real time process is afforded the highest CPU priority and is not pre empted by any competing tasks other than the core operating systems functions 10 The data received on the Client PC is then immediately transmitted to the Server PC The Server PC runs MATLAB s Simulink along with the Wincon server to supply the user with a graphical interface for data monitoring and recording Custom S Functions 48 were written which Wincon allows the user to save data files in standard MATLAB formats which greatly simplifies post processing The Client Server communication is accomplished via the standard TCP IP network protocol
115. frequencies in particular at steady state when higher order model effects can be neglected the bicycle model still does not match the data In order to force a match at low frequencies the bicycle model DC gain equations were investigated The DC gain of the model was forced to match that of the data and this relationship was used to calculate front and rear cornering stiffness values which would be necessary for such a match The frequency response method is particularly useful because the inherent averaging of the response tends to eliminate the 64 undesired effects of super elevation and non steady state behavior The DC gain method of determining cornering stiffness values is presented in the following sections 5 3 1 Bicycle Model DC Gain Derivations The bicycle model can be represented in standard state space form X AX BU 5 12 Y CX DU 5 13 Where equation 5 12 was presented for the bicycle model previously in Chapter 3 as equation 3 14 Equation 5 13 will vary depending on which state lateral velocity or yawrate is desired as an output By presenting the bicycle model in state space form the DC gain equations for yawrate or lateral velocity are easily written by G D CA B 5 14 The lateral velocity DC gain is computed with the A and B matrices presented in equation equation 3 14 and the following C and D matrices c 1 0 5 15 D 0 The lateral velocity DC gain is then directly written U C Cy 0
116. fts bits over 8 MessageID MessageIDByte2 MessageIDBytel1 The last two lines of the above code combines the two bytes corresponding to the message ID by bit shifting the second byte and then performing a bitwise OR between the two values The header also gives the message length which is specific to each log and has stored in the first element of the UART1HeaderArray array MessageLength UART1HeaderArray 0 IntValue With the message length and ID known the log content can be read This is done in the function UART1MessageCollection in the same manner as reading the message header void UART1MessageCollection void UARTImessagecollect 0 while UART1messagecollect lt MessageLength checkfornewcharUART1 amp UARTIreceivechar SYS_FOREVER UART1MessageArray UARTImessagecollect IntValue char UARTIreceivechar amp OxFF UARTImessagecollect ee of function UART1MessageCollection After the message collection is complete the task UART1ReceiveCharTask posts a semaphore SEM_UART1MessageReady to initiate a second task NetReceiveMessageTask which is used parses the messages and send them over the CAN bus B 2 DL 4plus Log Parsing For each available log NovAtel supplies a table indicating the breakdown of all of its contents 1 2 Since binary messages have been used for speed purposes the data parsing is not as straight forward as one may assume In order to accomplish the 177 processing in binary
117. g Angle to Vlat 20 F 15 J S wL 2 e 4 D OS ae Z yk OF a 5 0 1 L F 7 10 10 w rad s o J t oe 3 amp SB 50b es 4 a Hi 8 FO 8 igh Amplitude Pe aoo Low Amplitude ca J Bicycle Model Kus Method I ni T T ni L 1 1 1 L 10 10 w rad s Figure 5 9 Lateral Velocity Frequency Response Kus Method Yet again the bicycle model shows better matches to the yawrate data than the lateral velocity data The yawrate prediction matches very well for both magnitude and phase for frequencies lower than 10 rad s However the lateral velocity magnitude and phase plots do not match at all This will be further discussed in the next section 5 2 4 Bicycle Model Results Discussion In the previous three sections the bicycle model s accuracy was investigated in various situations The overall poor data fits for each time domain maneuver and the poor match in the frequency domain both suggests an error in the mode the model parameters or both An initial comparison between cornering stiffness values determined in section 5 1 and those used other works 1 4 5 suggest that although the numbers used here are reasonable they may be lower than the actual value 63 Further investigation into the cornering stiffness method used in section 5 1 uncovered some interesting issues This method is highly dependent on the understeer gradient determined in section 5 1 2 and a
118. g its reference signals to those received from the satellites the receiver can calculate the phase lags between the two signals This phase lag corresponds to the signal travel time from the satellite to the phase center of the GPS antenna This time multiplied by the speed of 14 light gives the receiver satellite range If the receiver s onboard clock could exactly match that of the satellite a receiver would be able to precisely calculate its position from only three satellite ranges In practice this is not possible because the quartz clock has an inherent time drift which creates a timing offset from true GPS time Because of this offset the distance measured to the satellite is slightly longer or shorter than the true range 2 Thus the calculated distance is not the true range but a pseudorange The pseudorange measurement can typically be modeled as P t t c 2 1 Where P is the pseudorange between the receiver and satellite n t is the receiver clock time 7 is the satellite transmit time and c is the speed of light Both the receiver and satellite have their own clock biases which create errors in the true range calculation The satellite clock bias can be modeled as a polynomial whose coefficients are transmitted to the receiver in the Navigation message 2 The satellite bias can then be easily removed from the range calculation The receiver can then estimate its own clock bias by calculating pseudoranges
119. gation Washington D C Ford T J Neumann and M Bobye OEM4 Inertial An Inertial GPS Navigation System on the OEM4 Receiver 2001 Banff Alberta Ford T J Hamilton and M Bobye Injected Alignment for an INS System for Trackmodel Data in a Race Car Environment in Proceedings of ION GPS 03 2003 Portland Oregon Janet Neumann J Z G Beutler J Kouba Real Time Carrier Phase Positioning Using the RTCM Standard Message Types 20 21 and 18 19 in Proceedings of ION GPS 97 1997 Kansas City Missouri NovAtel OEM4 Family of Receivers User Manual Vol 2 Command and Log Reference OM 20000047 Rev 18 2005 Alberta Canada Cameron J T Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover 2005 The Pennsylvania State University Quanser Wincon Product Information Sheet 2004 Ontario Canada Chapter 5 Vehicle Parameter and State Estimation Measurements and Bicycle Model Predictions The GPS INS sensing and data acquisition system described in the previous chapter was used to measure vehicle roll pitch yaw velocity direction velocity magnitude and position in order to verify various models This chapter will first present methods of vehicle parameter estimation based on bicycle model theory and the results of an investigation into the bicycle models accuracy An alternate way of estimating cornering stiffness is then presented and the new method is tested A comparison between two c
120. gh speeds The frequency of this low pass filtering effect is dependent on the vehicle s mass distribution and suspension characteristics To directly see the low 115 pass filtering effect of the vehicles suspension a Fourier Fast Transform FFT can be performed on the raw unfiltered pitch measurements The data used for the FFT must be a function of distance Frequency Content of Pitch Measurements 0 45 5 mph 40 mph 65 mph 0 35 0 25 02 i 0 1L TT aos NT a yy N Ww RAYS ARE EDS 4 LV NE 0 0 05 0 1 0 15 0 2 0 25 0 3 0 35 Frequency cycles meter Figure 8 12 Unfiltered Pitch Measurement FFT The above figure shows that the low speed data has a higher power density at high frequency than does the high speed data Conversely the high speed data has higher power density at low frequencies than the low speed data This division occurs at approximately 0 1 cycles meter This is shift in the signal s frequency content directly demonstrates the suspension s speed dependent low pass filtering effects Another interesting observation from the above FFT is the obvious similarity between the low frequency content of the signals This low frequency content is precisely what is sought after for the correlation routine In order to remove the unwanted high 116 frequencies an additional low pass spatial filter with a cutoff frequency of 0 1 cycles meter i
121. gle high precision map for their correlation routines so that manufacturers do not have to generate a map for all major roads and for all vehicles This type of positioning routine is demonstrated below Vehicle A Measured Pitch Low Pass Filter Vehicle B Measured Pitch Low Pass Filter Position Figure 8 14 Implementation Diagram Low Pass Filter The routine presented in Figure 8 14 would only be appropriate if the low frequency pitch content of all vehicles was the same for a given road profile However since the mass distribution and suspension parameters will vary from vehicle to vehicle the same road profile will not cause the same pitch measurements across different vehicle models Although the road grade estimates for the test vehicle in this work did not vary with speed this will not be the case for all vehicles In the next chapter this will be shown in simulation In order for a single map to be used for all vehicles this positioning routine must include a vehicle model that accounts for pitch plane dynamics By inverting the pitch plane model the vehicle dynamics can be removed from the pitch readings and more accurate 118 road grade estimations can be made that are independent of the vehicle and its velocity A more realistic implementation routine is given in Figure 8 15 Vehicle A Measured Pitch Model Inversion Vehicle B Disturbance Map Measured Pitch Model Inversion Figur
122. has acquired four or more satellites calibrated the IMU and started to transmit the pre programmed 186 logs INSPVASB INSSPDSB If after 10 minutes the green light does not begin flashing or if the red light is lit please see section C 2 If the base station has been setup at this time you will also observe the red light above the COM2 port blinking This shows the base station receiver communication via the radio modems If this red light is not flashing please see section C 2 12 Connect the COM1 port of the rover receiver to the serial input of the Interface DSP via the black serial null modem cable 13 Rover GPS INS setup complete C 49 2 2 Data Acquisition System The Data Acquisition system consists of the two DSP s and the two PC s If the Rover GPS INS calibration above has been complete then the Client PC should already be powered on and will require no further setup The following steps explain the DSP and Server PC setup 1 Connect the batteries of both the DPS s usually the negative terminal of each battery is disconnected after each use 2 Verify that the interface DSP has been connected to the COM1 port of the rover receiver via the serial cable 3 Verify that the Interface DSP is connected to the Master DSP via the two CAN wires purple blue and the ground wire brown as shown in Figure C 6 These connections are as follows a CAN wire orientation must be the same on either end of the CAN bus Th
123. he above algorithm A brief description of the algorithm described here and a detailed example of this code has been included in Appendix B 46 The DSP continually monitors the serial ports of the Digital I O board for incoming messages in the Message Receive Task When specific sync characters specified by NovAtel are detected this Task fills arrays with the message header and content When the message is ready Message Receive Task calls the Message Processing Task In this second task the DSP can identify the message content from the ID number extracted from the 9 byte header Then variables such as roll pitch and yaw can be extracted from their respective logs by their individual bytes according to the log format specified by NovAtel In the current setup the interface board decodes the receivers messages extracts the desired variables and then transmits the ones needed for post processing over a CAN bus to the second DSP The Interface DSP also reads the two steering sensor string potentiometers through its analog I O channels The DSP is setup to perform the analog to digital conversion and read the converted value off of the ADC7864 chip at 50 Hz Since the highest input frequency used in this work was approximately 4 5 Hz the 50 Hz sampling rate is fast enough to capture all data without aliasing according to the Nyquist Shannon Sampling Theorem Sample rates above 50Hz were observed to cause system delays for unknown reasons and th
124. hen satellite visibility is limited This integration of these sensors is system specific but is usually performed though a Kalman filtering process which corrects the INS positioning solution with that of the GPS This integration will be discussed in more detail in Chapter 4 Logsdon T Understanding the NAVSTAR GPS GIS and IVHS Second ed 1995 NY NY Van Nostrand Reinhold Hofmann Wellenhof B H Lichtenegger and J Collins GPS Theory and Practice Fourth revised edition ed 1997 Austria Springer Verlag Wien New York Parkinson B W and J S J eds Global Positioning System Theory and Applications Volume IT In Progress in Astronautics and Aeronautics Vol 164 ed P Zarachan 1996 Washington D C American Institute of Aeronautics and Astronautics Inc Novatel OEM4 Family of Receivers User Manual Vol 1 Installation and Operation OM 20000046 Rev 19 2005 Alberta Canada Janet Brown Neumann A M Thomas Ford Orest Mulyk Test Results from a New 2 cm Real Time Kinematic GPS Positioning System 1996 The Institute of Navigation Washington DC p 183 Chatfield A B Fundamentals of High Accuracy Inertital Navigation Progress in Astronautics and Aeronautics Vol 174 ed P Zarchan 1997 Washington D C American Institute of Aeronautics and Astronautics Inc Tom Ford J N P Fenton M Bobye J Hamilton OEM4 Inertial A Tightly Integrated Decentralised Inertial GPS Navigation System 2001 Salt Lake
125. his is most easily done by declaring these variables as Structs and making them part of a Union as demonstrated below struct DoubleBits unsigned sb0 unsigned sb1 unsigned sb2 unsigned sb3 unsigned sb4 unsigned sb5 unsigned sb6 unsigned sb7 we wv v we we v eee er eee v s union DoubleBitsType double DoubleValue struct DoubleBits bits volatile union DoubleBitsType horSpd trkGnd vertSpd The above code allows easy access to each of the 8 bytes of the double variables horSpd trkGnd and vertSpd In the case of trkGnd the 8 bytes have been read and stored in elements 13 through 20 of the UART1MessageArray array These bytes are recombined into the double value in the parseINSSPDS functions as follows trkGnd bits sb0 UART1MessageArray 12 bits sb0 trkGnd bits sb1 UART1MessageArray 13 bits sb0 trkGnd bits sb2 UART1MessageArray 14 bits sb0 trkGnd bits sb3 UART1MessageArray 15 bits sb0 trkGnd bits sb4 UART1MessageArray 16 bits sb0 trkGnd bits sb5 UART1MessageArray 17 bits sb0 trkGnd bits sb6 UART1MessageArray 18 bits sb0 trkGnd bits sb7 UART1MessageArray 19 bits sb0 Where UART1MessageArray s first element has an index of 0 Each byte of the trkGnd variable can be access as shown above or the full double value can be accessed calling trkGnd DoubleValue This process is performed for each of the variables that need to be transmitted After they have been proce
126. his particular vehicle does not change drastically with increasing speed Therefore the inclusion of a model on this vehicle would not be as beneficial as the one shown in simulation Regardless the Identical Suspension Model was used in an inversion process The resulting road grade estimate from the model inversion and the 151 road grade estimate from the low frequency content of the pitch measurements are displayed in Figure 9 29 Filtered Pitch Angle 0 4 bas 5 mph p 0 2 F 40 mph D l 65 mph S o lt x pl ey 2 0 2 lt 0 4 i i il il l l l 0 20 40 60 80 100 120 140 160 180 Estimated Road Grade from Inversion 0 4 g 02h hf Mi g oL A Oo l ig ke WN S 0 2 0 4 Vi l i i i i i i 0 20 40 60 80 100 120 140 160 180 Distance m Figure 9 29 Road Grade Estimation Method Comparison Experimental Data Since the model inversion accounts for the vehicle dynamics no additional low pass filter has been applied to the inverted data For this particular data set the correlation for the road grade data is lower than that of the low frequency pitch measurements These correlations are Corr _ LowFregPitch 0 7150 Corr _ Inversion 0 6349 9 35 Although the correlation between data sets has not improved it is interesting to note the recovered trends which were not present in the raw pitch data due to the suspension s filtering This is sh
127. ing methodology possible on any passenger vehicle 1 1 Motivation Over the past several years vehicle research groups in the automotive industry and academia have turned their focus to integrating computer based systems into vehicles in order to increase safety by assisting the driver in high risk situations Today driver 2 assist systems such the Anti lock Brake System ABS and Electronic Stability Program ESP come standard in many vehicle makes and models These two systems use various sensors to detect excessive wheel slip and automatically apply or adjust braking forces when deemed appropriate These systems are successful because the control actions can be applied faster and more consistently by a computer than by the average driver As computer processing power increases and cost decreases more advanced sensing technology can be integrated into the vehicle The increased computational power allows for data processing in real time and for the development of model based predictive algorithms By continuously monitoring the vehicle states and using this data in vehicle models running onboard the vehicle advanced safety systems such as Rollover Detection and Lane Detection become possible In order for these systems to be successful accurate vehicle models must be developed It is critical that the models are sufficiently complex to accurately predict the vehicle s dynamics while still remaining as simple as possible to allow
128. is means that if the purple wire is next to the jumper on the Interface board it must also be next to the jumper on the Master board In both cases the CAN wire is set on the top row of pins on both boards as shown in Figure C 6 b In order to ensure a proper voltage potential between the two boards ground pins on each board have been connected together Presumably this can be done at the battery terminals but this has not been verified In the current setup the brown GND wire is connected from the bottom row of the analog input pins on the Interface CAN board all pins on this row are grounds to the bottom row of pins on the Master CAN board pictured in Figure C 6 187 CAN Master DSP Figure C 6 DSP DSP Connections 4 Verify that the steering sensors are properly connected to the Inteface DSP The steering sensors have three connections power ground and output voltage The power and ground are connected to the 15V and 15V lines of the Astrodyne circuit while the output voltage is connected to the analog input pins of the Interface CAN board This can be seen in Figure C 7 as well as in the GND Interface DSP section of Figure C 6 Further clarification is given below a Figure C 7 shows the steering sensors connected to analog input channels 3 and 4 of the CAN board The pins used are the rightmost pins on the tops row of the analog input section 188 4 Digi VO Connections y Mii y i g Steering Sen
129. itch measurements to remove high frequency content of the signal The cutoff frequency was chosen by looking at the FFT of the vehicle s pitch measurements On the experimental data used in that chapter there was a relatively obvious distinction between the high and low frequency content and the cutoff frequency was chosen accordingly When the FFT of the simulated pitch measurements is performed the results are quite different Frequency Content of Pitch Measurements 1 5 mph 10 45 mph 80 mph Hi li j I i all l N N AUVAA A A ANa l i 0 0 05 0 1 O15 02 025 0 3 035 04 045 0 5 Frequency cycles meter Figure 9 21 Simulated Pitch Measurements FFT 145 In Figure 9 21 there no obvious frequency that can be used in a low pass filter to make the low pitch measurements at different speeds fit for correlation Because of this the cutoff frequency was varied to see its effect on the data Filtered Pitch fo 0 1 cycles meter F 5 mph Z UPS JIL OY PLZ A EPRI NNA 45 mph 2 80 mph a 1 i i l i i i i 0 20 40 60 80 100 120 140 160 180 200 Distance m Filtered Pitch fo 0 05 cycles meter 0 5 a 0 5 i i i i i i 0 20 40 60 80 100 120 140 160 180 200 Distance m Filtered Pitch fo 0 03 cycles meter 0 5 i i i 20 40 60 80 100 120 140 160 180 200 Distance m Figure 9 22 Identical Suspension Model Low Frequenc
130. j Y y 4 Y A h EIRAS m y gt an E N 0 024 yy at Y H HW NY x 1g if NM y W i j l 0 L i 0 20 40 60 80 100 120 140 160 180 Distance m Figure 9 23 Pitch Angle and Extracted Rear Road Disturbance Figure 9 23 clearly shows that the extracted rear road disturbance remains relatively constant over a wide range of vehicle speeds In contrast to the low frequency pitch method presented earlier this disturbance estimation requires no additional filtering Therefore this signal will allow for a better correlation than the low frequency content of the pitch measurement It is also important to note that the extracted road disturbance U matches the actual sample disturbance input This is shown in Figure 9 24 147 0 06 Recovered 5 mph Recovered 45 mph 0 05 i Recovered 80 mph 1 Original Disturbance hy h ji 0 04 hhi oai ji fi f i j nh I E AL M AN Wia ANA y gt Y i y i hy z oos V V Hy fh ni N 2 T il j i l I h h l i i Veil Y AW y 1 0 02 AJ S TER i y 0 01 l l 0 L 1 i ii 0 20 40 60 80 100 120 140 160 180 Distance m Figure 9 24 Identical Suspension Model Extracted and Actual Rear Disturbance From the road dis
131. l Increasing o o glu z _ 1 Lag X 10 10 w rad s Ofer as Ey 50 F 4 o k a 100F 4 L L 10 10 w rad s Figure 6 2 Lateral Velocity Frequency Response Varying Relaxation Length Figures 6 1 and 6 2 clearly show the effects of tire lag most notably on high frequency inputs The tire lag model captures some of the higher order dynamics present at frequencies around 10 rad s After the above parametric variation the value of the relaxation length which created the best match was extracted However the value which corresponded to the best match for the yawrate frequency response was different than that of the lateral velocity frequency response Table 6 1 Best Fit Relaxation Lengths Freq Response Sigma m Yawrate 0 7 Lateral Velocity 1 2 Plots showing simulations with only these two values are shown below 83 Phase deg Figure 6 3 Yawrate Frequency Response Best Fit Relaxation Lengths Phase deg Figure 6 4 Lateral Velocity Frequency Response Best Fit Relaxation Lengths Steering Angle to Yaw Rate with Tire Lag Model Lag 7 Increasing Lag Model Lag 1 2 I 1 1 L 10 10 w rad s 50 H 100 50 100 w rad s Steering Angle to Vlat with Tire Lag Fl Model Lag 7 Model Lag 1 2 1 Lag Increasing 10 10 w rad s w rad s Since it is known
132. le Model Comparison SS Circle It is nearly impossible to tell the two models apart in these cases The Lag Model shows no real improvement over the standard bicycle model and both still show poor model matching in the lateral velocity plots There still exists a somewhat constant offset in the lateral velocity data in the steady state circle maneuver which is not present in the chirp or frequency response plots As mentioned in chapter 5 this offset is believed to be due to the significant amount of body roll the vehicle sees in a steady state circle maneuver The effect of vehicle roll angle on tire force generation has been supported and investigated by others 8 and will be presented in detail in the next chapter 6 4 Conclusions e While tire relaxation length for the front and rear tires can be modeled independently this significantly increases parametric variation difficulty and only has a minor effect on the model matching NWN 91 The addition of rear relaxation length captures the higher order dynamics present at high frequencies This was not apparent in previous work 3 where the first order lag model was only introduced on the front steering input Since lateral velocity is more strongly coupled with roll than yawrate and the bicycle model does not model roll effects the model is expected to fit yawrate data better than lateral velocity The Lag Model does not improve the fit of steady state circle data The consta
133. lect the files and move them to an appropriately named folder NOTE If the files are left in the GPS_Wincon folder they will be overwritten on the next saving command 3 Go back to the plots and click Update gt Real Time to resume Real Time data Acquisition i ls Cat PeP WON as atie posi md Sitor mat sad Poller Tasks S WSs ladies Poot veld mat SE oe Den the sectei teres ii script baing poutine sev se Adash the selected Heres soe Seg tre othe Web no te Lnalthe siecedtens SO ee 1 Freeze All eite he selected tons igo horteut to tw A ve e Freen 3 Files Saved a Plots Option in GPS Wincon Folder sanl Ham SGO Amna Eb Wasitari o ued 1 sege os sran e aswon E see OD a Figure C 9 Saving Active Plots C 2 Troubleshooting If all the steps described in the previous section are followed the system should be up and running in approximately 10 minutes However it is necessary to include a trouble shooting section incase something does not go as planned Table C 1 and the subsequent troubleshooting sections can be used if necessary 191 Troubleshooting Table 1 Table C Component Symtom o O O Base Station Not in FIX mode No Correction Transmission COM2 Green Light not Flashing Rover GPSANS No Log Transmission COM1 Green Light not flashing No Corrections being received COM2 Red Light not flashing Data Acquisiton Server will not
134. lignment Complete to INS Solution Good Data collection should only be performed after this occurs as the yaw angle will not be accurate until then It must also be noted that this frame detection procedure does not zero the IMU s attitudes roll pitch yaw after mounting Therefore the angular offsets due to mounting the IMU will show as constant offsets in the attitude data This is accounted for by subtracting these values off the readings in data post processing The second stage the rover station calibration is to estimate the leverarm The leverarm is defined as the three dimensional distance between the GPS antenna s phase center and the IMU s center The leverarm estimate is given to the DL 4plus through the GPSolution software via the SETIMUTOANTOFFSET command After an accurate leverarm estimate is given the receiver can precisely calculate the given leverarm through the built in LEVERARMCALIBRATE routine NovAtel recommends the antenna s phase center and IMU center be as close as possible and if possible should only be offset in the vertical direction The antenna IMU alignment and the accuracy of the initial estimate directly affect the accuracy of the calculated leverarm Because of this the initial measurement was taken carefully Since the antenna and IMU are separated by the vehicle windshield an accurate initial leverarm estimate was not as straight forward as one may assume Because the entire sys
135. ll not greatly influence the system behavior For this equation only one pole is needed to make the function causal This pole is added at p by multiplying the denominator by s p and rescaling the numerator by a factor of p as shown below U s a b Pi ns n s n 9 19 0 s s p 2 n s When expanded this becomes 2 U s a 4 b PMS Phs p 9 20 0 s 2 n s 2 pns This transfer function is now causal and can be easily simulated in MATLAB Care must be taken to ensure the pole at p does not greatly affect the response 9 3 Model 2 Identical Suspensions No Rotational Inertia As an initial approximation of suspension behavior the front and rear suspensions can be assumed to be identical If the rotational inertia of the vehicle is neglected the model in Figure 9 1 reduces to two identical quarter car models The pitch angle can then be calculated from the kinematic formulation in equation 9 15 This system can be seen pictorially in the following block diagram Road Input Figure 9 5 Identical Suspension Model Block Diagram Where the blocks labeled represent the transfer function which relates the road disturbance to the vertical displacement of the sprung mass These transfer functions can 129 be derived from a simple mass spring damper system known as the quarter car model Its Free Body Diagram is given in Figure 9 6 aaa Bt TE k N i r
136. locity Vector Summation Assuming small angles we can then write Ve Very u af a 3 3 Vex Vir ar 3 4 And from geometry The lateral velocity vector for the front tire can be written as V sy V Par 3 5 Longitudinal velocity is approximately equal to the vehicles velocity at the center of gravity V ZU 3 6 By combining equations 3 5 3 5 3 5 and 3 6 the equation for front slip angle can be formed Vrat y a 3 7 f U f By repeating the above procedure for the rear tire and recalling that there is no steering input at the rear the equation for rear slip angle can be written 26 a 3 8 Combining equations 3 2 3 2 3 7 and 3 8 Vt a r V b r m a c t a e U 3 9 dr Vt a r V b r IT C_ 6 a C b zz dt af U a d U 3 10 Lateral acceleration in body fixed coordinates can be expressed as dV a 4U r 3 11 dt Rearranging equations 3 9 3 11 expressions for lateral acceleration and the time rate of change of the yaw rate can be written C4 C a C_b C LA ae pg ae a E 3 12 dt m U m U m C a C b Coa C b C E An ace a el 3 13 dt I U IU m Equations 3 12 and 3 13 can be represented in standard state space form as in equation 3 14 a Sable Cut Cob_y fea dr C a C b Cya C b HE Cya 6 3 14 ZZ ZZ 3 1 1 Derivation of Understeer Gradient A vehicle s handling behavior can be
137. lt in 15 state Kalman filter which to smooth the IMU readings resulting in virtually noise free measurements 156 10 2 Planar Model State Identification A series of experiments were described which allow a user to accurately estimate vehicle states and hard to measure parameters such as cornering stiffness and tire lag A new method of cornering stiffness estimation was developed which combines the DC gains of experimental data with equations derived from the Bicycle Model This new method was shown to be more accurate than previous methods for model matching responses produced by low frequency steering inputs in both the time and frequency domain Another interesting result of this work is that large variations in cornering stiffness values result in only small variations in the time domain yaw rate plots This indicates that time domain yaw rate plots should not be used to fine tune cornering stiffness estimations High frequency model matches were obtained by incorporating tire lag into the bicycle model It was noted that while tire relaxation length for the front and rear tires can be modeled independently this significantly increases difficulty in parametric matching and only has a minor effect on the model output This work also showed that the most accurate matches for yaw rate occurred with different tire lag values than the most accurate matches of lateral velocity Since lateral velocity is more strongly coupled with roll
138. lthough this value was the average of four data sets the initial assumption of steady state was violated At the current testing facility the skid pad used for both the understeer gradient calculation and zero sidelslip velocity measurement is not perfectly level In fact the elevation of varies 0 84 meters while traveling around the circle This super elevation leads to constant acceleration deceleration of the vehicle in both the lateral and longitudinal directions as it travels around the path These accelerations invalidate the steady state assumption Although this superelevation may seem small it plays a large effect in the understeer gradient value which is only on the order of 10 By simply increasing the magnitude of the cornering stiffness values an improvement can be seen in all of the plots presented in section 5 1 Because of this an alternative method of determining cornering stiffness was developed 5 3 Bicycle Model Cornering Stiffness Correction As demonstrated in 1 the effect of cornering stiffness variation can most easily be seen in the frequency domain The figures presented in section 5 2 3 clearly show that the bicycle model with the current parameter values mismatches the data at nearly all frequencies At the vehicles natural frequency and above higher order dynamics which are not modeled by the planar bicycle model such as tire lag roll and camber effects will greatly affect the model matching However at low
139. meant to be used by anyone who follows this work and needs to change the systems current data logging configuration This should be read simultaneously with the commented code in order to gain a complete understanding of how it works Once again this section is only an outline of the overall DSP code B 1 Data Retrieval from DL 4plus The Interface DSP communicates with the DL 4plus receiver over standard RS 232 serial protocol To do this the DSP utilized the serial port on the Digi I O board designed by Dan Block at the Control Systems Instructional Laboratory at the University of Illinois at Urbana Champaign The DSP is programmed with a high priority Task function to continuously monitor the serial port for incoming data void UART1ReceiveCharTask void while 1 Wait forever for new character sa The UART1ReceiveCharTask task first looks for three new characters on the serial port If three characters can be read in a row it stores these characters into variables called syncl sync2 and sync3 and sets a flag to indicate that three characters have been read if syncflag 0 checkfornewcharUART1 amp sync1 SYS_FOREVER checkfornewcharUART1 amp sync2 SYS_FOREVER 175 checkfornewcharUART1 amp sync3 SYS_FOREVER syncflag 1 NovAtel specifies that each log type has its own three specific sync characters In this example the log to be decoded is INSSPDSB which is a short binary INS log NovAtel provides th
140. n the velocity vector and the vehicles heading Therefore the total velocity vector can be broken down into it longitudinal and lateral components by looking at the velocity triangle as shown in Figure 5 10 A U Vegt Figure 5 10 Sideslip Vector U V oiiicg cos 2 ere i 5 23 p V otal cg sin V otat U B Where the lateral velocity is shown in the negative direction in Figure 5 10 in accordance with the SAE sign convention Equation 5 23 can be used with equation 5 22 to solve for the steady state lateral velocity y u 2 a 5 24 R The lateral velocity DC gain can then be written U 4 a R G L 1 b mU R 1 a mU ii R CyL R Cla R 67 Equations 5 21 and 5 25 can be rearranged to check their equivalence to equations 5 18 and 5 16 First Equations 3 21 and 3 22 can be substituted for a in Equation 5 25 2 U b mwega U R L C gR Sa 5 26 L 1 b mU i a mU R Cnt R C L R ar Next L can be replaced by the sum of a and b and the Equation 5 25 can be multiplied by 5 27 After simplification i b at b Cup Cy g a a b mgU C Cy a b C g 5 28 CuCap a b C mU b C mU a G Which can be further simplified to the expression obtained in section 5 3 1 E U CyCa ab Cy a m U PPr Cy Ca b a 2ab m U C a C b A similar procedure can be followed to show the equivalence of Equations
141. ndependent of vehicle velocity The accuracy of the inversion is dependent on several factors such as the accuracy of the time delay estimate and how accurately the pitch plane model can predict the vehicle s behavior In the above simulations these parameters were known exactly so the best possible inversion was achieved A brief simulation was performed to investigate the quality of the inversion process when the model does not exactly match that of the vehicle To do this the Identical Suspension 149 inversion was performed on pitch measurements that were generated using different suspension parameters in the front and rear The results are show in Figure 9 27 Pitch Angle and Recovered Road Grade 0 54 h Pitch Angle deg 0 5 0 20 40 60 80 100 120 140 160 180 200 Distance m hf l ony Nh Y Ny i lf IN My 0 5 F Recovered Road Grade deg L I i i i I 20 40 60 80 100 120 140 160 180 200 Distance m Figure 9 27 Model Inversion Incorrect Model The above figure shows that even though the model did not exactly match that of the vehicle the extracted road grade is still more consistent with varying velocities than the pitch measurements It should be noted that the parameters used in this simulation were the estimates of test vehicle parameters As mentioned previously for this car the estimated spring stiffness and damping values for the front and rear s
142. nerated are due to the front and rear road disturbances Uy and U e The front and rear suspension forces act on the vehicle body at locations a and b respectively Figure 9 1 e The road disturbance at the rear of the vehicle U is a time delayed version of the disturbance acting at the front of the vehicle U 9 2 Model 1 Kinematic Model The simplest version of pitch plane model neglects suspension forces altogether The result is a kinematic model which implies that the road disturbance directly acts on the vehicle chassis This system can be represented pictorially with the following block diagram 123 Figure 9 2 Kinematic Model Block Diagram As indicted in the figure the front and rear sprung mass vertical displacements are equal to their respective road inputs 9 1 Expressions relating the front and rear sprung mass vertical displacements to the vertical displacement at the center of gravity can be written directly from the kinematics of the free body diagram of Figure 9 1 Zy Z a0 9 2 Z Z b0 Solving for Z and rearranging these two equations leads to Zy Z 9 a b 9 3 Combining Equations 9 3 and 9 1 U U 0 a b 9 4 During forward motion the sensor measuring the pitch angle is located behind the vehicle s front axle Therefore the front road disturbance Up occurs before in time the sensor reaches the location of that disturbance Since the initial rear disturbance
143. ness values determined in the previous section were then used in a model fitting routine to determine the front and rear damping coefficients The procedure was similar to that used in 2 to determine the roll stiffness and damping The procedure is outlined here 1 2 Start the vehicle on a flat surface with the GPS INS system measuring pitch angle Forcibly oscillate the vehicle in the vertical direction at the front axle Continue the forced oscillation until the system reaches an approximate steady state response to the sinusoidal input Terminate force input and allow the vehicle to come to rest 134 4 Plot the vertical displacements at axle with the free response of the quarter car model Vary the damping coefficient value until the best model match is achieved 6 Repeat steps 1 4 for rear axle Nn For the experiment outlined above it can be assumed that the vehicle rotates about the axle which is not being oscillated e g for the front suspension oscillation the vehicle rotates about the rear axle It is also assumed that the forced oscillations cause no vertical motion at the opposing suspension This is shown for the front oscillation in Figure 9 9 Figure 9 9 Front Oscillation Diagram With the assumptions listed above the pitch angle which is measured at the center of gravity is equal to the angle the vehicle makes with respect to the horizontal measured at the rear rotation point Therefore from i
144. ng results are presented in both the time and frequency domain A novel method of longitudinal positioning has also been developed The method uses pitch angle measurements to estimate the disturbances input to the system from the road surface An estimation of road grade can then be made to increase the accuracy of the longitudinal positioning solution A model inversion process is used to make this positioning routine possible for any road vehicle By utilizing a road grade map the measurements of commercial grade inertial sensors may achieve positioning accuracy equivalent to that of a high end differential GPS system TABLE OF CONTENTS BIST OFP FIGURES aae a E nd nae nee ONUR Vili EISFOF TABLES Reece amend semen np rene Mest nett A Meee ear ERs etree xiii ACKNOWLEDGEMENT Setari n o EEE E E EE oua eee xiv Chapter Mateo cue tO iiss xsi nene a E E R nhac nln 1 TAP Motivatio sienose iacned dhs aaa bases paxoanaaetaladan hasan vanoraass AATE DRESS 1 1 2 Outline of Remaining Chapters 0 ccccecccecsseceseceeeceeeeeeseecseecceaecneeeeeeenseees 4 Chapter 2 Introduction to GPS and INS History Background and Basic FUNCIONS iaeaea a a a Aaa fas E Gay de UA EA ashen cae 7 2 1 GPS Background jy 0s5cdysksshecey ck Santas BacMads darisbaie sty his ieee aes 7 Zhe MS PACS Seement aniele no e E E ES 7 2 1 2 Control Segmenti neei a E ak outa otal T 8 Dil OWS CMI IM Rak a ae E a a E E N a aes 9 2 2 GPS Fynctionality isnin atsan iata a ERRE EO K K
145. ngles PF Calculated Ackerman deg Best fit Ackerman deg Error deg Small Circles 4 58 4 95 0 37 Large Circles 3 75 4 11 0 36 54 The over predicted Ackerman angle as presented in Table 5 2 suggests a constant steering offset error This error can be applied as a correction later if necessary 5 1 3 Cornering Stiffness Estimation Throughout the course of this work several methods were used in order to accurately determine the front and rear cornering stiffness values An initial estimate of cornering stiffness was made by using the understeer gradient derived above By using the bicycle model formulation an expression can be derived to relate the understeer gradient to the rear cornering stiffness This derivation is presented below As a vehicle negotiates a steady state turn its total velocity vector at the center of gravity is offset from the vehicle s longitudinal axis by an angle known as the sideslip angle B As a vehicle s speed increases the sideslip angle moves from a positive angle to a negative angle In Figure 5 2 a vehicle in a high speed turn is shown Figure 5 2 Bicycle Model SS Turn Sideslip View 55 By summing the interior angles of the triangle an expression for sideslip in a steady state turn can be written B t a 5 6 The expression for rear slip angle derived in equation 3 8 can be substituted into equation 5 6 1 W U bt 5 7 gt f z At the speed a
146. nominator of the inverted transfer functions 153 These inversions can only be used for vehicles with specific suspension configurations and mass distributions Even though it has not been shown with experimental data simulations have shown that with a more accurate model and model parameters the inversion method can accurately estimate road profile when the low frequency pitch method cannot The model inversion method results in velocity and vehicle independent estimations of road grade 9 8 Conclusions e Several pitch plane models were derived and inverted to estimate road grade from vehicle pitch measurements e A method of estimating vehicle suspension parameters such as spring stiffness and damping has been presented e Simulation results show that the low frequency portion of the pitch angle measurements will not always be consistent with increasing vehicle speed e The model inversion process successfully recovers known road disturbances in simulation where the model parameters are exactly known e The model inversion was not completely successful in experiment This failure is likely due to model uncertainties and un modeled parameters 154 Ozbay H Introduction to Feedback Control Theory 1999 Boca Raton FL CRC Press Inc 232 Cameron J T Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover 2005 The Pennsylvania State University Chapter 10 Conclusions The conclusions of this th
147. ns n S n P s Z 9 11 2 ns gs n Equation 9 7 can be solved for Uy and combined with 9 10 125 U s U s P 8 9 12 Taking the Laplace transform of equation 9 4 and combining it with equation 9 12 U s P s U s 0 s a 9 13 Equation 9 13 can then be solved for the transfer function between 6 and U A s _ PF s 9 14 U s a b Combining equation 9 14 with equation 9 11 and simplifying leads to 0 s 2 g n S ha 9 15 U s a b ns n 5 71 Equation 9 15 is the transfer function which relates the pitch angle measured at the center of gravity to the road disturbance input at the rear wheels for the Kinematic model In order to compare each of the models derived in this chapter once can look at each model s frequency response The frequency response for the Kinematic Model given by equation 9 15 for a vehicle moving at 25 mph is shown below 126 Pitch Model Frequency Response Pitch Angle Rear Disturbance Input o 10 L 4 220 4 P 30 J 40 L 4 50 1 1 1 10 10 10 10 w rad s 300 2501 Kinematic Model J G 200 J oO 2 150 J E Oo 100 J 50 i Li 10 10 10 10 w rad s Figure 9 3 Kinematic Model Frequency Response Further insight into the inversion problem can be shown through inspection of equation 9 15 At low frequencies the denominator of equation 9 15 will be
148. nspection of the figure and by assuming small angles the equation relating Zy to the pitch angle can be written Zy at b 0 9 29 Similarly for the rear Z a b 0 9 30 135 To ensure the above assumptions are valid the vertical displacement at the CG was also recorded during the experiment using the DGPS system With the previously mentioned assumptions this vertical displacement is related to the pitch angle by Z b 0 9 31 The measured vertical displacement at the CG and the estimated displacement from equation 9 31 are plotted together in Figure 9 10 Measured and Estimated Zg Front Oscillation Part 1 0 03 r r Measured Z eg 0 02 b Pitch Angle I 0 01 J 0 01 J Z og 0 03 0 04 0 05 0 0 5 1 1 5 2 2 5 3 time s Figure 9 10 Measured and Estimated Vertical Displacement at CG This figure shows that the assumptions used for this experiment are valid The front and rear vertical displacement values calculated from equations 9 29 and 9 30 were compared to those predicted by the free response of the quarter car model The free body diagram for the quarter car model with a road disturbance input was given in Figure 9 6 The free response of the system at the front axle is determined by MZ oy CZ k Zy 0 9 32 136 This system was simulated in MATLAB s Simlink using the following block diagram Figure 9 11 Quar
149. nt offset on the lateral velocity plots should be investigated Gillespie T D Fundamentals of Vehicle Dynamics 1992 Society of Automotive Engineers SAE 495 Heydinger G J et al Dynamic Effects of Tire Lag on Simulation Yaw Predictions Journal of Dynamic Systems Measurement and Control Transactions of the ASME 1994 116 2 p 249 256 Cameron J T Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover 2005 The Pennsylvania State University Carlson C R and J C Gerdes Optimal Rollover Prevention with Steer by Wire and Differential Braking in Proceedings of IMECHE 2003 Washington D C Pacejka H B Tire and Vehicle Dynamics 2002 Warrendale PA SAE Press Karnopp D Vehicle Stability 2004 New York Marcel Dekker Inc Laws S and J C Gerdes High Frequency Vehicle Characteristics Modeling and Experimental Validation of Yaw Sideslip and Roll Modes To be presented at AVEC 2006 8th International Symposium on Advanced Vehicle Control 2006 Taipei Taiwan Kim H J and Y P Park Investigation of robust roll motion control considering varying speed and actuator dynamics Mechatronics 2003 Chapter 7 Bicycle Model Camber Correction In order to correct the model data discrepancy in steady state turns a correction for roll camber was added into the two degree of freedom planar bicycle model In a steady state state turn a vehicle exhibits a significant amount of roll due
150. o cause problems in vehicle applications Because of these shortcomings alternate sensing configurations have been investigated for many years Due to their complimentary nature much attention has been paid to the integration of an Inertial Navigation System INS to existing GPS systems 2 3 INS Background Chatfield 6 defines Inertial Navigation as the computation of current velocity and position from initial velocity and position and the time history of the kinematic acceleration This definition is based on the concept that a vehicles current velocity is equal to the initial velocity plus the integral of the vehicles acceleration with respect to time Similarly the vehicles position is equal to its initial position plus the integral of the vehicles velocity with respect to time Therefore if an initial velocity and position is 19 known it is possible to position a vehicle by simply measuring accelerations and performing the integration and addition described above Inertial Navigation Systems which perform this type of positioning were initially developed in the late 1940 s for aircraft navigation The systems have since been refined for high accuracy and small size 2 4 INS Functionality INS systems use measurements captured from an Inertial Measurement Unit IMU to calculate position of a vehicle in the inertial frame The IMU is a sensor which uses three accelerometers X Y Z and three rate gyros roll pitch
151. odel esesceeseeeeecseeeneeeeeeeeeeeeeaeeneeeaee 94 Figure 7 3 Yawrate Camber Model SS Circle 00 cecscsssceseesoseerceesceneesseeseeeees 99 Figure 7 4 Lateral Velocity Camber Model SS Circle eeecesesceeseereeereeeeeeee 99 Figure 8 1 Initial Observation of Terrain Disturbance ceeeeseeseereeeeeeeeeeeeneeeaee 101 Fig re tea Pitch and Road Grade cccavenssitcacisuataaorsburaaegrnastvarauaseantvoessunvannadioonsseigunialors 102 Figure 8 3 Road Grade Estimation Method Comparison cscceseseeeeeeeteeeeeenee 104 Figure 8 4 Road Grade Repeatability ox sinccssaseacsiensenassesnenearensencanasaundevendescenoansncardenteces 106 Figure 5 Road Grade ssesssisscasetanienteiadcsauvssvnciapseanssess ahaatstan anana a ea aeeai 106 Figure 8 6 View of Error Calculation sisccsisseccissssssvsasssncsasasasivserssuesasassandeescsatsvatsseneanes 109 Figure 8 7 Road Grade Matches 4 yus assnccacvcenicesscnenaesaerearieaeaceaneaedacanaenads 111 Figure 8 8 Position Match Sample 3 ssssesessesseseessssresssseseesesesseserssrseesesseseesessese 112 Figure 8 9 Error Histogram Sample 3 ssssssessseessssersseessessrssressessrssressessresresseeseese 112 Figure 8 10 Single Lane Experiment actcesseccacasacadarcecasteasseancavesaseeensadtenteeacctacaseeesace 113 Figure 8 11 Road Grade Velocity Dependence 0 ce ceeeecceesceeteeceeceeeeeeeeeesseesneees 114 Figure 8 12 Unfiltered Pitch M
152. odeless or quasi codeless techniques for reconstruction of the unmodulated carrier wave from which the phase of the base carrier is measured 1 The codeless and quasi codeless techniques are inherently less accurate than the coded method Another advantage of dual frequency receivers are their ability to estimate ionospheric and atmospheric delays In the previous cases it was assumed that the satellite signal propagated at the speed of light It must be noted that this is only true in a vacuum In practice satellite signals see a delay while traveling though the ionosphere which is approximately proportional to the amount of free electrons the signal encounters 1 In the dual frequency system differences in the Ll and L2 observations are used directly solve for the ionospheric delay thus reducing ionospheric effects 5 2 2 3 Differential GPS Differential GPS DGPS was initially developed to eliminate the errors introduced through SA It is a system which combines two GPS receivers to produce a position solution accurate to 3 5 meters even when only standard L1 C A code is used One receiver referred to as the base station is setup at a fixed known location and remains stationary at that point for its entire operation This receiver s job is to receive data from the L phase carriers compute the position indicated by the received data as in ordinary GPS operation and then calculate the error between the computed solution and the kn
153. odels are used in an inversion process to increase the accuracy of the positioning routine and to generalize measurement of a single vehicle at a single velocity to any vehicle with known model at any velocity To identify pitch model characteristics a method of estimating vehicle spring constants and damping coefficients is given and the effects of the model inversion are demonstrated through simulation and experimental data Chapter 10 will present the thesis conclusions as well as the future work Appendix A consists of the detailed portions of the Pitch plane model derivations from Chapter 9 6 Appendix B outlines a detailed example of the data acquisition code This is necessary for users who will follow this work and need to adjust the system to accommodate additional system inputs Appendix C is a data acquisition system troubleshooting guide to be used as necessary 10 11 12 Cameron J T Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover 2005 The Pennsylvania State University Chen G and D A Grejner Brzezinska Land Vehicle Navigation Using Multiple Model Carrier Phase DGPS INS in Proceedings of the 2001 American Control Conference 2001 Arlington Virginia Farrell J T Givargis and M Barth Differential Carrier Phase GPS Aided INS for Automotive Applications in Proceedings of the 1999 American Control Conference 1999 San Diego California Ryu J E J Rossetter
154. odels are then investigated and an attempt is made to use each of these models to extract the true road grade from the pitch measurements These are compared across different velocities to determine repeatability of the road grade estimate as a function of speed 9 1 Free Body Diagram and Assumptions Figure 9 1 shows the free body diagram of the pitch plane model used in this chapter Each version of model presented in this chapter will utilize the same base set of 121 assumptions These models will then vary in complexity by applying additional simplifying assumptions a b Figure 9 1 Pitch Plane Model Free Body Diagram The notation is as follows 122 Table 9 1 Pitch Model Parameter Definitions Symbol Symbol Vertical Displacement of Front Sprung Force Due to Front Spring Mass Deflection Vertical Displacement of Rear Sprung Force Due to Rear Spring Mass Deflection Vertical Displacement of Center of Gravity Front Damping Force Vehicle Pitch Angle Rear Damping Force Front Road Disturbance Input CG to Front Axle Distance Rear Road Disturbance Input CG to Rear Axle Distance Front Spring Stiffness Rear Spring Stiffness Front Damping Coefficient Rear Damping Coefficient Each model in this chapter will be derived with the following assumptions e The un sprung mass wheels tires etc is neglected e The vehicle pitch angle is measured at the center of gravity e The suspension forces ge
155. or Connection ssesessssessessesseessesstesresseestesressesstesresseesee 188 Figure C8 Connecting to The Cheni sesswuxssonvuncsveavnntusesned sritis iasanen 189 Figure C 9 Saving Active Plots sesssssessessesersesseseesststesttsessestestssesesesersessrsersesse 190 Figure C 10 Base Station Modem Operation Mode c cesccesesceereeereeeeeeeeeeaeeneeeaee 194 Figure C 11 Base Station Modem Baud Rate Settings 0 00 0 ceeeeeseceteeneeeeeeeeeteenaes 194 xiii LIST OF TABLES Table 3 1 Bicycle Model Parameters iccss ssssssicessdsancsasncadeesaendcxsedstnesandasnadentetedeepiusacciass 23 Tabledi Leverarn Estimate sisssrsastiria ciani inaia E e aa SAE Ta 37 Table 2 Calculated Leverai Mansen a a aa aes 37 Table 4 3 Vehicle Angular Offsets sacvaccsvysteceeiisarestuaennnccaiiacameannameneatin 38 Table 44 Base Station POSMIOM sw iniccuciassnrerdavccvadrenscaannsansaasvensduay pu iiaiai eisoes iiaa 39 Table 5 1 NHTSA and Measured Vehicle Parameters c cccsccssecsteceeeeeeeeeeneees 51 Table 5 2 Understeer Gradient Calculation Results cseeseecceseceteceeeeteeeeeeeeeeaees 53 Table 5 3 Calculated and Best Fit Ackerman Angles ssnssesesessesseseressessresresseesee 53 Table 5 4 Bicycle Model Parameters ixcss issssaccseainctiascsassteshiatssealanessepaontasndavacesouheatotacs 57 Table 3 8 Measured DC Gains iiss sscciasissivaanss sieeatanaceaseshsavetanssdevanspsertasisananaiecansewiag 69 Table 6 1 Best Fit
156. oratory at Auburn University Although the hardware components used in these other projects are not the same as used here it must be noted that these research groups laid important ground work on the subject and therefore their work will be referenced extensively in this thesis With this new sensing system in place it was necessary to re perform all experimental tests presented in Cameron s work This includes both frequency and time domain analysis As a parallel to Cameron s work 1 the planar Bicycle Model is revisited This work will show significant differences between the results presented in 1 and those determined with the new sensing architecture Perhaps the most important model based result presented here is a new method of cornering stiffness estimation Common methods of cornering stiffness estimation presented in 1 as well as in vehicle dynamics texts such as 10 11 were attempted first before a new method is developed The differences between the previous methods and the one developed for this work are explained and discussed After the basic low order planar model is established higher order dynamics such as tire lag and camber effects are investigated and found to be necessary for adequate model fit These effects are most easily seen in the frequency domain Results show that the addition of these phenomena increases the model s accuracy without greatly increasing its complexity Throughout the analysis of th
157. ornering stiffness estimation methods is given followed by the chapter conclusions 5 1 Vehicle Parameter Estimation 5 1 1 Mass and Vehicle Dimensions The 1992 Mercury Tracer used in this study has been used in previous research 1 for which several of the vehicles parameters were estimated Many of these parameters have been confirmed against the NHTSA database of a 1998 Tracer and therefore they will be assumed accurate for this study In particular easily measured parameters such as vehicle mass length track width and CG location will be used from the previous study These parameters have been repeated from 1 in table 5 1 51 Table 5 1 NHTSA and Measured Vehicle Parameters 5 1 2 Understeer Gradient With a more accurate sensing system in place it was necessary to recalculate important vehicle dynamic properties such as the understeer gradient In order to estimate the understeer gradient data was collected from several steady state turning maneuvers The Constant Radius Method as described in 1 and 2 was used The methodology is repeated below According to the bicycle model derivation in Chapter 3 the required steering input to negotiate a steady state turn was derived to be L 2 E 5 1 R gR with U i 5 2 J gR Where a is the lateral acceleration in a steady state turn Taking the derivative of 5 1 with respect to lateral acceleration gives d d L d 6 K a da F d
158. ove hard work and dedication have made me who I am today I hope that one day I can be as good of a parent to my children as both of you are to me I love you both Chapter 1 Introduction This thesis outlines the development integration and implementation of a real time data acquisition system which utilizes the Global Positioning System and inertial sensors for vehicle state identification The system is capable of accurately estimating vehicle states and supplying control efforts in real time for modeling control and guidance This work then uses the real time data acquisition system to investigate the planar dynamics of a passenger vehicle through the Bicycle Model Several methods of estimating front and rear cornering stiffness values are presented and their effects on the Bicycle Model are shown through model comparisons The Bicycle Model is then modified to account for higher order phenomena such as tire lag and camber thrust to increase the model s accuracy The effects of these changes are investigated in both the time and frequency domains The data collection and modeling efforts of this work revealed very strong terrain influences on vehicle state measurement This dependence suggested a new method of vehicle localization through the analysis of road input disturbances Pitch plane vehicle models were derived and used in an inversion process to assist in this positioning routine and made the generalization of this position
159. own in Figure 9 30 152 Unfiltered Pitch Angle 0 4 5 mph Ej 0 26 A A r 40 mph 1 fin 65 mph gt of Yh arn TN lt x Wy E j 2 0 2 i o 0 4 i l l i i i li li 0 20 40 60 80 100 120 140 160 180 e Estimated Road Grade from Inversion 04 4 v z N f 02t 2 Vine 0 0 j W N Wh al 8 iI ier l A O th NG E Ne 3 20 2 vu W L 0 4 _ E l l f 0 20 40 60 80 100 120 140 160 180 Distance m Figure 9 30 Model Inversion Trend Recovery In the circled portion of the lower figure the inversion has recovered some of the road grade peaks which the vehicle suspension filtered out of the high speed pitch data These peaks can be assumed to be true road grade measurements because they are also present in the 5 mph data The pitch measurements at low speed can be assumed to be the true representation of the Road Grade since the vehicle s suspension dynamics will not be excited at these speeds Although the correlation has not improved this figure re iterates the inversion technique s ability to estimate true road grade The model s inability to generate consistent road grade estimations for the same vehicle at various speeds is likely due to it un modeled parameters such as rotational inertia Although more complex models were derived in Appendix A the inversion of these models fails due to unstable poles in the de
160. own location The base station estimates the slowly varying error components of each satellite range measurement and forms a correction for each GPS satellite in view 3 These error and bias calculations are then broadcasted on a communication link to the second GPS receiver known as the rover station 4 The rover is free to move and receives these corrections via radio internet or other communication means The rover uses the base stations corrections for every satellite used in its position calculations 18 DGPS operation drastically increases accuracy and almost entirely removes timing biases due to satellite clock error ionospheric and tropospheric and ephemeris prediction errors 2 2 3 1 DGPS Issues When considering the use of DGPS as a sensor for vehicle state identification there are several issues which need to be resolved Perhaps the most important issue is the possibility of GPS outages when a direct line of sight to satellites is not available A GPS receiver is not capable of accurate positioning when less than 4 satellites are available for its calculations Tunnels buildings trees and other environmental factors make GPS outages common in vehicle applications This lack of signal requires the use of additional sensors to compliment the DGPS system Another issue with GPS is the relatively slow update rate of the sensor only 5 to 20Hz at best The low update rate of GPS leads the system to high frequency errors which als
161. phase fixed integer mode and with continuous presence of GPS data the system achieves a position solution with an accuracy of 2 cm one sigma Attitude can be estimated with an accuracy of 0 013 degrees for roll and pitch and 0 04 degrees for yaw while velocity error is a mere 0 007 m s one sigma 1 33 The GPS portion of the Rover system is a NovAtel DL4plus receiver which has modified software and hardware to accommodate interfacing with the HG1700 over a standard RS 232 serial port The DL4plus is a dual frequency L1 L2 receiver capable of both pseudorange and carrier phase positioning These receivers can transmit GPS measurements at a rate of 20 Hz In situations where GPS outages occur they typically have L1 and L2 frequency reacquisition times of 0 5 and 1 second respectively The DL4plus is equipped with NovAtel s patented Pulse Aperture Correlator PAC technology to virtually eliminate the effects of multipath errors seen in environments where buildings or other signal obstacles may exist 2 Figure 4 2 NovAtel DL 4 Plus Receiver The INS portion of the system consists of the Honeywell HG1700 AG17 strap down ring laser gyro IMU used primarily in missile guidance systems unmanned aerial vehicles and standoff weapons This IMU exhibits a gyro bias of only 10 deg hr and an acceleration bias of 3 milli g 3 The HG1700 is mounted in a 160 x 160 x 100mm case from which it can measure accelerations and rotational rates
162. r effects in other driving situations 7 3 Conclusions e A method of incorporating roll steer camber effects into the bicycle model has been presented e Roll steer is clearly affecting the lateral velocity measurements in high roll maneuvers such as the steady state turn 1 Gillespie T D Fundamentals of Vehicle Dynamics 1992 Society of Automotive Engineers SAE 495 2y Kim H J and Y P Park Investigation of robust roll motion control considering varying speed and actuator dynamics Mechatronics 2003 Chapter 8 Terrain Disturbances for Longitudinal Positioning While performing the state estimation described in the previous chapters it became apparent that the terrain was greatly affecting the collected data This was most obvious when viewing sideslip roll and pitch data during the steady state circle maneuvers which were used to experimentally determine understeer gradient The repetitive location dependent nature of these terrain disturbances allows them to be used in a localization routine This chapter will outline the theory of using road grade for longitudinal positioning 8 1 Initial Terrain Disturbance Observations The repetitive nature of the disturbances caused by the vehicle terrain interaction was first observed during post processing of steady state circle data This data was collected at various speeds for two different circles traveling in two different directions When the data was aligned to st
163. real time implementation onboard vehicle processors A large portion of this work was motivated by a previous study by John Cameron 1 In Cameron s study a sensing system architecture was developed and used in a vehicle model comparison between several 3 Degree of Freedom DOF roll models found in literature The system was used to analyze rollover mitigation algorithms The sensing system was based on commercial grade rate sensors and accelerometers which were inherently noisy and susceptible to drift Therefore an accurate estimation of vehicle attitude roll pitch and yaw was difficult to obtain through integration of these sensor readings At the conclusion of Cameron s work the quality of the test data was brought into question as the system exhibited a poor Sensor to Noise ratio It was determined that a more accurate sensing architecture was needed for a more thorough model comparison 3 This thesis began with the development and integration of a military grade GPS INS based data acquisition system for vehicle dynamic studies A detailed description of the system components functionality and capabilities is presented GPS INS based sensing has been used extensively in literature with a vehicle dynamics focus 2 9 Most relevant to this work are those of Ryu and Bae 4 9 of Chris Gerdes group at the Dynamic Design Laboratory at Stanford University and the research group of Dave Bevly 7 of the GPS and Vehicle Dynamics Lab
164. reement of phase in the low 39 frequencies for lateral velocity and poor matching in both phase and amplitude at high frequencies 5 2 2 Steady State Circles The bicycle model was then used to fit steady state circle data at 25 miles per hour The results are below Figure 5 6 Yawrate Model Comparison Circle Using Kus 25 Measurement Predicted from Bicycle Model deg s 5 L 1 L L i L 5 10 15 20 25 30 35 40 time s Yawrate Steady State Circle Response Kus Method 60 Lateral Velocity Prediction and Measurement Circle Using Kus 0 3 m s 0 1 F 0 05 Measurement Predicted from Bicycle Model 0 i p L I I I L 5 10 15 20 25 30 35 40 time s Figure 5 7 Lateral Velocity Steady State Circle Response Kus Method Once again there is poor model matching for both yawrate and lateral velocity Both model predictions are offset from the measured value and show some disagreement in transient regions As with the chirp response the yawrate shows better matching than lateral velocity 5 2 3 Frequency Response A frequency response routine was successfully developed and implemented in 1 and a similar procedure was followed here Fifteen evenly spaced on logarithmic scale frequencies of sinusoidal steering inputs were given to the vehicle ranging from 0 15 Hz to 3 5 Hz The steering inputs were synchronized with a digital metronome an
165. referred to as an understeer vehicle The steering input required for an understeer vehicle to negotiate a steady state turn increases as the speed of the vehicle increases On the other hand a vehicle with a negative understeer gradient is known as an oversteer vehicle An oversteer vehicle actually requires decreasing steering inputs to negotiate a turn for increasing speeds Production vehicles are predominately understeer since oversteer vehicles become unstable in certain turning maneuvers Further discussion of this topic can be found in many vehicle dynamics text books 1 2 or in previous work 3 and will not be presented here 30 Gillespie T D Fundamentals of Vehicle Dynamics 1992 Society of Automotive Engineers SAE 495 Karnopp D Vehicle Stability 2004 New York Marcel Dekker Inc Cameron J T Vehicle Dynamic Modeling for the Prediction and Prevention of Vehicle Rollover 2005 The Pennsylvania State University Chapter 4 Vehicle Systems and Integration This chapter will outline the sensing system layout and then present each component of the system Pictures of the system are presented at the end of the chapter A 1992 five door Mercury Tracer has been selected as the test vehicle for this study The vehicle is equipped with a military grade GPS INS system linear string potentiometer steering sensors and an onboard DSP based data acquisition system The integrated system currently measures roll pitch yaw
166. rements and Model Inversion As a vehicle travels over a particular road profile the frequency of the road disturbance input into the system will vary with the vehicle s forward velocity Since the vehicle s suspension acts a low pass filter the vertical displacement of the sprung mass above the front and rear suspensions will also be a function of vehicle speed Because the pitch angle is assumed to be kinematically related to the front and rear sprung mass displacements the pitch angle measurements can also be expected to change as the vehicle velocity increases This velocity dependent change in pitch measurements will be determined directly from the vehicle s mass distribution and suspension characteristics With an accurate vehicle model and well known suspension parameters the velocity independent road disturbance profile could be extracted from the velocity dependent pitch measurements It should also be noted that if multiple vehicles had highly accurate suspension models their road grade estimations would be identical after extraction of the dynamic influence of the suspension Therefore a single high accuracy road grade map could be used for all vehicles in their localization estimation 139 These effects can easily be seen through simulation shown in the next section 9 6 1 Model 1 Kinematic Model Since the Kinematic Model does not account for the vehicle s suspension dynamics and the road disturbance is directly
167. rences between approximations can be seen more clearly The legend shows the calculated root mean square error between the original disturbance input and each order of the approximation 0 045 L First order RMS error 0 0057078 Seconds order RMS error 0 002718 eo Third order RMS error 0 001827 0 04 P4 i Fourth order RMS error 0 0015703 Original 0 035 fr i i an 0 03 j N 0 025 0 02 i li li i li l li I 108 110 112 114 116 118 120 122 Figure A 2 Pad Approximations Rear Road Disturbance Zoomed The above plot clearly shows that the accuracy of the approximation increases with increasing order Ideally the highest order approximation would be used to obtain the most accurate results However it is obvious from the model derivations in Chapter 9 that a high order approximation would also lead to significantly more complicated models Therefore for this work the second order approximation was used as it was found to be less complex than the third and fourth order approximations while still being considerably more accurate than the simple first order approximation 164 A 2 Model 2 Identical Suspensions No Rotational Inertia In order to make equation 9 25 causal poles must be added to the denominator Continuing from 9 25 with the coefficients of the numerator replaced with A and the coefficients of the denominator replaced with B
168. ring stiffness values The results are plotted in the next three sections and a discussion of the results is presented afterwards 71 5 4 1 Chirp Response Yaw Rate Prediction and Measurement Chirp Using DC Gains 20 Measurement 15L Predicted from Bicycle Model 105 BE Yaw Rate deg s oO 20 L L L L L LA i L L L I 6 8 10 12 14 16 18 20 22 24 26 time s Figure 5 13 Yawrate Chirp Response DC Gain Method Lateral Velocity Prediction and Measurement Chirp Using DC Gains 0 2 0 1 F Lateral Velocity m s 9 w T7 Measurement Predicted from Bicycle Model I I I I 0 4 L L L I 6 8 10 12 14 16 18 20 22 24 26 time s Figure 5 14 Lateral Velocity Chirp Response DC Gain Method 72 5 4 2 Steady state Circles Yawrate Model Comparison Circle Using DC Gains 25r Measurement Predicted from Bicycle Model 20 5 1 1 L 1 5 10 15 20 25 30 35 40 time s Figure 5 15 Yawrate Steady State Circle Response DC Gain Method Lateral Velocity Prediction and Measurement Circle Using DC Gains T T T T T T 0 3 T l 0 25 AAN A l an a a o N T i Lateral Velocity m s oS a 1 2 pre T L 0 05 J Measurement Predicted from Bicycle Model I I I 0 L L L 5 10 15 20 25 30 35 40 time s Figure 5 16 Lateral Velocity
169. ror checking Although certain error messages are transmitted from the reciever to the DSP these messages are not decoded and therefore are not processed The Interface DSP should be programmed to accept these messages and to warn the user if any problems occur The DSP can be programmed to warn the user of dropped communication with the base station or of insufficient satellite observations These simple code additions will help make the system fail safe 10 4 2 Planar Model State Identification The planar model presented in this work shows excellent matches in yaw rate with experimental data There is however room for improvement on the lateral velocity matches As discussed previously lateral velocity is strongly coulped with roll so the planar models ability to match lateral velocity may be limited One possible way to improve the matching of lateral velocity would be to account for the sprung mass In the planar model the lateral velocity is defined for the vehicle chassis the unsprung mass In the current vehicle system the IMU is mounted in the vehicle cabin which is a sprung mass Therefore the lateral velocity match may improve if this difference is taken into account To do this a full roll model would be necessary This is currently be investigated by other students in the research group 10 4 3 Road Grade Positioning The next step needed in the investigation of road grade positioning would be to repeat the correlation
170. s applied to the to the pitch measurements The unfiltered and filtered pitch measurements are shown in Figure 8 13 Figure 8 13 0 4 0 2 Pitch Angle deg 0 4 0 4 0 2 Pitch deg 0 2 0 4 0 2k Measured Pitch Angle Unfiltered 5 mph 40 mph 65 mph ll L 1 1 ll ll i ll 20 40 60 80 100 120 140 160 180 Measured Pitch Angle Filtered ll 20 40 60 80 100 120 140 160 180 Distance m Unfiltered and Filtered Pitch Measurements Figure 8 13 shows that the low frequency portion of the vehicle s pitch measurements exhibits little variation with large variations of speed This indicates that this signal is well suited for use in a localization routine for this vehicle 8 6 Results Discussion This chapter has shown that road grade estimates can be obtained from the low frequency content of a vehicle s pitch measurement These estimates can be correlated with a road grade map as a localization routine For the test vehicle and data used in this study the low frequency portion of the pitch measurements did not vary significantly with speed when plotted against distance traveled This indicates that the low frequency content of 117 the pitch measurements is caused by changes in terrain and therefore can be used as an estimate of road grade In order to implement this routine in practice all vehicles should be able to use a sin
171. sented it is important for the users of the data acquisition system to have a fundamental understanding of the principles of operation of each component Chapter 3 will present the standard 2 DOF planar Bicycle Model which is used extensively throughout this work Its derivation will be given as well as an explanation of the physics behind the model 5 Chapter 4 will describe the vehicle instrumentation that is used in this study This includes the GPS INS system the steering sensors and the custom real time data acquisition system Chapter 5 outlines a methodology of vehicle parameter estimation utilizing data collection and the Bicycle Model The experiments performed will be explained and a discussion will be given on how the data is post processed for model comparison A new method of cornering stiffness estimation is explained and it is compared to more traditional methods that are common in literature Chapter 6 will present a modification to the Bicycle Model to incorporate tire lag while Chpater 7 will add the effects of camber Chapter 8 introduces the concept of using Road Grade and road disturbances to help assist in the positioning solution The preliminary analysis used as a proof of concept is described before the process is refined further in Chapter 9 Chapter 9 includes the refinement of the road disturbance positioning routine as well as the introduction and implementation to several Pitch plane models These m
172. sor Cables a 15V Connections _ Figure C 7 Steering Sensor Connection 5 Verify that the Master DSP is connected to the Client PC via the parallel port 6 If all the connections above have been made turn on the two DSP s by switching the external switch on each enclosure DOWN 7 Plug the laptop power cord into the power inverter and power on the Laptop 8 Plug the laptop into the Client PC via the blue crossover Ethernet cable located on the passenger side of the vehicle 9 Start MATLAB on Laptop Server PC 10 Change the MATLAB Directory to C MartiniGPSFiles GPS_Wincon 11 Start Simulink 12 Open the Simulink model named gps data rd 13 At the top of the model click on Wincon gt Build Model 14 When the model is built you will get 3 error messages about not being connected to a client click OK to all 15 In the Wincon dialog box click Client gt Recent Clients and select the IP Address of the client To verify that the Client Server connection has been made click Client in the Wincon box and see if the Disconnect option is available If so you have been successfully connected This step is shown in Figure C 8 where the server has already connected to the client 189 all Hj Untitled WinCon Server 215 xj File Client Model Plot Window wiew Help ir Connect 3 Disconnect Er A Recent Clients 0 130 203 244 67 v Close On Exit Threshold Ne
173. sponse Varying Relaxation Length 82 Figure 6 3 Yawrate Frequency Response Best Fit Relaxation Lengths 83 Figure 6 4 Lateral Velocity Frequency Response Best Fit Relaxation Lengths 83 Figure 6 5 Yawrate Chirp Response Lag Model ccesccssccsesceeseecseceseeeeeeeeneees 84 Figure 6 6 Lateral Velocity Chirp Response Lag Model ccccccccesseeeseeeteeeteees 84 Figure 6 7 Yawrate Steady State Circle Lag Model cccccecccecsseceseceeeeeeeeeeeees 85 Figure 6 8 Lateral Velocity Steady State Circle Lag Model 00 0 eeeeeeeeeeteeeeeeee 85 Figure 6 9 Yawrate Lag Model and Bicycle Model Comparison Freq Resp 86 Figure 6 10 Lateral Velocity Lag Model and Bicycle Model Comparison Freq Resp Figure 6 11 Yawrate Lag Model and Bicycle Model Comparison Chirp ix Figure 6 12 Lateral Velocity Lag Model and Bicycle Model Comparison CMP E at cence Rens icaacens E esuccuabent inact zalaseas eaisadebdvadtceretundel cadeaed 88 Figure 6 13 Yawrate Lag Model and Bicycle Model Comparison SS Circle 89 Figure 6 14 Lateral Velocity Lag Model and Bicycle Model Comparison SS TIS sascha N EE EEE E area sate wma ged ee cra a eke ped eae deanba el onbennne nese 90 Figure 7 1 Vehicle Exhibiting Camber isis siasscsasisasiaavisienaassaseatesnsdecasssaaveanibsacceaysaoocdian 93 Figure 7 2 Rotation Spring Suspension M
174. ssed the SendToCan function is called which sends them over the CAN bus to the Master DSP At the systems current state Float values are transmitted over CAN Because of this each variable of type double except latitude and longitude is truncated into type float since the extra precision is not necessary The SendToCan 179 function formats each of the values to agree with the current CAN protocol and transmits them to the Master DSP This was done in previous work by Vishisht Gupta and will not be explained here B 3 Data Read from Steering Sensors As discussed in chapter 4 the interface DSP is also responsible for processing the outputs of the steering sensors The sensors which are installed are linear string potentiometers In order to read these analog devices an Analog to Digital Conversion ADC needs to take place This is performed by the AD7864 chip on the custom CAN boards designed by Vishisht Gupta of The Pennsylvania State University The code needed to perform this task is briefly described in this section The Interface DSP has been programmed with a period function ADCStart which runs once at 50Hz This function only has one line void ADCStart ADC7864_StartQ The ADC7864_Start function has been written in the include file ad7864 c This function is used to pulse a signal to the CONVST pin on the ADC chip The CONVST pin initiates the analog to digital conversion on all four tracks of the ADC chip This
175. ssorsesscossescesnseens 23 Figure 3 3 Wheel Velocity Vector Summation s sssssssssssssseseesesstsresrstrsessrsersesseserse 25 Figure 3 4 Bicycle Model Steady State Turn cece eceeceeeeceeceeeeneeeeeeesecneeeneeens 27 Figure 4 1 System Layout seseesesseseesesseesessesetsessesetsesseesesseseestsseseesessesseseseesessesee 32 Figure 4 2 NovAtel DL 4 Plus Receiver is sscsasccsossacssiensasssanssasssievanpnsaussoscvaccsanncnevonas 33 Figure 4 3 Honeywell HG1700 IMU NovAtel Enclosure sssesseseeseeseeseserseeses eee 34 Figure 4 4 Base Station LO CAtl Oia sacse isc unieceaustedirentnatte Rina nae one 40 Figure 4 5 Steering Sensor Calor arti gacccssdjaciaspacetassushcasaasagarasangacaseansneiemssumerseaiaies 42 Figure 46 DAQ OSS scies sec pea iernii e ae EEA EEEE A EEEE E Ea 43 Figure 4 7 Interface DSP Ale ort issuscsossivcacsvnateneuneaerauiaundeonniataveaiiawinwastueniinassins 45 Figure 5 1 Understeer Gradient Calculation 30 5 m Circle Clockwise 4 52 Figure 5 2 Bicycle Model SS Turn Sideslip View cceeccesesceeseeeneeeeeeseceseeneeeaee 54 Figure 5 3 Sideslip Measurements Cornering Stiffness Estimation 0 ee 56 Figure 5 4 Yawrate Chirp Response Kus Method ccecesceceeseeeeeeeeeeeeeeeeeneeeaee 58 Figure 5 5 Lateral Velocity Chirp Response Kus Method csceesceeceeeeeteeeeenee 58 Figure 5 6 Yawrate Steady State Circle Response Kus Method c
176. t DN Be SS The measurements have been summarized in Table 9 2 Table 9 2 Spring Deflection Measurements Drivers Front Passenger Front Force N Distance m Force N Distance m Drivers Rear Passenger Rear Force N Distance m Force N Distance m With the hub center to fender distances and the corresponding force readings of the scales the spring constants can be determined by F k 9 27 dx 133 Where k is the spring constant and dx is the spring deflection This process was performed for both the front and rear springs Figure 9 8 shows the resulting plots of the additional force from the initial value at rest versus the spring displacement from rest 500 Aaaitional Force IN 2000 1000 1500 Front Spring Stiffness Estimation Driver Front Passenger Front Fit Kf 28024 Nim 2500 0 1 1 1 1 1 1 1 0 01 0 02 0 03 0 04 0 05 0 06 0 07 Displacement m Figure 9 8 Spring Stiffness Fits Additional Force N 2500 500 1000 1500 2000 Rear Spring Stiffness Estimation Driver Rear Passenger Rear Fit Kf 27765 Nim 1 0 01 1 0 02 1 1 fi 1 1 1 0 03 0 04 0 05 0 06 0 07 0 08 Displacement m The average per axle spring stiffness values were determined to be k 56048 m k 55530 m 9 5 2 Damping Coefficient Estimation 9 28 The front and rear spring stiff
177. t configuration one DSP is responsible for data collection off of the rover DL4plus as well as reading the analog steering sensors In order to accomplish this this Interface DSP has been fitted with a custom daughter card developed by Dan Block at the Control Systems Instructional Laboratory at the University of Illinois at Urbana Champaign This I O board gives the Interface DSP 4 analog I O s 8 Digital I O 2 RS 232 Serial Ports and an I2C Data bus Interfacing with the rover DL4plus is accomplished through standard serial RS 232 communication When programmed the DL4plus outputs its data logs in either ASCII or binary format Since the system was designed for real time processing the fastest possible communication was required therefore binary format messages are transmitted NovAtel s SPAN and OEM4 manuals present each log s header and message format which can be used to decode these logs on the processor side The algorithm used to process the incoming messages on the Interface DSP has been outlined in the form of a flow chart in Figure 4 7 and will be explained in the paragraphs which follow 45 Message Receiving Task While J Loop Data On Serial Port J Fill Array with Message Header 9 Bytes Fill Array with Message Content Based on Message Length Send Over CAN to Master DSP Figure 4 7 Interface DSP Algorithm Using the CCS programming environment the interface DSP was programmed with t
178. t which a vehicle s sideslip angle transitions from positive low speed to negative high speed the above equation can be solved for rear cornering stiffness W U Ca E 5 8 g Where the sideslip angle was set equal to zero and the cornering stiffness value is a negative quantity with units N rad By definition sideslip is the angle between the direction of velocity and vehicle body Therefore by measuring velocity direction and yaw angle the current sensing system can directly measure sideslip by p VelocityDirection Yaw 5 9 By measuring sideslip and velocity and using the measurements in equation 5 8 the rear cornering stiffness can be determined experimentally To do this the Tracer was put into a steady state turning maneuver and vehicle s speed was slowly increased in an attempt to keep approximate steady state behavior The speed continued to increase until the sideslip changed signs to a negative value The data was then post processed to determine the speed at which the zero crossing occurred Figure 5 3 shows the plot of sideslip versus time as vehicle speed was increased 56 Si slip Sideslip Zoomed In test r 7 r T T r Measured Sideslip i Measured Sidesiip y Put fi L 20 21 2 time 8 Sideslip Zoomed In More degrees Measured Sideslip 4 L 5 10 15 20 25 z 35 145 15 156 16 16 time Ss time S Figure
179. tch Model Derivations and Implementation cc eceeceeseceteeneeeeeeeees 120 9 1 Free Body Diagram and Assumptions ccccceccesccessceececeseceseceeeeeeaeeesaeoes 120 9 2 Model 1 inematic Mode lis c3oceict avin cecal cnauihooaucs deatasvateaveuaesd tines 122 9 3 Model 2 Identical Suspensions No Rotational Inertia cece 128 9 4 Additional Suspension Models j s 155 sccsssteiersseesdtastansetadssestacstendiuatandestavsdesactsas 131 9 5 Suspension Parameter Estimation cccscccceccsssccssccssccsssscseccssscesncesensens 131 9 5 1 Spring Stiffness Estimation ccccsccscsccsssscssccssscessecsesnsssssesscesacees 132 9 5 2 Damping Coefficient Estimation ix 3 30 csicaus soandivus ceans eave ddussaamenruandons 133 9 6 Effect of Forward Velocity on Pitch Measurements and Model Inversion 138 9 6 1 Model 1 Kinematic Model sca ses ese arco ectceashcySieastasdnctraceustaraseaa sass 139 9 6 2 Model 2 Identical Suspension Model ceccccsseeeseceeteceeeeeeeeeeseees 142 9 7 Model Inversion on Experimental Data ccccecceeceesceesceceeceeeeeeeeeeseeeeaeees 150 OSG ONCLUSIONS soeia e a a a a i ae nS 153 Chapter 10 Conclasions aisee a a a a a e eee i 155 10 1 System Integration sseeneeseesseeseeseesseessesesssessessesstessessrsstesseestssresseeseesressre 155 10 2 Planar Model State Identification s sseoessseesseseeesseeseseesseesesresseessesersseesse 156 10 3 Road Gra
180. ted together as a single front and single rear wheel respectively The vehicle is also assumed to have constant longitudinal velocity U and 24 tires which roll without slipping in the longitudinal direction This means there are no acceleration or braking forces being applied The front and rear tires are also assumed to produce lateral forces which are linearly proportional to their respective cornering stiffnesses Finally the model also assumes all angles are small and therefore the following simplifications can be applied cos 1 sin 0 The states or variables required to fully describe the motion of the bicycle model are V the vehicles lateral velocity at the CG and r the angular velocity about the z axis The equation of motion of the vehicle can be derived using Newtonian mechanics as described below Summing forces in the lateral direction summing moments about the Z axis and applying the small angle approximation the following equations are obtained m a LF F cos 6 F F F d 3 1 L a F cos a F b F a F b Under the assumption that the front and rear tire lateral forces are linearly dependent on their respective slip angles and cornering stiffnesses and negative cornering stiffness values are used Fr Cy ay 32 Telra r The front and rear slip angles can be solved for by looking at the lateral and longitudinal velocities at each tire as in Figure 3 3 25 Figure 3 3 Wheel Ve
181. tem has to be modular modifying the vehicle for this measurement such as removing the windshield was deemed inappropriate The easiest way to make this measurement was to use a plumb bob The plumb bob was fixed to the GPS antenna at its phase center and then lowered until the bob s point touched the windshield A mark was then made on the outside of the windshield at the point of contact and the strings length was measured Then the process was repeated from the inside of the vehicle with the string fixed at the point of contact marked from the previous step The bob was 37 lowered to the center of the IMU and once again the string length was measured Although this is not an exact distance calculation it was appropriate for an initial leverarm estimate Table 4 1 Leverarm Estimate Inertial Frame Coordinate Offset m Uncertainty m 0 03 0 03 0 03 After the initial leverarm estimate was measured and its X Y and Z offsets were given to the DL4plus via the SETIMUTOANTOFFSET command the receivers LEVERARMCALIBRATE routine could be run During this built in calibration routine the vehicle was driven in several maneuvers such as circles and figure eights The routine runs until the user specified uncertainty is met minimum 0 02 m for all three offsets After approximately 2 minutes the calibration returned the calculated lever arm and the settings were automatically saved in system memory Table 4 2
182. ter Car Model Simulink Diagram Where the initial conditions for the vertical velocity z and vertical position z were sf extracted from the collected data An example of the sample data collection and model matching is shown below in Figure 9 12 Pitch Plane Oscillation 0 015 Measured 0 01 Quarter Car Model EN 0 005 0 005 o te Pitch Angle rad 0 015 Approximate Release Time 0 02 0 025 0 03 0 0 5 1 1 5 2 2 5 3 3 5 Time s Figure 9 12 Example Pitch Plane Excitation 137 In the model fitting routine the damping value was allowed to vary while the spring stiffness values remained constant The fit which minimized the root mean square error between the simulated and measured displacements was chosen to be the best fit The best model fits for the three data sets for the front and rear are shown in Figure 9 13 Front Suspension Fit Data Set 1 Rear Suspension Fit Data Set 1 0 04 0 04 Measured Measured 0 03 Fit with Measured k 56048 and c 4670 Fit with Measured k 55530 and c 2810 0 03 0 02 2 __ 0 02 E 0 01 E 5 E amp oF 8 ooh g i 5 0 01 F ol amp 0 02 0 01 0 03 0 04 1 1 0 02 r 1 r 1 r 1 1 1 r 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 0 0 2 0 4 0 6
183. the LCD indicates FIX and this light is not flashing see section Base station setup complete C 49 2 Rover Station Setup The Rover Station setup consists of setting up both the Rover GPS INS system and the Data Acquisition system These will be described below C 49 2 1 GPS INS System 1 Mount the IMU to the custom mounting bracket located at the center of gravity using the supplied hardware A socket wrench and allen key will be needed these tools have been left in the ashtray When mounting the IMU be sure to mount it in the proper orientation with the Receiver IMU connection facing the rear of the car It is important that the receiver is seated properly in the mounting bracket The proper mounting location is pictured in Figure C 4 E Receiver IMU lt a af Connection h r Figure C 4 IMU Mounting 2 Plug the IMU into the AUX port of the Rover DL 4plus via the cable labeled 01017384 3 Mount the GPS antenna to the roof of the car On the Tracer a roof rack is used which is permanently fixed above the IMU center as pictured below Figure C 5 185 Figure C 5 GPS Antenna Mounting 4 5 6 7 8 9 Because of this recalibration of the leverarm is not necessary However if you are using the ChaseCam mounts re calibration of the lever arm is necessary as outlined in Chapter 4 of this thesis and in the SPAN Manual Plug the GPS antenna into the ANTENNA connection of the DL 4plus
184. the ability to record data to an onboard compact flash card for post processing This data acquisition routine would be sufficient for general vehicle dynamic studies and model matching However since the vehicle in this study will eventually require real time control capabilities it was necessary to setup a real time data acquisition system capable of regulating control efforts for future use The data acquisition system installed in the Tracer consists of two Texas Instruments TMS320C6713 Digital Signal Processor DSP Developer s Kits operating on a CAN bus and a remotely accessible and programmable standard PC platform consisting of two windows based PC s The DSP and PC platform functionality are described below To Rover Receiver To Stering Sensors Serial Data Acquisition Communication CAN Network Parallel Communication Client PC Wireless TCP IP Figure 4 6 DAQ Overview 4 1 4 1 DSP Operation The dual Texas Instrument DSP s are the heart of the current data acquisition system Interfacing with the DSP chips is accomplished through standard address and data bus pin headers The pin headers allow for expansion via custom designed daughter cards such as the Digital I O and CAN boards used in this project The TI DSP s allow for the 44 boards to be programmed via Code Composer Studio CCS a standard C code programming suite included with the developer s kit 4 1 4 1 1 Interface DSP In the curren
185. the base station is easy to setup Since the position has been 182 saved it must be placed in the same spot for each use The base station is to be placed on the loading dock next to the skidpad as described below 1 Locate and unlock the base station carrying case The combination has been left with Dr Brennan 2 Align the base station with the mounting brackets located on the loading dock as pictured in Figure C 1 Mounting Brackets Figure C 1 Base Station Mounting 3 Mount the radio antenna vertically using the supplied mounting brackets as pictured in Figure C 2 and connect it to the base station modem via the long cable labeled GPS C006 0002 183 Mounting Brackets Figure C 2 Radio Antenna Mounting 4 Run an extension cord from the base station to the outlet located to the left of the loading dock 5 Power the DL 4plus receiver and wait approximately 5 minutes After 5 minutes or less the receiver should display FIX on the bottom of the LCD as shown in Figure C 3 If after 5 minutes FIX is not displayed please see section C 2 Figure C 3 Receiver with Fixed Position 6 After the receiver indicates its position is fixed it can calculate and send differential corrections to the rover station This transmission can be 184 verified by observing a flashing green light above the COM2 port on the rear of the receiver This will occur only after the position is fixed If
186. the coupling between lateral velocity and roll is greater than that of yawrate and roll 7 and the bicycle model does not account for roll it was decided that the relaxation length which corresponded to the best match of the yawrate frequency 84 response would be used for further analysis o 0 7m With the relaxation length estimated from the frequency response the time domain responses were repeated 6 2 2 Chirp Response Yaw Rate Prediction and Measurement Chirp Using DC Gains 20 1 1 1 r r 1 1 1 1 Measurement 15L Predicted from Bicycle Model with Tire Lag il 10 Yaw Rate deg s Oo 20 6 time s Figure 6 5 Yawrate Chirp Response Lag Model 0 25 Lateral Velocity Prediction and Measurement Chirp Using DC Gains 0 2 0 1 F 0 05 0 05 Lateral Velocity m s oO 0 15 02 T T T T T T mM T T T oO Measuremen Predicted from Bicyc I I I L T e Model with Tire Lag I I I 0 25 6 8 10 12 14 16 18 time s 20 22 24 26 Figure 6 6 Lateral Velocity Chirp Response Lag Model 6 2 3 Steady State Circles Yaw Rate Model Comparison Circle Using DC Gains 25 Measurement Predicted from Bicycle Model with Tire Lag 20 Yaw Rate deg s a 5 L L L L 5 10 15 20
187. tiffness variation cannot be seen This is an interesting result that may not be apparent upon inspection of the model s equations 5 4 4 2 Steady state Circles By comparing Figure 5 7 with Figure 5 16 the understeer gradient method presented in section 5 2 may seem better than the DC gain method when matching the lateral velocity measurements for the steady state circle data However by looking at the transient portions of the plots one can see that the DC gain method more accurately represents the dynamics of the vehicle even though it is offset by a constant value The accurate match for low frequencies of the frequency response and chirp response data and poor match for the steady state circle maneuver suggests that there is a significant tire force generation mechanism that is dependent on whether or not the vehicle is in a steady turn A possible explanation for this is that the tire model may be dependent on the vehicle roll 76 angle which is significantly greater in a steady state turn than during low frequency sinusoidal steering inputs The effects of roll angle and tire camber will be investigated later in chapter 7 5 4 4 3 Frequency Response By using the DC gain method the bicycle model was forced to match yawrate and lateral velocity plots in the low frequency region of the frequency response As expected both lateral velocity and yawrate frequency response magnitudes are now accurate at low frequencies However
188. tion cccceeessssssssssssssssssssssssssssssnsssssseaes 39 4 1 3 Part 32 Steering Sensors encro a E Ana de ideas ares 40 4 1 3 1 Steering Sensor Cali PratiOnis atsizssscsgbacdsveeoresdacsiasestesseenetadtensetiaed 41 4 1 4 Data Acquisition System sssssessesseeseessessreseesseesesresseeseesresseesreseresse 43 4i Vb DSPOperation sonari eeii i ieia iS 43 441I nterface DSP sin sch tis eia E EA E 44 JA41 2 Master DSP orrena E E Adena ai 46 4142 PCOpera tona Sates e a eas spy n E E A O aS 47 4 2 Systeri Setup PictUTES mirioni E E E E E a E 48 Chapter 5 Vehicle Parameter and State Estimation Measurements and Bicycle Model Predictions onnsieiin deiir ei a ai a iA 50 5 1 Vehi le Paraincter Estimation essien an E ees 50 5 1 1 Mass and Vehicle Dimensions e sssessseseesessesseseesstsetstssesresessesresseseesesse 50 312 Und rsteer Gradient nereo iain a i aa iiet 51 5 1 3 Cornering Stiffness EsStimationicsaccedssceaasseccstccsavsestadensazedesdasdessedenacates 54 5 2 Bicycle Model Simulation Results o c0 scssaccssdecacsssaneaassasdacdsatesuctoscdeensvaaduesartens 57 521 Chirp RESPONSE iir y E O EE A E ae ERE 57 5 2 2 Steady State Cm Chess siiin gri eaa ER EA RE Ea an 59 5 2 3 Freg ency Response oa nenea a a A a a i ata 60 5 2 4 Bicycle Model Results Discussionissac 2i3 aseaersieinss csi anaes 62 5 3 Bicycle Model Cornering Stiffness Correction ss ssesessssesseserssressesseesees 63 5 3 1 Bicycle Mod
189. tion from satellite signals to its known position According to NovAtel a single stationary DL4plus receiver is capable of calculating its position accurate enough for base station operation in approximately 1 hour however to ensure accuracy the position calculation was allotted 24 hours After the calculation was complete a FIXPOSITION command was given to the DL4plus to save its current position into system memory Table 4 4 summarizes the calibrated base station position Table 4 4 Base Station Position WGS84 Coordinate Latitude degrees 40 86313783175 Longitude degrees 77 83490273560 Ellipsoid Height m 367 353 The base station location was chosen by allowing it to send RTCM corrections to the rover and then monitoring this communication as the vehicle was driven around the PTI test track It was confirmed that the FreeWave wireless radio modems could successfully communicate the RTCM corrections for the vehicle s entire route so the base station location was deemed appropriate The current position is located on the loading dock on the left side of the skid pad as shown in Figure 4 4 40 lt tzeresesss BESTEST TSS es boert i ae Figure 4 4 Base Station Location 4 1 3 Part 3 Steering Sensors As in 9 the sensors used to determine the steering angle of the vehicle were linear string potentiometers These sensors work well with this application because they are simple to use and can be re
190. turbance measurements it is also possible to generate a road grade angle A as defined in Chapter 8 This is done combining the U measurements at the current time with those of a future time and taking into account the vehicle length The diagram in Figure 9 25 clarifies this Figure 9 25 Road Grade from Road Disturbance Estimations Diagram From geometry using the small angle approximation 148 U t r U O _ 34 a b a sin The resulting Road Grade 4 from the extracted road disturbance U is presented in Figure 9 26 Pitch Angle deg Recovered Road Grade deg So a oO gt a Pitch Angle and Recovered Road Grade 5 mph 45 mph 80 mph f 4 M DS y J Nfi j ii ii i 1 0 20 40 60 80 100 120 140 160 180 200 Distance m H j M A j i f il I ue di amp HAR FW Pad TE EA AR Ala ACL AN A fl i y M IRANTI if INNI AT Pye Woy j A Y Ad yy y ji So WY y 4 Wy iy fh ll Wy f y J Yy j y i i gi i i i 1 I I i 20 40 60 80 100 120 140 160 180 200 Distance m Figure 9 26 Road Grade from Road Disturbance Estimations Plot Once again no additional filtering was required for this road grade estimate The simulations presented in this section show that with a proper model inversion accurate road disturbance and road grade estimations can be made i
191. twork Real Time WorkShop Driver eading doubles from Master O v 1 130 203 244 67 GPS Nanhle Nata Figure C 8 Connecting to the Client 16 With the Client now connected build the model again Wincon gt Build Model 17 When the model is done building the green Start button will become available 18 You can now select what you would like to plot by checking the options under the Plot dialog and clicking OK Click the start button and the data will be viewable in real time You may have to set the plot axes to make the data viewable in the given window If the data is not accurate e g you shake the car and the data does not show it please see C 49 2 3 Data Acquisition Saving Data A script has been written to automatically save each of the variables that are currently available for plotting The script is located in the GPS Wincon directory and is named script_saving routine m In order to save your open plots complete the following steps which have been illustrated in Figure C 9 1 In any open plot click Update gt Freeze All Plots and WAIT for them all to freeze this will be dependent on how many seconds of data you have saved In general this is about 3 4 seconds this process is NOT instant 2 Go to the MATLAB command prompt be sure you are in the C MartiniGPSFiles GPS_ Wincon folder and type script_saving routine This will save all the variables to the GPS_Wincon folder as mat files You can then se
192. uspensions are very close however the sprung mass over each suspension is considerably different In the next section this process is repeated with experimental data and estimated suspension parameters 150 9 7 Model Inversion on Experimental Data In this section the inversions described earlier are applied to in vehicle pitch measurements To perform this test the vehicle was driven over the same straight line path for speeds varying from 5 to 65 mph as discussed in chapter 8 To view measurements over this velocity range the pitch measurements were aligned using the GPS data recorded during the experiment The experimental data was then decimated in 30 cm increments As in chapter 8 the vehicle s suspension dynamics are removed from the pitch measurement by applying a low pass filter with a cutoff frequency of 0 1 cycles meter The resulting raw and filtered pitch measurements are displayed in Figure 9 28 Measured Pitch Angle Unfiltered 0 4 i 5 mph g 0 27 i 40 mph d YY f i 65 mph z lt 0 2 l 2 i ogh L 1 L L 1 L L i L 0 20 40 60 80 100 120 140 160 180 Measured Pitch Angle Filtered 0 4 0 2R F amp OF j E 2 y a 02 0 4 L L L L L i L L 0 20 40 60 80 100 120 140 160 180 Distance m Figure 9 28 Aligned Experimental Pitch Measurements As discussed previously the road grade estimation from the low frequency pitch measurements on t
193. utine This error calculation was performed for every Template Sample pair of points and the average error across all pairs was calculated This was then repeated for all five data sets which were collected This initial error estimate shows promising results All but one data sample set collected show an average error of ess than one meter Table 8 1 below summarized the correlation values and average error estimates for the five samples Table 8 1 Average Error Estimates and Correlation Values Sample Average Standard Average Lane Keeping Correlation Error Deviation Error l 134 cm 27 cm 48 6 cm 0 9105 2 15 cm 12 cm 11 5 cm 0 9898 3 9 cm 5 cm 9 7 cm 0 9893 4 66 cm 14 cm 16 7 cm 0 9610 5 13 cm 14 cm 9 1 cm 0 9889 The five 111 road grade matches corresponding to the highest correlation values for each of the sample sets are shown below Road Grade deg Road Grade deg Road Grade Correlation Sample 1 Road Grade Correlation Sample 2 0 2 r r r r r 1 5 r r r r r r Max Correlation 0 9105 map Max Correlation 0 9898 map 0 cece data data h 1L 4 0 2 ININA 4 Ma f 0 4L Y 4 J A 0 5 4 s P 0 6 73 Oo 0 8 B oF 4 oO Ahk 4 8 H 0 5 l af J 1 2 b 4 Ri ep 7 kl 1 J 1 6L M 1
194. vehicle s suspension dynamics and velocity effects from the pitch measurements Four pitch plane models of varying complexity were derived in this work A method of estimating suspension parameters such as spring stiffness and damping was also presented In simulation it has been shown that with an accurate model in place the inversion method extracts consistent road grade estimations over a wide range of speeds when the pitch measurements vary greatly When the inversion technique was performed on experimental data it was not as successful as in the simulation Although it recovered portions of the signal which were lost due to suspension filtering the resulting road grade estimation showed lower correlations than the low frequency pitch measurements It is believed that the inversion would be more successful when implemented on a vehicle which measures varying pitch measurements with increasing speed as was the case in the simulation As mentioned previously the model inversion is also dependent on how accurately the model represents the actual vehicle The Identical Suspension Model used in the inversions neglects rotational inertia and treats the vehicle as two separate but identical 158 quarter car models Although the vehicle in this study had suspension parameters which were approximately equal there was a significant difference in the mass distribution above the front and rear suspensions The uneven mass distribution combined with
195. via cable GPS C006 0002 Mount the small Radio antenna to the vehicle The mounting of the Radio antenna need not be exact Just be sure that it is in the upright position on the top of the vehicle not obstructed by anything On the Tracer a custom bracket is used but in the future a ChaseCam mount can be used Connect the Radio antenna to the FreeWave modem via the antenna cable Connect the FreeWave modem to the COM2 port of the DL 4plus via the brown RS 232 cable labeled ST Turn the vehicle on With nothing plugged into the AC outlet of the DC Inverter plug the inverter into the cigarette lighter It is important that there is nothing plugged into the Inverter on startup because of voltage spikes which occur This has damaged the PC power supplies in the past 10 After the inverter has started up plug the APC UPS Surge Protector into the inverters AC outlet When the surge protector is powered on the Client PC should start up 11 Power on the Rover DL 4plus receiver NOTE On startup the receiver will perform the IMU alignment routine outlined in Chapter 4 and the SPAN Manual During this time the vehicle should remain stationary If the vehicle is put in motion the calibration will stop thus resulting in an in motion calibration routine This should be avoided whenever possible When the calibration routine is finished only the green light above the COM1 port should begin flashing This indicates that the receiver
196. y Pitch The plot above shows that the filtering frequency required to successfully remove the vehicle s suspension dynamics from the pitch measurements also removes a large portion of the information contained within the signal Also it can be seen that the filtered signal in Figure 9 22 does not match the known road disturbances shown in Figure 9 15 Therefore it cannot be assumed that this method will correctly estimate the road profile for all vehicles This also suggests that this method of road grade estimation is ill suited for an accurate correlation routine 146 However it can be shown that true road profile can be extracted from the velocity dependent pitch measurements through the use of model inversion This inversion results in an accurate velocity independent measurement without excessive filtering To show this the Identical Suspension Model inversion is used The block diagram is identical to that given for the Kinematic Inversion in Figure 9 17 however the equation within the inversion block is replaced with that of the given in equation 9 25 Figure 9 23 shows a plot of the pitch angles and road disturbances extracted from the pitch angles at various speeds Pitch Angle and Extracted Road Disturbance Pitch Angle deg 1 1 1 1 1 L fi i 1 i 0 20 40 60 80 100 120 140 160 180 200 Distance m 0 06 E i 0 041 I Af A tAn MN ay A Y 5 Al J mH A g y ay f j

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