特異点適合法に基づいた ヒューマノイドロボットの静歩行
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1. HOUUUUUUUUUUUUUUUUUUUUUUd 0 000000000 MPO000 0 00000000 uj MPagusagaaguuudggggugguguud nm MPHOOOOUUOOOND Fig 3000 OoO00 0000 CeMpLDCUD HOUUUDUO MPOOUUUCUUUC e COMOOOUUC o OUUU eillilllilllilllll 5 0000 CoM BOO UD 6 HB HBBHgmtudutuuuu 7 MPQUUUUUUCUL e CoM B BU DU I elllllill elllilllillilllll 8 0000 CoMDB IU UD 9 LB H BB HL BH BL OLD UL EE D HE 10 HHBUOH TL 11 CoMQOO0000 O000000 Aa W N e 0000 MPOOO0OOOO s0000 00 0000 UUHHUUUUUUOUUUE UUYUUUUUUUUUO oggi 32 0000 HOHUOUUUUU MPIDODDUU UUUUDU UUYUOUUUUUUUUUUUUUUU OUUU 000 HOAP 200000000000000000 MPHOUUQOUUUUUUUUU0U UU0UUUUUOL 1 pulse ms 4 78 deg s OO OOOOU000 000 DOOOOU0 000 XOAP 20 000000000 Fig 3 Motion primitives uggpnaugagaggagadgagudunga duturt CoP rt ugugaggagnmnaggadunmuut Table 1 Tablel Static stablity margins for HOAP 2 Direction of motion Stability interval Front gt 6 68 deg Back lt 7 86 deg Left stable in whole motion Right gt 9 97 deg Front gt 6 18 deg Back lt 8 38 deg Left lt 10 54 deg Right stable in whole motion 33 0000 00000 HOAP 200000000 000000 upnapnpnpnunmnmuunmud Fig 40000 0000 NOOU OO0000000000 OOOO OdegfOO0 HOHOUUUUUUDOUOUUUE UOO Fig 5OOUUY HOUUHUUUUUUUUUUUUUL 2P1 B29 2 Joint angle deg Joint angle deg 0 WK _ 0123 4 5 6 7 8 9 10 0123 4 5 6 7 8 92. 10 Time s Time s Joint speed deg s Joint speed deg s 0123 4 5 67 8 9 10 0123 45 67 8 9 10 Time s Time s a b Fig 4 Knee motion data for a left leg b right leg 4 00 UHOUUUUUHUUUUUUUUUUUUUUUUUUO UUHUU UUUU UUUUUUUUUUUUUUUO UHUUUHUUUUUUUUUUUUUUUU dll HUUHHUHUUUUUUUY UUUUY UUUUUO UOUHUHUUUUUUUUUUUUUUE U D 1 M Vukobratovich B Borovac D Surla and D Sto kic Biped Locomotion Stability Control and Appli cation Springer Verlag 1990 2 uuuu uuggggggugu ZMP uguuuu 000000000 Vol 20 No 3 pp 229 232 2002 3 T Sugihara Y Nakamura and H Inoue Realtime Hu manoid Motion Generation through ZMP Manipulation based on Inverted Pendulum Control in Proc 2002 IEEE Int Conf on Robotics and Automation Wash ington DC May 2002 pp 1404 1409 4 Y Ogura T Kataoka K Shimomura H Lim and A Takanishi A Novel Method of Biped Walking Pattern Generation with Predetermined Knee Joint Motion in Proc 2004 IEEE RSJ Int Conf on Inteligent Robots and Systems Sendai Japan 2004 pp 2831 2836 5 T McGeer Passive Dynamic Walking The Interna tional Journal of Robotics Research Vol 9 No 2 pp 62 81 1990 6 K Ono and R Takahashi Self Excited Walking of a Biped Mechanism The International Journal of Robotics Research Vol 20 No 12 pp 953 966 2001 7 D N Nenchev Y Tsumaki and M Uc
3. 2P1 B29 UggiudtutluutL ut UgaubidtutitLutLut Static Walk of a Humanoid Robot Based on the Singularity Consistent Method ou 00 000 uuu ug 00 0000 O0 Dragomir N Nenchev G0 00 O Kentaro TAKAHASHI Masashi NODA Dragomir N NENCHEV Musashi Institute of Technology Abstract This paper addresses the problem of naturally looking and energy efficient walk of biped humanoids We presupose that such walk requires motion control capability around kinematic singularities such that the knee can be fully extended This problem is tackled by adopting the Singularity Consistent method devoloped for manipulator motion control at and around kinematic singularities We implemented the method with a HOAP 2 humanoid robot demonstrating stable static walk as a first step in this direction Key Words Humanoid robot Singularity Consistent approach Biped walking 1 OO ZHUOUUUUUOUUUUUUUUUUUUUUUO ZMP Zero Moment Point 1 TOOOO00COGO000 uu ZMPOO000O000000000 00000000L HOOOUCDCODCOOOOY 2 8 00000000 HOUOQUUDUUUUUUL UUUUUUUUUOUO HOUOUUUUUOUU UUUOUUUU UUUUOUU HOUOUOUUUOUUUUUUOD UUUUUUDUUO HOUO UUUUUUUUUUUUUUUUUUOUO HOUUUUU UUUUUUUU UUUUUUOUOU HOUOUUUUUUUUUUUUU UUUUUOUO HOOUUUUUUU VUYUOUODUUUUUUUUYL pougauggaggagagaguggagggmggaggugsua da ugaagggug dagg bJO0000000D ug uggbgamluliiliiitibltlliulLbtl tlit HOUOQUUUDUUUL UUUUUUUUUUUUOUO HOUOUUUUU OU UUUUUUOUUUUUOUOU pnugaggaggagaggauaggg legum HOU UUUUUUUUUUUUUUUUUUUOUO
4. HOUUUUUODOUUUUUUUUUUUUL ugmubluduliubulililulttLi utLtultu HOUOUUDUUUUUUUUUUUUUUUOUU O ugauugusullulliullui tuiiilli ilutlL tLtLu pnuggaggugagguggagg vuamam Bu ugguauuduiulullluLiublutliililitLutLitLilu pDuis agggagamgg nggagagamagg agnul HOUOUUUUUOUDUUUUUUUOUU UUO ULD uguauuduiuiullliuLiublutilibitLutiutLitlu POO panen 2 pDgggnmnaggutguubbadde ttnbdgegtl u ugagnggnaggugnggggmnanggaund 0 OOO0000000000000000000000 NOOO wfOboOoO0 o000000000000000 DNOOO O00000000000000000000 D000000 Fig 1000 u GO000000 0 ugnagggggngugpn gugngdgnagdugag u ugggggggagaggaugmndgdugguguanmgu nu ugagnggaggggdggagnggadggmgauuu OOO agogmjgggpnpmggaggguugngu NOOoOog 00000000 0000000000 Leg motion boundary Extended knee configuration Vanishing null space vector direction Fig 1 Condition for vanishing null space vector UU GUUUUUYUUUUUUUUUUUUY UUUO O E EU O OE O E E E e e ddl ugupaupgpgBggagpbdBg dgggiiiii D00000 Fig 2 Fig 2000000000000 uugggggggggggggg nugupgugd edil nnnnnnnnnnnnnnnnmnmnrn No 06 4 Proceedings of the 2006 JSME Conference on Robotics and Mechatronics Waseda Japan May 26 28 2006 2P1 B29 1 Control in joint space Control by SC method ee j Fig 2 Hybrid control approach 3 00 000 HOAP 2 0 000000000000000 ui uuuiuuluiu uiuiuiuiuiul uiulliillL 000 00 MP Motion Primitives D Hl B B D D U HOUOGOUUUUOOUUE MPOOUOUUUUUUUUE uuulullllill LE 3 1 Motion Primitives
5. hiyama Singularity Consistent Parameterization of Robot Mo tion and Control The International Journal of Robotics Research Vol 19 No 2 pp 159 182 2000 i 000 0000 D N Nenchev OO00 t UU 000000 HOAP 2Q90000 No 05 4 0000 005 0 0000 0000 D N Nenchev Q OOOQU000 No 05 4000000 000000500000 1P2 8 042 2005 0 2 Du ooo 000 000 m 10 S H Research Vol 20 No 7 pp 607 615 2001 HOOOOODODDODO0D0 600000 2P1 5 051 0 Collins M Wisse and A Ruina A Three Dimensional Passive Dynamic Walking Robot with Two Legs and Knees The International Journal of Robotics 10s Fig 5 Motion snapshots of walk with static stability M1 OHOO00 000 000 0000 200000000 DOOOOOOD No 05 4 O 000000000000 HOOD 000000 1A1 8 042 2005 HA DHOOOOOOO00OD0DO000 0000000000 OOOO HOAP 2000000 2P1 B29 3
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