AMAM2000 Kimura 1 4 What is legged locomotion? Adaptive Dynamic Walking of the Quadruped on Irregular Terrain Stabilization of autonomous adaptation Non-linear Oscillation using neural system model H.Kimura Univ. of Electro-Communications Tokyo, Japan juggling dynamic walking hopping 2 5 Inverted Pendulum ZMP Based vs. Decerebrated Cat Based Zero Moment Point ZMP ZMP Stable Limit Cycle on Phase Plane [1939] 3 6 Which is primitive? Current Staus in Static (or Dynamic) Walking Dynamic Walking based on ZMP based on Inverted Pendulum position control of ZMP limit cycle on a phase plane • Legged Locomotion Studies in Robotics Dynamic Walking using CPG + Reflexes model no explicit model • Neuro-Mechanics trajectory based torque based No passive static walking Passive dynamic walking Acquired by learning Genetically programmed 1
AMAM2000 Kimura 7 10 Studies on Neuro-Mechanics Sensory Feedback to CPGs Dynamic Coupling between Neural Controller and Musculoskeleton • Peripheral sensory input: • Simulation Taga, Ekeberg, Ijspeert, ….. – Somatic sensation (joint angle, torque, contact, …) • Manipulator – Vestibular sensation – Miyakoshi [TITECH] juggling – Williamson [MIT] crank, sawing, .. – Kotosaka [ERATO/JST] drumming • Directive signal from upper level: • Legged Robot – Vision – Lewis [USC] salamander type – Kimura [UEC] quadruped Why Matsuoka’s Neural Oscillators? – Ilg [Karlsruhe, Jena] quadruped Essential for Adaptation to Irregular Terrain – Miyakosi [ETL, U. Tokyo] biped – ….. 8 11 Dynamic Walking on Irregular Terrain What’s the output of CPG? Conventional Method • Torque precise model – Directly output to actuators trajectory planning variety of irregularity – Easily combined with reflexes control • Joint Angle/Velocities Problem ? – Inverse dynamics is necessary to calcuate Autonomous Adaptation output torque 9 12 Dual System vs. Single System Why Neural System Model? sensor information traj. planning ves tibul e CPG e xten so r fle xor Animals show marvelous ability of N _T r eq. (8) autonomous dynamic adaptation. eq. (6) eq. (5) eq. (5) x(t) N o Rob ot N _Tr > 0 Y e eq. (9) s control desir ed a n g l e 4 b o d y e q. (4) In spite of difference in sensors and angle | f | f | | z > thresho ld ? x > t hresho ld ? actuators, there exist same principles as a N o Y e s physical phenomenon between animals u u and robots. x(t) : jo int trajecto ry u : joint torque 2
AMAM2000 Kimura 13 16 Control Model A Quadruped Robot stereo camera Proposed by Taga[91] encoder Length:36cm, Width:24cm Fe ed CPG Height:33cm, Weight:4.8Kg tonic s t r e t c h Hip&Knee joint: active reflex DC motor:23W s o m a t i c sensation Gear Ratio:40 muscle length contact with floor Ankle joint: passive torque rate gyro not good for musculoskeletal irregular terrain force/torque system sensor 14 17 Control Mechanism in Animals CPG alone Lower Control Mechanism in Animals cer ebrum vison v i s i o n a n d vestibu le a s s o ciation vestibulospinal cort i c e s s p i n a l cord vestibula r reflex motor cortex sensation somatic Central Pattern Generator γ vestibular purkinje α n u c l e i α sensation n e ur o n s motor neurons cer ebellu m brain stem flexor stretch spinal cord reflex reflex somatic γ α α sensation motor neuro ns flexor stretch extens or reflex reflex mus cle muscle mus cle flex sor ex tenso r muscle spindle muscle mus cle muscle Golgi tendon flexsor spindle muscle organ Golgi tendon skin organ skin Walking on flat terrain 15 18 Neural Oscillator As a Model of CPG Σ w y u 0 CPG alone ij j u 0 u 0 Extensor Neuron , τ τ -1 u e β v e Feed e -1 -1 y = m a x (u , 0 ) e - e w fe + -1 N_T r y = m a x (u , 0 ) f f Feed f 1 : E xcita tory C onnection u f v f β -1 : Inhibitory Connection , τ τ L F : left fore leg L H : l e f t hi nd le g Flex or Neuron R F : right fore leg Σ w ij y u 0 R H : right hind leg Matsuoka[87], Taga[91] j (b ) Neural Osc illator Walking on simple irregular terrain (a) N e u ral Osc illator Network for Trot 3
AMAM2000 Kimura 19 22 New Control Model Control Model Reflexes Independent of CPG vestibule Reflexes via CPG v e s t i b u l e Feed Feed CPG CPG tonic stretch tonic stretch reflex reflex phase somatic sensation somatic sensation v e s t i b u l o s p i n a l r e f l e x p h a s i c s t r e t c h r e f l e x muscle le ngth muscle le ngth t e n d o n r e flex contact wit h floor v e s t i b u l o s p i n a l r e f l e x contact with floor e x t e n s o r / f l e x o r r e f l e x & obstacle f l e x o r r e f l e x torque tendon force torque v e s t i b u l a r s e n s a t i o n musculoskeletal musculoskeletal system Biology system ex. Grillner[83], Cohen[99] 20 23 CPG + Reflexes Independent of CPG Neural Oscillator (1) Walking over an obstacle by using flexor reflex 21 24 Sensor Feedback to CPG CPG + Reflexes Independent of CPG vestibuolospinal reflex: tendon reflex: extensor reflex: flexor reflex: extensor: Walking up a slope by using vestibulospinal reflex flexor: 4
AMAM2000 Kimura 25 28 vesti bule rate gyro Actual C PG CPG + Reflexes via CPG extensor flexor Control Diagram N_Tr Feed e e r e q . ( 8 ) Feed e tr Feed e t s r v s r Feed f tsr vsr e q . ( 6 ) e q . ( 5 ) e q . ( 5 ) v s r v s r v s r No N_Tr > 0 Feed f fr v s r Yes e q . ( 9 ) v s r 4 d e s ir e d a n g l e body e q . ( 4 ) slow angle force sensor motion f f x > threshold ? | | z > threshold ? | | Vestibulospinal, Tendon and Flexor Reflexes No Yes N_Tr > 0 26 29 Walking on Irregular Terrain with Fixed Parameters CPG + Reflexes via CPG Ability of Autonomous Adaptation 44 cm 5 cm 7 c m 12 12 3 c m 66cm 28 cm 30cm 2 cm 3cm 3 cm Vestibulospinal, Tendon and Flexor Reflexes 27 30 CPG + Reflexes via CPG CPG + Reflexes via CPG Vestibulospinal, Tendon and Flexor Reflexes Vestibulospinal, Tendon and Flexor Reflexes 5
AMAM2000 Kimura 31 34 Walking on terrain undulation flexor reflex CPG torque Visual Adaptation N_Tr [Nm] Programmed 3 Adaptation RF 2 tendon reflex LF flexor 1 0 -1 extensor Autonomous Adaptation of CPG Visual Processing Walking over an obstacle -2 0 1 2 3 4 5 time [sec] 32 35 Walking over an obstacle cer ebrum CPG torque: u vison N_Tr vision input u 0 vision and (Nm) external input to CPG: u 0 asso ciation 3 10 cortices vestibule motor ves tibulospinal cortex vestibular RF reflex sen sation 0 0 directive signal vestib ular nuclei purkinje adjustment of neuron s 10 3 cerebellum brain stem landing point LF Adjustment of spinal cord somatic 0 0 C P G γ sensation External Input to CPG α α m o t o r n e u r o n s 3 10 flexor str etch reflex ref lex based on Vision LH extensor 0 m u sc l e 0 muscle m u sc l e flexsor 3 10 sp i n d l e musc le G o l g i te n d o n o r g a n skin RH 0 0 autonomous motion generation (sec) 33 36 Adjustment of CPG Visual Adaptation • Period Adjusted by reflexes • Amplitude Adjusted by an external input • Phase Adjusted autonomously on a CPG network By increasing external input to CPGs 6
AMAM2000 Kimura 37 40 What is Dynamic Walking? Conclusion & Future Work Mechanism itself has ability of dynamic walking. Dynamic walking is generated by • Autonomous adaptive dynamic walking on terrain of medium degree of irregularity by external force : gravity internal force : CPG torque using reflexes via CPG • Effectiveness • Well coordinated system by centering CPG • 3D dynamic walking on 3D irregular terrain Passive Dynamic Walking (PDW) Neural System Model (NSM) 38 41 PDW vs. NSM 2 Externla/Internal Additional Torque Fz CPG Torque Torque [Nm] by G ravity in PDW 1 Fz [N] flexor 0 END extensor -1 -2 -3 swinging supporting -4 0 1 4 2 3 time [sec] 39 Mechanical Design & Coupling with a Neural System • Small gear ratio & Large torque motor – Backdrivability of a joint for passive adaptation – Quick motion • Dynamics of mechanical system is encoded into parameters of neural system – Relation between the leg length and the frequency of CPG 7
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