Goals. Musculoskeletal Model. Human Body Modeling. Muscles/Tendons/Ligaments. Skeleton 7/23/2013

Transcription

1 Goals Robotics and Animatronics in Disney Lecture 7: Human Modeling and Control Katsu Yamane Introduce basic physiology and describe how to model it using robotics techniques Introduce attempts to understand human motor control principles Discussion on dierences between simple vs. complex models or human motion analysis 2 Musculoskeletal Model Human Body Modeling [Nakamura et al. TRO 2005] [Yamane et al. ICRA 2005] Skeleton Musculo-tendon network Skeleton Muscles/Tendons/Ligaments 200 bones 53 rigid bodies (no ingers) 155 DOF by mechanical joints 997 muscles 50 tendons 117 ligaments 1

2 Musculo-Tendon Network Dynamics Mass-less, zero-radius wires with via-points Wire tensions Joint torques τ G J = l θ Moment arm τ G = a a l Principle o Virtual Work d Alembert s Principle τ G = J T Dynamics Simulation Wire Tension Estimation Wire tensions Joint torques Wire tensions Joint torques 1. Obtain equivalent joint torques τ G = J T 2. Forward dynamics computation or articulated rigid bodies 1. Inverse dynamics computation or articulated rigid bodies 2. Solve τ G = J T Ininite number o solutions! Unique solution Physiological reality Wire Tension Estimation Optimization [Challis 1997] [Rasmussen 2003] Minimize Subject to τ G J T + 0 via linear or quadratic programming Reerence muscle tension 0 numerically optimal tensions rom EMG data physiologically realistic tensions Linear Programming Consider EMG data or physiological reality Linear programming ormulation minimize T T Z a a a, a 0 subject to T J 0 0 G * 0 [Nakamura et al. 2005] [Yamane et al. 2005] Error o the mapping equation Error rom a reerence tension * 0 minimizes total orce Compute rom EMG data Muscles can only pull 2

3 Physiological Muscle Model Muscle model [Hill 1938] Physiological Muscle Model EMG to muscle tensions Numerical model [Stroeve 1999] 2 l l 0 l ( l) exp lsh F Fv ( l ) Vshv l length-tension relationship length-tension relationship 0 V shvshlv V v l sh V l V V v ml sh shl l l 0 l v v l 0 EMG data IEMG u u a a T muscle activity a length-tension relationship velocity-tension relationship F v F l (l) (l ) Muscle tensions ) F * afl ( l) Fv ( l cross-section area F [Hill 1938] [Stroeve 1999] Examples vertical contact orce let right let vastus lateralis let achilles toe walk toe walk heel walk heel walk Realtime Interace [Murai et al. EMBC 2009] Neuromuscular Control [Murai, Yamane, Nakamura EMBC 2007] [Murai and Yamane ICRA2011] 18 3

4 Understanding Motor Control Modeling the Relex Behavior How motor commands are generated Neuromuscular network model Parameter identiication Evaluation Simple relex Relex in walking motion [MacLean 1990] Peripheral nervous system (PNS) Inputs and outputs Inputs: motor command signals at spinal nerve rami Outputs: muscle tensions Two paths: CNS PNS: descending pathway PNS PNS: ascending and descending pathways (somatic relex network) Central nervous system (CNS) Motor Command Signals [Murai, Yamane, Nakamura EMBC 2007] 997 muscles: 997 independent control signals? A lot o work suggests that human motions are conined in smaller space Joint trajectories [Saonova et al. 2004] Muscle synergy [Bernstein 1967] Hypothesis: muscles are controlled by ewer independent signals Motor Command Signals [Murai, Yamane, Nakamura EMBC 2007] [Murai, Yamane, Nakamura EMBC 2007] Independent component analysis (ICA) = W ICA s Muscle tensions Independent signals Estimate mutually independent signal sources Order o the independent signals is undeined Dimension o s? 120, the number o relevant spinal nerve rami, is enough! 4

5 Somatosensory Inormation Somatosensory inormation or relex: Muscle spindle: senses muscle length and velocity, induces stretch relex, antagonistic inhibition, etc. Golgi tendon organ: senses muscle tension, induces Ib inhibition 120 independent signals All-to-all connection Anatomical connection Anatomical connection Muscle tensions Muscle length / orce sensors 5

6 Anatomical connection with time delay (30ms) Parameter identiication 5000 cycles Error average: 2.59% variance: 0.34% Experiment training data (2000 rames/10 seconds) Weight Parameter o Relex Loop rom Iliacus (hip lexion) to muscle weight Iliacus 4.20E+00 Sartorius 2.60E-01 Rectus Femoris 3.94E+00 Pectineus 4.60E-01 Gracilis -4.06E-01 Adductor Longus -1.69E-01 Adductor Brevis -3.59E-01 Adductor Magnus -4.10E-02 Weight Parameter o Relex Loop rom Tensor Fasciae Latae (hip lexion) to muscle Tensor Fasciae Latae Gluteus Maximus Biceps Femoris Semitendinosus Semimembranosus Gluteus Medius Gluteus Minimus weight 2.93E E E E E E E-01 hip lexion muscles hip extension muscles Patellar Tendon Relex hit! Relex in Walking Motion [Murai and Yamane 2011] 36 6

7 Further Validation o Relex Model Human Response to Trips [Pijnappels et al.05] More complex behavior: walking Videos rom Human response to trips [Eng et al. 1994] [Cham 2009] Elevating strategy: Trip at early stage o swing(5-25%) Swing leg is lited or collision avoidance Lowering strategy: Trip at later stage o swing(55-75%) Swing leg is lowered or immediate contact EMG within 100ms is observed involuntary response Induced by relex system? tripping 100ms Simpliied Model Parameter Identiication Saggital plane 7 muscles in each leg (14 muscles) (x0.03) Identiied Parameters Reconstruction Accuracy HAM GLU TA GAS RF VAS SOL HAM GLU TA GAS RF VAS SOL Positive orce eedback or synergistic muscle Negative orce eedback or antagonistic muscle average error: 2.0% 7

8 Additional Controller Dynamic Simulation o Locomotion Upper body control: Apply PD controller to ixed posture Mechanical joint limit: Strong spring is applied at knee joint limit Swing leg PD control: Ankle joint has weak spring and damper during swing phase Model cannot continue walking Similar to original joint motions despite lack o reerence trajectory dierence in the contact condition Simulation o Trip Response Summary 13% o swing phase 55% o swing phase Qualitatively similar to elevating / lowering strategies Simulated muscle activities match reported EMG in GAS, SOL, and GM [Pijnappels et al. 05] Detailed musculoskeletal model Modeling Dynamics Neuromuscular network model Control signal rom ICA Patellar tendon relex Relex in Walking Simpliied model or simulation Trip responses Discussion Level o details We started rom a very detailed human model Then used simpler model or urther validation Many researchers work with simple models Which model makes sense? Simple models can miss details? Parameter identiication? Signal/noise ratio? 8