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Angular Momentum Primitives for Human Walking: Biomechanics and Control

Angular Momentum Primitives for Human Walking: Biomechanics and Control. Marko Popovic 1,2 , Amy Englehart 1 and Hugh Herr 1,3 1) Biomechatronics Lab, The Media Lab, MIT 2) Computer Science and Artificial Intelligence Lab, MIT 3) MIT-Harvard Division of Health Sciences and Technology

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Angular Momentum Primitives for Human Walking: Biomechanics and Control

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  1. Angular Momentum Primitives for Human Walking: Biomechanics and Control Marko Popovic1,2, Amy Englehart1 and Hugh Herr1,3 1)Biomechatronics Lab, The Media Lab, MIT 2)Computer Science and Artificial Intelligence Lab, MIT 3)MIT-Harvard Division of Health Sciences and Technology IROS 2004, Sendai, Friday October 1, 2004

  2. Goal To develop robust biomimetic real-time controls for humanoid robots, leg prostheses/orthosis and exoskeleton. Many degrees of freedom, complex & often changing environment, zillion potential tasks and their parameters, superpositions and transitions => a) no library with all possible trajectories and grgb) detailed long range (a few seconds) real-time optimization unattainable. Obstacle

  3. How to simplify the problem? • Time-local optimization approach and hierarchical controls. • Small set of motion metrics (CM, CP/ZMP and FRI points, angular momentum, correct foot landing, metabolic energy…) & extremely simplified target values. • Tunable coefficients parametrizing cost function. • Cost function such that it communicates more • time-integral behavior than time-local behavior.

  4. How to simplify the problem? (continued) • -Problematic in time-local vs. time-integral sense. • Biomimetic motion not guaranteed! • (For simple PD control situation even worse.) • Optimization still computationally expensive. • Need to constrain space! • -Robot and task specificreductionthat is either: • manually chosen/tuned • long range optimized w/ & w/o noise • data driven

  5. Normalized Spin Angular Momentum Whole body Effective Angle Whole body effective angular velocity is Recipe: Integrate angular velocity to get whole body effective angle. Note – not directly measurable quantity! State reduction from the Angular Momentum Distribution • Angular Momentum highly regulated while: balancing in double support, • walking & running => zero spin as high level control target (Popovic et al.2002) (Popovic et al. 2004) (Kajita et al. 2004)

  6. How is angular momentum distributed throughout the links? 16-component angular momentum distribution vector • Apply Principal Component Analysis (PCA) on trajectory in • 16 dimensional angular momentum distribution space to get PCs=Angular Momentum Primitives & their data explained.

  7. Primitives and data explained Normalized tuning coefficients ci Left foot (1), right foot (2), left shin (3), right shin (4), left thigh (5), right thigh (6), left hand (7), right hand (8), left forearm (9), right forearm (10), left upper arm (11), right upper arm (12), abdomen and pelvis (13), thorax (14), neck (15) and head (16). Angular Momentum Primitives Invariant in respect to speed, stride length and subject!!! magnitude

  8. Applied control strategy • Command speed and stride length (high level specification). • Estimate gait phase based on CM position in respect to • stance foot. • Estimate angular momentum of all limbs for best guess solution based on angular momentum of the stance foot.

  9. Control Results Simulation joint angles (solid) & biological data (dotted) A) Swing ankle B) Swing knee C) Swing hip D) Stance ankle E) Stance knee and F) Stance hip.

  10. Alternatives & Future directions? • Lump initial and final optimizer into one. Work only with primitives. • Consider more than three if needed to address larger perturbations. • Build library of primitive sets (explaining ~99% of data) for various • tasks. See how much sets differ among themselves. Address smooth • tasks’ transition and superposition. • If biological data is not available perform long range optimization • with perturbation noise. Extract primitives. Construct real time control.

  11. Summary • Movementmotor primitives in angular momentum distribution space – for the first time whole body primitives. Invariant to speed, stride and subject! • Biomimetic motion generated in real time based on space reduction through motor primitives • Future work: controls by optimization of primitives’ tuning coefficients alone, perturbation test, study of concept for various task & transition/superposition, address control of robots w/o biological counterpart.

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