Reasoning about Human Motion: A Tutorial Overview

1. Reasoning about Human Motion: A Tutorial Overview Andreas Hofmann

2. Contents • Introduction • Architectures for motion control • Impedance control algorithms • Explaining and reproducing human motion trajectories • Disturbances - classification and strategies • Conclusion

3. Different kinds of human motion

4. Artificial human motion: Robotics

5. Artificial human motion: Animation

6. Artificial human motion: Assistive Devices

7. Goals of Motion Research • Understand biomechanical principles underlying control of motion • Biomimetic motion trajectories • Stability in presence of disturbances • Develop models and controllers based on such principles • Develop estimators based on these models • Compute trajectories, intent, from noisy sensor input (video, EMG, marker)

8. Contents • Introduction • Architectures for motion control • Impedance control algorithms • Explaining and reproducing human motion trajectories • Disturbances - classification and strategies • Conclusion

9. Motor control – functional hierarchy • High-level goals (conscious, flexible) • Win point vs. conserve energy (in tennis) • Strategic planning (conscious, flexible) • Note opponent’s position, return to right rear baseline • Tactical objectives (preconscious, learned) • Contact of racket with ball • Action (subconscious, automatic) • Desired force and position trajectories • Muscle activation

10. Motion execution architecture

11. Motion estimation architecture

12. Contents • Introduction • Architectures for motion control • Impedance control algorithms • Explaining and reproducing human motion trajectories • Disturbances - classification and strategies • Conclusion

13. Control of walking machines

14. Virtual Model Control • Impedance control of reaction point • Reaction point is control point of interest (COM, swing leg, end-effector) • Virtual elements used to express setpoint, impedance of reaction point • Compute desired force for reaction point • Jacobian used to compute joint torques that achieve desired reaction point force

15. Virtual Elements Specify translational and rotational force between action frame and reaction frame Force usually computed based on simple PD control law

16. Using Jacobian to Compute Joint Torques • Simple Jacobian-based equation • Derived using notion of virtual work • Jacobian computed from kinematic transforms

17. Model Kinematics Horizontal Plane Hy is hip yaw Frontal Plane Hr, ar are hip and ankle roll Joint angle vector for one leg: Sagittal Plane Hp, kp, ap are hip, knee, and ankle pitch

18. VMC Jacobian Transformation – Single Leg Jacobian used to relate reaction frame force to joint torques - Based on virtual work derivation (Paul, Craig) • so (simple equation requiring only matrix multiplication)

19. Caveats for torque computation using Jacobian • No limit on joint torques • (to model actuator limits, or to prevent foot slip or roll) • Not guaranteed to work for all poses • If leg completely straight, hp, kp, ap are all 0 • Jacobian not of full rank • Vertical force not feasible in this pose • Joint torques for hp, kp, and ap will be computed as 0, even if the desired vertical force is non-zero • In practice, such problems are avoided by bending the leg slightly in the computation

20. Hardware implementation • Requires use of special actuators • Series-elastic actuators

21. Jacobian Computation for Single Leg Forward kinematic transform built up using chain of homogeneous transforms for segments and joints Ankle pitch transform Shin transform Elements of J computed using partial derivative method (Paul, Craig)

22. Biological inspiration: equilibrium point hypothesis • Motion as sequence of poses (Bizzi, et. al.)

23. How can virtual element parameters be determined? • ”Intuitive” approaches are not adequate for locomotion applications

24. Contents • Introduction • Architectures for motion control • Impedance control algorithms • Explaining and reproducing human motion trajectories • Disturbances - classification and strategies • Conclusion

25. Achieving biomimetic motion • What should the parameters for the virtual elements be? • “Intuitive” control (tweaking parameters by hand) is tricky • Investigation of human motion and its underlying biomechanical control principles can provide useful guidance

26. Planar arm motion • Flash and Hogan, minimum jerk • Hasan, minimum effort • Both give good predictions (within noise range of biological data)

27. 3-D arm motion • Atkeson and Hollerbach, invariants of 3-D arm motion • Trajectories are curved, but • Invariant tangential velocity profile when normalized for speed and distance • Close to minimum-jerk • Hypothesized association with visual kinematic coordinate frame

28. Challenges with locomotion • Kinematic principles alone generally not adequate • Foot contact as semi-underactuated joint • Inverted pendulum analogy • Dynamics are important

29. Dynamic optimization techniques • Dynamic programming • Very general, can incorporate discrete as well as continuous variables, limitations with large state spaces, discretization • Space-time Dynamic Optimization • Witkin, Popovic brothers • SQP, control points

30. Space-Time Dynamic Optimization • Zoran Popovic animations

31. Space-Time Dynamic Optimization

32. Space-Time Dynamic Optimization • Angle position trajectories represented as splines with control points • Typically, 10 – 20 control points for a 1 – 5 second trajectory • Easy to differentiate to get velocity and acceleration splines • Control points are parameters to be optimized • SQP algorithm (constrained non-linear optimization) • Kinematic, dynamic constraints • Cost function in terms of state and force variables

33. Space-Time Optimization • Kinematic constraints • Relations of joint angles, angular velocities, and angular accelerations to segment positions, velocities, and accelerations • Minimum and maximum values for angles • Keep body upright • Keep swing foot off ground

34. Space-Time Optimization • Dynamic constraints • Relation of joint torques to angular accelerations • Associated ground reaction forces, center of pressure

35. Important Biomechanical Principle • Noticed interesting characteristics in test data collected at Spaulding Rehab Gait Lab • Hypothesize that conservation of angular momentum about COM is being actively and vigorously asserted (closely controlled) for many kinds of movements

36. Assuming strict conservation of angular momentum, torque about COM must be 0. Therefore, by torque balance,

37. Conservation of Angular Momentum about COM • This suggests a technique for computing COP if a desired COM trajectory is known • Differentiate COM trajectory twice to get desired stance leg(s) ground reaction forces • Use previous equation to compute corresponding COP

38. Conservation of Angular Momentum about COM • Tested this hypothesis using human test subject • Tests performed as Spaulding Rehab Gait Lab • Developed full-body kinematic model corresponding to dimensions of test subject • Used to compute COM • [Show test subject model movie] • Following plots show results averaged over 5 trials • (1/2 gait cycle, right toe-off to left toe-off

48. Conservation of Angular Momentum about COM • Tests show that COP can be predicted based on COM trajectory • Foot placement can be predicted based on COM trajectory • Suggests that dynamic optimizer should track COM, and derived ground reaction force and COP trajectories

49. Reduced-order Models

50. Sagittal Plane Model Dynamic Optimization • Initialize all trajectories to straight-line interpolation from initial pose to final pose angle values • Run dynamic optimization to get open-loop prediction of trajectories • Compare with biological results • [Play 100 movie.] • Following plots show results for toe-off to heel-strike