Safe Execution of Bipedal Walking Tasks from Biomechanical Principles

1. Safe Execution of Bipedal Walking Tasks from Biomechanical Principles Andreas Hofmann Cognitive Robotics – 04/27/2005

2. Introduction

3. Introduction Problem: For agile, underactuated systems, can’t ignore dynamics

4. Introduction Problem: For agile, underactuated systems, can’t ignore dynamics

5. Introduction Problem: For agile, underactuated systems, can’t ignore dynamics Problem: No notion of task plan, little flexibility to disturbances

6. Introduction • Gap: Large class of problems that require • ability to execute task-level plans • flexibility to disturbances during this execution • taking into account dynamic limitations; understanding relationship between acceleration limits, and time needed to achieve state-space goals

7. Challenging case – Bipedal Machines • Walk from location A to B in 30 seconds • Must be strong, fast enough

8. Challenging case – Bipedal Machines • Walk from location A to B in 30 seconds • Must be strong, fast enough • Should not fall, even if disturbed

9. Challenging case – Bipedal Machines • Should not fall, even if disturbed

10. Challenging case – Bipedal Machines • Should not fall, even on shaky ground

11. Challenging case – Bipedal Machines • Should not fall, even on shaky ground

12. Challenging case – Bipedal Machines • Should not fall, even on shaky ground • But there are limits!

13. Problem Statement • What balance strategies do humans use? • How can we build an autonomous system that • Understands qualitative walking task specifications • Translates such specifications into control actions • Rejects significant disturbances?

14. Humans use Three Balance Strategies • Stance ankle torque

15. Humans use Three Balance Strategies • Stepping • Stance ankle torque

16. Humans use Three Balance Strategies • Stepping • Stance ankle torque

17. Humans use Three Balance Strategies • Stepping • Stance ankle torque • Movement of non-contact segments

18. Humans use Three Balance Strategies • Stepping • Stance ankle torque • Movement of non-contact segments

19. Humans use Three Balance Strategies • Stepping • Stance ankle torque • Movement of non-contact limbs

20. Approach – walking task spec Qualitative State Plan

21. Computing torques to achieve a particular state goal is challenging

22. Hybrid executive and multivariable controller

23. Hybrid executive coordinates controllers to sequence plant through poses in qualitative state plan

24. Hybrid executive coordinates controllers to sequence plant through poses in qualitative state plan

25. Hybrid executive coordinates controllers to sequence plant through poses in qualitative state plan

26. Hybrid executive coordinates controllers to sequence plant through poses in qualitative state plan

27. Hybrid executive coordinates controllers to sequence plant through poses in qualitative state plan

28. Multivariable controller • makes state plan quantities, like CM, directly controllable • allows hybrid executive to control CM by adjusting linear gain parameters

29. Hybrid executive • Synthesizes dedicated controller for each qualitative pose • Rather than generating specific reference trajectories, generates “tubes” of valid operating regions Maximizing tubes maximizes robustness to disturbances

30. Approach Summary • To enhance balancing ability, use all 3 strategies • To simplify task specification, use qualitative state plan • To translate specification into actions, use model-based executive • Hybrid executive to sequence • Multivariable controller to decouple, linearize • To provide robustness, compute regions of operation, not just nominal trajectories

31. Innovations of Approach Previous Approach Uses primarily first strategy [Hirai, 1997]

32. Innovations of Approach Previous Approach Innovation Use all three strategies Uses primarily first strategy

33. Innovations of Approach Previous Approaches Innovation Use all three strategies Use primarily first strategy Detailed actuated trajectory spec.

34. Innovations of Approach Previous Approaches Innovation Use all three strategies Use primarily first strategy Detailed trajectory spec. Higher-level spec – Get to goal by specific time Qualitative specification - Dividing range of values of state variables into regions of interest [Williams, 1986]

35. Innovations of Approach Previous Approaches Innovation Use all three strategies Use primarily first strategy Detailed trajectory spec. Higher-level spec – Get to goal by specific time, using common gait

36. Innovations of Approach Previous Approaches Innovation Use all three strategies Use primarily first strategy Detailed actuated trajectory spec. Qualitative state trajectory spec.

37. Innovations of Approach Previous Approach Innovation Use all three strategies Uses primarily first strategy Use detailed trajectory spec. Use flexible trajectory spec. - Compute tubes [Sacks, 1987], [Bradley and Zhao, 1993]

38. Innovations of Approach Previous Approach – exploits waits [Morris, 2001]

39. Innovations of Approach Previous Approach Innovation Underactuated system - Control epochs have no equilibrium point (no ability to wait)

40. Innovations of Approach Previous Approach Innovation • Define continuous goal region in position/velocity state space • Find feasible range of times for presence in goal region

41. Innovations of Approach Previous Approach Innovation • Offline planning to generate detailed trajectories • Compilation of state-space and temporal requirements into control bounds • Executive adjusts control parameters within bounds • Compilation efficiency through use of a novel metric

42. Innovations of Approach Previous Approach Innovation • Offline planning to generate detailed trajectories

43. Roadmap • Analysis of three balance strategies • Model-based executive • Discussion

44. Analysis of three balance strategies • Study of human trial data • Which balance strategies are used during normal walking? • Are there simplifying relations that are useful for control?

45. Angular momentum tightly conserved • During normal walking [Popovic, Hofmann, and Herr, 2004] • Using strategies 1 and 2, not 3 • Ground reaction force vector points from ZMP through CM

46. Angular momentum tightly conserved • During normal walking [Popovic, Hofmann, and Herr, 2004] • Using strategies 1 and 2, not 3 • Horizontal ZMP can be used to accelerate horizontal CM • ZMP can be thought of as control input

47. Angular momentum tightly conserved • During normal walking [Popovic, Hofmann, and Herr, 2004] • Using strategies 1 and 2, not 3 • Approximate using spring constant

48. Validation of approximation • Lateral ZMP: prediction in red, average over 7 trials in green, standard deviation bounds in black and blue

49. Horizontal CM accelerated by horizontal ZMP • ZMP bounded by support polgon • Imposes controllability limit

50. Horizontal CM accelerated by horizontal ZMP • ZMP bounded by support polgon • Imposes controllability limit • What if this isn’t enough? • What if more horizontal force is needed, but foot placement can’t be changed?