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Safe Execution of Bipedal Walking Tasks from Biomechanical Principles

Safe Execution of Bipedal Walking Tasks from Biomechanical Principles. Andreas Hofmann and Brian Williams. Introduction. Introduction. Problem: For agile, underactuated systems, can’t ignore dynamics. Introduction. Problem: For agile, underactuated systems, can’t ignore dynamics.

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Safe Execution of Bipedal Walking Tasks from Biomechanical Principles

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  1. Safe Execution of Bipedal Walking Tasks from Biomechanical Principles Andreas Hofmann and Brian Williams

  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 – Problem Addressed • Gap: Large class of problems that require • ability to execute task-level plans • ability to deal with disturbances • taking into account dynamic limitations; understanding relationship between acceleration limits, and time needed to achieve state-space goals

  7. Challenging case – bipedal walking • Walk from location A to B in specified time • Observe foot placement restrictions imposed by terrain

  8. Challenging case – bipedal walking • Walk from location A to B in specified time • Observe foot placement restrictions imposed by terrain

  9. Challenging case – Bipedal Machines • Walk from location A to B in specified time

  10. Challenging case – Bipedal Machines • Walk from location A to B in specified time • Should not fall, even if disturbed

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

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

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

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

  15. Approach – walking task spec Qualitative State Plan

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

  17. Hybrid executive and multivariable controller

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

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

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

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

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

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

  24. Innovations • Requirement: Stable walking

  25. Innovations • Requirement: Stable walking Previous Approaches

  26. Innovations • Requirement: Stable walking Previous Approaches

  27. Innovations • Requirement: Stable walking • How to get to the right place at the right time? • What if terrain requires irregular foot placement? Previous Approaches

  28. Innovations • Requirement: Stable walking • How to get to the right place at the right time? • What if terrain requires irregular foot placement? Previous Approaches Innovation Execute a plan

  29. Innovations • Requirement: ability to execute task-level plans • How should walking plans be expressed? • What are the requirements for successful plan execution? Previous Approaches Detailed actuated trajectory spec.

  30. Innovations • Requirement: ability to execute task-level plans • How should walking plans be expressed? • What are the requirements for successful plan execution? Previous Approaches Innovation Detailed actuated trajectory spec. Qualitative state trajectory spec.

  31. Innovations • Requirement: ability to execute task-level plans • How should walking plans be expressed? • What are the requirements for successful plan execution? Previous Approaches Innovation Detailed actuated trajectory spec. Qualitative control plan

  32. Innovations • Requirement: ability to deal with disturbances • What balance strategies can bipeds (like humans) use?

  33. Innovations • Requirement: ability to deal with disturbances • What balance strategies can bipeds (like humans) use? Previous Approaches Uses primarily ankle torque strategy

  34. Innovations • Requirement: ability to deal with disturbances • What balance strategies can bipeds (like humans) use? Previous Approaches Innovation Use three balance strategies Uses primarily ankle torque strategy

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

  36. Innovations • Requirement: account for dynamic limitations • What is the relationship between acceleration limits, and timing needed to achieve state-space goals?

  37. Innovations • Requirement: account for dynamic limitations • What is the relationship between acceleration limits, and timing needed to achieve state-space goals? Previous Approach – exploits waits [Morris, 2001]

  38. Innovations • Requirement: account for dynamic limitations • What is the relationship between acceleration limits, and timing needed to achieve state-space goals? Previous Approach – exploits waits Innovation Underactuated system - no equilibrium point (no ability to wait) [Morris, 2001]

  39. Problem Solution Take state plan and plant state as input Generate plant control input that causes plant state to evolve in accordance with the state plan specification.

  40. Multivariable controller makes CM directly controllable

  41. Multivariable Controller Requirements • Want to specify coarse setpoint • Forward CM setpoint = 0 • Lateral CM setpoint = 0 • Controller should figure out detailed joint trajectories

  42. Hybrid executive decides CM setpoints, control gains • adjusts kp, kd gains of SISO abstraction

  43. Hybrid Executive Requirements • Multivariable controller accepts single setpoint

  44. Hybrid Executive Requirements • Multivariable controller accepts single setpoint • Can’t, by itself, sequence through multiple setpoints • Need hybrid executive for that

  45. At start of control epoch, hybrid exec. sets controller gains

  46. Hybrid Executive guides each variable to its goal

  47. Hybrid Executive transitions to next epoch • when goal for each variable is achieved

  48. What if there is a disturbance? • trip recovery

  49. Disturbances and Controllability • How can disturbances be handled? • Given some bound on disturbances, is it possible to guarantee successful execution of a plan? • Dispatchers for discrete systems

  50. Disturbances and Controllability • How can disturbances be handled? • Given some bound on disturbances, is it possible to guarantee successful execution of a plan? • Dispatchers for discrete systems • Guarantee successful execution • Even with temporal uncertainty • If uncertainty is bounded, [Morris, 2001]

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