Motion Planning: Generate Dynamic Motions for Legged Robots

1. Motion Planning: Generate Dynamic Motions for Legged Robots Mathieu Geisert MEMMO WS

2. Generate Dynamic Motions for Legged Robots

3. Generate Dynamic Motions for Legged Robots TOWR repository: https://github.com/ethz-adrl/towr VM: https://cloud.laas.fr/index.php/s/r8hu0GnFDxCfeX3

4. Dynamic Model Rigid Body Dynamics Representation Governing Equations Assumptions or • Rigid body, i.e. no deformation when forces are applied

5. Dynamic Model Centroidal Dynamics Representation Governing Equations Assumptions Torque motor feasible or

6. Dynamic Model Centroidal Dynamics Representation Governing Equations Assumptions Torque motor feasible or Underaction => plan trajectories Optimal Control

7. Dynamic Model Centroidal Dynamics Representation

8. Dynamic Models Contact constraints Representation Legged Robots Forces only when contact+ Friction cone Reachable contact positions

9. Contacts Discovering contact with optimal control? Local approximation Constant 0 force

10. Contacts Guiding optimization to contacts Local approximation Increase when closer

11. Contacts Predefining contacts Stance/swing phase for each leg. Contact Switching DS SS - right foot DS SS - left foot

12. Contacts Predefining contacts Stance/swing phase for each leg. Contact Switching DS SS - right foot DS SS - left foot Carpentier’s 3d Pattern Generator TOWR A. W. Winkler, C. D. Bellicoso, M. Hutter, and J. Buchli, ‘Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization’, IEEE Robotics and Automation Letters, vol. 3, no. 3, pp. 1560–1567, Jul. 2018. Justin Carpentier, Nicolas Mansard, “Multi-contact Locomotion of Legged Robots”, IEEE Transactions on Robotics 2018.

13. TOWR

14. Dynamic Models Single Rigid Body Dynamics Representation Governing Equations Assumptions • Negligible momentum due to joints, i.e. the effect of joints’ velocities is insignificant • Negligible change in full-body inertia, i.e. the effect of joints’ positions is insignificant Single Rigid Body Dynamics: End-effector position/forces:-Zero forces at swing phases.-Height at stance phase = height map.

15. Collocation, Parametrisation and Constraints Cubic (Hermite) Polynomial Parametrisation Collocation and Constraints

16. Range of Motion [1] A. W. Winkler, C. D. Bellicoso, M. Hutter, and J. Buchli, ‘Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization’, IEEE Robotics and Automation Letters, vol. 3, no. 3, pp. 1560–1567, Jul. 2018. [2] M. Hutter et al., ‘ANYmal - a highly mobile and dynamic quadrupedal robot’, in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2016, pp. 38–44.

17. Contact Model [1] S. Caron, ‘Computational Foundation for Planner-in-the-Loop Multi-Contact Whole-Body Control of Humanoid Robots’, The University of Tokyo, 2017. [2] A. W. Winkler, C. D. Bellicoso, M. Hutter, and J. Buchli, ‘Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization’, IEEE Robotics and Automation Letters, vol. 3, no. 3, pp. 1560–1567, Jul. 2018.

18. Gait Optimisation

19. Solving a Mathematical Feasibility Problem

20. TOWR - demonstration

21. TOWR - test Changing friction coefficient: towr/include/towr/terrain/height_map.h Changing maximum force: towr/src/parameters.cc

22. Contact Model Negligible Friction Actuator Force Limited

23. TOWR - test

24. Range of Motion Chaotic movement of end-effectors Cuboidal ranges not respected

25. Range of Motion Carpentier’s PG: -Compute the Range of Motion as a density of probability using random sampling. -Approximate the density using Gaussian Mixture Models. -Add a cost corresponding to -log(p) => The integration of this cost will allow a continuous checking of the constraint.

26. TOWR - test Changing the environment:towr/include/terrain/example/height_map_example.hhtowr/src/height_map_example.cc

27. Contact position Local approximation of the height map.

28. Contact position Local approximation of the height map: timestep 1

29. Contact position Local approximation of the height map: timestep 2

30. Contact position Local approximation of the height map: timestep 3

31. Contact position Local approximation of the height map: timestep 3 => Precomputed the contact surfaces using HPP contact planner..

32. Contact position: MEMMO pipeline Andrea Del Prete: TSIDNicolas Mansard/Carlos Mastalli Steve Tonneau : HPP rbprm

33. Reactive Replanning via Model Predictive Control (MPC) If motion planning is achieved through a high-raterecursive optimisation of the robot dynamics, the method is termed Model Predictive Control (MPC).

34. Reactive Replanning via Model Predictive Control (MPC) Reducing computation time:- Convex approximation of the angular momentum Ponton, B., Herzog, A., Schaal, S., Righetti, L. A, “Convex Model of Momentum Dynamics for Multi-Contact Motion Generation”, IEEE-RAS Humanoids 2016. - Quadratic approximation of the frictional wrench coneJustin Carpentier, Nicolas Mansard, “Multi-contact Locomotion of Legged Robots”, IEEE Transactions on Robotics 2018. - Better initial guess

35. Reactive Replanning via Model Predictive Control (MPC) Reducing computation time:- Convex approximation of the angular momentum Ponton, B., Herzog, A., Schaal, S., Righetti, L. A, “Convex Model of Momentum Dynamics for Multi-Contact Motion Generation”, IEEE-RAS Humanoids 2016. - Quadratic approximation of the frictional wrench coneJustin Carpentier, Nicolas Mansard, “Multi-contact Locomotion of Legged Robots”, IEEE Transactions on Robotics 2018. - Better initial guess Nicolas Mansard, Andrea Del Prete, Mathieu Geisert, Steve Tonneau, Olivier Stasse. “Using a Memory of Motion to Efficiently Warm-Start a Nonlinear Predictive Controller”, IEEE ICRA 2018. MEMMO