The Human Center Robotics Laboratory (HCRL) The University of Texas at Austin

1. Motion Planning of Extreme Locomotion Maneuvers Using Multi-Contact Dynamics and Numerical Integration Luis Sentis and Mike Slovich The Human Center Robotics Laboratory (HCRL) The University of Texas at Austin Humanoids 2011,Bled, Slovenia October 28th, 2011

2. What Are Extreme Maneuvers (EM)?(Generalization of recreational free-running) Tackles discrete surfaces and near-vertical terrains Needed for humanoids, assistive devices and biomechanical studies

3. Objectives of the research Develop new dynamical models and numerical techniques to predict, plan and analyze EM Develop whole-body adaptive torque controllers to execute the motion plans and the desired multi-contact behaviors Build a nimble bipedal robot to verify the methods

4. State of the art Rough terrain still dominated by methods that do not taking into account friction characteristics No generalization of gait to discrete terrains with near-vertical surfaces Multicontact dynamics are largely overlooked Linearization is too commonly used instead of tackling the full nonlinear problems

5. Our approach to EM Model multicontact and single-contact dynamics Develop geometric path dependencies Use path dependencies to reduce dimensionality of the dynamic problems Derive set of rules for feasiblegeometric paths Given step conditions, use numerical integration to predict the nonlinear behavior in forward and backward times Choose as the contact planning strategy the intersections in state space of maneuvering curves Conduct comparative analysis with a human

6. Let’s start with multicontact dynamics fr Hands and feet are in contact acom acom fr(LF) fr(RF) ft mn ft In IROS’09, TRO’10 we presented the Virtual Linkage Model and the Multi-Contact / Grasp Matrix for humanoids Only feet are in contact

7. Model for single-contact dynamics(established area of research) Non-linear pendulum dynamics (balance of inertial-gravitational-reaction moments) actuated linear motor cop = center of pressure (contact point) - The form of the model is: passive hinge Solving multivariate NL systems is difficult

8. Resort to modeling arbitrary geometric paths Geometric dependencies are model as:

9. Dimensional Reduction of Models Using the previous dependencies the actuated non-linear pendulum becomes The model becomes now an ODE:

10. Given the piecewise linear model analyze feasible geometric paths FALL!! is angle of attack

11. Example: design of geometric path GOOD! UNFEASIBLE

12. If we consider non-linear geometric paths, dynamics are non-linear

13. Then, prediction by Numerical Integration Establishing geometric dependencies: Consider discrete solutions (Taylor expansion): Time perturbation is: State space solution: Reduction of single contact dynamics (Non linear behavior):

14. Examples:(Forward/Backward Propagation)

15. Solving the multicontact behavior FRICTION CONE

16. Planning of contact transitions BWD Apex Search-based to reach apex with zero velocity FWD FWD Apex

17. Entire leaping planning strategy

18. Results and Comparison with Human PLANNER HUMAN HUMAN PLANNER

19. Movie

20. Details design of Hume

21. Design setpoint CoM Path Rough Terrain 0.4 m

22. Questions

23. Supporting slides

24. How is that possible? In the absence of forces -> parabola

25. Angle of attack negative

26. Angle of attack positive Details on forces

27. Side and Front of Hume

28. Mechatronics

29. Unused slides

30. Let’s start with multicontact dynamics fr Hands and feet are in contact acom acom fr(LF) fr(RF) ft mn ft In IROS’09, TRO’10 we presented the Virtual Linkage Model and the Multi-Contact / Grasp Matrix for humanoids Only feet are in contact