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)
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 feasible geometric 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 dynamicsfr
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)
Sagittal accels proportional to Vertical accels. Therefore, in sinusoidal, we accelerate more than decelerate

15. Solving the multicontact behavior
FRICTION
CONE
Search over acom and ft for feasible reaction forces

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 dynamicsfr
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