1. Capture Point: A Step toward Humanoid Push Recovery
Jerry Pratt1, John Carff1, Sergey Drakunov1, Ambarish Goswami2
1Florida Institute for Human and Machine Cognition
2 Honda Research Institute
Humanoids 2006
December 6, 2006

2. Capture Point: A Step toward Humanoid Push Recovery

3. Some Push Recovery Approaches
Replan trajectories.
Solve Constrained Optimization Problem.
Machine Learning.
Heuristics based on intuition and simple models.

4. Outline Push Recovery Overview Our Approach to Push Recovery.
Simulation Examples.
Ongoing and Future Work.

5. Importance of Push Recovery
Bipedal robots in human environments:
Bumping into objects.
Incidental contact when walking down a sidewalk.
Tripping over cluttered floors.
Contact during sports.
Intentional pushes.
Method of human input interface.
Understanding and Assisting Humans
Falls are a major cause of injury.

6. Theoretical and Practical Difficulties of Push Recovery
Non-linear dynamics
Multi-variable dynamics
Limited foot-ground interaction
Hybrid dynamics (dynamics are both continuous and change discretely during steps)
Quick detection of push required.
Fast reaction speed required.
Relatively large actuator power required.

7. Human Push Recovery Strategies
Move the Center of Pressure, predominately through ankle torques.
Accelerate Angular momentum by “lunging” and “windmilling”. [Video]
Take a step. [Video]
Combinations. [Video1, Video2]

8. Why these Strategies Work
Broomstick (Inverted Pendulum) Analogy
Tightrope Walker Analogy

9. Using Angular Momentum effectively increases the size of your footprint
[Popovic, Goswami, Herr IJRR2005]

10. Outline Push Recovery Overview Our Approach to Push Recovery.
Simulation Examples.
Ongoing and Future Work.

11. Capture Points and Capture Regions (Quick Definition)
Capture Point: Point that the biped can step to and stop in one step without falling down.
Capture Region: Set of all Capture Points. F

12. Balance Strategy 1: Center of Pressure
Kinematic Workspace
Of Swing Leg
Support
Foot
Capture Region

13. Balance Strategy 2: Accelerate Angular Inertia (“Windmill” or “Lunge”)
Kinematic Workspace
Of Swing Leg
Support
Foot
Capture Region

14. Balance Strategy 3: Take a Step
Kinematic Workspace
Of Swing Leg
Support
Foot
Capture Region

15. Balance Strategies 4,5,6: Multiple Steps, Run, or Fall
Kinematic Workspace
Of Swing Leg
Support
Foot
Capture Region

16. How to Compute Capture Points?
Simple Models with Closed-Form Solutions.
Numerical Search
Learning

17. Computing the Capture Point for the Linear Inverted Pendulum (Kajita and Tani 1991) Model

18. Computing Capture Points for the Linear Inverted Pendulum plus Flywheel Model

19. Deriving Linear Inverted Pendulum Plus Flywheel Dynamics using Similar TrianglesMg Fx z0
X- /Mg

20. Flywheel is torque-limited due to motors.
Computing Capture Points for the Linear Inverted Pendulum plus Flywheel Model
Flywheel is torque-limited due to motors.
Flywheel is position limited to model humanoid upper body.
Greatest effect the flywheel can have is through a bang-bang torque profile so that the flywheel accelerates and decelerates as quickly as possible, stopping at its maximum or minimum angle limit.

21. Computing Capture Points for the Linear Inverted Pendulum plus Flywheel Model
Bang-bang torque profile
Solve for TR1 and TR2 given initial and final states of the flywheel.
Since dynamics are linear and torque profile has Laplace Transform, everything can be computed in closed form.

22. State Trajectories

23. Projection of Phase Portrait

24. Dynamic Evolution of Capture Points
Using Linear Inverted Pendulum Model, dynamic evolution can be computed in closed form.

25. Outline Push Recovery Overview Our Approach to Push Recovery.
Simulation Examples.
Ongoing and Future Work.

26. Push Recovery from Impulsive Push

27. Stopping in one step by lunging

28. Applying Linear Inverted Pendulum based Capture Point to 12 dof 3D model

29. Stepping Stones by “guiding” the Capture Point to the Desired Stepping Point

30. Take Home Message 1
Precise foot placement is not necessary for push recovery, but good foot placement is.
If any point of the foot is placed inside the Capture Region, the humanoid can stop.
Larger feet and/or more angular momentum increase robustness to poor foot placement.

31. Take Home Message 2 Simple Models can be Useful!
Understanding of the fundamental principles.
Control Algorithm Development.

32. Future Work Apply to a real humanoid.
Derive closed form calculations of Capture Points for arbitrary CoM height trajectory.
Numerically compute Capture Regions for complex models and compare to simple models.
Extend to persistent pushes.
Expand techniques to other aspects of walking:
Dynamic Turning.
Rough Terrain.

33. Capture Point: A Step toward Humanoid Push Recovery
Jerry Pratt1, John Carff1, Sergey Drakunov1, Ambarish Goswami2
1Florida Institute for Human and Machine Cognition
2 Honda Research Institute
Humanoids 2006
December 6, 2006