Capture Point: A Step toward Humanoid Push Recovery

Jerry Pratt1, John Carff1, Sergey Drakunov1,

Ambarish Goswami2

1Florida Institute for Human and Machine Cognition2 Honda Research Institute

Humanoids 2006December 6, 2006

Capture Point: A Step toward Humanoid Push Recovery

Some Push Recovery Approaches

• Replan trajectories.

• Solve Constrained Optimization Problem.

• Machine Learning.

• Heuristics based on intuition and simple models.

Outline• Push Recovery Overview

• Our Approach to Push Recovery.

• Simulation Examples.

• Ongoing and Future Work.

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.

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.

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]

Why these Strategies Work

• Broomstick (Inverted Pendulum) Analogy

• Tightrope Walker Analogy

Using Angular Momentum effectively increases the size of

your footprint

[Popovic, Goswami, Herr IJRR2005]

Outline

• Push Recovery Overview

• Our Approach to Push Recovery.

• Simulation Examples.

• Ongoing and Future Work.

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

Balance Strategy 1: Center of Pressure

Kinematic Workspace Of Swing Leg

Support Foot

Capture Region

Balance Strategy 2:Accelerate Angular Inertia

(“Windmill” or “Lunge”)Kinematic Workspace Of Swing Leg

Support Foot

Capture Region

Balance Strategy 3:Take a Step

Kinematic Workspace Of Swing Leg

Support Foot

Capture Region

Balance Strategies 4,5,6:Multiple Steps, Run, or Fall

Kinematic Workspace Of Swing Leg

Support Foot

Capture Region

How to Compute Capture Points?

• Simple Models with Closed-Form Solutions.

• Numerical Search

• Learning

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

Computing Capture Points for the Linear Inverted Pendulum plus Flywheel Model

Deriving Linear Inverted Pendulum Plus Flywheel Dynamics using

Similar Triangles

Mg

z0

X- /Mg

Fx

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.

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.

State Trajectories

Projection of Phase Portrait

Dynamic Evolution of Capture Points

• Using Linear Inverted Pendulum Model, dynamic evolution can be computed in closed form.

Outline• Push Recovery Overview

• Our Approach to Push Recovery.

• Simulation Examples.

• Ongoing and Future Work.

Push Recovery from Impulsive Push

Stopping in one step by lunging

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

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

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.

Take Home Message 2

• Simple Models can be Useful!– Understanding of the fundamental principles.– Control Algorithm Development.

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.

Capture Point: A Step toward Humanoid Push Recovery

Jerry Pratt1, John Carff1, Sergey Drakunov1,

Ambarish Goswami2

1Florida Institute for Human and Machine Cognition2 Honda Research Institute

Humanoids 2006December 6, 2006