Capture Point: A Step toward Humanoid Push Recovery Jerry Pratt 1, John Carff 1, Sergey Drakunov 1,...
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Transcript of Capture Point: A Step toward Humanoid Push Recovery Jerry Pratt 1, John Carff 1, Sergey Drakunov 1,...
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