Capture Point: A Step toward Humanoid Push Recovery

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

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Capture Point A Step toward Humanoid Push
Recovery
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Some Push Recovery Approaches

• Replan trajectories.
• Solve Constrained Optimization Problem.
• Machine Learning.
• Heuristics based on intuition and simple models.

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Outline

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

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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.

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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.

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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

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Why these Strategies Work

• Broomstick (Inverted Pendulum) Analogy
• Tightrope Walker Analogy

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Using Angular Momentum effectively increases the
size of your footprint
Popovic, Goswami, Herr IJRR2005
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Outline

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

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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
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Balance Strategy 1 Center of Pressure
Kinematic Workspace Of Swing Leg
Support Foot

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

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

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

Capture Region
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How to Compute Capture Points?

• Simple Models with Closed-Form Solutions.
• Numerical Search
• Learning

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Computing the Capture Point for the Linear
Inverted Pendulum (Kajita and Tani 1991) Model
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Computing Capture Points for the Linear Inverted
Pendulum plus Flywheel Model
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Deriving Linear Inverted Pendulum Plus Flywheel
Dynamics using Similar Triangles
Mg
Fx
z0
X- /Mg
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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.

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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.

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State Trajectories
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Projection of Phase Portrait
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Dynamic Evolution of Capture Points

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

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Outline

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

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Push Recovery from Impulsive Push
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Stopping in one step by lunging
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Applying Linear Inverted Pendulum based Capture
Point to 12 dof 3D model
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Stepping Stones by guiding the Capture Point to
the Desired Stepping Point
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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.

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Take Home Message 2

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

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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.

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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