A' L' Schwab1 and M' Wisse2

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Basin of Attraction of the Simplest Walking Model
A. L. Schwab1 and M. Wisse2 1Laboratory for
Engineering Mechanics 2Delft Biped
Laboratory Delft University of Technology The
Netherlands
DETC01 ASME 2001, Sep 9-12, Pittsburgh PA, 2001
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Walking Robots

• Anthropomorphic Design
• Energy Efficient

Passive Dynamic Walking ( T. McGeer 1990 )
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Passive Dynamic Walking
G.T.Fallis Patent (1888)
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Problem
Mostly Falls Down Hard to Start (initial
conditions) Sensitive to Small Disturbances
Why?
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Simplest Walking Model
Garcia, Chatterjee, Ruina and Coleman (1998)
Scaling with M, l and g
Limit case m/M 0
Leaves one free parameter g
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Walking Motion
Walking Motion in Phase Plane
g 0.004
Swing phase
Stance phase
Cyclic Motion if
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Cyclic Motions
Stable Cyclic Motions
Stability of Cyclic Motion Determined by
Characteristic Multipliers llt1
How Stable ?
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Basin of Attraction
Failure Modes
Poincare Section
Fixed Point (Cyclic Motion)
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Basin of Attraction
(continued)
Basin of Attraction, askew enlarged
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Towards Cyclic Motion
A Number of Steps in the Basin of Attraction
x Fixed Point
1 Start
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Effect of Slope
Basin of Attraction gt Slope Angle g
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How Stable?
Basin of Attraction lt gt Stability Cyclic Motion
l Characteristic Multiplier
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Conclusion
Simplest Walking Model

• Very small Basin of Attraction
• No Relation between Basin of Attraction and
  Cyclic Motion Stability l

Increase the Basin of Attraction ?