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A. L. Schwab1 and M. Wisse2

1Laboratory for Engineering Mechanics2Delft Biped Laboratory

Delft University of TechnologyThe Netherlands

Basin of Attractionof the Simplest Walking Model

DETC’01 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

Leaves one free parameter:

Limit case: m/M 0

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Walking Motion

Walking Motion in Phase Plane

Cyclic Motion ifnn

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Stance phase

Swing phase

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Cyclic Motions

Stable Cyclic Motions

How Stable ?

Stability of Cyclic Motion Determined by Characteristic Multipliers |

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Basin of Attraction

Failure Modes

Poincare Section

Fixed Point (Cyclic Motion): )1561.0,1534.0(),(

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Basin of Attraction

Basin of Attraction, askew & enlarged

(continued)

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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 > Slope Angle

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How Stable?

Basin of Attraction < > Stability Cyclic Motion

Characteristic Multiplier

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Conclusion

• Very small Basin of Attraction

• No Relation between Basin of Attraction and Cyclic Motion Stability

Simplest Walking Model

Increase the Basin of Attraction ?