Download - A. L. Schwab 1 and M. Wisse 2 1 Laboratory for Engineering Mechanics 2 Delft Biped Laboratory
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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 ?