of the Simplest Walking Model 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 DETC’01 ASME 2001, Sep 9-12, Pittsburgh PA, 2001

Walking Robots Anthropomorphic Design Energy Efficient Passive Dynamic Walking ( T. McGeer 1990 )

Passive Dynamic Walking G.T.Fallis Patent (1888)

Problem Mostly Falls Down Hard to Start (initial conditions) Sensitive to Small Disturbances Why?

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

Walking Motion Walking Motion in Phase Plane Cyclic Motion if Swing phase Stance phase Cyclic Motion if

Cyclic Motions How Stable ? Stable Cyclic Motions Stability of Cyclic Motion Determined by Characteristic Multipliers |l|<1 How Stable ?

Basin of Attraction Failure Modes Fixed Point (Cyclic Motion): Poincare Section Fixed Point (Cyclic Motion):

Basin of Attraction (continued) Basin of Attraction, askew & enlarged

Towards Cyclic Motion A Number of Steps in the Basin of Attraction x = Fixed Point 1 = Start

Effect of Slope Basin of Attraction > Slope Angle g

How Stable? Basin of Attraction < > Stability Cyclic Motion l Characteristic Multiplier

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 ?