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Classification of periodic and chaotic passive limit cycles for a compass-gait biped with gait asymmetries

Published online by Cambridge University Press:  23 March 2011

Jae-Sung Moon  and
Mark W. Spong
Jae-Sung Moon
Affiliation:
Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
Mark W. Spong*
Affiliation:
Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX 75080, USA
*
*Corresponding author. E-mail: [email protected]
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Abstract

In this paper we study the problem of passive walking for a compass-gait biped with gait asymmetries. In particular, we identify and classify bifurcations leading to chaos caused by the gait asymmetries because of unequal leg masses. We present bifurcation diagrams showing step period versus the ratio of leg masses at various walking slopes. The cell mapping method is used to find stable limit cycles as the parameters are varied. It is found that a variety of bifurcation diagrams can be grouped into six stages that consist of three expanding and three contracting stages. The analysis of each stage shows that marginally stable limit cycles exhibit period-doubling, period-remerging, and saddle-node bifurcations. We also show qualitative changes regarding chaos, i.e., generation and extinction of chaos follow cyclic patterns in passive dynamic walking.

Keywords

Passive dynamic walkingBifurcations and chaosGait asymmetriesSix stages of bifurcationsComposite hybrid systems
Type
Articles
Information
Robotica , Volume 29 , Issue 7 , December 2011 , pp. 967 - 974
Copyright
Copyright © Cambridge University Press 2011

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