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Tracking a joint path for the walk of an underactuated biped

Published online by Cambridge University Press:  05 January 2004

Christine Chevallereau ,
Alexander Formal'sky  and
Dalila Djoudi
Christine Chevallereau
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes, BP 92101, 1 rue de la Noë, 44321 Nantes Cedex 03 (France). E-mail: [email protected]. Website: http://www.irccyn.ec-nantes.fr
Alexander Formal'sky
Affiliation:
Institute of Mechanics, Moscow State Lomonosov University, 1, Michurinsky Prospect, Moscow 119899 (Russia). E-mail: [email protected]
Dalila Djoudi
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes, BP 92101, 1 rue de la Noë, 44321 Nantes Cedex 03 (France).
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Abstract

This paper presents a control law for the tracking of a cyclic reference path by an under-actuated biped robot. The robot studied is a five-link planar biped. The degree of under-actuation is one during the single support phase. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. To achieve this objective, we consider a parametrized control. When a joint path is given, a five degree of freedom biped in single support becomes similar to a one degree of freedom inverted pendulum. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple analytical conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced. These conditions are defined on the reference trajectory path. The analytical considerations are illustrated with some simulation results.

Keywords

Biped robotWalkingUnder-actuated systemReference joint pathControlLimit cycleStability
Type
Research Article
Information
Robotica , Volume 22 , Issue 1 , January 2004 , pp. 15 - 28
Copyright
© 2004 Cambridge University Press

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