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Effect of circular arc feet on a control law for a biped

Published online by Cambridge University Press:  01 July 2009

T. Kinugasa ,
C. Chevallereau  and
Y. Aoustin
T. Kinugasa*
Affiliation:
Okayama University of Science, 1-1, Ridai-cho, Okayama, 700-0005, Japan
C. Chevallereau
Affiliation:
IRCCyN, Ecole Centrale de Nantes, CNRS, Université de Nantes BP 92101, 1, rue de la Noë, 44321 Nantes cedex 3, France
Y. Aoustin
Affiliation:
IRCCyN, Ecole Centrale de Nantes, CNRS, Université de Nantes BP 92101, 1, rue de la Noë, 44321 Nantes cedex 3, France
*
*Corresponding author. E-mail: kinugasa@mech.ous.ac.jp
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Summary

The purpose of our research is to study the effects of circular arc feet on the biped walk with a geometric tracking control. The biped studied is planar and is composed of five links and four actuators located at each hip and each knee thus the biped is underactuated in single support phase. A geometric evolution of the biped configuration is controlled, instead of a temporal evolution. The input-output linearization with a PD control law and a feed forward compensation is used for geometric tracking. The controller virtually constrains 4 degrees of freedom (DoF) of the biped, and 1 DoF (the absolute orientation of the biped) remained. The temporal evolution of the remained system with impact events is analyzed using Poincaré map. The map is given by an analytic expression based on the angular momentum about the contact point. The effect of the radii of the circular arc feet on the stability is studied. As a result, the speed of convergence decreases when the radii increases, if the radius is larger than the leg length the cyclic motion is not more stable. Among the stable cyclic motion, larger radius broadens the basin of attraction. Our results agree with those obtained for passive dynamic walking on stability, even if the biped is controlled through the geometric tracking.

Keywords

under-actuated bipedcircular arc feetnonlinear controlstability analysis
Type
Article
Information
Robotica , Volume 27 , Issue 4 , July 2009 , pp. 621 - 632
Copyright
Copyright © Cambridge University Press 2008

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