A passive 2-DOF walker: hunting for gaits using virtual holonomic constraints

Authors:
Leonid B. Freidovich;Uwe Mettin;Anton S. Shiriaev;Mark W. Spong
Affiliations:
Department of Applied Physics and Electronics, Umeå University, Umeå, Sweden;Department of Applied Physics and Electronics, Umeå University, Umeå, Sweden;Department of Applied Physics and Electronics, Umeå University, Umeå, Sweden and Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway;Erik Jonsson School of Engineering and Computer Science, University of Texas, Dallas, TX
Venue:
IEEE Transactions on Robotics
Year:
2009

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Abstract

A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that has attractedmany researchers who are motivated by various aspects of passive and active dynamic walking. We propose a new approach to find stable as well as unstable hybrid limit cycles without integrating the full set of differential equations and, at the same time, without approximating the dynamics. The procedure exploits a time-independent representation of a possible periodic solution via a virtual holonomic constraint. The description of the limit cycle obtained in this way is useful for the analysis and characterization of passive gaits as well as for design of regulators to achieve gaits with the smallest required control efforts. Some insights into the notion of hybrid zero dynamics, which are related to such a description, are presented as well.