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Running With Symmetry

Department of Computer Science and The Robotics Institute Carnegie-Mellon University Pittsburgh, Pennsylvania 15213

Symmetry can simplify the control of dynamic legged sys tems. In this paper, the symmetries studied describe motion of the body and legs in terms of even and odd functions of time. A single set of equations describes symmetric running for systems with any number of legs and for a wide range of gaits. Techniques based on symmetry have been used in laboratory experiments to control machines that run on one, two, and four legs. In addition to simplifying the control of legged machines, symmetry may help us to understand legged locomotion in animals. Data from a cat trotting and galloping on a treadmill and from a human running on a track conform reasonably well to the predicted symmetries.

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