04-27 Heinz Hanßmann, Naomi Ehrich Leonard, Troy R. Smith
Symmetry and Reduction for Coordinated Rigid Body Networks (168K, PostScript, gzipped and uuencoded) Feb 6, 04
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Abstract. Motivated by interest in the collective behavior of autonomous agents, we study networks of rigid bodies and the problem of coordinated orientation and position across the group. Our main result is the reduction of the networked system in the case that individuals are coupled by control inputs that depend only on relative configuration. We use reduction theory based on semi-direct products; this yields flat Poisson spaces which enable efficient formulation of control laws. In the second part of the paper, we apply the reduction results to particular choices of kinetic energy and prove stability of coordinated behaviors.

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