Heinz Hanßmann, Naomi Ehrich Leonard, Troy R. Smith
Symmetry and Reduction for Coordinated Rigid Body Networks
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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.