Symmetry and Reduction for Coordinated Rigid Bodies
Heinz Hanssmann, Naomi Ehrich Leonard and Troy R. Smith
European Journal of Control, Volume 12, No. 2, 2006, p 176-194.
Motivated by interest in the collective behavior of autonomous agents, we
lay foundations for a study of
networks of rigid bodies and, specifically, the problem of aligning orientation and
controlling relative position across the group.
Our main result is the reduction of the
system in the case that
are coupled by control inputs that depend only on relative configuration.
We use reduction theory based on
semi-direct products, yielding Poisson spaces that enable
efficient formulation of control laws. We apply these reduction results
to satellite and underwater vehicle dynamics, proving stability of coordinated behaviors
such as the case of two underwater vehicles moving at constant speed with their
orientations stably aligned.
(1.8 MB pdf)
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