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Stable Synchronization of Rigid Body Networks

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Sujit Nair and Naomi Ehrich Leonard,

* Networks and Heterogeneous Media, * American
Institute of Mathematical Sciences, Vol. 2, No. 4, December 2007, 595-624.
We address stable synchronization of a network of rotating and
translating rigid bodies in three-dimensional space. Motivated by
applications that require coordinated spinning spacecraft or diving
underwater vehicles, we prove control laws that stably couple and
coordinate the dynamics of multiple rigid bodies. We design
decentralized, energy shaping control laws for each individual rigid
body that depend on the relative orientation and relative position of
its neighbors. Energy methods are used to prove stability of the
coordinated multi-body dynamical system. To prove exponential
stability, we break symmetry and consider a controlled dissipation term
that requires each individual to measure its own velocity. The
control laws are illustrated in simulation for a network of spinning rigid bodies.

(452 KB pdf)
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