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Stabilization of Three-Dimensional Collective Motion (2008)
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BibTeX
@MISC{Scardovi08stabilizationof,
author = {Luca Scardovi and Naomi Leonard and Rodolphe Sepulchre},
title = {Stabilization of Three-Dimensional Collective Motion },
year = {2008}
}
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Abstract
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in threedimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the stabilization problem is reduced to a consensus problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical formations. We first derive the stabilizing control laws in the presence of all-to-all communication. Providing each agent with a consensus estimator, we then extend the results to a general setting that allows for unidirectional and time-varying communication topologies.
Keyphrases
three-dimensional collective motion consensus problem all-to-all communication threedimensional euclidean space dynamical system relative equilibrium time-varying communication topology equilibrium correspond lie group structure consensus estimator general setting control law stabilization problem helical formation lie algebra
