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arXiv · 0806.3442

Stabilization of Three-Dimensional Collective Motion

Luca Scardovi·Naomi Leonard·Rodolphe Sepulchre
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Abstract

This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional 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.

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Luca Scardovi, Naomi Leonard, Rodolphe Sepulchre. 2008-06-21. Stabilization of Three-Dimensional Collective Motion. https://arxiv.org/abs/0806.3442

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