Stabilization of Collective Motion in Three Dimensions: A Consensus Approach

Luca Scardovi, Naomi Ehrich Leonard and Rodolphe Sepulchre

Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, December 2007.
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. We first derive the stabilizing control laws in the presence of allto- 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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