Stabilization of Three Dimensional Collective Motion

Luca Scardovi, Naomi Leonard and Rodolphe Sepulchre

Communications in Information and Systems, Brockett Legacy issue, vol. 8, no. 4, pp. 473-500, 2008.  Also see arXiv:0806.3442v2 [math.OC] 
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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