Communications in Information and Systems

Volume 8 (2008)

Number 4

Stabilization of Three-Dimensional Collective Motion

Pages: 473 – 500



Naomi Leonard

Luca Scardovi

Rodolphe Sepulchre


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.


Motion coordination; nonlinear systems; multi-agent systems; consensus; multi-vehicle formations

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