Stabilization of collective motion in three dimensions: A consensus approach

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 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.