STABILIZATION OF THREE-DIMENSIONAL COLLECTIVE MOTION

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.