  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.
