Stabilization of Three-Dimensional Collective Motion
Naomi Ehrich Leonard, Luca Scardovi, Rodolphe J. Sepulchre · Communications in Information and Systems · 2008
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.