Consensus control for dynamic systems on lie groups

This paper addresses the consensus problem of multi-agent systems with a complete communication topology consisting of second order dynamics defined on Lie groups. The specific results are illustrated on SE(3) and SE(2) (the special Euclidean groups of rigid body motions and each of which shares the geometric structure of a Lie group). The control algorithm proposed in the paper drive the multi-agent systems toward consensus of position as well as attitude simultaneously with specific motion patterns. Several numerical simulations are included to verify the theoretical results.