Consensus based formation control laws for systems on Lie groups

This paper designs the consensus based formation control laws for multi-agent systems defined on Lie groups. The specific results are illustrated on S E ( 2 ) and S E ( 3 ) (the special Euclidean groups of rigid body motions and each of which shares the geometric structure of a Lie group). The paper develops the control laws for the problem concerned under the assumption that the communication topologies of the multi-agent systems are spanning-tree-shaped, ring-shaped and complete, respectively. At last, several examples are included in the numerical simulations to verify the theoretical results.