A barycentric coordinate based approach to formation control of multi-agent systems under directed and switching topologies

This paper studies the formation control problem for a leader-follower network in 3D. The objective is to control the agents to form a globally rigid formation, for which the sensing graph is directed and switching while the communication graph is undirected and switching. Under such a setup, a barycentric coordinate based approach is proposed for the design of formation control laws ensuring global convergence. A necessary and sufficient graphical condition is obtained to guarantee that the followers converge to form a globally rigid formation together with the leaders. By this approach, the formation of the whole group, namely, the orientation, translation and formation scale, can be reconfigured by the leaders.