Cooperative control of nonlinear multi-agent systems with only relative position measurements

In this paper, we study the distributed cooperative control of second-order multi-agent systems with intrinsic nonlinear dynamics under an undirected graph that characterizes the interaction among the followers or agents. By introducing a distributed filter for each follower or agent, the proposed control algorithms use only relative position measurements. Both the coordination tracking problem with a dynamic leader and the leaderless consensus problem are considered. In the special case when the intrinsic nonlinear dynamics are zero, i.e., for multi-agent systems with second-order integrators, we further derive results for the leaderless consensus problem under a directed graph. We present a necessary and sufficient condition such that the systems achieve consensus using only relative position measurements.