Controllability of Second Order Leader-Follower Systems

In this paper we study formation control of a network of communicating mobile agents with double integrator dynamics. All agents run a consensus algorithm, several leader agents are further subject to an external input. We put this problem in a control theoretical framework and show that the controllability of the entire system via external control input depends only on the controllability of the follower system through the leaders. We then show necessary and sufficient conditions for the follower system to be controllable and relate the obtained conditions to the existing results on topological properties of the follower communication graph.