Controllability of formations over directed graphs

In this paper, we investigate the controllability of a class of formation control systems. Given a directed graph, we assign an agent to each of its vertices and let the edges of the graph describe the information flow in the system. We relate the strongly connected components of this graph to the reachable set of the formation control system. Moreover, we show that the formation control model is approximately path-controllable over a path-connected, open dense subset as long as the graph is weakly connected and satisfies some mild assumption on the numbers of vertices of the strongly connected components.