Multi-agent coordination under connectivity constraints

We study the problem of motion coordination of multiple agents, under a graph connectivity constraint. We develop a framework for the problem based on partial ordering of graphs and embedding of constraint sets and identify a certain convexity property of the constraint set induced by the graph connectivity constraint. This property is used to solve two instances of the coordination problem. In the first instance, the agents are required to converge from an arbitrary position to a formation characterized by its adjacency matrix. In the second instance, we study the specific problem of moving from one formation to another formation so that the formation graph remains connected at all times. We show that both these problems can be reduced to static convex optimization problems. Existence and uniqueness of solutions are also investigated.