Information Flow and Cooperative Control of Vehicle Formations

We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. We apply tools from graph theory to relate the topology of the communication network to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the graph on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that states that formation stability is achieved if the information flow is stable for the given graph and if the local controller stabilizes the vehicle. The information flow can be rendered highly robust to changes in the graph, thus enabling tight formation control despite limitations in intervehicle communication capability.