Formation control for a cooperative multi-agent system using decentralized navigation functions

We propose a decentralized cooperative controller for a group of mobile agents. The control design is based on the navigation function formalism. The aim of the group control law is to generate a pattern or formation in a given workspace while avoiding obstacles and collisions. The desired goal is specified in terms of distances among the agents. We show that it is always possible to design a control law as the gradient of a suitably-defined navigation function whose minimum corresponds to the desired configuration. Furthermore in certain cases, such as when the topology of the interconnection is an acyclic graph, this minimum is unique. Some simulations are shown to test the strategy