Multi-agent formation maintenance and target tracking

In this paper, we introduce distance-based control laws for the multi-agent formation maintenance and target tracking problems. Using a single-integrator agent model, the proposed controls consist of a formation acquisition term, dependent on the potential function and graph rigidity matrix, and a formation maintenance or target tracking term. The control laws are only a function of the relative position of agents in an infinitesimally and minimally rigid graph, and either the desired velocity of the formation or the target´s relative position to the leader and absolute velocity. A Lyapunov analysis shows that the origin of the distance error dynamics is locally exponentially stable, and, as a consequence, formation maintenance or target tracking can be readily proven.