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.