Formation control of mobile agents based on inter-agent distance dynamics

We propose a novel formation control strategy based on inter-agent distances for single-integrator modeled agents in the plane. Attempting to directly control the inter-agent distances, we derive a control law from the distance dynamics. The proposed control law achieves the local asymptotic stability of infinitesimally rigid formations. Triangular infinitesimally rigid formations are globally asymptotically stable under the proposed control law, with all squared distance errors exponentially and monotonically converging to zero. As an extension of existing results, the stability analysis in this paper reveals that any control laws related with the gradient law by multiplication of a positive matrix ensure the local asymptotic stability of infinitesimally rigid formations.