Distributed control of cyclic formations with local relative position measurements

We propose a distributed control scheme for cyclic formations of multi-agent systems using relative position measurements in local coordinate frames. It is assumed that agents cannot communicate with each other and do not have access to global position information. For the case of three and four agents with desired formation defined as a regular polygon, we prove that under the proposed control, starting from almost any initial condition, agents converge to the desired configuration. Moreover, it is shown that the control is robust to the failure of any single agent. From Monte Carlo analysis, a conjecture is proposed to extend the results to any number of agents.