Regular Polygon Formations With Fixed Size and Cyclic Sensing Constraint

We propose a distributed control strategy for a team of agents to autonomously achieve a regular polygon formation with a desired size. Our strategy does not require global position measurements, common sense of orientation, or communication capability among agents. We assume that the graph that describes the sensing among agents is cyclic, which is the minimum required sensing to achieve the desired formation. We analyze the stability properties of the proposed control for an arbitrary number of agents, and prove that the desired polygon formation is a locally asymptotically stable equilibrium. We further demonstrate that while a finite number of undesired equilibria exist, they are unstable. This gives an advantage over the distance-based methods in which often undesired equilibria are stable. Experiments performed using the Robotarium platform demonstrate the effectiveness of the proposed control strategy.