Control of a three-coleader formation in the plane

This paper considers a formation of three point agents moving in the plane, where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbour; further, each agent is allowed to determine its movement strategy using local knowledge only of the direction of its neighbour, and the current and desired distance from its neighbour. The motion of the formation is studied when distances are initially incorrect. A convergence result is established, to the effect that provided agents never become collinear, the correct distances will be approached exponentially fast, and the formation as a whole will rotate by a finite angle and translate by a finite distance.