Global asymptotic stabilization of a triangle formation

This paper considers formation shape control of three agents moving in the plane, where the formation shape is controlled by actively controlling a certain set of inter-agent distances using relative position measurements. It is shown that the proposed novel bidirectional control law can not only guarantee that the desired formation shape is globally asymptotically stable, but also ensure that the collision between each agent is avoided. Simulation results are provided to illustrate the effectiveness of the control algorithm.