Globally asymptotically stable formation control of three agents

This paper considers the formation-shape control of three agents moving in the plane. By adding an adaptive vector perturbation to any agent's movement direction, a novel control strategy is proposed. It is shown that the proposed novel bidirectional control law can not only guarantee the global asymptotical stability of the desired formation shape, but also ensure the collision avoidance of agents between each other. Simulation results are provided to illustrate the effectiveness of the control algorithm.