Formation control of three-coleader agents in the plane via backstepping design

This paper deals with a directed formation control problem of three agents moving in the plane, where the agents have a cyclic ordering with each one required to maintain a nominated distance from its neighbor. The agent dynamics under consideration is a double integrator. Firstly, a directed formation control law based on the knowledge only of the direction of its neighbor, is designed by using the integrator backstepping technique, which can not only accomplish the desired triangle formation, but also ensure all agent speeds converge to a common velocity without collision between all agents during the motion. Secondly, with the purpose of relaxing and even overcoming the restriction of initial conditions of the agents owing to collision avoidance, we introduce the inter-agent potential functions into the design. Finally, convergence guarantees are provided by using tools from LaSalle´s invariance principle. Simulation results are provided to illustrate the effectiveness of the proposed control laws.