A backstepping design for directed formation control of three‐coleader agents in the plane

Abstract

Abstract 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, and each agent is described by a double integrator. Firstly, a directed formation control law based on the knowledge only of the neighbor's direction is designed by using the integrator backstepping technique, which can not only accomplish the desired triangle formation but also ensure that speeds of all agents converge to a common value without collision between each other during the motion. Then, 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. The convergence of the proposed control algorithms is proved by using tools from LaSalle's invariance principle. Simulation results are provided to illustrate the effectiveness of the control laws. Copyright © 2008 John Wiley & Sons, Ltd.