Design and Realization of Distributed Adaptive Formation Control Law for Multi-Agent Systems With Moving Leader

Abstract

In this paper, distributed formation control laws for the multi-agent systems are proposed when the leader is moving constantly with unknown velocity. The proposed control laws are based on the distance-based formation control; therefore, each distance between agents is controlled measuring the relative position. Because the control laws use only local information such as relative position with respect to their own local reference frame, the control laws are completely decentralized. The proposed control laws are designed to make a group of agents keep the desired formation and move with a constant reference velocity in two-dimensional space. The considered system consists of three types of agents: 1) leader; 2) first follower; and 3) follower. The leader knows the reference velocity value, whereas the other agents do not know the reference velocity. For this reason, the first follower and follower estimate the reference velocity by using the adaptive method. Using graph theory and nonlinear control theory, the control laws are verified mathematically. Additionally, the three-agent case is extended to $N$ -agent case by an inductive way. The stability and convergence of the system are theoretically analyzed, and the validity of the proposed control laws is clarified by performing simulations and real experiments.