Distributed Estimation and Control for Leader-Following Formations of Nonholonomic Mobile Robots

Abstract

The problem of the leader-following formation control of nonholonomic mobile robots is addressed in this paper. A distributed formation control strategy using explicitly the coordination errors among robots is proposed without assuming that each follower robot knows the full state of the leader. First, a distributed estimation law is proposed for each follower robot to estimate the states, including the position, orientation, and linear velocity of the leader. The distributed formation control law is then designed based on the estimated states of the leader, and the neighborhood formation tracking error. Under some mild assumptions on the interaction graph among the leader and the follower robots, and the velocity of the leader, asymptotic convergence of formation tracking errors to zero can be achieved. Finally, some numerical simulations and experiments on a group of nonholonomic mobile robots are presented to demonstrate the effectiveness of the proposed strategy. Note to Practitioners —The motivation of this paper is to investigate a practical control strategy for the leader-following formation of multiple autonomous mobile robots subjected to nonholonomic constraints. In most of the existing leader-following formation control schemes for nonholonomic mobile robots, having access to the full state of the leader is a requirement. However, due to limitations in communication bandwidth and range, it is reasonable to assume that the information of the leader is available only to a subset of followers. Hence, this paper suggests a new distributed leader-following formation control strategy based on the distributed estimation of the leader’s states. Moreover, the coordination error between a pair of interacting robots is explicitly used in the control design to weaken the dependence on the estimated state of the leader, and enhance the decentralized nature of the proposed control scheme. The stability and convergence of the system are analyzed mathematically and the experiment using unicycles provides promising results. In ongoing research, we are addressing the issues of collision avoidance and communication delays to provide more realistic setup for the industrial applications of multivehicle systems.