Decentralized leader-following formation control of nonholonomic mobile robots by local measurement: A small-gain approach

This paper considers the leader-following formation control problem of multiple nonholonomic mobile robots by local measurement. The sensor network among the multi-robot system is described by a general directed graph, which contains a directed spanning tree with the root node denoting the leader. A dynamic control law consisting of an observer and a velocity controller, is designed based on the feedback of measurements on the relative positions and orientations. Particularly, the proposed control law can be implemented without using any communication provided that the reference velocities are prior set, which makes it feasible in a decentralized manner. The small-gain theorem is employed to deal with stability analysis on the augmented closed-loop system. A low-gain parameter in the observer ensures that the small-gain condition can be satisfied. The global asymptotic stability of the augmented multi-robot closed-loop system is guaranteed by the proposed small-gain approach. More interestingly, the proposed dynamic control law is robust to measurement errors in relative positions and orientations. Finally, the effectiveness is illustrated by the simulation results of examples.