Global consensus-based formation control of perturbed nonholonomic mobile robots with time varying delays

Abstract

This paper proposes a smooth time-variant PID-like control scheme for networks composed of nonholonomic vehicles modeled as differential drive robots affected by unknown input constant disturbances and transmission variable time-delays in the communication channel. Using Barbalat’s Lemma and under the fact that the interconnecting graph is undirected and connected, it is proved that all robots positions asymptotically converge to a position in a given desired formation and they all agree on the center of this formation, while the orientations asymptotically reach a consensus value. Besides, it is proved that given the structure of the proposed new integral action, the external constant disturbances are rejected (exactly estimated) and that velocities converge to zero. Simulation results, with a robot network composed of eight nonholonomic vehicles and considering disturbances subjected to step changes, are presented to illustrate the robustness of the proposed control scheme.