Formation Control of Nonholonomic Vehicles Under Time Delayed Communications

This document considers the formation control problem for a group of nonholonomic mobile robots under time delayed communications. The agents are assumed to be working under a directed and fixed communication topology. A recently developed formation control technique, based on a consensus protocol for linear systems is revisited. The stability analysis of this control technique, in the domain of the time delays, is performed using the Cluster Treatment of Characteristic Roots paradigm under the Spectral Delay Space approach. This analysis leads to an exact declaration of the stability boundaries in the domain of the delays. This linear control law is adapted to the nonlinear dynamics of the nonholonomic carts by means of feedback linearization. Simulation results show the applicability of this method to the class of agents considered here. Note to Practitioners-The problem dealt with in this paper is the coordinated motion of a group of mobile robots. Without a leader or a central authority, the members of the team attempt to converge into a predefined formation by exchanging information about position and velocities among themselves. The particularity here is that the communication among agents is corrupted by two time delays. One delay is considered to affect the measurement of the position of the agents and the second the determination of their velocity. We present a methodology to study the effect of the delay in the stability of the formation. This technique allows an exact declaration of the delay compositions that guarantee convergence to the formation in a finite time. The methodology is applied to a group of nonholonomic differential drive mobile robots.