Stable Formation Control of Multi-Robot System with Communication Delay

In this paper, a distributed formation control algorithm with delayed information exchange is discussed. The algorithm, which is derived from the flocking behaviour of birds and consensus theory, enables robots to move in formation at a desired velocity. After a series of orthogonal transformations to the original formation system, the upper bound tolerable delay is obtained by using matrix theory and the Nyquist criterion. According to the results, the upper bound tolerable delay depends on the control parameters and eigenvalues of the Laplacian matrix. Therefore, the effect of the parameters on the maximum tolerable delay is analysed, obtaining the following conclusions: the upper bound tolerable delay is proportional to the parameters associated with the velocity, inversely proportional to the parameters associated with the position, and inversely proportional to the difference between the eigenvalue of Laplacian matrix and 1. The simulation results of a four-robot formation system with different communication delays verify the effectiveness of the formation control algorithm and the correctness of the theoretical analysis