Displacement-Based Formation Control with Measurement Noises

Multi-agent formations have many practical applications. Measurement noises are inevitable in multi-agent formations, in which, however, the existing results mainly focus on special types of noises, and the analytical discussion on the effect of general noises is challenging and remains open. This motivates us to study the effect of stochastic measurement noises on displacement-based multi-agent formations, which are described by a general form of stochastic processes with finite second-order moments. First, for the case of unbiased measurement noises, a sufficient and necessary condition is derived for the existence of solutions in the stochastic dynamics of multi-agent formations. Then, several statistical features and convergence of formation errors are analyzed. In particular, for the case of unbiased measurement noises described by zero-mean wide-sense stationary processes, an upper bound on the mean square convergence of formation errors is obtained. Finally, we demonstrate the effectiveness of our theoretical results through a simulation example.