Fixed-time formation tracking for multiple nonholonomic wheeled mobile robots based on distributed observer

This paper studies the distributed fixed-time formation tracking problem of multiple nonholonomic wheeled mobile robots system over directed fixed and switching topologies. Through a classical nonlinear transformation, the formation control problem is transformed into a consensus problem. New control protocols based on a distributed observer are proposed. The communication topology between multiple nonholonomic wheeled mobile robots is directed, which can reduce the energy loss of communication. Some sufficient conditions of multiple robots achieving the expected formation pattern are given. All follower robots can track the leader's trajectory, form the desired formation shape within a fixed settling time, and make the leader in the geometric center of the formation. By adopting graph theory, Lyapunov stability method and fixed time theory, one can obtain an upper bound of the settling time, and the settling time is independent of the system's initial states. Finally, two examples are presented to illustrate the potential correctness of the main results.