Trajectory tracking control for nonholonomic mobile robots under arbitrary reference input

This paper studies the tracking control problem for nonholonomic mobile robots based on second order dynamics, with application to consensus tracking and formation tracking. The greatest novelty in this paper is that the reference trajectory can be arbitrarily chosen, in the sense that the condition of persistency excitation and any other requirements are not imposed on the leader. In this paper, at first, the tracking control of one leader with single follower is taken into consideration, which is converted to the stabilization of two relative subsystems by the design of an adjoint system. Then, the single follower tracking controller is extended to the consensus tracking of multiple nonholonomic mobile robots connected by a directed acyclic graph, in which the convex combination in nonlinear manifolds is introduced to construct a virtual leader for each follower. Next, the relationship between consensus control and formation control is established for multiple nonholonomic mobile robots, with the result that a new transformed system is constructed so as to obtain the formation tracking control strategy from the consensus tracking result. Finally, simulations are presented to verify the effectiveness of the control laws.