Fixed-Time Formation Control of Multiple Wheeled Mobile Robots for Circumnavigating a Moving Target

This paper addresses the dynamic target tracking and circumnavigation problem for multiple Wheeled Mobile Robots (WMRs) while considering both kinematic and dynamic models, and proposes a fixed-time circumnavigation controller. The control system consists of two parts: Firstly, it formulates an error model of relative velocity between the target and WMRs, transforming the cooperative circumnavigation problem into a tracking problem. A dynamic feedback linearization method is employed to generate suitable linear and angular velocity. Secondly, based on the dynamic model, the error vector is redefined to represent relative position and orientation between the trajectory generated by the kinematic controller and the WMRs. A torque control law is designed using backstepping and fixed-time stability theory to track this trajectory, ultimately achieving circumferential velocity, circumferential radius, and relative angular spacing tracking during circumnavigation control. Additionally, the integration of an adaptive term into the controller, aimed at estimating unknown parameters, facilitates the attainment of effective control performance even when confronted with parameter uncertainties. Furthermore, Lyapunov tools are utilized for fixed-time stability analysis. Finally, the efficacy of the designed controller is validated via numerical simulations.