Prescribed-time Cooperative Formation Control of Unmanned Surface Vessels for Multi-target Encirclement and Tracking

Objectives The paper investigates the multi-objective collaborative encirclement tracking control problem of underactuated unmanned surface vehicles (USVs) under unknown time-varying environmental disturbances. A decoupled control method for position and velocity is proposed based on the prescribed-time control approach. Methods In the position control layer, considering the real-time changes in the positions of multiple targets and the underactuated nature of the USVs, a prescribed-time cooperative encirclement tracking guidance law is designed to enable the USVs to track the convex combination of multiple targets with a time-varying scaling of the encirclement. In the velocity control layer, a prescribed-time sliding mode encirclement control law is designed to track the desired velocity signal output by the guidance law. To mitigate the impact of unknown time-varying disturbances on the control system, the prescribed-time theory is incorporated into the weight update law of the Radial Basis Function Neural Network (RBFNN). A prescribed-time RBFNN disturbance estimator is designed to estimate and compensate for the disturbances experienced by the system. The Lyapunov stability theory is employed to analyze and prove that the proposed control method ensures the prescribed-time stability of the system. Results Simulation results demonstrate that the proposed method can achieve the convergence of position tracking errors, velocity tracking errors, and disturbance estimation errors to zero within the prescribed-time. The disturbance estimation method used reduces the longitudinal velocity integral absolute error and the yaw rate integral absolute error of the USV formation by 13.55% and 24.46%, respectively. Conclusions In conclusion, the proposed method is capable of stabilizing the multi-objective tracking control system of the USV formation within the prescribed-time. It also demonstrates certain advantages in estimating unknown time-varying environmental disturbances and enhancing the dynamic performance of the system.