Time-domain mapping-based prescribed-time formation control for the heterogeneous unmanned surface vehicles with collision-free

This paper investigates the prescribed-time formation control problem for heterogeneous unmanned surface vehicles (USVs) under uncertain external disturbances. Firstly, we transform the prescribed-time formation control problem into an asymptotic convergence problem through time-domain mapping. Subsequently, we design a prescribed-time formation controller using backstepping and dynamic surface control (DSC) methods, and employ adaptive control method to estimate the upper bounds of the uncertainties. Furthermore, by leveraging Lyapunov stability theory, the proposed control strategy ensures that the heterogeneous USVs can achieve leader–follower formation control with prescribed performance and collision-free. In a prescribed-time frame, the formation tracking errors can converge to a small neighborhood of zero. Finally, simulation results are provided to validate the effectiveness of the designed prescribed-time formation controller.