Equivalent-control-based discrete-time sliding mode trajectory tracking control for the underactuated USV

This paper studies the discrete-time sliding mode control (DSMC) for the trajectory tracking of the underactuated USV with external disturbances. In this work, a improved equivalent-control-based DSMC with a discrete-time virtual velocity control law is proposed to address the trajectory tracking. Initially, using the forward Euler discretization method, the discrete-time dynamics and kinematic mathematical models of the unmanned surface vessel (USV) are derived. Then, with the help of a double closed-loop control technology, a novel discrete virtual velocity control (DVVC) law is designed in the outer loop to convert trajectory tracking control into virtual velocity tracking control. In the inner loop, a equivalent-control-based DSMC is suggested to suppress the external disturbance of the USV. Afterward, the theoretical analysis is given to show that the closed-loop system is uniformly bounded stable after the introduction of the control strategy. Finally, the effectiveness of the proposed control scheme is verified by the comparative simulation results.