An Improved Dynamic Surface Sliding Mode Method for Autonomous Cooperative Formation Control of Underactuated USVS with Complex Marine Environment Disturbances

Abstract In this paper, a novel dynamic surface sliding mode control (DSSMC) method, combined with a lateral velocity tracking differentiator (LVTD), is proposed for the cooperative formation control of underactuated unmanned surface vehicles (USVs) exposed to complex marine environment disturbances. Firstly, in view of the kinematic and dynamic models of USVs and the design idea of a virtual control law in a backstepping approach, the trajectory tracking control problem of USVs’ cooperative formation is transformed into a stabilisation problem of the virtual control law of longitudinal and lateral velocities. Then, aiming at the problem of differential explosion caused by repeated derivation in the process of backstepping design, the first-order low-pass filter about the virtual longitudinal velocity and intermediate state quantity of position is constructed to replace differential calculations during the design of the control law, respectively. In order to reduce the steady-state error when stabilising the virtual lateral velocity control law, the integral term is introduced into the design of the sliding mode surface with a lateral velocity error, and then the second-order sliding mode surface with an integral is structured. In addition, due to the problem of controller oscillation and the role of the tracking differentiator (TD) in active disturbance rejection control (ADRC), the LVTD is designed to smooth the state quantity of lateral velocity. Subsequently, based on the dynamic model of USV under complex marine environment disturbances, the nonlinear disturbance observer is designed to observe the disturbances and compensate the control law. Finally, the whole cooperative formation system is proved to be uniformly and ultimately bounded, according to the Lyapunov stability theory, and the stability and validity of the method is also verified by the simulation results.