Continuous nonsingular terminal sliding mode control for trajectory tracking of underactuated AUVs with mismatched disturbance

Achieving precise trajectory tracking with practical applicability for underactuated autonomous underwater vehicles (AUVs) is challenging due to uncertainties and inherent underactuation. This paper presents a finite-time control framework with continuous inputs to address this issue. By incorporating a sliding mode observer, the framework estimates lumped disturbances – including mismatched lateral velocity disturbances – to facilitate effective control law design. A key feature is the direct dependence of the control input on the sliding manifold, which avoids chattering and yields a continuous dynamical control law. Furthermore, the controller utilises an integral form to obtain the equivalent sign-function of sliding variables, eliminating the need for saturation function approximations. This design guarantees finite-time convergence and reduces the reliance on high-order state derivatives. Simulation on the REMUS AUV verifies that the proposed controller achieves favorable performance in the convergence of both position and velocity tracking errors. These results robustly validate the practical value of the proposed controller for real-world AUV applications.