Adaptive Fixed-Time Anti-Saturation Nonsingular Terminal Sliding Mode Control for Multi-AUV Formation Tracking Under Actuator Saturation and Lumped Disturbances

This paper investigates formation trajectory tracking control for multiple autonomous underwater vehicles (AUVs) subject to actuator saturation and unknown lumped disturbances. An adaptive fixed-time nonsingular terminal sliding mode (AFxTNTSM) control method is proposed to achieve formation tracking under input constraints. First, a fixed-time nonsingular terminal sliding mode (FxTNTSM) surface is constructed to improve the convergence behavior of the position and velocity tracking errors while avoiding the singularity associated with conventional terminal sliding mode control. Second, a fixed-time dynamic auxiliary system (FxTDAS) is designed to compensate for the input deviation caused by actuator saturation. In addition, an adaptive robust compensation law is incorporated to handle unknown lumped disturbances without requiring prior knowledge of their upper bounds. Lyapunov-based analysis proves that the closed-loop tracking errors are practically fixed-time stable, and the settling-time upper bound is independent of the initial conditions. At this stage, validation is limited to numerical simulations, which illustrate that the proposed AFxTNTSM control method maintains the prescribed formation, attenuates time-varying lumped disturbances, and keeps the actual control inputs within the actuator saturation limits.