Homogeneity-based fixed-time path following control for unmanned surface vehicles with uncertainties and asymmetric actuator saturation

This paper proposes a novel Adaptive Nonsingular Fixed-Time Path Following Control scheme for underactuated unmanned surface vehicles navigating under unknown uncertainties, environmental disturbances, and asymmetric input saturation constraints. The main contribution is the integration of a Fixed-Time Line-of-Sight guidance law with a homogeneity-based Adaptive Full-order Integral Terminal Sliding Mode control framework to achieve robust fixed-time path-following performance. Unlike conventional Line-of-Sight guidance methods with fixed or empirically selected look-ahead distances, the proposed Fixed-Time Line-of-Sight guidance law incorporates adaptive sideslip compensation and a dynamically adjusted look-ahead distance based on real-time cross-track error, enabling rapid and accurate heading correction under time-varying disturbances. Furthermore, a novel variable-exponent Adaptive Full-order Integral Terminal Sliding Mode controller is developed to guarantee nonsingular fixed-time convergence while simultaneously ensuring accurate tracking of both the desired heading angle and yaw rate. An adaptive gain mechanism is introduced to estimate and compensate unknown uncertainties online, eliminating the requirement for conservative prior bounds and mitigating control-gain overestimation. To address practical implementation issues, an asymmetric saturation function is incorporated directly into the control design to explicitly account for actuator limitations. Compared with existing fixed-time and finite-time path-following approaches, the proposed method simultaneously addresses adaptive sideslip compensation, fixed-time convergence, uncertainty rejection, singularity avoidance, second-order heading dynamics tracking, and asymmetric actuator saturation within a unified framework. A homogeneity-based variable-exponent Lyapunov analysis is developed to rigorously establish Fixed-Time Stability of the closed-loop system. Comparative simulation studies demonstrate that the proposed Adaptive Nonsingular Fixed-Time Path Following Control scheme achieves superior path-following accuracy, robustness, and disturbance-rejection capability compared with existing benchmark methods under constrained and uncertain marine environments.