Quaternion-Based Modeling and Predefined-Time Tracking Control of a Fully Actuated Autonomous Underwater Vehicle

This paper investigates the modeling and the practical predefined-time (PdT) tracking control problems for a fully actuated disk-shaped autonomous underwater vehicle (AUV) with six degrees of freedom. To overcome the gimbal lock problem inherent in Euler angle representation, unit quaternions are adopted to model the AUV, accounting for internal uncertainties and external disturbances. Then, an improved time-varying function is introduced, which serves as the basis for designing a non-singular sliding surface and sliding mode controller with PdT stability. This approach ensures that the tracking errors converge within a predefined time, independent of initial conditions and design parameters. Compared with traditional PdT controllers, the proposed method eliminates singularities, enhances the precision of convergence time estimation, and typically yields smaller, smoother initial control inputs, thus improving its potential for engineering applications. Numerical simulations validate the effectiveness and performance of the proposed controller.