Adaptive Second-Order Fast Nonsingular Terminal Sliding Mode Tracking Control for Fully Actuated Autonomous Underwater Vehicles

Abstract

This paper focuses on the design of an adaptive second-order fast nonsingular terminal sliding mode control (ASOFNTSMC) scheme for the trajectory tracking of fully actuated autonomous underwater vehicles (AUVs) in the presence of dynamic uncertainties and time-varying external disturbances. First, a second-order fast nonsingular terminal sliding mode (SOFNTSM) manifold is designed to achieve a faster convergence rate than the existing second-order nonsingular terminal sliding mode (SONTSM) manifold. Then, by using this SOFNTSM manifold, an ASOFNTSMC scheme is developed for the fully actuated AUVs to track the desired trajectory. The designed SOFNTSM manifold yields local exponential convergence of the position and attitude tracking errors to zero, and the developed ASOFNTSMC scheme ensures that the error trajectories always move toward the SOFNTSM manifold and once they hit the manifold, remain on it in the presence of dynamic uncertainties and time-varying external disturbances. By deriving the expression of the bounding function of the system uncertainty and using adaptive technique to estimate the unknown parameters of the system uncertainty bounds, the ASOFNTSMC scheme does not require the prior knowledge of the upper bound of the system uncertainty. Meanwhile, through involving the discontinuous sign function into the time derivative of the control input, the ASOFNTSMC scheme eliminates the chattering without reducing the tracking precision. Compared with the existing adaptive SONTSM control (ASONTSMC) scheme, the proposed ASOFNTSMC scheme offers a faster convergence rate for the trajectory tracking control of fully actuated AUVs. Two comparative simulation cases performed respectively on two fully actuated AUVs demonstrate the superiority of the ASOFNTSMC scheme over the ASONTSMC scheme.