An adaptive nonsingular fast terminal sliding mode control scheme with extended state observer (ESO) is proposed for the trajectory tracking of an underwater vehicle-manipulator system (UVMS), where the system is subjected to the lumped disturbances associating with both parameter uncertainties and external disturbances. The inverse kinematics for the system is obtained by the quaternion-based closed-loop inverse kinematic algorithm. The proposed controller consists of the modified nonsingular fast terminal sliding mode surface (NFTSMS) and ESO, and the adaptive control law. The utilized NFTSMS can ensure the fast convergence of the tracking errors, together with avoiding the singularity in the derivation. According to the ESO method, the estimation error of the lumped disturbance vector can realize the fixed-time convergence to the origin, along with replacing the sign function with the saturation function to attenuate the chattering. A continuous fractional PI-type robust term with adaptive laws is introduced to handle the unknown bound of the estimation error. The closed-loop system is proved to be asymptotically stable by the Lyapunov theory. Simulations are performed on a ten degree-of-freedom UVMS under four different strategies. Comparative simulation results show that the proposed controller can achieve better tracking performance and stronger robustness of the disturbance rejection.

This paper proposes a composite controller (CC) to improve the accuracy of trajectory tracking and suppress the vibration of two-link underwater flexible manipulators. A dynamic model of the flexible manipulators considering hydrodynamic force is established by combining the Lagrange equation and Morison formula. Then, the dynamic model is divided into a flexible dynamic subsystem and rigid dynamic subsystem, and a decomposed dynamic control strategy is presented for the two subsystems. In particular, an adaptive fuzzy sliding mode control scheme (AFSMC) with good robustness to compensate for uncertain factors is designed to track the joint trajectory and suppress vibration. Next, the trajectory tracking control of two-link underwater flexible manipulators is simulated to investigate the performance of the framework. The results show that the hydrodynamic force and flexible deformation markedly affect the input torque of the joint, and the traditional sliding mode controller (SMC) is superior to proportional integral derivative (PID) control in managing hydrodynamic force disturbance and inferior in suppressing flexible vibration. The proposed composite controller based on adaptive fuzzy sliding mode control CC(AFSMC) is more effective in restraining the vibration of flexible manipulators and resisting hydrodynamic force disturbance than PID and CC(SMC).