## 1 Introduction  
With increasing interest in the field of marine research, autonomous underwater vehicle manipulator systems (UVMSs) [1] have rapidly developed into important devices for exploring the ocean, completing underwater tasks, underwater sampling and so on. It is a challenging problem to accurately control the UVMS in an energy-efficient manner due to the kinematic redundancy and underwater environment with hydrodynamic uncertainties, unknown external disturbances (such as ocean currents) and inaccurate sensor information. For solving these problems, inverse kinematics and robust coordinated control techniques have been developed for the UVMS. For the inverse kinematics of the UVMS, the solution can be obtained through mapping the end-effector's velocities to the velocities of the vehicle and manipulator. As the UVMS has redundant degrees of freedom (DOFs), there are various combinations of vehicle and manipulator velocities without affecting the end-effector velocities. A common solution is to adopt the pseudo-inverse Jacobian matrix of the UVMS or its weighted form [2]. However, this method is not desirable for redundant exploration to avoid joint limits, improve system manipulability or save energy. Therefore, the task-priority redundancy resolution technique [3] was proposed in such a way that the fulfillment of the primary task has a higher priority than that of a secondary task. Generally, the secondary task is to optimize the performance index through assigning additional motion in the null space of the primary task. [PERSON] and [PERSON] [4] solved the inverse kinematics of the UVMS on the acceleration level to minimize the total hydrodynamic drag; however, the performance index of this method requires dynamic equations which can not be modeled exactly. [PERSON] et al. [5] proposed a new performance index designed to minimize restoring moments without using dynamic equations. However, this method was implemented for a specific configuration of the UVMS. The task-priority strategy can be extensible to chain multiple tasks which have a lower order of priority ([PERSON] and [PERSON] [6]). [PERSON] et al. [7] used a fuzzy inference system (FIS) to handle multiple secondary tasks, such as reduction of fuel consumption and improvement of system manipulability. In such a way, a secondary task can be activated by FIS when the corresponding variable is without the safe range. [PERSON] et al. [8] used a fuzzy logic algorithm to decide the priorities of secondary objectives, such as manipulator singularity avoidance and attitude optimization of the UVMS. The experimental validation of three difference kinematic control schemes was presented in [9]. In [10], a multitask kinematic control of the underwater biomimetic vehicle-manipulator system (UBVMS) was designed. A unifying framework for the kinematic control of UVMSs was proposed in [11]. A very recent work dedicated to motion planning for the UVMS was presented in [12]. To achieve trajectory tracking, it is very important to design a coordinated motion controller for the UVMS. The simple control methods (e.g., proportional-integral-derivative (PID) control) are not suitable for the UVMS due to the inherent nonlinear and coupled dynamics of the system [13; 14; 15]. [PERSON] and [PERSON] [16] proposed a control strategy in terms of feedback linearization. [PERSON] and [PERSON] [4] utilized a computed torque controller (CTC) for trajectory tracking of the UVMS. [PERSON] et al. [17] proposed a model-based motion control for the UVMS, which can be applicable to three types of servo systems; i.e., a voltage-controlled, a torque-controlled and a velocity-controlled servo system. [PERSON] et al. [18] presented a trajectory tracking control for an underactuated underwater vehicle manipulator system (U-UVMS) based on the inverse dynamics. However, these model-based controllers are poor in terms of robustness against model uncertainties. In [19], a fuzzy logic control method was designed for a hybrid-driven UVMS to grasp marine products on the seabed.