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).

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It is of great significance to expand the functions of submarines by carrying underwater manipulators with a large working space. To suppress the flexible vibration of underwater manipulators, an improved sparrow search algorithm (ISSA) combining an elite strategy and a sine algorithm is proposed for the trajectory planning of underwater flexible manipulators. In this method, the vibration evaluation function is established based on the precise dynamic model of the underwater flexible manipulator and considering complex motion and vibration constraints. Simulation results show that the ISSA algorithm requires only 1/3.68 of the time of PSO. Compared to PSO, SSA and the opposition-based learning sparrow search algorithm (OBLSSA), the optimization performance is improved by 17.3%, 13.1% and 9.7%, respectively. However, because the complex dynamics model of the underwater flexible manipulator leads to large computational effort and a long optimization time, ISSA is difficult to apply directly in practice. To obtain a large number of optimization results in a shorter time, an incremental Kriging-assisted ISSA (IKA-ISSA) is proposed in this paper. Simulation results show that IKA-ISSA has good nonlinear approximation ability and the optimization time is only 3% of that of the ISSA.

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