In this paper, the precise control of the underwater manipulator has studied under the conditions of uncertain underwater dynamics and time-varying external interference. An improved adaptive model predictive control (MPC) method is proposed for a multiple-degrees-of-freedom (DOF) underwater manipulator. In this method, the Gaussian process regression (GPR) algorithm has been embedded into the precise trajectory tracking control of the underwater manipulator. The GPR algorithm has been used to predict the water resistance, additional mass, buoyancy and external interference in real time, and the control law has been calculated by the terminal constraint MPC to realize the adaptive internal and external interference compensation. In addition, a more accurate dynamic model of the underwater 6-DOF manipulator is established by combining Lagrange equation with Morrison formula. Finally, the effectiveness of the adaptive MPC using GPR method is verified by a series of comparative simulations.

This study introduces an innovative double closed-loop 3D trajectory tracking approach, integrating deep neural networks (DNN) with event-triggered nonlinear model predictive control (ENMPC), specifically designed for remotely operated vehicles (ROVs) under external disturbance conditions. In contrast to single-loop model predictive control, the proposed double closed-loop control system operates in two distinct phases: (1) The outer loop controller uses a DNN controller to replace the LMPC controller, overcoming the uncertainties in the kinematic model while reducing the computational burden. (2) The inner loop velocity controller is designed using a nonlinear model predictive control (NMPC) algorithm with its closed-loop stability proven. A DNN + ENMPC 3D trajectory tracking method is proposed, integrating a velocity threshold-triggered mechanism into the inner-loop NMPC controller to reduce computational iterations while sacrificing only a small amount of tracking control performance. Finally, simulation results indicate that compared with the ENMPC algorithm, NMPC + ENMPC can better track the desired trajectory, reduce thruster oscillations, and further minimize the computational load.