Due to the growing interest using model predictive control (MPC), there are more and more researches about the applications of MPC on autonomous underwater vehicle (AUV), and these researches are mainly focused on simulation and simple application of MPC on AUV. This paper focuses on the improvement of MPC based on the state space model of an AUV. Unlike the previous approaches using a fixed weighting matrix, in this paper, a coefficient, varied with the error, is introduced to adjust the control increment vector weighting matrix to reduce the settling time. Then, an analysis on the effect of the adjustment to the stability is given. In addition, there is always a lag between the AUV real trajectory and the desired trajectory when the AUV tracks a continuous trajectory. To solve this problem, a simple re-planning of the desired trajectory is developed. Specifically, the point certain steps ahead from current time on the desired trajectory is treated as the current desired point and input to the controller. Finally, experimental results for depth control are given to demonstrate the feasibility and effectiveness of the improved MPC. Experimental results show that the method of real-time adjusting control increment weighting matrix can reduce settling time by about 2 s when tracking step trajectory of 1 m, and the simple re-planning of the desired trajectory method can reduce the average of absolute error by about 15% and standard deviation of error by about 17%.

The joint control problem of the underwater manipulator is addressed in this paper, under the influence of uncertainty factors such as model uncertainty, external disturbance, and manipulator joint lag. In general, for the uncertainty factors, it is usually approximated online, but it is difficult to select a reasonable value for the approximation error boundary, too conservative estimated values would cause chattering problem easily. And the influence of joint lag on the manipulator control should be considered in actual work. Unlike most previous control method, in this paper, the function approximation technique (FAT), which uses the Legendre polynomial, is adopted to approximate the uncertainty factors online. Then, based on the proportion integral differential (PID) sliding manifold with the integral and differential of tracking error, a sliding model PID controller is designed to speed up the response and reduce the effects of joint lag. For the error boundary, the adaptive law is proposed, and it will reduce chattering of the control quantity under the steady state of the system. It was proved that the joint error of the control system is uniformly asymptotic convergence through the stability analysis. Finally, the effectiveness of the proposed approach is demonstrated with pool comparison experiments of the underwater manipulator installed in the autonomous underwater vehicles (AUVs).