To address the limitations of traditional controllers for the considered six-degree-of-freedom multi-thruster underwater robot under strong nonlinearities and environmental disturbances, this paper proposes a particle swarm optimization–radial basis function–proportional–integral–derivative (PSO-RBF-PID) control algorithm. The proposed method combines the nonlinear identification capability of the RBF neural network, the global optimization capability of PSO, and the stable closed-loop structure of PID control, thereby enabling adaptive parameter tuning and disturbance compensation. Unlike existing PSO-PID- and RBF-based controllers, the proposed method combines offline global optimization and online adaptive gain tuning within a unified control framework. Although the framework is modular and can be extended to underwater robotic systems with different degrees of freedom by redefining the state vector, controller channels, and thrust allocation matrix, the present study validates the method through a six-degree-of-freedom multi-thruster underwater robot case study. Comparative simulations were conducted under the same model, disturbance conditions, sampling settings, and evaluation indices for six controllers: PID, cascade PID, fuzzy PID, FOPID, PSO-PID, and PSO-RBF-PID. For the considered 6-DOF multi-thruster underwater robot, PSO-RBF-PID achieved the best overall performance in steady-state error, settling time, overshoot, and IAE. This improvement is mainly attributed to the combination of PSO-based offline optimization and RBF-based online adaptive compensation.
Chen et al. (Thu,) studied this question.