Hydrodynamic modeling is the basis of the precise control research of underwater manipulators. Viscous hydrodynamics, an important part of the hydrodynamic model, directly affects the accuracy of the dynamic model and the control model of the manipulator. Considering the limited research on viscous hydrodynamics of underwater manipulators and the difficulty in measuring viscous hydrodynamic coefficients, the viscous hydrodynamic model in the form of Taylor expansion is analyzed and established. Through carrying out simulation calculations, curve fitting and regression analysis, positional derivatives, rotational derivatives, and coupling derivatives in the viscous hydrodynamic model, are determined. This model provides a crucial theoretical foundation and reference data for subsequent related research.

It is challenging to accurately judge the actual end position of the manipulator—regarded as a rigid body—due to the influence of micro-deformation. Its precise and efficient control is a crucial problem. To solve the problem, the Hamilton principle was used to establish the partial differential equation (PDE) dynamic model of the manipulator system based on the infinite dimension of the working environment interference and the manipulator space. Hence, it resolves the common overflow instability problem in the micro-deformable manipulator system modeling. Furthermore, an infinite-dimensional radial basis function neural network compensator suitable for the dynamic model was proposed to compensate for boundary and uncertain external interference. Based on this compensation method, a distributed boundary proportional differential control method was designed to improve control accuracy and speed. The effectiveness of the proposed model and method was verified by theoretical analysis, numerical simulation, and experimental verification. The results show that the proposed method can effectively improve the response speed while ensuring accuracy.