Unsteady hydrodynamic parameter identification for underwater continuum manipulators: A structure-embedded PINN approach

Continuum manipulators offer significant compliance for underwater interventions, but their configuration-dependent unsteady hydrodynamics complicate modeling and real-time control. This paper presents a novel cable-driven rigid–flexible coupled manipulator and proposes a hydrodynamic parameter identification framework based on a Structure-Embedded Physics-Informed Neural Network (SE-PINN). For reliable computational fluid dynamics (CFD) data generation, a 3-RRRR-based multi-segment joint mechanism provides a physical basis for the constant-curvature assumption while preventing unintended buckling. A conjugate term reconstruction algorithm is also proposed to eliminate initial kinematic singularities, ensuring moving-mesh stability under extreme bending. A feature-decoupled virtual sampling strategy is subsequently employed to eliminate multicollinearity at the data source. To mitigate gradient flow pathologies in parameter inversion, the SE-PINN internalizes the generalized Morison equation as a hard constraint and embeds a dual-branch architecture for independently predicting drag and inertia coefficients. Results demonstrate that the SE-PINN successfully reconstructs physically consistent hydrodynamic manifolds and accurately characterizes unsteady hysteresis phenomena. Compared to the constant-coefficient model and standard Multilayer Perceptrons (MLPs), the proposed framework exhibits robust cross-regime generalization, overcoming amplitude overshoots and non-physical divergence in high-frequency extrapolation tests. Furthermore, the surrogate model significantly reduces inference latency, establishing a computationally efficient dynamic foundation for the real-time feedforward torque compensation of underwater continuum robots.