Research on hydrodynamic-load-aware trajectory planning for an underwater hydraulic manipulator under directional currents

Hydrodynamic loading affects the motion performance and hydraulic compatibility of underwater manipulators operating in current-disturbed environments. Because the resultant water-induced joint torque depends on both manipulator motion and incident-current direction, this study develops a hydrodynamic-load-aware trajectory-planning method for a three-degree-of-freedom underwater hydraulic manipulator. A planning-level optimal control problem is formulated in joint space and transcribed using a fixed-grid Legendre-Gauss-Radau (LGR) pseudospectral method. The objective minimizes the time-integrated squared norm of the resultant hydrodynamic torque formed by the vector superposition of the self-motion-induced and current-induced components, thereby retaining their reinforcement and cancellation during optimization. Numerical convergence across five LGR collocation orders and sensitivity tests using multiple initial guesses support the consistency of the obtained solutions. The method is first evaluated under 41 principal flow conditions, including still water and currents in the positive and negative x- and y-directions. Under identical motion duration, endpoint conditions, and joint-space constraints, the proposed trajectory produces a lower resultant hydrodynamic index than both the no-hydrodynamic-objective LGR trajectory and the quintic-polynomial baseline in every case. Relative to the no-hydrodynamic-objective LGR trajectory, the case-averaged reduction is 13.78%, and the maximum absolute reduction reaches 28.21 (N⋅m) 2 s. Mechanism analysis shows that the reduction under the x-direction currents is dominated by weakened flow-force excitation, whereas that under the y-direction currents is achieved mainly through reduced configuration-dependent force-to-torque transmission. The same dominant mechanisms are retained across four additional motion tasks, for which all 160 directional-current cases yield positive reductions and task-averaged reductions of 11.29%-14.93%. Posterior hydraulic assessment further shows a maximum pump-speed utilization of 68.0% and a maximum pump-flow demand of 0.326 L/min. By scaling the model-computed cylinder-force demands using experimentally measured pressure references from an 8 s trapezoidal-velocity trajectory, the resulting pressure-feasibility indicator remains within 0.497–2.79 MPa. These results demonstrate that the proposed method consistently reduces direction-dependent hydrodynamic loading across the investigated motion tasks while maintaining compatibility with the prescribed hydraulic actuation envelope.