Underwater vehicle manipulator system (UVMS) mathematical modeling and force optimization

This study presents a unified dynamic modeling, control, and optimization framework for underwater vehicle-manipulator systems (UVMSs) that explicitly captures vehicle-manipulator coupling and realistic hydrodynamic effects. A recursive Newton–Euler formulation combined with Denavit–Hartenberg (DH) kinematics is developed to model the coordinated motion of a fully actuated underwater vehicle equipped with a manipulator, using CFD-derived hydrodynamic coefficients to improve model fidelity. Strongly coupled inverse kinematics are solved using an adaptive task-priority damped-least-squares Newton–Raphson algorithm for singularity-robust redundancy resolution through null-space projection. Trajectory tracking is evaluated using nonlinear backstepping and finite-time sliding mode control (FTSMC), with FTSMC providing superior robustness and disturbance rejection under hydrodynamic disturbances and ocean currents. At the propulsion level, constrained thrust allocation is formulated as a quadratic programming problem and solved using the alternating direction method of multipliers (ADMM), with performance benchmarked against interior-point and active-set methods, demonstrating comparable computational performance and scalability for embedded implementation. The proposed framework reduces RMS end-effector tracking error by 8.3% and maximum tracking error by 6.4% relative to nonlinear backstepping while maintaining comparable control effort, demonstrating its suitability for realistic UVMS operations.