Dynamics Of Underwater Manipulator: A Recursive Lagrangian Formulation

This article presents a method for computation of a unified inverse dynamics and hydrodynamics of a serial link manipulator, completely submerged in water using Lagrangian formulation. The derivation is based on recurrence relation for the velocities, accelerations and generalized forces including hydrodynamic forces. In dealing with the fluid dynamic effects of both uniform and accelerated motion of a body submerged in water, this paper makes use of empirical formulations/relations available in standard literature. As an exemplar implementation, the recursive formulation for a two-link planar underwater manipulator, moving in a vertical plane against gravity, is presented using the proposed algorithm to obtain the motion equations. A free-fall experiment of the chosen two-link manipulator is carried out in simulation through solving the equations of motion numerically with initial conditions set at rest. The two-link manipulator is physically built with straight cylindrical links and free joints (on antifriction bearings). The free-fall experiment same as the simulation experiment is again carried out physically, keeping the whole assembly completely submerged underwater in a glass tank. The time-varying evolution of manipulator configurations is recorded using high-speed motion capture and then analyzed to obtain time evolution of manipulator configurations and kinematic states. The paper concludes by stating the effectiveness of the proposed recursive procedure for inverse dynamics formulation through comparative study of the simulation and experimental results.