Development of an Algorithm for Solving the Inverse Dynamics Problem for Underwater Manipulators

Abstract

The paper discusses the development of a new method for calculating load moments for all joints of underwater multi-link manipulators installed on unmanned underwater vehicles. By introducing additional terms into the equations of motion, it takes into account all the key features of the interaction of the manipulator links with a viscous medium, including the effects of currents. To achieve this, the attached masses and moments of inertia are represented as symmetric positive-definite matrices with constant coefficients. This distinguishes the proposed approach from known methods that use variable coefficients dependent on the instantaneous velocity and direction of motion. This representation ensures the linearity of the dynamic model with respect to the identifiable hydrodynamic parameters, creating the basis for their subsequent precise determination. To account for constant underwater currents in the proposed modified algorithm, the linear velocity of the manipulator base is assumed to be equal to the difference between the vehicle speed and the current velocity, allowing for the determination of the longitudinal and transverse components of the viscous friction forces and moments. Furthermore, a correction is introduced into the expressions for the acceleration of the link's center, accounting for the constant current velocity. This corrects the calculation of the forces and moments due to the attached masses and moments of inertia. Thanks to these modifications, the proposed algorithm enables the correct modeling of the manipulator's dynamics in a real underwater environment, where the presence of currents is a significant factor influencing the formation of moments in the joints.