Dynamic analysis of flexible-link manipulator in underwater applications using Gibbs-Appell formulations

Abstract

The dynamic model of a flexible robotic chain by considering its motion in a fluid medium is developed in this study. The use of flexible manipulators in fluid applications offers several advantages, but the fluid-manipulator interaction forces, as well as the elasticity of each link, complicates the modeling process. To tackle this issue, the dynamic effects of the fluid on the performance of flexible arms are identified and expressed mathematically so that the resulting interaction during the robot motion can be modeled simultaneously. In this regard, the dynamic interaction between the links and the fluid as a result of link flexibility is modeled as a distributed load along the arm length. In addition to the structural damping of the links, the effect of fluid damping along with its added mass affects the performance of the considered robotic system. Thus, compared to a flexible robotic arm in the air or a rigid robotic arm in the fluid, the flexible deformation of the robot links during motion is affected by the fluid flow. The recursive Gibbs-Apple formulation is used to derive the equations of motion of an N-link robotic chain. Not only does this formulation reduce the computational complexity compared to similar algorithms, but it also allows us to consider the effect of forces exerted on the joints and robot links in the form of the Rayleigh dissipation function. The final equations of motion are simulated using MATLAB for a two-link flexible arm. Simulations of robot links are conducted for different elasticities, different initial conditions, and different media with different viscosities. According to the obtained results, the deformation of flexible manipulators decreases from 5 mm (in the air) to 3 mm (in the fluid), while the displacement in water is 10% of that in the air under similar conditions.