Robot Manipulator Control for Rigid and Assumed Mode Flexible Dynamics Models

Abstract

rigid Euler-Lagrange dynamics model but are extended here to a flexible dynamics model based on the first assumed mode calculated using Euler-Bernoulli pinnedpinned beam theory. A square trajectory presents an ideal case for studying intense vibration effects and their control at the four orthogonal direction switches. 7 Operational problems with robots in space relate to several factors. One most important is the structural flexibility problem of a robot manipulator and subsequently significant difficulties with its control systems, especially, position control. Typically, small elastic vibrations of the links coupled with their large rigid link rotations and non-linear dynamics primarily cause these difficulties. This paper presents a control scheme for positioning the endpoint of a two-link robot manipulator modeled with assumed modes flexible dynamics while tracking a square trajectory. The dominant assumed mode vibration is derived for an Euler-Bernoulli pinned-pinned beam to model link flexibility then, coupled with nonlinear dynamics for large rotations of rigid links to formulate an EulerLagrange inverse dynamics robot model. A control law derived using the Jacobian transpose provides joint actuation for both rigid and flexible dynamics. Comparison of output trajectories shows some differences in control performance between the rigid and flexible dynamics models with the transient response characteristics demonstrating a reduction in maximum overshoot for the flexible dynamics over the rigid dynamics models but a lengthier settling time with a consistent albeit slight oscillation about the entire desired steady-state ttrajectory .