On Dynamics and Control of Multi-Link Flexible Manipulators

Abstract

This paper presents solutions of dynamics, inverse dynamics, and control problems of multi-link flexible manipulators. In deriving the manipulator dynamics, flexible deformations are assumed to be small in relation to the link length, angular rates of the links are assumed to be much smaller than their fundamental frequencies, and nonlinear terms (centrifugal and Coriolis forces) in the flexible manipulator model are assumed to be the same as those in the rigid body model. Flexible displacements are measured with respect to the rigid body configuration, obtained from its rigid body inverse kinematics. As a result, a linear time-varying system is obtained. The inverse dynamics problem consists of determination of joint torques for a given tip trajectory such that joint angles in the flexible configuration are equal to the angles in the rigid body configuration. The manipulator control system consists of the feedforward compensation and feedback control loops. Simulation results of a two-link space crane with a large payload show that the performance of this linearized dynamics and control approach is accurate, and at the same time is robust when subjected to parameter variations during slew operations.