Optimal motion of flexible objects with oscillations elimination at the final point

Abstract

In this article, a theoretical justification of one type of skew-symmetric optimal translational motion (moving in the minimal acceptable time) of a flexible object carried by a robot from its initial to its final position of absolute quiescence with the exception of the oscillations at the end of the motion is presented. The Hamilton-Ostrogradsky principle is used as a criterion for searching an optimal control. The data of experimental verification of the control are presented using the Orthoglide robot for translational motions and several masses were attached to a flexible beam.