Optimal Motion of Flexible Objects with Oscillations Elimination at the Final Point

TL;DR

This paper presents a theoretical framework for optimal, time-minimal motion of flexible objects carried by robots, ensuring oscillations are eliminated at the final position, verified experimentally with a robotic setup.

Contribution

It introduces a skew-symmetric optimal control method for flexible object motion that minimizes time and eliminates oscillations at the endpoint, supported by experimental validation.

Findings

Optimal control law derived for flexible object motion

Experimental verification with Orthoglide robot

Oscillations successfully eliminated at 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.