Steering Flexible Linear Objects in Planar Environments by Two Robot Hands Using Euler's Elastica Solutions

TL;DR

This paper presents a novel method for controlling flexible linear objects in planar environments using two robot hands, leveraging Euler's elastica solutions for shape modeling, obstacle avoidance, and stability, with practical implementation and demonstrations.

Contribution

It introduces a closed-form elastica-based control framework for steering flexible objects with two robot hands, including criteria for non self-intersection and obstacle avoidance.

Findings

Successfully derived elastica solutions under optimal control.

Developed a planning scheme for obstacle avoidance in planar environments.

Demonstrated the approach with detailed robotic manipulation examples.

Abstract

The manipulation of flexible objects such as cables, wires and fresh food items by robot hands forms a special challenge in robot grasp mechanics. This paper considers the steering of flexible linear objects in planar environments by two robot hands. The flexible linear object, modeled as an elastic non-stretchable rod, is manipulated by varying the gripping endpoint positions while keeping equal endpoint tangents. The flexible linear object shape has a closed form solution in terms of the grasp endpoint positions and tangents, called Euler's elastica. This paper obtains the elastica solutions under the optimal control framework, then uses the elastica solutions to obtain closed-form criteria for non self-intersection, stability and obstacle avoidance of the flexible linear object. The new tools are incorporated into a planning scheme for steering flexible linear objects in planar environments populated by sparsely spaced obstacles. The scheme is fully implemented and demonstrated with detailed examples.