A minimum swept-volume metric structure for configuration space

TL;DR

This paper introduces a novel metric structure on configuration spaces based on swept-volume, enabling natural geodesic computation for articulated objects and applications in path planning amidst obstacles.

Contribution

It presents a new swept-volume based metric for configuration spaces, with methods to compute geodesics applicable to robotic manipulators and free-flying objects.

Findings

Geodesic paths can be computed efficiently for articulated objects.

The metric aids in obstacle-aware path planning.

Applicable to various robotic systems and configurations.

Abstract

Borrowing elementary ideas from solid mechanics and differential geometry, this presentation shows that the volume swept by a regular solid undergoing a wide class of volume-preserving deformations induces a rather natural metric structure with well-defined and computable geodesics on its configuration space. This general result applies to concrete classes of articulated objects such as robot manipulators, and we demonstrate as a proof of concept the computation of geodesic paths for a free flying rod and planar robotic arms as well as their use in path planning with many obstacles.