Characterizing minimum-length coordinated motions for two discs
Abstract
We study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization of a shortest collision-avoiding motion for all initial and final configurations of the robots. The individual paths are composed of at most six (straight or circular-arc) segments, and their total length can be expressed as a simple integral with a closed form solution depending only on the initial and final configuration of the robots. Furthermore, the paths can be parametrized in such a way that (i) only one robot is moving at any given time (decoupled motion), or (ii) the angle between the two robots' centres changes monotonically.
Cite
@article{arxiv.1607.04005,
title = {Characterizing minimum-length coordinated motions for two discs},
author = {David Kirkpatrick and Paul Liu},
journal= {arXiv preprint arXiv:1607.04005},
year = {2017}
}
Comments
long-form of conference submission, 26 pages, 18 figures