Geodesics in the configuration spaces of two points in R^n
Differential Geometry
2020-07-07 v3 Algebraic Topology
Abstract
We determine explicit formulas for geodesics (in the Euclidean metric) in the configuration space of ordered pairs (x,x') of points in R^n which satisfy d(x,x')>=epsilon. We interpret this as two or three (depending on the parity of n) geodesic motion-planning rules for this configuration space. In the associated unordered configuration space, we need not prescribe that the points stay apart by epsilon. For this space, with a Euclidean metric, we show that geodesic motion-planning rules correspond to ordinary motion-planning rules on RP^{n-1}.
Cite
@article{arxiv.2001.00850,
title = {Geodesics in the configuration spaces of two points in R^n},
author = {Donald M Davis},
journal= {arXiv preprint arXiv:2001.00850},
year = {2020}
}
Comments
Replacement of paper which just did the ordered case