/Path-Connectivity of the Free Space

Path-Connectivity of the Free Space

Alberto Rodriguez and Matthew T. Mason
Journal Article, Carnegie Mellon University, IEEE Transactions on Robotics (TRO), Vol. 28, No. 5, pp. 1177-1180, October, 2012

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This paper revisits the notion of free configuration space and reviews some of its path-connectivity related properties. Literature on motion planning reveals at least three different definitions for the free configuration space of a robot in the presence of obstacles. This paper shows that, assuming regularity of both object and obstacles, those three definitions are equivalent. We show the three definitions regularize the free space and therefore prevent the existence of “thin bits”, or low dimensional strata. The paper concludes discussing a series of properties regarding the existence and smoothability of contact-free paths between pairs of configurations.

BibTeX Reference
author = {Alberto Rodriguez and Matthew T. Mason},
title = {Path-Connectivity of the Free Space},
journal = {IEEE Transactions on Robotics (TRO)},
year = {2012},
month = {October},
volume = {28},
number = {5},
pages = {1177-1180},
keywords = {Configuration space, Path planning},