New perspective on sampling-based motion planning via random geometric graphs

Kiril Solovey, Oren Salzman, Dan Halperin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Roadmaps constructed by many sampling-based motion planners coincide, in the absence of obstacles, with standard models of random geometric graphs (RGGs). Those models have been studied for several decades and by now a rich body of literature exists analyzing various properties and types of RGGs. In their seminal work on optimal motion planning Karaman and Frazzoli [31] conjectured that a sampling-based planner has a certain property if the underlying RGG has this property as well. In this paper we settle this conjecture and leverage it for the development of a general framework for the analysis of sampling-based planners. Our framework, which we call localization-tessellation, allows for easy transfer of arguments on RGGs from the free unit-hypercube to spaces punctured by obstacles, which are geometrically and topologically much more complex. We demonstrate its power by providing alternative and (arguably) simple proofs for probabilistic completeness and asymptotic (near-)optimality of probabilistic roadmaps (PRMs). Furthermore, we introduce two variants of PRMs, analyze them using our framework, and discuss the implications of the analysis.

Original languageEnglish
Title of host publicationRobotics
Subtitle of host publicationScience and Systems XII, RSS 2016
EditorsDavid Hsu, Nancy Amato, Spring Berman, Sam Jacobs
PublisherMIT Press
ISBN (Electronic)9780992374723
StatePublished - 2016
Event2016 Robotics: Science and Systems, RSS 2016 - Ann Arbor, United States
Duration: 18 Jun 201622 Jun 2016

Publication series

NameRobotics: Science and Systems
ISSN (Electronic)2330-765X


Conference2016 Robotics: Science and Systems, RSS 2016
Country/TerritoryUnited States
CityAnn Arbor


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