Motion planning via manifold samples

Oren Salzman*, Michael Hemmer, Barak Raveh, Dan Halperin

*Corresponding author for this work

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

6 Scopus citations


We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with sampling-based approaches that are appropriate for higher dimensions. We suggest taking samples that are entire low-dimensional manifolds of the configuration space. These samples capture the connectivity of the configuration space much better than isolated point samples. Geometric algorithms then provide powerful primitive operations for complete analysis of the low-dimensional manifolds. We have implemented our framework for the concrete case of a polygonal robot translating and rotating amidst polygonal obstacles. To this end, we have developed a primitive operation for the analysis of an appropriate set of manifolds using arrangements of curves of rational functions. This modular integration of several carefully engineered components has lead to a significant speedup over the PRM sampling-based algorithm, which represents an approach that is prevalent in practice.

Original languageAmerican English
Title of host publicationAlgorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Number of pages13
StatePublished - 2011
Event19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany
Duration: 5 Sep 20119 Sep 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6942 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th Annual European Symposium on Algorithms, ESA 2011

Bibliographical note

Funding Information:
This work has been supported in part by the 7th Framework Programme for Research of the European Commission, under FET-Open grant number 255827 (CGL—Computational Geometry Learning), by the German-Israeli Foundation (grant no. 969/07), and by the Hermann Minkowski–Minerva Center for Geometry at Tel Aviv University.


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