Motion planning via manifold samples

Oren Salzman; Michael Hemmer; Barak Raveh; Dan Halperin

doi:10.1007/978-3-642-23719-5_42

Motion planning via manifold samples

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

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Scopus citations

Abstract

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 language	English
Title of host publication	Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings
Pages	493-505
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-642-23719-5_42
State	Published - 2011
Event	19th Annual European Symposium on Algorithms, ESA 2011 - Saarbrucken, Germany Duration: 5 Sep 2011 → 9 Sep 2011

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	6942 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th Annual European Symposium on Algorithms, ESA 2011
Country/Territory	Germany
City	Saarbrucken
Period	5/09/11 → 9/09/11

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.

Access to Document

10.1007/978-3-642-23719-5_42

Cite this

Salzman, O., Hemmer, M., Raveh, B., & Halperin, D. (2011). Motion planning via manifold samples. In Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings (pp. 493-505). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6942 LNCS). https://doi.org/10.1007/978-3-642-23719-5_42

@inproceedings{0d506e8e2cdf4f4a85a63c4de08a9d73,

title = "Motion planning via manifold samples",

abstract = "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.",

author = "Oren Salzman and Michael Hemmer and Barak Raveh and Dan Halperin",

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.; 19th Annual European Symposium on Algorithms, ESA 2011 ; Conference date: 05-09-2011 Through 09-09-2011",

year = "2011",

doi = "10.1007/978-3-642-23719-5_42",

language = "אנגלית",

isbn = "9783642237188",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

pages = "493--505",

booktitle = "Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings",

}

Salzman, O, Hemmer, M, Raveh, B & Halperin, D 2011, Motion planning via manifold samples. in Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6942 LNCS, pp. 493-505, 19th Annual European Symposium on Algorithms, ESA 2011, Saarbrucken, Germany, 5/09/11. https://doi.org/10.1007/978-3-642-23719-5_42

Motion planning via manifold samples. / Salzman, Oren; Hemmer, Michael; Raveh, Barak et al.
Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings. 2011. p. 493-505 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6942 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Motion planning via manifold samples

AU - Salzman, Oren

AU - Hemmer, Michael

AU - Raveh, Barak

AU - Halperin, Dan

N1 - 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.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80052811551&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-23719-5_42

DO - 10.1007/978-3-642-23719-5_42

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:80052811551

SN - 9783642237188

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 493

EP - 505

BT - Algorithms, ESA 2011 - 19th Annual European Symposium, Proceedings

T2 - 19th Annual European Symposium on Algorithms, ESA 2011

Y2 - 5 September 2011 through 9 September 2011

ER -

Motion planning via manifold samples

Abstract

Publication series

Conference

Bibliographical note

Access to Document

Other files and links

Fingerprint

Cite this