Motion planning for unlabeled discs with optimality guarantees

Kiril Solovey; Jingjin Yu; Or Zamir; Dan Halperin

doi:10.15607/RSS.2015.XI.011

Motion planning for unlabeled discs with optimality guarantees

Kiril Solovey, Jingjin Yu, Or Zamir, Dan Halperin

School of Computer Science

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

61 Scopus citations

Abstract

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time Õ(m⁴ + m²n²), where m is the number of robots and n is the total complexity of the workspace. Moreover, the total length of the returned solution is at most OPT+4m, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency.

Original language	English
Title of host publication	Robotics
Subtitle of host publication	Science and Systems XI, RSS 2015
Editors	Jonas Buchli, David Hsu, Lydia E. Kavraki
Publisher	MIT Press
ISBN (Electronic)	9780992374716
DOIs	https://doi.org/10.15607/RSS.2015.XI.011
State	Published - 2015
Event	2015 Robotics: Science and Systems Conference, RSS 2015 - Rome, Italy Duration: 13 Jul 2015 → 17 Jul 2015

Publication series

Name	Robotics: Science and Systems
Volume	11
ISSN (Electronic)	2330-765X

Conference

Conference	2015 Robotics: Science and Systems Conference, RSS 2015
Country/Territory	Italy
City	Rome
Period	13/07/15 → 17/07/15

Funding

Funders	Funder number
Computer Science and Artificial Intelligence Lab
Hermann Minkowski-MINERVA Center for Geometry
Office of Naval Research	N00014-09-1-1051, N00014-12-1-1000
German-Israeli Foundation for Scientific Research and Development	1150-82.6/2011
Israel Science Foundation	1102/11
Tel Aviv University

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10.15607/RSS.2015.XI.011

Cite this

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title = "Motion planning for unlabeled discs with optimality guarantees",

abstract = "We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time {\~O}(m4 + m2n2), where m is the number of robots and n is the total complexity of the workspace. Moreover, the total length of the returned solution is at most OPT+4m, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency.",

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AB - We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time Õ(m4 + m2n2), where m is the number of robots and n is the total complexity of the workspace. Moreover, the total length of the returned solution is at most OPT+4m, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency.

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Motion planning for unlabeled discs with optimality guarantees

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