Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds

Bahareh Banyassady*, Mark de Berg*, Karl Bringmann*, Kevin Buchin*, Henning Fernau*, Dan Halperin*, Irina Kostitsyna*, Yoshio Okamoto*, Stijn Slot*

*Corresponding author for this work

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

4 Scopus citations

Abstract

We consider the unlabeled motion-planning problem of m unit-disc robots moving in a simple polygonal workspace of n edges. The goal is to find a motion plan that moves the robots to a given set of m target positions. For the unlabeled variant, it does not matter which robot reaches which target position as long as all target positions are occupied in the end. If the workspace has narrow passages such that the robots cannot fit through them, then the free configuration space, representing all possible unobstructed positions of the robots, will consist of multiple connected components. Even if in each component of the free space the number of targets matches the number of start positions, the motion-planning problem does not always have a solution when the robots and their targets are positioned very densely. In this paper, we prove tight bounds on how much separation between start and target positions is necessary to always guarantee a solution. Moreover, we describe an algorithm that always finds a solution in time O(n log n + mn + m2) if the separation bounds are met. Specifically, we prove that the following separation is sufficient: any two start positions are at least distance 4 apart, any two target positions are at least distance 4 apart, and any pair of a start and a target positions is at least distance 3 apart. We further show that when the free space consists of a single connected component, the separation between start and target positions is not necessary.

Original languageEnglish
Title of host publication38th International Symposium on Computational Geometry, SoCG 2022
EditorsXavier Goaoc, Michael Kerber
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772273
DOIs
StatePublished - 1 Jun 2022
Externally publishedYes
Event38th International Symposium on Computational Geometry, SoCG 2022 - Berlin, Germany
Duration: 7 Jun 202210 Jun 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume224
ISSN (Print)1868-8969

Conference

Conference38th International Symposium on Computational Geometry, SoCG 2022
Country/TerritoryGermany
CityBerlin
Period7/06/2210/06/22

Funding

FundersFunder number
Blavatnik Computer Science Research Fund
US-Israel-BSF2019754
Yandex Machine Learning Initiative for Machine Learning
National Science Foundation
Japan Society for the Promotion of ScienceJP20K11670, JP20H05795
Nederlandse Organisatie voor Wetenschappelijk OnderzoekNETWORKS-024.002.003
Israel Science Foundation1736/19
Tel Aviv University
Ministry of Science and Technology, Israel103129

    Keywords

    • computational geometry
    • motion planning
    • simple polygon

    Fingerprint

    Dive into the research topics of 'Unlabeled Multi-Robot Motion Planning with Tighter Separation Bounds'. Together they form a unique fingerprint.

    Cite this