Shortest Coordinated Motion for Square Robots

Guillermo Esteban*, Dan Halperin, Víctor Ruíz, Vera Sacristán, Rodrigo I. Silveira

*Corresponding author for this work

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

3 Scopus citations

Abstract

We study the problem of determining minimum-length coordinated motions for two axis-aligned square robots translating in an obstacle-free plane: Given feasible start and goal configurations, find a continuous motion for the two squares from start to goal, comprising only robot-robot collision-free configurations, such that the total Euclidean distance traveled by the two squares is minimal among all possible such motions. We present an adaptation of the tools developed for the case of discs by Kirkpatrick and Liu [Characterizing minimum-length coordinated motions for two discs. Proceedings 28th CCCG, 252-259, 2016; CoRR abs/1607.04005, 2016.] to the case of squares. Certain aspects of the case of squares are more complicated, requiring additional and more involved arguments over the case of discs. Our contribution can serve as a basic component in optimizing the coordinated motion of two squares among obstacles, as well as for local planning in sampling-based algorithms, which are often used in practice, in the same setting.

Original languageEnglish
Title of host publicationAlgorithms and Data Structures - 18th International Symposium, WADS 2023, Proceedings
EditorsPat Morin, Subhash Suri
PublisherSpringer Science and Business Media Deutschland GmbH
Pages430-443
Number of pages14
ISBN (Print)9783031389054
DOIs
StatePublished - 2023
Event18th International Symposium on Algorithms and Data Structures, WADS 2023 - Montreal, Canada
Duration: 31 Jul 20232 Aug 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14079 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference18th International Symposium on Algorithms and Data Structures, WADS 2023
Country/TerritoryCanada
CityMontreal
Period31/07/232/08/23

Funding

FundersFunder number
Blavatnik Computer Science Research Fund
Center for Foundations of Modern Computer ScienceUNCE/SCI/004
Digital Research Centre Denmark
Lynn and William Frankel Center for Computer Sciences
US-Israel-BSF2019754
Yandex Machine Learning Initiative for Machine Learning
National Science FoundationCCF-2153723, 2212129, CCF 2049010, CCF-2300356, CCF-2005323, CCF 2107434, CCF-2007275, CCF 2046730
Defense Advanced Research Projects Agency
California Community Foundation
Microsoft
United States - Israel Binational Science Foundation
Horizon 2020 Framework Programme101019564
Innovationsfonden9142-00001B
Natural Sciences and Engineering Research Council of Canada
European Commission
Deutsche ForschungsgemeinschaftDI 2041/2
Japan Society for the Promotion of ScienceJP20K11670, JP20K11692, JP19K11814, JP22H05001, JP20H05793, JP20H05795, JP21H03397, JP23K10982
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung204320
Grantová Agentura České Republiky22-19073S
Nederlandse Organisatie voor Wetenschappelijk OnderzoekNETWORKS-024.002.003
Ministero dell’Istruzione, dell’Università e della RicercaPNRR CN00000013, PRIN 20174LF3T8
Università degli Studi di Padova
Ministry of Science, ICT and Future Planning
National Research Foundation of Korea
Israel Science Foundation1736/19
Tel Aviv University
Ministerio de Ciencia e Innovación
Ministry of Science and Technology, Israel103129
Danmarks Frie Forskningsfond9131-00113B
Exploratory Research Center on Life and Living Systems, National Institutes of Natural SciencesDFF-0135-00018B
National Science and Technology Council110-2221-E-007-043

    Keywords

    • Coordinated motions
    • Geometric algorithms
    • Motion planning

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