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


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
Number of pages14
ISBN (Print)9783031389054
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


Conference18th International Symposium on Algorithms and Data Structures, WADS 2023


  • Coordinated motions
  • Geometric algorithms
  • Motion planning


Dive into the research topics of 'Shortest Coordinated Motion for Square Robots'. Together they form a unique fingerprint.

Cite this