Symmetry of anonymous Robots

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Symmetry of anonymous mobile Robots imposes many impossibilities. We focus on the formation problem that requires the Robots to form a target pattern. We consider the Robots moving in the three-dimensional space and the two-dimensional space (3D and 2D space, respectively) and introduce the notion of symmetricity of a set of points that represents the set of rotation groups that the Robots cannot resolve. However, the symmetricity does not always match the rotational symmetry of geometric positions of the Robots. We demonstrate that the Robots are capable of breaking symmetry by their movement in some cases. The goal of this chapter is to present the following characterization of formable patterns; anonymous synchronous mobile Robots in 3D space or 2D space can form a target pattern from an initial configuration if and only if the symmetricity of an initial configuration is a subset of the symmetricity of the target pattern.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages109-133
Number of pages25
DOIs
Publication statusPublished - Jan 1 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11340 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Fingerprint

Robot
Robots
Symmetry
Mobile Robot
Mobile robots
Target
Rotation Group
Configuration
Rotational symmetry
Symmetry Breaking
Set of points
Resolve
If and only if
Three-dimensional
Subset
Demonstrate

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yamauchi, Y. (2019). Symmetry of anonymous Robots. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 109-133). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11340 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-11072-7_6

Symmetry of anonymous Robots. / Yamauchi, Yukiko.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag, 2019. p. 109-133 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11340 LNCS).

Research output: Chapter in Book/Report/Conference proceedingChapter

Yamauchi, Y 2019, Symmetry of anonymous Robots. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11340 LNCS, Springer Verlag, pp. 109-133. https://doi.org/10.1007/978-3-030-11072-7_6
Yamauchi Y. Symmetry of anonymous Robots. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2019. p. 109-133. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-11072-7_6
Yamauchi, Yukiko. / Symmetry of anonymous Robots. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag, 2019. pp. 109-133 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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