### 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 language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 109-133 |

Number of pages | 25 |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11340 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*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

}

TY - CHAP

T1 - Symmetry of anonymous Robots

AU - Yamauchi, Yukiko

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

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UR - http://www.scopus.com/inward/citedby.url?scp=85061117610&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-11072-7_6

DO - 10.1007/978-3-030-11072-7_6

M3 - Chapter

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 109

EP - 133

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -