### Abstract

Creating a swarm of mobile computing entities frequently called robots, agents or sensor nodes, with self-organization ability is a contemporary challenge in distributed computing. Motivated by this, this paper investigates the plane formation problem that requires a swarm of robots moving in the three dimensional Euclidean space to reside in a common plane. The robots are fully synchronous and endowed with visual perception. But they have neither identifiers, access to the global coordinate system, any means of explicit communication with each other, nor memory of past. Though there are plenty of results on the agreement problem for robots in the two dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first result for robots in the three dimensional space. This paper presents a necessary and sufficient condition to solve the plane formation problem. An implication of the result is somewhat counter-intuitive: The robots cannot form a plane from most of the semi-regular polyhedra, while they can from every regular polyhedron (except a regular icosahedron), which consists of the same regular polygon faces and the robots on its vertices are “more” symmetric than semi-regular polyhedra.

Original language | English |
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Title of host publication | Distributed Computing - 29th International Symposium, DISC 2015, Proceedings |

Editors | Yoram Moses |

Publisher | Springer Verlag |

Pages | 92-106 |

Number of pages | 15 |

ISBN (Print) | 9783662486528 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Event | 29th International Symposium on Distributed Computing, DISC 2015 - Tokyo, Japan Duration: Oct 7 2015 → Oct 9 2015 |

### 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 | 9363 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 29th International Symposium on Distributed Computing, DISC 2015 |
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Country | Japan |

City | Tokyo |

Period | 10/7/15 → 10/9/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Distributed Computing - 29th International Symposium, DISC 2015, Proceedings*(pp. 92-106). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9363). Springer Verlag. https://doi.org/10.1007/978-3-662-48653-5_7

**Plane formation by synchronous mobile robots in the three dimensional Euclidean space.** / Yamauchi, Yukiko; Uehara, Taichi; Kijima, Shuji; Yamashita, Masafumi.

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

*Distributed Computing - 29th International Symposium, DISC 2015, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9363, Springer Verlag, pp. 92-106, 29th International Symposium on Distributed Computing, DISC 2015, Tokyo, Japan, 10/7/15. https://doi.org/10.1007/978-3-662-48653-5_7

}

TY - GEN

T1 - Plane formation by synchronous mobile robots in the three dimensional Euclidean space

AU - Yamauchi, Yukiko

AU - Uehara, Taichi

AU - Kijima, Shuji

AU - Yamashita, Masafumi

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Creating a swarm of mobile computing entities frequently called robots, agents or sensor nodes, with self-organization ability is a contemporary challenge in distributed computing. Motivated by this, this paper investigates the plane formation problem that requires a swarm of robots moving in the three dimensional Euclidean space to reside in a common plane. The robots are fully synchronous and endowed with visual perception. But they have neither identifiers, access to the global coordinate system, any means of explicit communication with each other, nor memory of past. Though there are plenty of results on the agreement problem for robots in the two dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first result for robots in the three dimensional space. This paper presents a necessary and sufficient condition to solve the plane formation problem. An implication of the result is somewhat counter-intuitive: The robots cannot form a plane from most of the semi-regular polyhedra, while they can from every regular polyhedron (except a regular icosahedron), which consists of the same regular polygon faces and the robots on its vertices are “more” symmetric than semi-regular polyhedra.

AB - Creating a swarm of mobile computing entities frequently called robots, agents or sensor nodes, with self-organization ability is a contemporary challenge in distributed computing. Motivated by this, this paper investigates the plane formation problem that requires a swarm of robots moving in the three dimensional Euclidean space to reside in a common plane. The robots are fully synchronous and endowed with visual perception. But they have neither identifiers, access to the global coordinate system, any means of explicit communication with each other, nor memory of past. Though there are plenty of results on the agreement problem for robots in the two dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first result for robots in the three dimensional space. This paper presents a necessary and sufficient condition to solve the plane formation problem. An implication of the result is somewhat counter-intuitive: The robots cannot form a plane from most of the semi-regular polyhedra, while they can from every regular polyhedron (except a regular icosahedron), which consists of the same regular polygon faces and the robots on its vertices are “more” symmetric than semi-regular polyhedra.

UR - http://www.scopus.com/inward/record.url?scp=84946042376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84946042376&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-48653-5_7

DO - 10.1007/978-3-662-48653-5_7

M3 - Conference contribution

AN - SCOPUS:84946042376

SN - 9783662486528

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

SP - 92

EP - 106

BT - Distributed Computing - 29th International Symposium, DISC 2015, Proceedings

A2 - Moses, Yoram

PB - Springer Verlag

ER -