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

Yukiko Yamauchi, Taichi Uehara, Shuji Kijima, Masafumi Yamashita

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

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 languageEnglish
Title of host publicationDistributed Computing - 29th International Symposium, DISC 2015, Proceedings
EditorsYoram Moses
PublisherSpringer Verlag
Pages92-106
Number of pages15
ISBN (Print)9783662486528
DOIs
Publication statusPublished - Jan 1 2015
Event29th International Symposium on Distributed Computing, DISC 2015 - Tokyo, Japan
Duration: Oct 7 2015Oct 9 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9363
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other29th International Symposium on Distributed Computing, DISC 2015
CountryJapan
CityTokyo
Period10/7/1510/9/15

Fingerprint

Mobile Robot
Mobile robots
Euclidean space
Robot
Robots
Three-dimensional
Semiregular polyhedron
Swarm
Regular Icosahedron
Regular polyhedron
Regular polygon
Visual Perception
Mobile computing
Mobile Computing
Distributed computer systems
Self-organization
Pattern Formation
Distributed Computing
Sensor nodes
Intuitive

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Yamauchi, Y., Uehara, T., Kijima, S., & Yamashita, M. (2015). Plane formation by synchronous mobile robots in the three dimensional Euclidean space. In Y. Moses (Ed.), 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.

Distributed Computing - 29th International Symposium, DISC 2015, Proceedings. ed. / Yoram Moses. Springer Verlag, 2015. p. 92-106 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9363).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yamauchi, Y, Uehara, T, Kijima, S & Yamashita, M 2015, Plane formation by synchronous mobile robots in the three dimensional Euclidean space. in Y Moses (ed.), 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
Yamauchi Y, Uehara T, Kijima S, Yamashita M. Plane formation by synchronous mobile robots in the three dimensional Euclidean space. In Moses Y, editor, Distributed Computing - 29th International Symposium, DISC 2015, Proceedings. Springer Verlag. 2015. p. 92-106. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-662-48653-5_7
Yamauchi, Yukiko ; Uehara, Taichi ; Kijima, Shuji ; Yamashita, Masafumi. / Plane formation by synchronous mobile robots in the three dimensional Euclidean space. Distributed Computing - 29th International Symposium, DISC 2015, Proceedings. editor / Yoram Moses. Springer Verlag, 2015. pp. 92-106 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{2497895996bb4672b8413d045a37dd43,
title = "Plane formation by synchronous mobile robots in the three dimensional Euclidean space",
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.",
author = "Yukiko Yamauchi and Taichi Uehara and Shuji Kijima and Masafumi Yamashita",
year = "2015",
month = "1",
day = "1",
doi = "10.1007/978-3-662-48653-5_7",
language = "English",
isbn = "9783662486528",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "92--106",
editor = "Yoram Moses",
booktitle = "Distributed Computing - 29th International Symposium, DISC 2015, Proceedings",
address = "Germany",

}

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 -