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

12 Citations (Scopus)


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
Number of pages15
ISBN (Print)9783662486528
Publication statusPublished - 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)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other29th International Symposium on Distributed Computing, DISC 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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