Plane formation by synchronous mobile robots without chirality

Yusaku Tomita, Yukiko Yamauchi, Shuji Kijima, Masafumi Yamashita

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

5 Citations (Scopus)


We consider a distributed system consisting of autonomous mobile computing entities called robots moving in the three-dimensional space (3D-space). The robots are anonymous, oblivious, fully-synchronous and have neither any access to the global coordinate system nor any explicit communication medium. Each robot cooperates with other robots by observing the positions of other robots in its local coordinate system. One of the most fundamental agreement problems in 3D-space is the plane formation problem that requires the robots to land on a common plane, that is not predefined. This problem is not always solvable because of the impossibility of symmetry breaking. While existing results assume that the robots agree on the handedness of their local coordinate systems, we remove the assumption and consider the robots without chirality. The robots without chirality can never break the symmetry consisting of rotation symmetry and reflection symmetry. Such symmetry in 3D-space is fully described by 17 symmetry types each of which forms a group. We extend the notion of symmetricity [Suzuki and Yamashita, SIAM J. Compt. 1999] [Yamauchi et al., PODC 2016] to cover these 17 symmetry groups. Then we give a characterization of initial configurations from which the fully-synchronous robots without chirality can form a plane in terms of symmetricity.

Original languageEnglish
Title of host publication21st International Conference on Principles of Distributed Systems, OPODIS 2017
EditorsJames Aspnes, Joao Leitao, Alysson Bessani, Pascal Felber
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770613
Publication statusPublished - Mar 1 2018
Event21st International Conference on Principles of Distributed Systems, OPODIS 2017 - Lisboa, Portugal
Duration: Dec 18 2017Dec 20 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Other21st International Conference on Principles of Distributed Systems, OPODIS 2017

All Science Journal Classification (ASJC) codes

  • Software


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