Search by a Metamorphic Robotic System in a Finite 3D Cubic Grid

Ryonosuke Yamada, Yukiko Yamauchi

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

Abstract

We consider search in a finite 3D cubic grid by a metamorphic robotic system (MRS), that consists of anonymous modules. A module can perform a sliding and rotation while the whole modules keep connectivity. As the number of modules increases, the variety of actions that the MRS can perform increases. The search problem requires the MRS to find a target in a given finite field. Doi et al. (SSS 2018) demonstrate a necessary and sufficient number of modules for search in a finite 2D square grid. We consider search in a finite 3D cubic grid and investigate the effect of common knowledge. We consider three different settings. First, we show that three modules are necessary and sufficient when all modules are equipped with a common compass, i.e., they agree on the direction and orientation of the x, y, and z axes. Second, we show that four modules are necessary and sufficient when all modules agree on the direction and orientation of the vertical axis. Finally, we show that five modules are necessary and sufficient when all modules are not equipped with a common compass. Our results show that the shapes of the MRS in the 3D cubic grid have richer structure than those in the 2D square grid.

Original languageEnglish
Title of host publication1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022
EditorsJames Aspnes, Othon Michail
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772242
DOIs
Publication statusPublished - Apr 1 2022
Event1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022 - Virtual, Online
Duration: Mar 28 2022Mar 30 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume221
ISSN (Print)1868-8969

Conference

Conference1st Symposium on Algorithmic Foundations of Dynamic Networks, SAND 2022
CityVirtual, Online
Period3/28/223/30/22

All Science Journal Classification (ASJC) codes

  • Software

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