License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.DISC.2018.19
URN: urn:nbn:de:0030-drops-98086
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Di Luna, Giuseppe A. ; Flocchini, Paola ; Santoro, Nicola ; Viglietta, Giovanni

TuringMobile: A Turing Machine of Oblivious Mobile Robots with Limited Visibility and Its Applications

LIPIcs-DISC-2018-19.pdf (0.5 MB)


In this paper we investigate the computational power of a set of mobile robots with limited visibility. At each iteration, a robot takes a snapshot of its surroundings, uses the snapshot to compute a destination point, and it moves toward its destination. Each robot is punctiform and memoryless, it operates in R^m, it has a local reference system independent of the other robots' ones, and is activated asynchronously by an adversarial scheduler. Moreover, the robots are non-rigid, in that they may be stopped by the scheduler at each move before reaching their destination (but are guaranteed to travel at least a fixed unknown distance before being stopped).
We show that despite these strong limitations, it is possible to arrange 3m+3k of these weak entities in R^m to simulate the behavior of a stronger robot that is rigid (i.e., it always reaches its destination) and is endowed with k registers of persistent memory, each of which can store a real number. We call this arrangement a TuringMobile. In its simplest form, a TuringMobile consisting of only three robots can travel in the plane and store and update a single real number. We also prove that this task is impossible with fewer than three robots.
Among the applications of the TuringMobile, we focused on Near-Gathering (all robots have to gather in a small-enough disk) and Pattern Formation (of which Gathering is a special case) with limited visibility. Interestingly, our investigation implies that both problems are solvable in Euclidean spaces of any dimension, even if the visibility graph of the robots is initially disconnected, provided that a small amount of these robots are arranged to form a TuringMobile. In the special case of the plane, a basic TuringMobile of only three robots is sufficient.

BibTeX - Entry

  author =	{Giuseppe A. Di Luna and Paola Flocchini and Nicola Santoro and Giovanni Viglietta},
  title =	{{TuringMobile: A Turing Machine of Oblivious Mobile Robots with Limited Visibility and Its Applications}},
  booktitle =	{32nd International Symposium on Distributed Computing  (DISC 2018)},
  pages =	{19:1--19:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-092-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{121},
  editor =	{Ulrich Schmid and Josef Widder},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-98086},
  doi =		{10.4230/LIPIcs.DISC.2018.19},
  annote =	{Keywords: Mobile Robots, Turing Machine, Real RAM}

Keywords: Mobile Robots, Turing Machine, Real RAM
Collection: 32nd International Symposium on Distributed Computing (DISC 2018)
Issue Date: 2018
Date of publication: 04.10.2018

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