Convergence of even simpler robots without position information

Debasish Pattanayak, Kaushik Mondal, Partha Sarathi Mandal, Stefan Schmid

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

The design of distributed gathering and convergence algorithms for tiny robots has recently received much attention. In particular, it has been shown that the convergence problem, that is, the problem of moving robots close to each other (i.e., inside an area of some maximum size, where the position of the area is not fixed beforehand), can even be solved for very weak, oblivious robots: robots which cannot maintain state from one round to the next. The oblivious robot model is hence attractive from a self-stabilization perspective, where the state is subject to adversarial manipulation. However, to the best of our knowledge, all existing robot convergence protocols rely on the assumption that robots, despite being “weak”, can measure distances. We in this paper initiate the study of convergence protocols for even simpler robots, called monoculus robots: robots which cannot measure distances. In particular, we introduce two natural models which relax the assumptions on the robots’ cognitive capabilities: (1) a Locality Detection (LD) model in which a robot can only detect whether another robot is closer than a given constant distance or not, (2) an Orthogonal Line Agreement (OLA) model in which robots only agree on a pair of orthogonal lines (say North-South and West-East, but without knowing which is which). The problem turns out to be non-trivial, as simple strategies like median and angle bisection can easily increase the distances among robots (e.g., the area of the enclosing convex hull) over time. Our main contribution is deterministic self-stabilizing convergence algorithms for these two models. We also show that in some sense, the assumptions made in our models are minimal: by relaxing the assumptions on the monoculus robots further, we run into impossibility results.

Original languageEnglish
Title of host publicationNetworked Systems - 5th International Conference, NETYS 2017, Proceedings
EditorsAmr El Abbadi, Benoit Garbinato
PublisherSpringer Verlag
Pages69-85
Number of pages17
ISBN (Print)9783319596464
DOIs
StatePublished - 1 Jan 2017
Externally publishedYes
Event5th International Conference on Networked Systems, NETYS 2017 - Marrakech, Morocco
Duration: 17 May 201719 May 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10299 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference5th International Conference on Networked Systems, NETYS 2017
Country/TerritoryMorocco
CityMarrakech
Period17/05/1719/05/17

Keywords

  • Asynchronous
  • Convergence
  • Distributed algorithm
  • Oblivious mobile robots
  • Weak robots

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