Gathering on a circle with limited visibility by anonymous oblivious robots

Giuseppe A. Di Luna, Ryuhei Uehara, Giovanni Viglietta, Yukiko Yamauchi

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

Abstract

A swarm of anonymous oblivious mobile robots, operating in deterministic Look-Compute-Move cycles, is confined within a circular track. All robots agree on the clockwise direction (chirality), they are activated by an adversarial semi-synchronous scheduler (SSYNCH), and an active robot always reaches the destination point it computes (rigidity). Robots have limited visibility: each robot can see only the points on the circle that have an angular distance strictly smaller than a constant ϑ from the robot's current location, where 0 < ϑ ≤ π (angles are expressed in radians). We study the Gathering problem for such a swarm of robots: that is, all robots are initially in distinct locations on the circle, and their task is to reach the same point on the circle in a finite number of turns, regardless of the way they are activated by the scheduler. Note that, due to the anonymity of the robots, this task is impossible if the initial configuration is rotationally symmetric; hence, we have to make the assumption that the initial configuration be rotationally asymmetric. We prove that, if ϑ = π (i.e., each robot can see the entire circle except its antipodal point), there is a distributed algorithm that solves the Gathering problem for swarms of any size. By contrast, we also prove that, if ϑ ≤ π/2, no distributed algorithm solves the Gathering problem, regardless of the size of the swarm, even under the assumption that the initial configuration is rotationally asymmetric and the visibility graph of the robots is connected. The latter impossibility result relies on a probabilistic technique based on random perturbations, which is novel in the context of anonymous mobile robots. Such a technique is of independent interest, and immediately applies to other Pattern-Formation problems.

Original languageEnglish
Title of host publication34th International Symposium on Distributed Computing, DISC 2020
EditorsHagit Attiya
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771689
DOIs
Publication statusPublished - Oct 1 2020
Event34th International Symposium on Distributed Computing, DISC 2020 - Virtual, Online
Duration: Oct 12 2020Oct 16 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume179
ISSN (Print)1868-8969

Conference

Conference34th International Symposium on Distributed Computing, DISC 2020
CityVirtual, Online
Period10/12/2010/16/20

All Science Journal Classification (ASJC) codes

  • Software

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