Abstract
A swarm of anonymous oblivious mobile robots, operating in deterministic LookComputeMove cycles, is confined within a circular track. All robots agree on the clockwise direction (chirality), they are activated by an adversarial semisynchronous 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 PatternFormation problems.
BibTeX  Entry
@InProceedings{diluna_et_al:LIPIcs:2020:13090,
author = {Giuseppe A. Di Luna and Ryuhei Uehara and Giovanni Viglietta and Yukiko Yamauchi},
title = {{Gathering on a Circle with Limited Visibility by Anonymous Oblivious Robots}},
booktitle = {34th International Symposium on Distributed Computing (DISC 2020)},
pages = {12:112:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771689},
ISSN = {18688969},
year = {2020},
volume = {179},
editor = {Hagit Attiya},
publisher = {Schloss DagstuhlLeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13090},
URN = {urn:nbn:de:0030drops130907},
doi = {10.4230/LIPIcs.DISC.2020.12},
annote = {Keywords: Mobile robots, Gathering, limited visibility, circle}
}
Keywords: 

Mobile robots, Gathering, limited visibility, circle 
Collection: 

34th International Symposium on Distributed Computing (DISC 2020) 
Issue Date: 

2020 
Date of publication: 

07.10.2020 