---
_id: '22510'
abstract:
- lang: eng
text: 'Over the past decades, the Gathering problem, which asks to gather a group
of robots in finite time given some restrictions, has been intensively studied.
In this paper, we are given a group of n autonomous, dimensionless, deterministic,
and anonymous robots, with bounded viewing range. Assuming a continuous time model,
the goal is to gather these robots into one point in finite time. We introduce
a simple convergence criterion that defines a new class of algorithms which perform
gathering in O(nd) time, where d is the diameter of the initial robot configuration.
We show that some gathering algorithms in the literature belong to this class
and propose two new algorithms that belong to this class and have quadratic running
time, namely, Go-To-The-Relative-Center algorithm (GTRC) and Safe-Go-To-The-Relative-Center
algorithm (S-GTRC). We prove that the latter can perform gathering without collision
by using a slightly more complex robot model: non oblivious, chiral, and luminous
(i.e. robots have observable external memory, as in [8]). We also consider a variant
of the Gathering problem, the Near-Gathering problem, in which robots must get
close to each other without colliding. We show that S-GTRC solves the Near-Gathering
problem in quadratic time and assumes a weaker robot model than the one assumed
in the current state-of-the-art.'
author:
- first_name: Shouwei
full_name: Li, Shouwei
last_name: Li
- first_name: Christine
full_name: Markarian, Christine
last_name: Markarian
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
- first_name: Pavel
full_name: Podlipyan, Pavel
last_name: Podlipyan
citation:
ama: Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. A continuous strategy
for collisionless gathering. *Theoretical Computer Science*. 2021;852:41-60.
doi:10.1016/j.tcs.2020.10.037
apa: Li, S., Markarian, C., Meyer auf der Heide, F., & Podlipyan, P. (2021).
A continuous strategy for collisionless gathering. *Theoretical Computer Science*,
*852*, 41–60. https://doi.org/10.1016/j.tcs.2020.10.037
bibtex: '@article{Li_Markarian_Meyer auf der Heide_Podlipyan_2021, title={A continuous
strategy for collisionless gathering}, volume={852}, DOI={10.1016/j.tcs.2020.10.037},
journal={Theoretical Computer Science}, author={Li, Shouwei and Markarian, Christine
and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={41–60}
}'
chicago: 'Li, Shouwei, Christine Markarian, Friedhelm Meyer auf der Heide, and Pavel
Podlipyan. “A Continuous Strategy for Collisionless Gathering.” *Theoretical
Computer Science* 852 (2021): 41–60. https://doi.org/10.1016/j.tcs.2020.10.037.'
ieee: S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan, “A continuous
strategy for collisionless gathering,” *Theoretical Computer Science*, vol.
852, pp. 41–60, 2021.
mla: Li, Shouwei, et al. “A Continuous Strategy for Collisionless Gathering.” *Theoretical
Computer Science*, vol. 852, 2021, pp. 41–60, doi:10.1016/j.tcs.2020.10.037.
short: S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer
Science 852 (2021) 41–60.
date_created: 2021-06-28T09:24:15Z
date_updated: 2021-06-28T09:47:26Z
department:
- _id: '63'
doi: 10.1016/j.tcs.2020.10.037
intvolume: ' 852'
keyword:
- Local algorithms
- Distributed algorithms
- Collisionless gathering
- Mobile robots
- Multiagent system
language:
- iso: eng
page: 41-60
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
status: public
title: A continuous strategy for collisionless gathering
type: journal_article
user_id: '15415'
volume: 852
year: '2021'
...
---
_id: '22511'
abstract:
- lang: eng
text: "In this paper, we reconsider the well-known discrete, round-based Go-To-The-Center
algorithm due to Ando, Suzuki, and Yamashita [2] for gathering n autonomous mobile
robots with limited viewing range in the plane. Remarquably, this algorithm exploits
the fact that during its execution, many collisions of robots occur. Such collisions
are interpreted as a success because it is assumed that such collided robots behave
the same from now on. This is acceptable under the assumption that each robot
is represented by a single point. Otherwise, collisions should be avoided. In
this paper, we consider a continuous Go-To-The-Center algorithm in which the robots
continuously observe the positions of their neighbors and adapt their speed (assuming
a speed limit) and direction. Our first results are time bounds of O(n2) for gathering
in two dimensions Euclidean space, and Θ(n) for the one dimension. Our main contribution
is the introduction and evaluation of a continuous algorithm which performs Go-To-The-Center
considering only the neighbors of a robot with respect to the Gabriel subgraph
of the visibility graph, i.e. Go-To-The-Gabriel-Center algorithm. We show that
this modification still correctly executes gathering in one and two dimensions,
with the same time bounds as above. Simulations exhibit a severe difference of
the behavior of the Go-To-The-Center and the Go-To-The-Gabriel-Center algorithms:
Whereas lots of collisions occur during a run of the Go-To-The-Center algorithm,
typically only one, namely the final collision occurs during a run of the Go-To-The-Gabriel-Center
algorithm. We can prove this “collisionless property” of the Go-To-The-Gabriel-Center
algorithm for one dimension. In two-dimensional Euclidean space, we conjecture
that the “collisionless property” holds for almost every initial configuration.
We support our conjecture with measurements obtained from the simulation where
robots execute both continuous Go-To-The-Center and Go-To-The-Gabriel-Center algorithms.\r\n"
author:
- first_name: Shouwei
full_name: Li, Shouwei
last_name: Li
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
- first_name: Pavel
full_name: Podlipyan, Pavel
last_name: Podlipyan
citation:
ama: Li S, Meyer auf der Heide F, Podlipyan P. The impact of the Gabriel subgraph
of the visibility graph on the gathering of mobile autonomous robots. *Theoretical
Computer Science*. 2021;852:29-40. doi:10.1016/j.tcs.2020.11.009
apa: Li, S., Meyer auf der Heide, F., & Podlipyan, P. (2021). The impact of
the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous
robots. *Theoretical Computer Science*, *852*, 29–40. https://doi.org/10.1016/j.tcs.2020.11.009
bibtex: '@article{Li_Meyer auf der Heide_Podlipyan_2021, title={The impact of the
Gabriel subgraph of the visibility graph on the gathering of mobile autonomous
robots}, volume={852}, DOI={10.1016/j.tcs.2020.11.009},
journal={Theoretical Computer Science}, author={Li, Shouwei and Meyer auf der
Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={29–40} }'
chicago: 'Li, Shouwei, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “The
Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile
Autonomous Robots.” *Theoretical Computer Science* 852 (2021): 29–40. https://doi.org/10.1016/j.tcs.2020.11.009.'
ieee: S. Li, F. Meyer auf der Heide, and P. Podlipyan, “The impact of the Gabriel
subgraph of the visibility graph on the gathering of mobile autonomous robots,”
*Theoretical Computer Science*, vol. 852, pp. 29–40, 2021.
mla: Li, Shouwei, et al. “The Impact of the Gabriel Subgraph of the Visibility Graph
on the Gathering of Mobile Autonomous Robots.” *Theoretical Computer Science*,
vol. 852, 2021, pp. 29–40, doi:10.1016/j.tcs.2020.11.009.
short: S. Li, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer Science
852 (2021) 29–40.
date_created: 2021-06-28T09:34:45Z
date_updated: 2021-06-28T09:44:28Z
department:
- _id: '63'
doi: 10.1016/j.tcs.2020.11.009
intvolume: ' 852'
keyword:
- Local algorithms
- Distributed algorithms
- Collisionless gathering
- Mobile robots
- Multiagent system
language:
- iso: eng
page: 29-40
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
status: public
title: The impact of the Gabriel subgraph of the visibility graph on the gathering
of mobile autonomous robots
type: journal_article
user_id: '15415'
volume: 852
year: '2021'
...