---
res:
bibo_abstract:
- "In this work, we initiate the research about the Gathering problem for robots\r\nwith
limited viewing range in the three-dimensional Euclidean space. In the\r\nGathering
problem, a set of initially scattered robots is required to gather at\r\nthe same
position. The robots' capabilities are very restricted -- they do not\r\nagree
on any coordinate system or compass, have a limited viewing range, have\r\nno
memory of the past and cannot communicate. We study the problem in two\r\ndifferent
time models, in FSYNC (fully synchronized discrete rounds) and the\r\ncontinuous
time model. For FSYNC, we introduce the 3D-Go-To-The-Center-strategy\r\nand prove
a runtime of $\\Theta(n^2)$ that matches the currently best runtime\r\nbound for
the same model in the Euclidean plane [SPAA'11]. Our main result is\r\nthe generalization
of contracting strategies (continuous time) from\r\n[Algosensors'17] to three
dimensions. In contracting strategies, every robot\r\nthat is located on the global
convex hull of all robots' positions moves with\r\nfull speed towards the inside
of the convex hull. We prove a runtime bound of\r\n$O(\\Delta \\cdot n^{3/2})$
for any three-dimensional contracting strategy, where\r\n$\\Delta$ denotes the
diameter of the initial configuration. This comes up to a\r\nfactor of $\\sqrt{n}$
close to the lower bound of $\\Omega (\\Delta \\cdot n)$\r\nwhich is already true
in two dimensions. In general, it might be hard for\r\nrobots with limited viewing
range to decide whether they are located on the\r\nglobal convex hull and which
movement maintains the connectivity of the swarm,\r\nrendering the design of concrete
contracting strategies a challenging task. We\r\nprove that the continuous variant
of 3D-Go-To-The-Center is contracting and\r\nkeeps the swarm connected. Moreover,
we give a simple design criterion for\r\nthree-dimensional contracting strategies
that maintains the connectivity of the\r\nswarm and introduce an exemplary strategy
based on this criterion.@eng"
- Best Student Paper Award@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Michael
foaf_name: Braun, Michael
foaf_surname: Braun
- foaf_Person:
foaf_givenName: Jannik
foaf_name: Castenow, Jannik
foaf_surname: Castenow
foaf_workInfoHomepage: http://www.librecat.org/personId=38705
- foaf_Person:
foaf_givenName: Friedhelm
foaf_name: Meyer auf der Heide, Friedhelm
foaf_surname: Meyer auf der Heide
foaf_workInfoHomepage: http://www.librecat.org/personId=15523
bibo_doi: 10.1007/978-3-030-54921-3_4
dct_date: 2020^xs_gYear
dct_language: eng
dct_publisher: Springer@
dct_title: Local Gathering of Mobile Robots in Three Dimensions@
...