Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case
We consider the distributed setting of <i>N</i> autonomous mobile robots that operate in <i>Look-Compute-Move</i> (LCM) cycles and use colored lights (the <i>robots with lights</i> model). We assume <i>obstructed visibility</i> where a robot cannot see...
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doaj-62e670f4d46b4543b5fb1f5240d79df12021-02-10T00:04:36ZengMDPI AGAlgorithms1999-48932021-02-0114565610.3390/a14020056Constant-Time Complete Visibility for Robots with Lights: The Asynchronous CaseGokarna Sharma0Ramachandran Vaidyanathan1Jerry L. Trahan2Department of Computer Science, Kent State University, Kent, OH 44242, USAElectrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA 70803, USAElectrical Engineering and Computer Science, Louisiana State University, Baton Rouge, LA 70803, USAWe consider the distributed setting of <i>N</i> autonomous mobile robots that operate in <i>Look-Compute-Move</i> (LCM) cycles and use colored lights (the <i>robots with lights</i> model). We assume <i>obstructed visibility</i> where a robot cannot see another robot if a third robot is positioned between them on the straight line segment connecting them. In this paper, we consider the problem of positioning <i>N</i> autonomous robots on a plane so that every robot is visible to all others (this is called the <span style="font-variant: small-caps">Complete Visibility</span> problem). This problem is fundamental, as it provides a basis to solve many other problems under obstructed visibility. In this paper, we provide the first, asymptotically optimal, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> time, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> color algorithm for <span style="font-variant: small-caps">Complete Visibility</span> in the asynchronous setting. This significantly improves on an <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula>-time translation of the existing <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> time, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> color semi-synchronous algorithm to the asynchronous setting. The proposed algorithm is <i>collision-free</i>, i.e., robots do not share positions, and their paths do not cross. We also introduce a new technique for moving robots in an asynchronous setting that may be of independent interest, called Beacon-Directed Curve Positioning.https://www.mdpi.com/1999-4893/14/2/56distributed algorithmsautonomous mobile robotsrobots with lightscomplete visibilitycollisionsconvex hull |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Gokarna Sharma Ramachandran Vaidyanathan Jerry L. Trahan |
spellingShingle |
Gokarna Sharma Ramachandran Vaidyanathan Jerry L. Trahan Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case Algorithms distributed algorithms autonomous mobile robots robots with lights complete visibility collisions convex hull |
author_facet |
Gokarna Sharma Ramachandran Vaidyanathan Jerry L. Trahan |
author_sort |
Gokarna Sharma |
title |
Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case |
title_short |
Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case |
title_full |
Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case |
title_fullStr |
Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case |
title_full_unstemmed |
Constant-Time Complete Visibility for Robots with Lights: The Asynchronous Case |
title_sort |
constant-time complete visibility for robots with lights: the asynchronous case |
publisher |
MDPI AG |
series |
Algorithms |
issn |
1999-4893 |
publishDate |
2021-02-01 |
description |
We consider the distributed setting of <i>N</i> autonomous mobile robots that operate in <i>Look-Compute-Move</i> (LCM) cycles and use colored lights (the <i>robots with lights</i> model). We assume <i>obstructed visibility</i> where a robot cannot see another robot if a third robot is positioned between them on the straight line segment connecting them. In this paper, we consider the problem of positioning <i>N</i> autonomous robots on a plane so that every robot is visible to all others (this is called the <span style="font-variant: small-caps">Complete Visibility</span> problem). This problem is fundamental, as it provides a basis to solve many other problems under obstructed visibility. In this paper, we provide the first, asymptotically optimal, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> time, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> color algorithm for <span style="font-variant: small-caps">Complete Visibility</span> in the asynchronous setting. This significantly improves on an <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mi>N</mi><mo>)</mo></mrow></semantics></math></inline-formula>-time translation of the existing <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> time, <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> color semi-synchronous algorithm to the asynchronous setting. The proposed algorithm is <i>collision-free</i>, i.e., robots do not share positions, and their paths do not cross. We also introduce a new technique for moving robots in an asynchronous setting that may be of independent interest, called Beacon-Directed Curve Positioning. |
topic |
distributed algorithms autonomous mobile robots robots with lights complete visibility collisions convex hull |
url |
https://www.mdpi.com/1999-4893/14/2/56 |
work_keys_str_mv |
AT gokarnasharma constanttimecompletevisibilityforrobotswithlightstheasynchronouscase AT ramachandranvaidyanathan constanttimecompletevisibilityforrobotswithlightstheasynchronouscase AT jerryltrahan constanttimecompletevisibilityforrobotswithlightstheasynchronouscase |
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