Separating Bounded and Unbounded Asynchrony for Autonomous Robots: Point Convergence with Limited Visibility
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| Title: | Separating Bounded and Unbounded Asynchrony for Autonomous Robots: Point Convergence with Limited Visibility |
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| Authors: | Kirkpatrick D., Kostitsyna I., Navarra A., Prencipe G., Santoro N. |
| Source: | Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing. :9-19 |
| Publication Status: | Preprint |
| Publisher Information: | ACM, 2021. |
| Publication Year: | 2021 |
| Subject Terms: | Computational Geometry (cs.CG), FOS: Computer and information sciences, 0102 computer and information sciences, 02 engineering and technology, distributed geometric algorithms, 01 natural sciences, Computer Science - Robotics, Computer Science - Distributed, Parallel, and Cluster Computing, mobile robots, asynchrony, 0202 electrical engineering, electronic engineering, information engineering, Computer Science - Computational Geometry, Distributed, Parallel, and Cluster Computing (cs.DC), Robotics (cs.RO) |
| Description: | Among fundamental problems in the context of distributed computing by autonomous mobile entities, one of the most representative and well studied is {\sc Point Convergence}: given an arbitrary initial configuration of identical entities, disposed in the Euclidean plane, move in such a way that, for all $\eps>0$, a configuration in which the separation between all entities is at most $\eps$ is eventually reached and maintained. The problem has been previously studied in a variety of settings, including full visibility, exact measurements (like distances and angles), and synchronous activation of entities. Our study concerns the minimal assumptions under which entities, moving asynchronously with limited and unknown visibility range and subject to limited imprecision in measurements, can be guaranteed to converge in this way. We present an algorithm that solves {\sc Point Convergence}, for entities in the plane, in such a setting, provided the degree of asynchrony is bounded: while any one entity is active, any other entity can be activated at most $k$ times, for some arbitrarily large but fixed $k$. This provides a strong positive answer to a decade old open question posed by Katreniak. We also prove that in a comparable setting that permits unbounded asynchrony, {\sc Point Convergence} in the plane is impossible, contingent on the natural assumption that algorithms maintain the (visible) connectivity among entities present in the initial configuration. This variant, that we call {\sc Cohesive Convergence}, serves to distinguish the power of bounded and unbounded asynchrony in the control of autonomous mobile entities, settling at the same time a long-standing question whether in the Euclidean plane synchronously scheduled entities are more powerful than asynchronously scheduled entities. |
| Document Type: | Article Conference object |
| File Description: | application/pdf |
| DOI: | 10.1145/3465084.3467910 |
| DOI: | 10.48550/arxiv.2105.13042 |
| Access URL: | http://arxiv.org/abs/2105.13042 https://dblp.uni-trier.de/db/journals/corr/corr2105.html#abs-2105-13042 https://research.tue.nl/en/publications/separating-bounded-and-unbounded-asynchrony-for-autonomous-robots https://research.unipg.it/handle/11391/1495720 https://www.podc.org/podc2021/list-of-accepted-papers/#11 https://dl.acm.org/doi/pdf/10.1145/3465084.3467910 https://doi.org/10.1145/3465084.3467910 https://dl.acm.org/doi/10.1145/3465084.3467910 https://doi.org/10.1145/3465084.3467910 https://hdl.handle.net/11568/1115021 https://hdl.handle.net/11391/1495720 https://doi.org/10.1145/3465084.3467910 |
| Rights: | CC BY URL: https://www.acm.org/publications/policies/copyright_policy#Background |
| Accession Number: | edsair.doi.dedup.....8e152965cac3f3fc71df7f804df221ba |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | Among fundamental problems in the context of distributed computing by autonomous mobile entities, one of the most representative and well studied is {\sc Point Convergence}: given an arbitrary initial configuration of identical entities, disposed in the Euclidean plane, move in such a way that, for all $\eps>0$, a configuration in which the separation between all entities is at most $\eps$ is eventually reached and maintained. The problem has been previously studied in a variety of settings, including full visibility, exact measurements (like distances and angles), and synchronous activation of entities. Our study concerns the minimal assumptions under which entities, moving asynchronously with limited and unknown visibility range and subject to limited imprecision in measurements, can be guaranteed to converge in this way. We present an algorithm that solves {\sc Point Convergence}, for entities in the plane, in such a setting, provided the degree of asynchrony is bounded: while any one entity is active, any other entity can be activated at most $k$ times, for some arbitrarily large but fixed $k$. This provides a strong positive answer to a decade old open question posed by Katreniak. We also prove that in a comparable setting that permits unbounded asynchrony, {\sc Point Convergence} in the plane is impossible, contingent on the natural assumption that algorithms maintain the (visible) connectivity among entities present in the initial configuration. This variant, that we call {\sc Cohesive Convergence}, serves to distinguish the power of bounded and unbounded asynchrony in the control of autonomous mobile entities, settling at the same time a long-standing question whether in the Euclidean plane synchronously scheduled entities are more powerful than asynchronously scheduled entities. |
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| DOI: | 10.1145/3465084.3467910 |