Gathering of Opaque Robots in 3D Space

Bhagat, Subhash; Chaudhuri, Sruti Gan; Mukhopadyaya, Krishnendu

doi:10.1145/3154273.3154322

Cited by 9 publications

(6 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As future work, it would be interesting to extend our results to consider robots with non-zero extent, as in the fat robots studied in [1,7,16]. Other natural constraints worth investigating include occlusion, as in [3,5], and collision avoidance, as in [26].…”

Section: Discussionmentioning

confidence: 99%

Separating Bounded and Unbounded Asynchrony for Autonomous Robots

Kirkpatrick

Kostitsyna

Navarra

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

We consider distributed computations, by identical autonomous mobile entities, that solve the Point Convergence problem: given an arbitrary initial configuration of entities, disposed in the Euclidean plane, move in such a way that, for all ε > 0, a configuration is eventually reached and maintained in which the separation between all entities is at most ε. The problem has been previously studied in a variety of settings. 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 Point Convergence, provided the degree of asynchrony is bounded by some arbitrarily large but fixed constant. This provides a strong positive answer to a decade old open question posed by Katreniak.We also prove that, in an otherwise comparable setting, Point Convergence is impossible with unbounded asynchrony. This 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 synchronous entities are more powerful than asynchronous ones.

show abstract

Section: Discussionmentioning

confidence: 99%

Separating Bounded and Unbounded Asynchrony for Autonomous Robots

Kirkpatrick

Kostitsyna

Navarra

et al. 2021

Proceedings of the 2021 ACM Symposium on Principles of Distributed Computing

View full text Add to dashboard Cite

show abstract

“…As future work, it would be interesting to extend our results to consider robots with non-zero extent, as in the fat robots studied in [1,7,17]. Other natural constraints worth investigating include occlusion, as in [3,5], and collision avoidance, as in [28].…”

Section: Discussionmentioning

confidence: 99%

“…Robots are (i) autonomous: that is, they operate without a central control or external supervision, (ii) identical: that is, they are indistinguishable by their appearance, they do not have distinct identities that can be used during the computation, and they all have and execute the same algorithm; and (iii) silent: they have no means of direct communication of 3 If P and Q are points in R d , we denote by P Q the line segment joining P and Q, by |P Q| the length of this segment, and by − − → P Q the ray from P to Q.…”

Section: Robotsmentioning

confidence: 99%

See 1 more Smart Citation

Separating Bounded and Unbounded Asynchrony for Autonomous Robots: Point Convergence with Limited Visibility

Kirkpatrick¹,

Kostitsyna²,

Navarra³

et al. 2021

Preprint

View full text Add to dashboard Cite

Among fundamental problems in the context of distributed computing by autonomous mobile entities, one of the most representative and well studied is Point Convergence: given an arbitrary initial configuration of identical entities, disposed in the Euclidean plane, move in such a way that, for all ε > 0, a configuration in which the separation between all entities is at most ε 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 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, 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 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.

show abstract

“…We summarize the literature briefly. In [2] the authors show that gathering of robots in the three-dimensional Euclidean space is possible -under the assumptions that robot have a global view but are not transparent and that the robots agree on one axis of their coordinate systems. Tomaita et al study a different problem -the plane formation problem [12].…”

Section: Related Workmentioning

confidence: 99%

Local Gathering of Mobile Robots in Three Dimensions

Braun¹,

Castenow²,

Heide³

2020

Preprint

View full text Add to dashboard Cite

In this work, we initiate the research about the Gathering problem for robots with limited viewing range in the three-dimensional Euclidean space. In the Gathering problem, a set of initially scattered robots is required to gather at the same position. The robots' capabilities are very restricted -they do not agree on any coordinate system or compass, have a limited viewing range, have no memory of the past and cannot communicate.We study the problem in two different time models, in Fsync (fully synchronized discrete rounds) and the continuous time model. For Fsync, we introduce the 3d-Go-To-The-Centerstrategy and prove a runtime of Θ n 2 that matches the currently best runtime bound for the same model in the Euclidean plane [SPAA'11] .Our main result is the generalization of contracting strategies (continuous time model) from [Algosensors'17] to the three-dimensional case. In contracting strategies, every robot that is located on the global convex hull of all robots' positions moves with full speed towards the inside of the convex hull. We prove a runtime bound of O ∆ • n 3/2 for any three-dimensional contracting strategy, where ∆ denotes the diameter of the initial configuration. This comes up to a factor of √ n close to the lower bound of Ω (∆ • n) which is already true in two dimensions. In general, it might be hard for robots with limited viewing range to decide whether they are located on the global convex hull and which movement maintains the connectivity of the swarm, rendering the design of concrete contracting strategies a challenging task. We prove that the continuous variant of 3d-Go-To-The-Center is contracting and keeps the swarm connected. Moreover, we give a simple design criterion for three-dimensional contracting strategies that maintains the connectivity of the swarm and introduce an exemplary strategy based on this criterion.

show abstract

Gathering of Opaque Robots in 3D Space

Cited by 9 publications

References 25 publications

Separating Bounded and Unbounded Asynchrony for Autonomous Robots

Separating Bounded and Unbounded Asynchrony for Autonomous Robots

Separating Bounded and Unbounded Asynchrony for Autonomous Robots: Point Convergence with Limited Visibility

Local Gathering of Mobile Robots in Three Dimensions

Contact Info

Product

Resources

About