A Distributed Algorithm for Pattern Formation by Autonomous Robots, with No Agreement on Coordinate Compass

Ghike, Swapnil; Mukhopadhyaya, Krishnendu

doi:10.1007/978-3-642-11659-9_16

Cited by 9 publications

(6 citation statements)

References 5 publications

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“…There are two possible options. As in [24], the pattern can be specified as a list of ratios of its sides and angles between the sides. Another option is to provide the list of distances among all points.…”

Section: Our Resultsmentioning

confidence: 99%

“…m 24 Let r be the robot closest to c(R), and t be a point on C g (R) s.t. t is not on an axis of symmetry and (t, c(R), r ) = α for any r ∈ ∂C(R).…”

Section: Phase Fmentioning

confidence: 99%

“…-A first study can be found in [24]. The authors provide a distributed algorithm that can form many patterns, subject to significant restrictions in the input configurations.…”

Section: Motivation and Related Workmentioning

confidence: 99%

“…[28,30,31]) or asynchronous (cf. [2,14,22,21,24]): pendently, and the duration of each phase is finite but unpredictable. As a result, robots do not have a common notion of time.…”

Section: Introductionmentioning

confidence: 99%

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Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

2018

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Given any multiset F of points in the Euclidean plane and a set R of robots such that |R| = |F|, the Arbitrary Pattern Formation (APF) problem asks for a distributed algorithm that moves robots so as to reach a configuration similar to F. Similarity means that robots must be disposed as F regardless of translations, rotations, reflections, uniform scalings. Initially, each robot occupies a distinct position. When active, a robot operates in standard Look-ComputeMove cycles. Robots are asynchronous, oblivious, anonymous, silent and execute the same distributed algorithm. So far, the problem has been mainly addressed by assuming chirality, that is robots share a common left-right orientation. We are interested in removing such a restriction.While working on the subject, we faced several issues that required close attention. We deeply investigated how such difficulties were overcome in the literature, revealing that crucial arguments for the correctness proof of the existing algorithms have been neglected. The systematic lack of rigorous arguments with respect to necessary conditions required for providing correctness proofs deeply affects the The work has been supported in part by the European project "Geospatial based Environment for Optimisation Systems Addressing Fire Emergencies" (GEO-SAFE), contract no. H2020-691161, and by the Italian National Group for Scientific Computation (GNCS-INdAM). Here we design a new deterministic distributed algorithm that fully characterizes APF showing its equivalence with the well-known Leader Election problem in the asynchronous model without chirality. Our approach is characterized by the use of logical predicates in order to formally describe our algorithm as well as its correctness. In addition to the relevance of our achievements, our techniques might help in revising previous results.

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Section: Our Resultsmentioning

confidence: 99%

“…m 24 Let r be the robot closest to c(R), and t be a point on C g (R) s.t. t is not on an axis of symmetry and (t, c(R), r ) = α for any r ∈ ∂C(R).…”

Section: Phase Fmentioning

confidence: 99%

“…-A first study can be found in [24]. The authors provide a distributed algorithm that can form many patterns, subject to significant restrictions in the input configurations.…”

Section: Motivation and Related Workmentioning

confidence: 99%

“…[28,30,31]) or asynchronous (cf. [2,14,22,21,24]): pendently, and the duration of each phase is finite but unpredictable. As a result, robots do not have a common notion of time.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

2018

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“…We assume that cycles are performed according to the weakest Asynchronous scheduler (Async) (cf. [1,6,8,9,14,19,20]): the robots are activated independently, and the duration of each phase is finite 3 No randomization features are allowed. but unpredictable (the activation of each robot can be thought of as decided by the adversary).…”

Section: Arxiv:201014152v1 [Csdc] 27 Oct 2020mentioning

confidence: 99%

Arbitrary Pattern Formation on Infinite Regular Tessellation Graphs

Cicerone

Fonso

Stefano

et al. 2021

Proceedings of the 22nd International Conference on Distributed Computing and Networking

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Given a set R of robots, each one located at different vertices of an infinite regular tessellation graph, we aim to explore the Arbitrary Pattern Formation (APF ) problem. Given a multiset F of grid vertices such that |R| = |F |, APF asks for a distributed algorithm that moves robots so as to reach a configuration similar to F . Similarity means that robots must be disposed as F regardless of translations, rotations, reflections. So far, as possible graph discretizing the Euclidean plane only the standard square grid has been considered in the context of the classical Look-Compute-Move model. However, it is natural to consider also the other regular tessellation graphs, that are triangular and hexagonal grids. We provide a resolution algorithm for APF when the initial configuration is asymmetric and the considered topology is any regular tessellation graph.

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A Distributed Algorithm for Pattern Formation by Autonomous Robots, with No Agreement on Coordinate Compass

Cited by 9 publications

References 5 publications

Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

Arbitrary Pattern Formation on Infinite Regular Tessellation Graphs

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