Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots

Bose, Kaustav; Adhikary, Ranendu; Kundu, Manash Kumar; Sau, Buddhadeb

doi:10.1007/978-3-030-10564-8_28

Cited by 12 publications

(15 citation statements)

References 14 publications

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“…In discrete spaces, typically graphs like grids or rings, similar problems have been studied, see for example: gathering [11,20]; exploration [22]; pattern formation [3]; and deployment [14]. Unlike in our paper, in all these studies, only a subset of the nodes of the graph is occupied by agents, and typically agents are identical, and not partitioned into colour classes.…”

Section: Related Workmentioning

confidence: 95%

Distributed Pattern Formation in a Ring

Ehresmann

Lafond

Narayanan

et al. 2019

Structural Information and Communication Complexity

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Motivated by concerns about diversity in social networks, we consider the following pattern formation problems in rings. Assume n mobile agents are located at the nodes of an n-node ring network. Each agent is assigned a colour from the set {c 1 , c 2 , . . . , c q }. The ring is divided into k contiguous blocks or neighbourhoods of length p. The agents are required to rearrange themselves in a distributed manner to satisfy given diversity requirements: in each block j and for each colour c i , there must be exactly n i (j) > 0 agents of colour c i in block j. Agents are assumed to be able to see agents in adjacent blocks, and move to any position in adjacent blocks in one time step.When the number of colours q = 2, we give an algorithm that terminates in time N 1 /n * 1 + k + 4 where N 1 is the total number of agents of colour c 1 and n * 1 is the minimum number of agents of colour c 1 required in any block. When the diversity requirements are the same in every block, our algorithm requires 3k + 4 steps, and is asymptotically optimal. Our algorithm generalizes for an arbitrary number of colours, and terminates in O(nk) steps. We also show how to extend it to achieve arbitrary specific final patterns, provided there is at least one agent of every colour in every pattern.

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Section: Related Workmentioning

confidence: 95%

Distributed Pattern Formation in a Ring

Ehresmann

Lafond

Narayanan

et al. 2019

Structural Information and Communication Complexity

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“…The subject of efficient uniform scattering is of extensive research in several fields (e.g. [6], [7], [4], [13], [23], [9], [18], [11], [10]). Depending on the assumptions they make, the existing protocols differ greatly from each other.…”

Section: Earlier Work and Our Contributionmentioning

confidence: 99%

Uniform Scattering of Robots on Alternate Nodes of a Grid

Mondal¹,

Chaudhuri²,

Chatterjee³

2020

Preprint

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In this paper, we propose a distributed algorithm to uniformly scatter the robots along a grid, with robots on alternate nodes of this grid distribution. These homogeneous, autonomous mobile robots place themselves equidistant apart on the grid, which can be required for guarding or covering a geographical area by the robots. The robots operate by executing cycles of the states "look-compute-move". In the look phase, it looks to see the position of the other robots; in the compute phase, it computes a destination to move to; and then in the move phase, it moves to that computed destination. They do not interact by message passing and can recollect neither the past actions nor the looked data from the previous cycle, i.e., oblivious. The robots are semi-synchronous, anonymous and have unlimited visibility. Eventually, the robots uniformly distribute themselves on alternate nodes of a grid, leaving the adjacent nodes of the grid vacant. The algorithm presented also assures no collision or deadlock among the robots.

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“…The Arbitrary Pattern Formation problem has been extensively studied in the literature in various settings (See [2,4,6,7,9,11] and references therein). Until recently, the problem had only been The first two authors are supported by NBHM, DAE, Govt.…”

Section: Introductionmentioning

confidence: 99%

“…Procedure ArbitraryPatternFormation()2 if there is a robot with light set to leader then //PatternFormationFromLeaderConfiguration(the first batch has two robots with light set to terminal) and (the lights of all robots of the second batch are set to same color) and (the distance between the first and second batch is at least n+3 if there is at least one robot with light set to failed, symmetry, ready, move or switch off then 8…”

mentioning

confidence: 99%

Arbitrary Pattern Formation by Opaque Fat Robots with Lights

Bose

Adhikary

Kundu³

et al. 2020

Algorithms and Discrete Applied Mathematics

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Arbitrary Pattern Formation is a widely studied problem in autonomous robot systems. The problem asks to design a distributed algorithm that moves a team of autonomous, anonymous and identical mobile robots to form any arbitrary pattern given as input. The majority of the existing literature investigates this problem for robots with unobstructed visibility. In a few recent works, the problem has been studied in the obstructed visibility model, where the view of a robot can be obstructed by the presence of other robots. However, in these works, the robots have been modelled as dimensionless points in the plane. In this paper, we have considered the problem in the more realistic setting where the robots have a physical extent. In particular, the robots are modelled as opaque disks. Furthermore, the robots operate under a fully asynchronous scheduler. They do not have access to any global coordinate system, but agree on the direction and orientation of one coordinate axis. Each robot is equipped with an externally visible light which can assume a constant number of predefined colors. In this setting, we have given a complete characterization of initial configurations from where any arbitrary pattern can be formed by a deterministic distributed algorithm.

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Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots

Cited by 12 publications

References 14 publications

Distributed Pattern Formation in a Ring

Distributed Pattern Formation in a Ring

Uniform Scattering of Robots on Alternate Nodes of a Grid

Arbitrary Pattern Formation by Opaque Fat Robots with Lights

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