Mutual Visibility by Asynchronous Robots on Infinite Grid

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

doi:10.1007/978-3-030-14094-6_6

Cited by 16 publications

(15 citation statements)

References 14 publications

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“…Then, the moving group moves up towards the top-right beacon robot. Next, the moving group turns left, and the robot in C i 2 is translated by a vector (1,1). Finally, the moving group reaches the top-left beacon robot and forms the first configuration of the sequence described in Fig.…”

Section: An Algorithm Using Five Robots and Five Modifiable Colorsmentioning

confidence: 99%

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Infinite Grid Exploration by Disoriented Robots

Bramas

Devismes

Lafourcade

2019

Structural Information and Communication Complexity

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We deal with a set of autonomous robots moving on an infinite grid. Those robots are opaque, have limited visibility capabilities, and run using synchronous Look-Compute-Move cycles. They all agree on a common chirality, but have no global compass. Finally, they may use lights of different colors that can be seen by robots in their surroundings, but except from that, robots have neither persistent memories, nor communication mean.We consider the infinite grid exploration (IGE) problem. For this problem we give two impossibility results and three algorithms, including one which is optimal in terms of number of robots.In more detail, we first show that two robots are not sufficient in our settings to solve the problem, even when robots have a common coordinate system. We then show that if the robots' coordinate systems are not self-consistent, three or four robots are not sufficient to solve the problem neither.Finally, we present three algorithms that solve the IGE problem in various settings. The first algorithm uses six robots with constant colors and a visibility range of one. The second one uses the minimum number of robots, i.e., five, as well as five modifiable colors, still under visibility one. The last algorithm requires seven oblivious anonymous robots, yet assuming visibility two. Notice that the two last algorithms also achieve exclusiveness.

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Section: An Algorithm Using Five Robots and Five Modifiable Colorsmentioning

confidence: 99%

“…Various terminating problems have been investigated in infinite grids such as arbitrary pattern formation [4], mutual visibility [1], and gathering [9,11]. The possibly closest related work is that of Emek et al [13].…”

Section: Introductionmentioning

confidence: 99%

Infinite Grid Exploration by Disoriented Robots

Bramas

Devismes

Lafourcade

2019

Structural Information and Communication Complexity

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“…Furthermore, robots were given a fixed point on the grid so that they can form a connected configuration containing it. Other specific types of formation problems that have been studied in the infinite grid set up, are the Gathering problem [11], i.e., the point formation problem and the Mutual Visibility problem [1], where a set of opaque robots have to form a pattern in which no three robots are collinear.…”

Section: Earlier Workmentioning

confidence: 99%

Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots

Bose

Adhikary

Kundu

et al. 2018

WALCOM: Algorithms and Computation

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The ARBITRARY PATTERN FORMATION problem asks to design a distributed algorithm that allows a set of autonomous mobile robots to form any specific but arbitrary geometric pattern given as input. The problem has been extensively studied in literature in continuous domains. This paper investigates a discrete version of the problem where the robots are operating on a two dimensional infinite grid. The robots are assumed to be autonomous, identical, anonymous and oblivious. They operate in Look-Compute-Move cycles under a fully asynchronous scheduler. The robots do not agree on any common global coordinate system or chirality. We have shown that a set of robots can form any arbitrary pattern, if their starting configuration is asymmetric.

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“…Arbitrary Pattern Formation Input : The configuration of robots visible to me 1. Procedure ArbitraryPatternFormation()2 if there is a robot with light set to leader then // PatternFormationFromLeaderConfigurationthere are two robots with light set to candidate on the same vertical line or at least one robot with light set to symmetry then 6…”

mentioning

confidence: 99%

“…Pattern Formation from Leader Configuration Input : The configuration of robots visible to me 1. Procedure PatternFormationFromLeaderConfiguration() l ← the robot with light leader4 if r.light = off then 5 if r l ∈ H O B (r) ∩ H O L (r) then if there are no robots in H O B (r) ∩ H O U (r l ) ∩ H O R (r l ) and r is the leftmost robot on LH (r) ∩ H O R (r l ) then 9if there is no robot on LV (r l ) then10 p ← the point of intersection of the lines LH (r) and LV (r l ) there are k ≥ 0 robots on LH (r l ) with light off then 14 Move to (Ψ (k + 2), −1) 15 else if r l ∈ LH (r), there is a robot on LV (r l ), and there are no robots with light off in H O U (r) ∩ H O R (r l ) then 16 if r.pos = (Ψ (i), −1) and PartialFormation(i) = True then 17 r.light ← done 18 Move to P[i] 19 else if r l ∈ LV (r) then 20 if there is no other robot with light off in H C U (r) and there are no robots in H O B (r) except r l then 21 Move to P[1] 22 else if r.light = leader then 23 if there are no robots with light off then a robot with light done at ti−1 then Suppose that at time t 1. a robot r with light set to off finds itself eligible to become leader, and 2. for all r ∈ R \ {r}, r is stable and r .light = off,…”

mentioning

confidence: 99%

Arbitrary Pattern Formation by Asynchronous Opaque Robots with Lights

Bose

Kundu

Adhikary

et al. 2019

Structural Information and Communication Complexity

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The Arbitrary Pattern Formation problem asks for a distributed algorithm that moves a set of autonomous mobile robots to form any arbitrary pattern given as input. The robots are assumed to be autonomous, anonymous and identical. They operate in Look-Compute-Move cycles under a fully asynchronous scheduler. The robots do not have access to any global coordinate system. The existing literature that investigates this problem, considers robots with unobstructed visibility. This work considers the problem in the more realistic obstructed visibility model, where the view of a robot can be obstructed by the presence of other robots. The robots are assumed to be punctiform and equipped with visible lights that can assume a constant number of predefined colors. We have studied the problem in two settings based on the level of consistency among the local coordinate systems of the robots: two axis agreement (they agree on the direction and orientation of both coordinate axes) and one axis agreement (they agree on the direction and orientation of only one coordinate axis). In both settings, we have provided a full characterization of initial configurations from where any arbitrary pattern can be formed.

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Mutual Visibility by Asynchronous Robots on Infinite Grid

Cited by 16 publications

References 14 publications

Infinite Grid Exploration by Disoriented Robots

Infinite Grid Exploration by Disoriented Robots

Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots

Arbitrary Pattern Formation by Asynchronous Opaque Robots with Lights

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