Infinite Grid Exploration by Disoriented Robots

Bramas, Quentin; Devismes, Stéphane; Lafourcade, Pascal

doi:10.1007/978-3-030-67087-0_9

Cited by 10 publications

(17 citation statements)

References 17 publications

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“…Direct open questions to this work are to determine whether Vone 3 3 is also optimal with respect to the number of colors and whether Vone 5 1 is optimal with respect to the number of robots. Also, it would be interesting to extend the investigation on other topologies such as torus shaped networks.…”

Section: Discussionmentioning

confidence: 99%

“…We retrieve, the previous discussed case. We present here all the rules of algorithm Vtwo 5 1 and when they are used.…”

Section: B Correctness Proof Of Vonementioning

confidence: 99%

“…Th exploration problem is a well known problem that has been excessively investigated. Various topoligies have been considered, e.g., lines [13], rings [2,14,10,15,7], trees [12], torus [9], finite [8,3] and infinite grids [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…In such a context, robots are always assumed to be anonymous and oblivious, i.e., they have no state and cannot remember past actions. Exploration algorithms satisfying exclusiveness are proposed in both finite [2,3] and infinite graphs [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…six) synchronous robots are necessary and sufficient to explore an infinite grid with (resp. without) the common chirality assumption [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Exclusive Perpetual Grid Exploration by Luminous Myopic Robots Without Common Chirality

et al. 2021

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We consider swarms of luminous myopic robots that run in synchronous Look-Compute-Move cycles. These robots evolve in a finite grid and are disoriented i.e., they have no global compass nor a common chirality. In this context, we propose optimal solutions to the perpetual exploration of a finite grid. Precisely, we investigate optimality in terms of the visibility range and number of robots. In more detail, under the optimal visibility range one, we give an algorithm which is optimal w.r.t. the number of robots: it uses three robots and three colors. Under visibility two, we design an algorithm that uses only one color (i.e., robots are oblivious).

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Section: Discussionmentioning

confidence: 99%

“…We retrieve, the previous discussed case. We present here all the rules of algorithm Vtwo 5 1 and when they are used.…”

Section: B Correctness Proof Of Vonementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…six) synchronous robots are necessary and sufficient to explore an infinite grid with (resp. without) the common chirality assumption [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Optimal Exclusive Perpetual Grid Exploration by Luminous Myopic Robots Without Common Chirality

et al. 2021

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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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Perpetual Torus Exploration by Myopic Luminous Robots

Darwich

Ulucan²,

Bramas³

et al. 2022

Lecture Notes in Computer Science

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We study perpetual torus exploration for swarm of autonomous, anonymous, uniform, luminous robots with a common chirality. We consider robots with only few capabilities. They have a finite limited vision (myopic), they can only see robots at distance one or two. We show that the problem is impossible with only two luminous robots and also with three oblivious robots (without light). We design an optimal algorithm for three luminous robots using two colors and with visibility one. We also propose an optimal algorithm with visibility two with four oblivious robots.

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Infinite Grid Exploration by Disoriented Robots

Cited by 10 publications

References 17 publications

Optimal Exclusive Perpetual Grid Exploration by Luminous Myopic Robots Without Common Chirality

Optimal Exclusive Perpetual Grid Exploration by Luminous Myopic Robots Without Common Chirality

Infinite Grid Exploration by Disoriented Robots

Perpetual Torus Exploration by Myopic Luminous Robots

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