Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

Cicerone, Serafino; Stefano, Gabriele Di; Navarra, Alfredo

doi:10.1007/s00446-018-0325-7

Cited by 46 publications

(40 citation statements)

References 27 publications

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“…The ability to make circular moves is crucial to our algorithm. Although the standard model for mobile robots in the plane assumes rectilinear robot movement, it is not completely uncommon to allow the robots to move along circular trajectories (e.g., [7,17]). It would be interesting to see if the same result can be achieved without the ability to make circular moves.…”

Section: Resultsmentioning

confidence: 99%

Positional Encoding by Robots with Non-rigid Movements

Bose

Adhikary

Kundu

et al. 2019

Structural Information and Communication Complexity

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Consider a set of autonomous computational entities, called robots, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant δ > 0, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than δ amount. This model is known in literature as non-rigid movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having O(1) bits of persistent memory and ability to make circular moves.

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Section: Resultsmentioning

confidence: 99%

Positional Encoding by Robots with Non-rigid Movements

Bose

Adhikary

Kundu

et al. 2019

Structural Information and Communication Complexity

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“…A robot infers that it is in Phase 1 if ¬(C 1 ∧C 2 ) ∧ ¬(C 3 ∧C 4 ) is true 3 . In this case, the tail will move to the right and all other robots will remain static.…”

Section: Phasementioning

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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“…When active, a robot operates in standard Look-Compute-Move (LCM) computational cycles, see e.g. [8], [39], [52]. Within one cycle, a robot acquires a snapshot of the current global positioning of the other robots (Look phase) with respect to its own coordinate system.…”

Section: Introductionmentioning

confidence: 99%

“…This, of course, extraordinarily affects also the arguments necessary to provide the proofs of correctness of the proposed algorithms. To this respect, see [11] for an extended discussion related to the difficulties encountered when dealing with ASYNC.…”

Section: Introductionmentioning

confidence: 99%

“Semi-Asynchronous”: A New Scheduler in Distributed Computing

2021

Self Cite

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The study of mobile entities that based on local information have to accomplish global tasks is of main interest for the scientific community. Classic models for the activation and synchronization of mobile entities are the fully-synchronous (FSYNC), semi-synchronous (SSYNC), and asynchronous (ASYNC) models, where entities alternate between active and inactive states with different timing. According to the assumed synchronization model, very different results have been achieved in the field of distributed computing. One of the main outcomes is the big gap between the ASYNC and the other models in terms of manageability and algorithm design. In fact, there are still many problems for which it is not known whether synchronicity is crucial for designing resolution algorithms or not. In order to better understand the ASYNC case, here we propose a further model referred to as the semiasynchronous (SASYNC). This slightly deviates from SSYNC. In fact, like in SSYNC (and FSYNC), the duration of the activation of an entity is kept of fixed time whereas, like in ASYNC, the starting instant of the activation is not fully synchronized with the possible activation of other entities. We show that for entities moving on graphs, the SSYNC model allows accomplishing more tasks than the SASYNC that in turn allows accomplishing more tasks than the ASYNC. Furthermore, our results show that, especially to tackle problems in the Euclidean plane, the SASYNC model is already quite challenging, therefore there is no need to get involved with complications arising in the ASYNC model.

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Asynchronous Arbitrary Pattern Formation: the effects of a rigorous approach

Cited by 46 publications

References 27 publications

Positional Encoding by Robots with Non-rigid Movements

Positional Encoding by Robots with Non-rigid Movements

Arbitrary Pattern Formation on Infinite Grid by Asynchronous Oblivious Robots

“Semi-Asynchronous”: A New Scheduler in Distributed Computing

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