Uniform Circle Formation by Swarm Robots Under Limited Visibility

Mondal, Moumita; Chaudhuri, Sruti Gan

doi:10.1007/978-3-030-36987-3_28

Cited by 6 publications

(4 citation statements)

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“…Such a problem has been investigated and solved under different combinations of system assumptions in order to point out the minimal sets of features for its solution. In [35,37], the problem is solved for fat robots, but (partially) oriented. Specifically, the authors of [37] cope with transparent and fat robots, which agree on one axis of their coordinate systems, operating in the SSYNCH mode.…”

Section: Related Work and Main Contributionsmentioning

confidence: 99%

“…Specifically, the authors of [37] cope with transparent and fat robots, which agree on one axis of their coordinate systems, operating in the SSYNCH mode. The algorithm in [35] solves the UCF problem for a swarm of fat, opaque, but oriented (they share a common coordinate system) robots in the ASYNCH mode. In [30], the authors provide a solution for transparent, disoriented, and non-rigid robots, in the ASYNCH mode.…”

Section: Related Work and Main Contributionsmentioning

confidence: 99%

“…In the Uniform Circle Formation (UCF) problem [26,30,[35][36][37], robots are required to move to the vertices of a common regular polygon whose number of vertices-which can or cannot be known in advance-is exactly the number of robots in the system. This problem has received a lot of attention (see, e.g., [36] for a survey) for both theoretical and practical reasons.…”

Section: Introductionmentioning

confidence: 99%

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Uniform Circle Formation for Fully, Semi-, and Asynchronous Opaque Robots with Lights

2023

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In the field of robotics, a lot of theoretical models have been settled to formalize multi-agent systems and design distributed algorithms for autonomous robots. Among the most investigated problems for such systems, the study of the Uniform Circle Formation (UCF problem earned a lot of attention for the properties of such a convenient disposition. Such a problem asks robots to move on the plane to form a regular polygon, running a deterministic and distributed algorithm by executing a sequence of look–compute–move cycles. This work aims to solve the UCF problem for a very restrictive model of robots: they are punctiform, anonymous, and indistinguishable. They are completely disoriented, i.e., they share neither the coordinate system nor chirality. Additionally, they are opaque, so collinearities can hide important data for a proper computation. To tackle these system limitations, robots are equipped with a persistent light used to communicate and store a constant amount of information. For such a robot model, this paper presents a solution for UCF for each of the three scheduling modes usually studied in the literature: fully synchronous, semi-synchronous, and asynchronous. Regarding the time complexity, the proposed algorithms use a constant number of cycles (epochs) for fully synchronous (semi-synchronous) robots, and linearly, many epochs in the worst case for asynchronous robots.

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Section: Related Work and Main Contributionsmentioning

confidence: 99%

Section: Related Work and Main Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Uniform Circle Formation for Fully, Semi-, and Asynchronous Opaque Robots with Lights

2023

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“…Much less is known about formation tasks for robots with limited visibility that aim to achieve a contrary goal: to expand the robots' positions. One example is the Uniform-Circle-Formation problem in which n robots are to move such that their positions form a regular polygon [11,18]. Another, very recent example and the main inspiration for this work is the Max-Chain-Formation problem [5].…”

Section: Introductionmentioning

confidence: 99%

The Max-Line-Formation Problem

Castenow¹,

Götte²,

Knollmann³

et al. 2021

Preprint

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We consider n robots with limited visibility: each robot can observe other robots only up to a constant distance denoted as the viewing range. The robots operate in discrete rounds that are either fully synchronous (Fsync) or semi-synchronized (Ssync). Most previously studied formation problems in this setting seek to bring the robots closer together (e.g., Gathering or Chain-Formation). In this work, we introduce the Max-Line-Formation problem, which has a contrary goal: to arrange the robots on a straight line of maximal length.First, we prove that the problem is impossible to solve by robots with a constant sized circular viewing range. The impossibility holds under comparably strong assumptions: robots that agree on both axes of their local coordinate systems in Fsync. On the positive side, we show that the problem is solvable by robots with a constant square viewing range, i.e., the robots can observe other robots that lie within a constant-sized square centered at their position. In this case, the robots need to agree on only one axis of their local coordinate systems. We derive two algorithms: the first algorithm considers oblivious robots (OBLOT ) and converges to the optimal configuration in time O(n 2 • log(n/ε)) under the Ssync scheduler (ε is a convergence parameter). The other algorithm makes use of locally visible lights (LUMI). It is designed for the Fsync scheduler and can solve the problem exactly in optimal time Θ(n). We also argue how a combination of the two algorithms can solve the Max-Line-Formation exactly in time O(n 2 ) under the Ssync scheduler with the help of the LUMI model.Afterward, we show that both the algorithmic and the analysis techniques can also be applied to the Gathering and Chain-Formation problem: we introduce an algorithm with a reduced viewing range for Gathering and give new and improved runtime bounds for the Chain-Formation problem.

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