Uniform Circle Formation by Fat Robots Under Non-Uniform Visibility Ranges

Mondal, Moumita; Chaudhuri, Sruti Gan

doi:10.1145/3369740.3372779

Cited by 2 publications

(2 citation statements)

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“…The special case of the Square Formation has been solved in [24]. Recently, UCF has been studied with additional objectives or features: minimizing the maximum distance traveled by a robot [1] and considering transparent/opaque fat robots (of diameter 1) [8,25,26].…”

Section: Related Workmentioning

confidence: 99%

“…Related to UCF, it is noteworthy to mention its precursor, the Circle Formation problem [1,8]: robots are required to relocate on the boundaries of the same circle, without any other requirement. The uniform version of this problem, namely UCF, has been investigated by multiple works [4,9,10,12,13,14,21,22,24,25,26] in the classic oblivious-transparent robot model (see [33] for an excellent survey). Many of the cited works focused mostly on the solvability of the problem in finite time, considering different model assumptions (e.g.…”

Section: Introduction 1background and Motivationmentioning

confidence: 99%

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Uniform Circle Formation for Swarms of Opaque Robots with Lights

Feletti

Mereghetti

Palano

2018

Lecture Notes in Computer Science

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We study the Uniform Circle Formation (UCF) problem for a swarm of n autonomous mobile robots operating in Look-Compute-Move (LCM) cycles on the Euclidean plane. We assume our robots are luminous, i.e. embedded with a persistent light that can assume a color chosen from a fixed palette, and opaque, i.e. not able to see beyond a collinear robot. Robots are said to collide if they share positions or their paths intersect within concurrent LCM cycles. To solve UCF, a swarm of n robots must autonomously arrange themselves so that each robot occupies a vertex of the same regular n-gon not fixed in advance. In terms of efficiency, the goal is to design an algorithm that optimizes (or provides a tradeoff between) two fundamental performance metrics: (i) the execution time and (ii) the size of the color palette. There exists an O(1)-time O(1)-color algorithm for this problem under the fully synchronous and semi-synchronous schedulers and a O(log log n)-time O(1)-color or O(1)-time O( √ n)-color algorithm under the asynchronous scheduler, avoiding collisions. In this paper, we develop a deterministic algorithm solving UCF avoiding collisions in O(1)-time with O(1) colors under the asynchronous scheduler, which is asymptotically optimal with respect to both time and number of colors used, the first such result. Furthermore, the algorithm proposed here minimizes for the first time what we call the computational SEC, i.e. the smallest circular area where robots operate throughout the whole algorithm.

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