Arbitrary pattern formation on a continuous circle by oblivious robot swarm

IF 0.9 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science Pub Date : 2024-09-21 DOI:10.1016/j.tcs.2024.114882

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引用次数: 0

Abstract

In the field of distributed systems, the Arbitrary Pattern Formation (APF) problem is an extensively studied problem. The purpose of APF is to design an algorithm to move a swarm of robots to a particular position in an environment (discrete or continuous) such that the swarm can form a specific but arbitrary pattern given previously to every robot as an input. In this paper, the solvability of the APF problem on a continuous circle is discussed for a swarm of oblivious and silent robots without chirality under a semi-synchronous scheduler. Firstly a class of configurations (the initial placements of the robots on the circle) called Formable Configuration (FC) has been provided which is necessary to solve the APF problem on a continuous circle. Then considering the initial configuration to be an FC, a deterministic and distributed algorithm has been provided that solves the APF problem for n robots on a continuous circle of fixed radius within

O (n)

epochs without collision, where an epoch is considered to be a time interval in which all robots are activated at least once.

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遗忘机器人群在连续圆上形成任意图案

在分布式系统领域，任意模式形成（APF）问题是一个被广泛研究的问题。任意模式形成问题的目的是设计一种算法，将机器人群移动到环境（离散或连续）中的某个特定位置，使机器人群能够形成一个特定但任意的模式，并将该模式事先作为输入提供给每个机器人。本文讨论了在半同步调度程序下，无手性的遗忘沉默机器人群在连续圆上的 APF 问题的可解性。首先，本文提供了一类称为可形成配置（FC）的配置（机器人在圆圈上的初始位置），这是解决连续圆圈上的 APF 问题所必需的。然后，将初始配置视为 FC，提供了一种确定性分布式算法，可在 O(n) 个历时内解决半径固定的连续圆上 n 个机器人的 APF 问题，且不会发生碰撞，其中历时被视为所有机器人至少被激活一次的时间间隔。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical Computer Science 工程技术-计算机：理论方法

CiteScore

2.60

自引率

18.20%

发文量

471

审稿时长

12.6 months

期刊介绍： Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.