离散运动规划的离散拓扑复杂性

IF 0.5 4区 数学 Q3 MATHEMATICS
Hadi Hassanzada, Hamid Torabi, Hanieh Mirebrahimi, Ameneh Babaee
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引用次数: 0

摘要

在本文中,我们提出了一个为以离散方式操作的机器人量身定制的离散运动规划框架。进一步,我们将r-离散同伦的概念推广为离散(s,r)-同伦。利用这个框架,我们研究了离散拓扑复杂性的概念,它被定义为离散运动所需的最少数量的运动规划算法。我们建立了与离散拓扑复杂性相关的几个性质;例如,我们证明了度量空间X内的离散运动规划当且仅当X是一个离散可收缩空间时是可行的。此外,我们还证明了离散拓扑复杂度完全取决于所涉及空间的严格离散同伦类型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A discrete topological complexity of discrete motion planning
In this paper, we present a framework for discrete motion planning tailored for robots that operate in a discrete manner. Furthermore, we extend the concept of r-discrete homotopy as discrete (s,r)-homotopy. Utilizing this framework, we investigate the notion of discrete topological complexity, which is defined as the least number of motion planning algorithms necessary for discrete movement. We establish several properties related to discrete topological complexity; for example, we demonstrate that discrete motion planning within a metric space X is feasible if and only if X is a discrete contractible space. Additionally, we show that the discrete topological complexity is solely determined by the strictly discrete homotopy type of the spaces involved.
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来源期刊
CiteScore
1.20
自引率
33.30%
发文量
251
审稿时长
6 months
期刊介绍: Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.
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