Topological complexity of the work map-Reference-Cited by-同舟云学术

Topological complexity of the work map

Published:2019-02-28 Issue:01 Volume:13 Page:219-238
ISSN:1793-5253
Container-title:Journal of Topology and Analysis
language:en
Short-container-title:J. Topol. Anal.

Author:

Murillo Aniceto¹,Wu Jie²³⁴^ORCID

Affiliation:

1. Departamento de Algebra, Geometría y Topología, Universidad de Málaga Ap. 59, 29080 Málaga, Spain

2. School of Mathematical Sciences, Hebei Normal University, No. 20 Road East. 2nd Ring South, Yuhua District, Shijiazhuang, Hebei, 050024 China

3. Center For Topology and Geometry Based Technology, Hebei Normal University, No. 20 Road East, 2nd Ring South, Yuhua District, Shijiazhuang, 050024, China

4. Department of Mathematics, National University of Singapore, Block S17 Lower Kent Ridge Road 119076, Singapore

Abstract

We introduce the topological complexity of the work map associated to a robot system. In broad terms, this measures the complexity of any algorithm controlling, not just the motion of the configuration space of the given system, but the task for which the system has been designed. From a purely topological point of view, this is a homotopy invariant of a map which generalizes the classical topological complexity of a space.

Funder

Ministry of Education

National Natural Science Foundation of China

Spanish MINECO research grants

Publisher

World Scientific Pub Co Pte Lt

Subject

Geometry and Topology,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S179352532050003X

Reference20 articles.

1. Robotics

2. Lusternik-Schnirelmann Category

3. C. Ehresmann , Les connexions infinitésimales dans un espace fibré différentiable, Colloque de topologie (espaces fibrés) (Georges Thone, Liège; Masson et Cie., Paris, 1951), pp. 29–55.

Cited by 10 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the sequential topological complexity of group homomorphisms;Topology and its Applications;2024-10

2. Relative sectional category revisited;Expositiones Mathematicae;2024-09

3. Strong digital topological complexity of digital maps;Topology and its Applications;2024-06

4. Higher topological complexity of a map;Turkish Journal of Mathematics;2023-09-25

5. On the Targeted Complexity of a Map;Hacettepe Journal of Mathematics and Statistics;2022-12-31