On the targeted complexity of a map

Year 2023, , 572 - 584, 30.05.2023

Seyyed Abolfazl Aghili , Hanıeh Mırebrahımı , Ameneh Babaee

https://doi.org/10.15672/hujms.1132283

Abstract

We study the topological complexity of work maps with respect to some subspaces of the configuration space and a workspace considered as the target set of the motion of robots. The motivation is to optimize and reduce the number of motion planners for work maps. In this regard, we focus on the useful set of works. We check some basic properties of the targeted complexity of maps, such as homotopical invariance, reduction, the product of maps, and so on. Then we compare these targeted complexities, and we find some inequalities in reducing the number of motion planners. We show that the relative topological complexity of pair of spaces defined by Short is a special case of the targeted complexity of work maps.

Keywords

Topological complexity, work map, configuration space, motion planning.

Supporting Institution

Ferdowsi University of Mashhad

Project Number

3/57099

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