Motion planning algorithms for Configuration Spaces

TL;DR

This paper presents explicit motion planning algorithms for Euclidean configuration spaces, enabling the calculation of their topological complexity and Lusternik-Schinirelman category, which are important in robotics and topological analysis.

Contribution

It introduces explicit motion planners for Euclidean configuration spaces, facilitating the computation of key topological invariants.

Findings

Recovered known topological complexity values

Calculated Lusternik-Schinirelman category for these spaces

Provided explicit algorithms for motion planning

Abstract

We provide explicit motion planners for Euiclidean configuration spaces. This allows us to recover some known values of the topological complexity and the Lusternik-Schinirelman category of these spaces.