Some geometric and topological data-driven methods in robot motion path planning
Abstract
Motion path planning is an intrinsically geometric problem which is central for design of robot systems. Since the early years of AI, robotics together with computer vision have been the areas of computer science that drove its development. Many questions that arise, such as existence, optimality, and diversity of motion paths in the configuration space that describes feasible robot configurations, are of topological nature. The recent advances in topological data analysis and related metric geometry, topology and combinatorics have provided new tools to address these engineering tasks. We will survey some questions, issues, recent work and promising directions in data-driven geometric and topological methods with some emphasis on the use of discrete Morse theory.
Keywords
Cite
@article{arxiv.2403.12725,
title = {Some geometric and topological data-driven methods in robot motion path planning},
author = {Boris Goldfarb},
journal= {arXiv preprint arXiv:2403.12725},
year = {2024}
}
Comments
21 pages, 6 figures, to appear in a book project on Topology, Geometry and AI in the EMS Series in Industrial and Applied Mathematics, edited by Michael Farber and Jes\'us Gonz\'alez