@inproceedings{e4abf343473148ef9ab70d96d5c415a3,
title = "Parametrized Motion Planning and Topological Complexity",
abstract = "In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are viewed as parameters and serve as part of the input of the algorithm. Continuing the recent paper [2], we study further the concept of parametrized topological complexity. We analyse in full detail the problem of controlling a swarm of robots in the presence of multiple obstacles in Euclidean space which served for us a natural motivating example. We present an explicit parametrized motion planning algorithm solving the motion planning problem for any number of robots and obstacles in Rd. This algorithm is optimal, it has minimal possible topological complexity for any d≥ 3 odd. Besides, we describe a modification of this algorithm which is optimal for d≥ 2 even. We also analyse the parametrized topological complexity of sphere bundles using the Stiefel - Whitney characteristic classes.",
keywords = "Collision free motion of swarms of robots, Motion planning algorithm, Parametrized topological complexity, Stiefel – Whitney characteristic classes, Topological complexity",
author = "Michael Farber and Shmuel Weinberger",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 15th Workshop on the Algorithmic Foundations of Robotics, WAFR 2022 ; Conference date: 22-06-2022 Through 24-06-2022",
year = "2023",
doi = "10.1007/978-3-031-21090-7_1",
language = "אנגלית",
isbn = "9783031210891",
series = "Springer Proceedings in Advanced Robotics",
publisher = "Springer Nature",
pages = "1--17",
editor = "LaValle, {Steven M.} and O{\textquoteright}Kane, {Jason M.} and Michael Otte and Dorsa Sadigh and Pratap Tokekar",
booktitle = "Algorithmic Foundations of Robotics XV - Proceedings of the Fifteenth Workshop on the Algorithmic Foundations of Robotics",
address = "ארצות הברית",
}