Parametrized Motion Planning and Topological Complexity

Michael Farber*, Shmuel Weinberger

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publicationAlgorithmic Foundations of Robotics XV - Proceedings of the Fifteenth Workshop on the Algorithmic Foundations of Robotics
EditorsSteven M. LaValle, Jason M. O’Kane, Michael Otte, Dorsa Sadigh, Pratap Tokekar
PublisherSpringer Nature
Number of pages17
ISBN (Print)9783031210891
StatePublished - 2023
Externally publishedYes
Event15th Workshop on the Algorithmic Foundations of Robotics, WAFR 2022 - College Park, United States
Duration: 22 Jun 202224 Jun 2022

Publication series

NameSpringer Proceedings in Advanced Robotics
Volume25 SPAR
ISSN (Print)2511-1256
ISSN (Electronic)2511-1264


Conference15th Workshop on the Algorithmic Foundations of Robotics, WAFR 2022
Country/TerritoryUnited States
CityCollege Park


  • Collision free motion of swarms of robots
  • Motion planning algorithm
  • Parametrized topological complexity
  • Stiefel – Whitney characteristic classes
  • Topological complexity


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