Parametrized topological complexity of collision-free motion planning in the plane

Daniel C. Cohen*, Michael Farber, Shmuel Weinberger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying motion planning problem. In this paper, we analyze the parametrized motion planning problem for the motion of many distinct points in the plane, moving without collision and avoiding multiple distinct obstacles with a priori unknown positions. This complements our prior work Cohen et al. [3] (SIAM J. Appl. Algebra Geom. 5, 229–249), where parametrized motion planning algorithms were introduced, and the obstacle-avoiding collision-free motion planning problem in three-dimensional space was fully investigated. The planar case requires different algebraic and topological tools than its spatial analog.

Original languageEnglish
JournalAnnals of Mathematics and Artificial Intelligence
StateAccepted/In press - 2022
Externally publishedYes


  • Obstacle-avoiding collision-free motion
  • Parametrized topological complexity


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