Document Type
Article
Publication Date
10-1-2022
Abstract
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.
Publication Source (Journal or Book title)
Annals of Mathematics and Artificial Intelligence
First Page
999
Last Page
1015
Recommended Citation
Cohen, D., Farber, M., & Weinberger, S. (2022). Parametrized topological complexity of collision-free motion planning in the plane. Annals of Mathematics and Artificial Intelligence, 90 (10), 999-1015. https://doi.org/10.1007/s10472-022-09801-6