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

被引：0
作者：
Daniel C. Cohen
Michael Farber
Shmuel Weinberger
机构：
[1] Louisiana State University,Department of Mathematics
[2] Queen Mary University of London,School of Mathematical Sciences
[3] The University of Chicago,Department of Mathematics
来源：
Annals of Mathematics and Artificial Intelligence | 2022年 / 90卷
关键词：
Parametrized topological complexity; Obstacle-avoiding collision-free motion; 55S40; 55M30; 55R80; 70Q05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：999 / 1015
页数：16
相关论文
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