Topology of Parametrized Motion Planning Algorithms

被引：12

作者：

Cohen, Daniel C. ^{[1
]}

Farber, Michael ^{[2
]}

Weinberger, Shmuel ^{[3
]}

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[2] Queen Mary Univ London, Sch Math Sci, London E1 4NS, England

[3] Univ Chicago, Dept Math, Chicago, IL 60637 USA

来源：

SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY | 2021年 / 5卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

parametrized topological complexity; topological robotics; obstacle-avoiding collision-free motion planning; COMPLEXITY;

D O I：

10.1137/20M1358505

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce and study a new concept of parametrized topological complexity: a topological invariant motivated by the motion planning problem of robotics. In the parametrized setting, a motion planning algorithm has a high degree of universality and flexibility and can function under a variety of external conditions (such as positions of obstacles). We explicitly compute the parametrized topological complexity of obstacle-avoiding collision-free motion of many particles (robots) in 3-dimensional space. Our results show that the parametrized topological complexity can be significantly higher than the standard (nonparametrized) invariant.

引用

页码：229 / 249

页数：21

共 21 条

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