The classification of homotopy classes of bounded curvature paths

被引：9

作者：

Ayala, Jose ^{[1
]}

Rubinstein, Hyam ^{[2
]}

机构：

[1] Univ Arturo Prat, FIA, Iquique, Chile

[2] Univ Melbourne, Dept Math & Stat, Parkville, Vic 3010, Australia

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2016年 / 213卷 / 01期

关键词：

Unit Circle; Minimal Length; Homotopy Class; Curvature Path; Proximity Condition;

D O I：

10.1007/s11856-016-1321-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A bounded curvature path is a continuously differentiable piecewise C (2) path with bounded absolute curvature that connects two points in the tangent bundle of a surface. In this note we give necessary and sufficient conditions for two bounded curvature paths, defined in the Euclidean plane, to be in the same connected component while keeping the curvature bounded at every stage of the deformation. Following our work in [3], [2] and [4] this work finishes a program started by Lester Dubins in [6] in 1961.

引用

页码：79 / 107

页数：29