论文标题
有界曲率路径的普查
Census of bounded curvature paths
论文作者
论文摘要
有界曲率路径是一个连续可区分的零件$ c^2 $路径，具有有界的绝对曲率，在表面的切线束中连接两个点。这些路径在计算机科学和工程中已被广泛考虑，因为弯曲模型在转弯圆约束下机器人运动的轨迹。分析有界曲率路径空间的整体性质并不是一个简单的物质，因为在许多情况下，任意关闭终点或方向的长度最小化之间的长度变化是不连续的。在本说明中，我们开发了一项简单的技术，使我们可以将有限曲率路径的空间划分为单参数家族。这些空间家族根据我们的元素具有的连接组件（同喻类别，同位素类别或隔离点）的类型进行分类，因为我们改变了真实的参数。因此，我们回答了杜宾（Dubins）提出的一个问题（Pac J Math 11（2），1961年）。
A bounded curvature path is a continuously differentiable piece-wise $C^2$ path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These paths have been widely considered in computer science and engineering since the bound on curvature models the trajectory of the motion of robots under turning circle constraints. Analyzing global properties of spaces of bounded curvature paths is not a simple matter since the length variation between length minimizers of arbitrary close endpoints or directions is in many cases discontinuous. In this note, we develop a simple technology allowing us to partition the space of spaces of bounded curvature paths into one-parameter families. These families of spaces are classified in terms of the type of connected components their elements have (homotopy classes, isotopy classes, or isolated points) as we vary a parameter defined in the reals. Consequently, we answer a question raised by Dubins (Pac J Math 11(2), 1961).
