论文标题
运动计划的测量复杂性
Geodesic complexity of motion planning
论文作者
论文摘要
我们引入了度量空间的地球复杂性，灵感来自拓扑空间的拓扑复杂性。它们俩都是数值不变的，但是，尽管TC仅取决于同型类型，但GC是异构体下不变的。我们表明，在许多情况下它们是重合的，但我们还开发了在一系列示例中区分两者的工具。为此，我们研究了我们表示的总切割基因座，在文献中似乎并未明确考虑。据作者所知，GC是度量空间的新不变。此外，就像TC一样，GC在机器人技术领域也具有潜在的应用。
We introduce the geodesic complexity of a metric space, inspired by the topological complexity of a topological space. Both of them are numerical invariants, but, while the TC only depends on the homotopy type, the GC is an invariant under isometries. We show that in many cases they coincide but we also develop tools to distinguish the two in a range of examples. To this end, we study what we denote the total cut locus, which does not appear to have been explicitly considered in the literature. To the knowledge of the author, the GC is a new invariant of a metric space. Furthermore, just like the TC, the GC has potential applications to the field of robotics.
