Directed topological complexity
Directed topological complexity
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有向拓扑复杂度
DOI：
10.1007/s41468-019-00034-x
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Aurélien Sagnier
中科院分区：
文献类型：
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作者：
É. Goubault;M. Farber;Aurélien Sagnier
已经观察到，机器人的运动规划问题在数学上归结为找到路径空间纤维化的一部分的问题，导致拓扑复杂性的概念，如M.法伯在这种方法中，假设任何连续运动都是允许的，对系统的运动没有限制。然而，在许多应用中，物理装置可能具有受约束的控制，导致对其潜在动态的约束。在本文中，我们适应的拓扑复杂性的概念的情况下，有向拓扑空间，其中包括这样的控制系统，也出现在并发理论的系统。我们研究这个新概念的性质，并计算了一些有趣的例子。
It has been observed that the motion planning problem of robotics reduces mathematically to the problem of finding a section of the path-space fibration, leading to the notion of topological complexity, as introduced by M. Farber. In this approach one imposes no limitations on motion of the system assuming that any continuous motion is admissible. In many applications, however, a physical apparatus may have constrained controls, leading to constraints on its potential dynamics. In the present paper we adapt the notion of topological complexity to the case of directed topological spaces, which encompass such controlled systems, and also systems which appear in concurrency theory. We study properties of this new notion and make calculations for some interesting classes of examples.