Sequential parametrized motion planning and its complexity
Sequential parametrized motion planning and its complexity
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顺序参数化运动规划及其复杂性
DOI：
10.1016/j.topol.2022.108256
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发表时间：
2022
影响因子：
0.6
通讯作者：
Farber M
中科院分区：
文献类型：
--
作者：
Farber M
本文提出了一种序列参数化运动规划理论，将[3]中介绍的参数化运动规划方法进行了推广。序列参数化运动规划算法产生系统的运动，该运动要求在指定的时刻以一定的顺序访问指定的状态序列。序列参数化算法具有通用性，因为外部条件不是预先确定的，而是构成算法输入的一部分。在这篇文章中，我们给出了一个详细的分析顺序参数化拓扑复杂性的Fadell-Neuwirth纤维。在机器人语言中，Fadell-Neuwirth纤维的部分是移动多个机器人的算法，以避免与其他机器人和欧几里得空间中的障碍物发生碰撞。在本文的最后一节，我们引入了纤维的tc生成函数的新概念，考察了一些例子，并就其解析性质提出了一些令人兴奋的一般问题。
In this paper we develop a theory of sequential parametrized motion planning generalising the approach of parametrized motion planning, which was introduced recently in [3]. A sequential parametrized motion planning algorithm produced a motion of the system which is required to visit a prescribed sequence of states, in a certain order, at specified moments of time. The sequential parametrized algorithms are universal as the external conditions are not fixed in advance but rather constitute part of the input of the algorithm. In this article we give a detailed analysis of the sequential parametrized topological complexity of the Fadell-Neuwirth fibration. In the language of robotics, sections of the Fadell-Neuwirth fibration are algorithms for moving multiple robots avoiding collisions with other robots and with obstacles in the Euclidean space. In the last section of the paper we introduce the new notion of TC-generating function of a fibration, examine examples and raise some exciting general questions about its analytic properties.