论文标题
顺序参数化运动计划及其复杂性
Sequential Parametrized Motion Planning and its Complexity
论文作者
论文摘要
在本文中，我们开发了顺序参数化运动计划的理论，该理论概括了参数化运动计划的方法，该方法最近在[3]中引入。顺序的参数化运动计划算法产生了系统的运动，该运动需要在指定的时间时刻以某些顺序访问规定的状态序列。顺序参数化算法是通用的，因为外部条件不是预先固定的，而是构成算法输入的一部分。本文的第二部分包括对Fadell -Neuwirth振动的顺序参数化拓扑复杂性的详细分析。用机器人的语言，Fadell的部分 - Neuwitrh纤维化是移动多个机器人的算法，避免了与其他机器人发生碰撞以及在欧几里得空间中遇到障碍的算法。在本文的最后一部分中，我们介绍了TC生成功能的新概念，检查示例并提出有关其分析特性的一些一般性问题。
In this paper we develop theory of sequential parametrized motion planning which generalises 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 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. The second part of this article consists of a detailed analysis of the sequential parametrized topological complexity of the Fadell - Neuwirth fibration. In the language of robotics, sections of the Fadell - Neuwitrh fibration are algorithms for moving multiple robots avoiding collisions with other robots and with obstacles in 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 general questions about its analytic properties.
