论文标题
顺序参数化运动计划及其复杂性，II
Sequential parametrized motion planning and its complexity, II
论文作者
论文摘要
这是我们最近的论文的延续，在该论文中，我们发展了顺序参数化运动计划的理论。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矩中以一定顺序访问规定的状态序列。在上一个出版物中，我们分析了Fadell的顺序参数化拓扑复杂性 - Neuwirth纤维化，这与移动多个机器人的问题避免了与其他机器人碰撞以及欧几里得空间中的障碍有关的问题。此外，在前面的论文中，我们发现了Fadell的顺序参数式拓扑复杂性-Euclidean Space $ \ bbb r^d $的neuwirth捆绑包以及奇数尺寸以及情况$ d = 2 $。在本文中，我们为任意的$ d \ ge 2 $提供完整的答案。此外，我们提出了一种明确的运动计划算法，用于控制$ \ bbb r^d $中的多个机器人，具有最小的拓扑复杂性；该算法适用于任何数字$ n $的机器人和任何数字$ m \ ge 2 $的障碍物。
This is a continuation of our recent paper in which we developed the theory of sequential parametrized motion planning. 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. In the previous publication we analysed the sequential parametrized topological complexity of the Fadell - Neuwirth fibration which in relevant to the problem of moving multiple robots avoiding collisions with other robots and with obstacles in the Euclidean space. Besides, in the preceeding paper we found the sequential parametrised topological complexity of the Fadell - Neuwirth bundle for the case of the Euclidean space $\Bbb R^d$ of odd dimension as well as the case $d=2$. In the present paper we give the complete answer for an arbitrary $d\ge 2$ even. Moreover, we present an explicit motion planning algorithm for controlling multiple robots in $\Bbb R^d$ having the minimal possible topological complexity; this algorithm is applicable to any number $n$ of robots and any number $m\ge 2$ of obstacles.
