论文标题
部分可观测时空混沌系统的无模型预测
Parametrized motion planning and topological complexity
论文作者
论文摘要
在本文中，我们研究了对运动计划的参数性运动计划算法，这些算法为各种运动计划问题提供了通用和灵活的解决方案。这种算法旨在在各种外部条件下起作用，这些外部条件被视为参数，并用作算法输入的一部分。继续最近的论文，我们进一步研究了参数化拓扑复杂性的概念。我们全面详细分析了在欧几里得空间中有多个障碍的存在下控制一群机器人的问题，这为我们提供了一个自然的激励榜样。我们提出了一种明确的参数化运动计划算法解决任何数量的机器人和障碍的运动计划问题。该算法是最佳的，对于任何D奇数，它具有最小的拓扑复杂性。此外，我们描述了该算法的修改，该算法对D甚至最佳。我们还使用Stiefel -Whitney特性类别分析球体束的参数化拓扑复杂性。
In this paper we study paramertized motion planning algorithms which provide universal and flexible solutions to diverse motion planning problems. Such algorithms are intended to function under a variety of external conditions which are viewed as parameters and serve as part of the input of the algorithm. Continuing a recent paper, we study further the concept of parametrized topological complexity. We analyse in full detail the problem of controlling a swarm of robots in the presence of multiple obstacles in Euclidean space which served for us a natural motivating example. We present an explicit parametrized motion planning algorithm solving the motion planning problem for any number of robots and obstacles.. This algorithm is optimal, it has minimal possible topological complexity for any d odd. Besides, we describe a modification of this algorithm which is optimal for d even. We also analyse the parametrized topological complexity of sphere bundles using the Stiefel - Whitney characteristic classes.
