Algorithmic Foundations of Robotics XV - Proceedings of the Fifteenth Workshop on the Algorithmic Foundations of Robotics
Algorithmic Foundations of Robotics XV - Proceedings of the Fifteenth Workshop on the Algorithmic Foundations of Robotics
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机器人算法基础 XV - 第十五届机器人算法基础研讨会论文集
DOI：
10.1007/978-3-031-21090-7_1
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Farber M
中科院分区：
文献类型：
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作者：
Farber M
在本文中，我们研究的参数化运动规划算法，提供了通用和灵活的解决方案，以不同的运动规划问题。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的输入的一部分。在最近的文章的基础上，我们进一步研究了参数化拓扑复杂性的概念。我们详细分析了在欧几里得空间中存在多个障碍物的情况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例子。提出了一种显式参数化运动规划算法，解决了机器人和障碍物的运动规划问题。该算法是最优的，对任意奇数都具有最小可能的拓扑复杂度。此外，我们描述了一个修改的算法，这是最佳的foreven。利用Stiefel-Whitney特征类分析了球丛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 the 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 in. This algorithm is optimal, it has minimal possible topological complexity for anyodd. Besides, we describe a modification of this algorithm which is optimal foreven. We also analyse the parametrized topological complexity of sphere bundles using the Stiefel - Whitney characteristic classes.