论文标题
参数化运动计划算法的拓扑
Topology of parametrised motion planning algorithms
论文作者
论文摘要
在本文中，我们介绍并研究了一个新的参数化拓扑复杂性的概念，这是一个由机器人技术的运动计划问题激励的拓扑结构。在参数设置中，运动计划算法具有高度的普遍性和灵活性，它可以在各种外部条件（例如障碍物的位置等）下起作用。我们明确计算了3维空间中许多颗粒（机器人）的无障碍碰撞运动的参数化拓扑复杂性。我们的结果表明，参数化的拓扑复杂性可以显着高于标准（未参数）不变性。
In this paper we introduce and study a new concept of parametrised topological complexity, a topological invariant motivated by the motion planning problem of robotics. In the parametrised setting, a motion planning algorithm has high degree of universality and flexibility, it can function under a variety of external conditions (such as positions of the obstacles etc). We explicitly compute the parameterised topological complexity of obstacle-avoiding collision-free motion of many particles (robots) in 3-dimensional space. Our results show that the parameterised topological complexity can be significantly higher than the standard (nonparametrised) invariant.
