论文标题
飞机上无碰撞运动计划的参数化拓扑复杂性
Parametrized topological complexity of collision-free motion planning in the plane
论文作者
论文摘要
参数化运动计划算法具有高度的通用性和灵活性，因为它们旨在在各种外部条件下工作，这些外部条件被视为参数并构成了基础运动计划问题的输入的一部分。在本文中，我们分析了平面中许多不同点的运动的参数化运动计划问题，而无需碰撞并避免具有先验未知位置的多个不同的障碍。这补充了我们先前的工作[ARXIV：2009.06023]，其中引入了参数化运动计划算法，并对三维空间中的无障碍碰撞运动计划问题进行了充分研究。与其空间类似物相比，平面案例需要不同的代数和拓扑工具。
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying motion planning problem. In this paper, we analyze the parameterized motion planning problem for the motion of many distinct points in the plane, moving without collision and avoiding multiple distinct obstacles with a priori unknown positions. This complements our prior work [arXiv:2009.06023], where parameterized motion planning algorithms were introduced, and the obstacle-avoiding collision-free motion planning problem in three-dimensional space was fully investigated. The planar case requires different algebraic and topological tools than its spatial analog.
