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.

翻译：组合式运动规划算法具有高度的普遍性和灵活性,因为设计这些算法是为了在各种外部条件下工作,这些外部条件被视为参数,并构成基本运动规划问题的一部分。在本文中,我们分析了飞机上许多不同点运动的参数化运动规划问题,没有碰撞地移动,并避免了具有先验未知位置的多重不同障碍。这补充了我们以前的工作[arXiv:2009.06.023],采用了参数化运动规划算法,充分调查了三维空间避免碰撞行动规划问题的障碍。 平板案需要与空间模拟不同的代数和地形学工具。