We present optimal motion planning algorithms which can be used in designing practical systems controlling objects moving in Euclidean space without collisions. Our algorithms are optimal in a very concrete sense, namely, they have the minimal possible number of local planners. Our algorithms are motivated by those presented by Mas-Ku and Torres-Giese (as streamlined by Farber), and are developed within the more general context of the multitasking (a.k.a.~higher) motion planning problem. In addition, an eventual implementation of our algorithms is expected to work more efficiently than previous ones when applied to systems with a large number of moving objects.

翻译：我们提出了最佳运动规划算法,可用于设计实用的系统,控制在不发生碰撞的欧几里德空间移动的物体。我们的算法在非常具体的意义上是最佳的,即它们拥有尽可能少的当地规划人员。我们的算法是由马斯库和托雷斯-吉塞(由法伯精简)提出的算法所驱动的,是在多任务(a.k.a.~higher)运动规划问题这一更为笼统的背景下制定的。此外,在应用有大量移动物体的系统时,预期最终实施我们的算法将比以往的算法更有效率。