  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.
