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We present optimal motion planning algorithms which can be used in designingpractical systems controlling objects moving in Euclidean space withoutcollisions. Our algorithms are optimal in a very concrete sense, namely, theyhave the minimal possible number of local planners. Our algorithms aremotivated by those presented by Mas-Ku and Torres-Giese (as streamlined byFarber), and are developed within the more general context of the multitasking(a.k.a.~higher) motion planning problem. In addition, an eventualimplementation of our algorithms is expected to work more efficiently thanprevious ones when applied to systems with a large number of moving objects.

Multitasking collision-free motion planning algorithms in Euclidean spaces