Multitasking collision-free motion planning algorithms in Euclidean spaces
This work addresses motion planning for controlling multiple objects without collisions, but it appears incremental as it builds on prior algorithms by Mas-Ku and Torres-Giese.
The authors tackled the problem of multitasking collision-free motion planning in Euclidean spaces by developing algorithms with the minimal possible number of local planners, which are expected to work more efficiently for systems with many moving objects.
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.