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Sequential collision-free optimal motion planning algorithms in punctured Euclidean spaces

In robotics, a topological theory of motion planning was initiated by M. Farber. The multitasking motion planning problem is new and its theoretical part via topological complexity has hardly been developed, but the concrete implementations are still non-existent, and in fact this work takes the first step in this last direction (producing explicit algorithms.) We present optimal motion planning algorithms which can be used in designing practical systems controlling objects moving in Euclidean space without collisions between them and avoiding obstacles. Furthermore, we present the multitasking version of the algorithms.