Parametrised collision-free optimal motion planning algorithms in Euclidean spaces
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We present optimal parametrised motion planning algorithms which can be used in designing practical systems controlling objects that move in Euclidean d-space, with d≥ 2 even, without collisions and in the presence of two obstacles with unknown a priori positions. Our algorithms are optimal in a very concrete sense, namely, they have the minimal possible number of local planners.
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