We recapitulate the achievement about the Dubins path as well as some precise proofs which are important but omitted by Dubins. Then we prove that the shortest path (R*-geodesic) in environments with an obstacle consists of no more than five segments, each of which is either an arc or a straight line. To obtain suchR*-geodesic, an effective algorithm is presented followed by a numerical simulation as verification.
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Yang et al. (2013) studied this question.
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