A procedure is presented for finding the shortest network connecting three given undirected points, subject to a curvature constraint on both the path joining two of the points and the path that connects to the third point. The problem is a generalisation of the Fermat–Torricelli problem and is related to a shortest curvature-constrained path problem that was solved by Dubins. The procedure has the potential to be applied to the optimal design of decline networks in underground mines.
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Grossman et al. (2024) studied this question.
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