In this paper, we address the problem of computing optimal paths throughthree consecutive points for the curvature-constrained forward moving Dubinsvehicle. Given initial and final configurations of the Dubins vehicle, and amidpoint with an unconstrained heading, the objective is to compute themidpoint heading that minimizes the total Dubins path length. We provide anovel geometrical analysis of the optimal path, and establish new properties ofthe optimal Dubins' path through three points. We then show how our method canbe used to quickly refine Dubins TSP tours produced using state-of-the-arttechniques. We also provide extensive simulation results showing theimprovement of the proposed approach in both runtime and solution quality overthe conventional method of uniform discretization of the heading at themid-point, followed by solving the minimum Dubins path for each discreteheading.
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