Optimal paths for a curvature-constrained vehicle on a unit sphere are CGC or concatenations of C segments, generalized from prior results to all r ≤ √3/2.
First, the expression for A2 + B2 can be obtained as A2 + B2 = 4 1 − 2r2 1 − r2 (1 + cβ) 2
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A New Approach to Motion Planning in 3D for a Dubins Vehicle: Special Case on a Sphere
Optimal paths for a curvature-constrained vehicle on a unit sphere are CGC or concatenations of C segments, generalized from prior results to all r ≤ √3/2.