A geometric approach to shortest bounded curvature paths (Q1784346)

A planar bounded curvature path corresponds to a C\(^{1}\) and piecewise C\(^{2}\) path lying in \(\mathbb{R}^{2}\) . These paths connect two elements in the tangent bundle TR\(^{2}\) and have curvature bounded by a positive constant curvature. The authors present a geometric proof for the classification of length minimizers in spaces of planar bounded curvature paths. They prove that length minimising bounded curvature paths have complexity at most three. Techniques developed in the paper allow to achieve the classification of the homotopy classes of bounded curvature paths and length minimizers therein.