The classification of homotopy classes of bounded curvature paths (Q314390)

Throughout other three papers and a PhD thesis [Classification of the homotopy classes and minimal length elements in spaces of bounded curvature paths. Melbourne: University of Melbourne (2014)], the authors developed techniques to answer questions about connectivity of the spaces of bounded curvature paths and to establish the minimal length elements in the spaces. Following this work and the program started by \textit{L. E. Dubins} [Pac. J. Math. 11, 471--481 (1961; Zbl 0123.15503)], this paper provides an answer finding necessary and sufficient conditions for two bounded curvature paths in the Euclidean space to lie in the same homotopy class while keeping the curvature bounded at every stage of the deformation.