On sub-Riemannian geodesics in \(\mathrm{SE}(3)\) whose spatial projections do not have cusps

DOI10.1007/s10883-016-9329-4zbMath1364.53033arXiv1305.6061OpenAlexW2465536258WikidataQ59460212 ScholiaQ59460212MaRDI QIDQ334633

T. C. J. Dela Haije, Remco Duits, Arpan Ghosh, Alexey P. Mashtakov

Publication date: 1 November 2016

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.6061

zbMATH Keywords

geodesicssub-Riemannian geometryPontryagin maximum principlespecial Euclidean motion group

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Existence theories for optimal control problems involving ordinary differential equations (49J15) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Sub-Riemannian geometry (53C17)

Related Items (8)

New exact and numerical solutions of the (convection-)diffusion kernels on \(\mathrm{SE}(3)\) ⋮ Time minimization problem on the group of motions of a plane with admissible control in a half-disc ⋮ Sub-Riemannian Geometry in Image Processing and Modeling of the Human Visual System ⋮ Tracking of lines in spherical images via sub-Riemannian geodesics in \(\mathrm{SO}(3)\) ⋮ Asymptotics of Extremal Controls in the Sub-Riemannian Problem on the Group of Motions of Euclidean Space ⋮ Extremal controls in the sub-Riemannian problem on the group of motions of Euclidean space ⋮ Optimal paths for variants of the 2D and 3D Reeds-Shepp car with applications in image analysis ⋮ HARDI segmentation via fourth-order tensors and anisotropy preserving similarity measures

Uses Software

• HamPath

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