{"paper":{"title":"On sub-Riemannian geodesics in $SE(3)$ whose spatial projections do not have cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.OC","authors_text":"Alexey Mashtakov, Arpan Ghosh, Remco Duits, Tom Dela Haije","submitted_at":"2013-05-26T19:43:06Z","abstract_excerpt":"We consider the problem $\\mathbf{P_{curve}}$ of minimizing $\\int \\limits_0^L \\sqrt{\\xi^2 + \\kappa^2(s)} \\, {\\rm d}s$ for a curve $\\mathbf{x}$ on $\\mathbb R$ with fixed boundary points and directions. Here the total length $L\\geq 0$ is free, $s$ denotes the arclength parameter, $\\kappa$ denotes the absolute curvature of $\\mathbf{x}$, and $\\xi>0$ is constant. We lift problem $\\mathbf{P_{curve}}$ on $\\mathbb R^3$ to a sub-Riemannian problem $\\mathbf{P_{mec}}$ on $\\operatorname{SE(3)}\\nolimits/(\\{\\mathbf{0}\\}\\times \\operatorname{SO(2)}\\nolimits)$. Here, for admissible boundary conditions, the spat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6061","kind":"arxiv","version":9},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}