On the topology of the spaces of curvature constrained plane curves

DOI10.1515/advgeom-2017-0015zbMath1386.53003arXiv1404.4378OpenAlexW2963887365MaRDI QIDQ1707397

José L. Ayala

Publication date: 29 March 2018

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.4378

zbMATH Keywords

homotopy classesbounded curvatureregular homotopy

Mathematics Subject Classification ID

Spaces of embeddings and immersions (58D10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Curves in Euclidean and related spaces (53A04) Topology of infinite-dimensional manifolds (57N20)

Related Items (4)

Curvature-constrained path elongation with expected length for Dubins vehicle ⋮ Elongation of curvature-bounded path ⋮ Spaces of curves with constrained curvature on hyperbolic surfaces ⋮ Census of bounded curvature paths

Uses Software

• Dubins explorer

Cites Work

• Unnamed Item
• The classification of homotopy classes of bounded curvature paths
• Reachability by paths of bounded curvature in a convex polygon
• Length minimising bounded curvature paths in homotopy classes
• A geometric approach to shortest bounded curvature paths
• Optimal paths for a car that goes both forwards and backwards
• Census of bounded curvature paths
• On plane curves with curvature
• On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents
• Plane Motion with Curvature Limitations
• An Application of the Maximum Principle to the Geometry of Plane Curves
• Plane Motion of a Particle Subject to Curvature Constraints
• Set of reachable positions for a car

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