10 citations · 12 across the 7 of their papers we have counts for
5 papers · 1 filter
On the topology of the spaces of curvature constrained plane curves
José Ayala
It is well known that plane curves with the same endpoints are homotopic. An analogous claim for plane curves with the same endpoints and bounded curvature still remains open. In t…
The classification of homotopy classes of bounded curvature paths
José Ayala, J. Hyam Rubinstein
A bounded curvature path is a continuously differentiable piecewise path with bounded absolute curvature that connects two points in the tangent bundle of a surface. In this…
Length minimising bounded curvature paths in homotopy classes
José Ayala
Choose two points in the tangent bundle of the Euclidean plane . In this work we characterise the immersed length minimising paths with a prescribed…
Non-uniqueness of the homotopy class of bounded curvature paths
José Ayala, Hyam Rubinstein
A bounded curvature path is a continuously differentiable piecewise path with a bounded absolute curvature that connects two points in the tangent bundle of a surface. In thi…
A geometric approach to shortest bounded curvature paths
José Ayala, David Kirszenblat, J. Hyam Rubinstein
Consider two elements in the tangent bundle of the Euclidean plane . In this work we address the problem of characterizing the paths of bounded curva…