Dubins' problem is intrinsically three-dimensional

Mittenhuber, D.. "Dubins' problem is intrinsically three-dimensional." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 1-22. <http://eudml.org/doc/197376>.

@article{Mittenhuber2010,
abstract = { In his 1957 paper [1] L. Dubins considered the problem of finding shortest differentiable arcs in the plane with curvature bounded by a constant and prescribed initial and terminal positions and tangents. One can generalize this problem to non-euclidean manifolds as well as to higher dimensions (cf. [15]). 
Considering that the boundary data - initial and terminal position and tangents - are genuinely three-dimensional, it seems natural to ask if the n-dimensional problem always reduces to the three-dimensional case. In this paper we will prove that this is true in the euclidean as well as in the noneuclidean case. At first glance one might consider this a trivial problem, but we will also give an example showing that this is not the case. 
},
author = {Mittenhuber, D.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Noneuclidean Dubins' problem; length-minimizing curves with bounded curvature; variational problems on Lie groups; Serret-Frenet differential system; maximum principle.; optimal arcs; Pontryagin's maximum principle; Dubins problem},
language = {eng},
month = {3},
pages = {1-22},
publisher = {EDP Sciences},
title = {Dubins' problem is intrinsically three-dimensional},
url = {http://eudml.org/doc/197376},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Mittenhuber, D.
TI - Dubins' problem is intrinsically three-dimensional
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 1
EP - 22
AB - In his 1957 paper [1] L. Dubins considered the problem of finding shortest differentiable arcs in the plane with curvature bounded by a constant and prescribed initial and terminal positions and tangents. One can generalize this problem to non-euclidean manifolds as well as to higher dimensions (cf. [15]). 
Considering that the boundary data - initial and terminal position and tangents - are genuinely three-dimensional, it seems natural to ask if the n-dimensional problem always reduces to the three-dimensional case. In this paper we will prove that this is true in the euclidean as well as in the noneuclidean case. At first glance one might consider this a trivial problem, but we will also give an example showing that this is not the case. 

LA - eng
KW - Noneuclidean Dubins' problem; length-minimizing curves with bounded curvature; variational problems on Lie groups; Serret-Frenet differential system; maximum principle.; optimal arcs; Pontryagin's maximum principle; Dubins problem
UR - http://eudml.org/doc/197376
ER -