The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. In the previous works [Moiseev and Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009004; Sachkov, ESAIM: COCV, DOI: 10.1051/cocv/2009031], extremal trajectories were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping is described. On this basis an explicit characterization of the cut locus and Maxwell set is obtained. The optimal synthesis is constructed.
Mots clés : optimal control, sub-riemannian geometry, differential-geometric methods, left-invariant problem, group of motions of a plane, rototranslations, cut locus, optimal synthesis
@article{COCV_2011__17_2_293_0,
author = {Sachkov, Yuri L.},
title = {Cut locus and optimal synthesis in the sub-riemannian problem on the group of motions of a plane},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {293--321},
publisher = {EDP-Sciences},
volume = {17},
number = {2},
year = {2011},
doi = {10.1051/cocv/2010005},
mrnumber = {2801321},
zbl = {1251.49057},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2010005/}
}
TY - JOUR AU - Sachkov, Yuri L. TI - Cut locus and optimal synthesis in the sub-riemannian problem on the group of motions of a plane JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2011 SP - 293 EP - 321 VL - 17 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2010005/ DO - 10.1051/cocv/2010005 LA - en ID - COCV_2011__17_2_293_0 ER -
%0 Journal Article %A Sachkov, Yuri L. %T Cut locus and optimal synthesis in the sub-riemannian problem on the group of motions of a plane %J ESAIM: Control, Optimisation and Calculus of Variations %D 2011 %P 293-321 %V 17 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2010005/ %R 10.1051/cocv/2010005 %G en %F COCV_2011__17_2_293_0
Sachkov, Yuri L. Cut locus and optimal synthesis in the sub-riemannian problem on the group of motions of a plane. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 2, pp. 293-321. doi : 10.1051/cocv/2010005. http://www.numdam.org/articles/10.1051/cocv/2010005/
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