# 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 (2011)

- Volume: 17, Issue: 2, page 293-321
- ISSN: 1292-8119

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topSachkov, 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 17.2 (2011): 293-321. <http://eudml.org/doc/276331>.

@article{Sachkov2011,

abstract = {
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.
},

author = {Sachkov, Yuri L.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Optimal control; sub-Riemannian geometry; differential-geometric methods; left-invariant problem; group of motions of a plane; rototranslations; cut locus; optimal synthesis; optimal control},

language = {eng},

month = {5},

number = {2},

pages = {293-321},

publisher = {EDP Sciences},

title = {Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*},

url = {http://eudml.org/doc/276331},

volume = {17},

year = {2011},

}

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

DA - 2011/5//

PB - EDP Sciences

VL - 17

IS - 2

SP - 293

EP - 321

AB -
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.

LA - eng

KW - Optimal control; sub-Riemannian geometry; differential-geometric methods; left-invariant problem; group of motions of a plane; rototranslations; cut locus; optimal synthesis; optimal control

UR - http://eudml.org/doc/276331

ER -

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- I. Moiseev and Yu. L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV (2009) DOI: . Zbl1217.49037DOI10.1051/cocv/2009004
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- Yu.L. Sachkov, Conjugate and cut time in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV (2009) DOI: . DOI10.1051/cocv/2009031
- A.M. Vershik and V.Y. Gershkovich, Nonholonomic Dynamical Systems. Geometry of distributions and variational problems, in Itogi Nauki i Tekhniki: Sovremennye Problemy Matematiki, Fundamental'nyje Napravleniya16, VINITI, Moscow (1987) 5–85 [in Russian]. [English translation in Encyclopedia of Math. Sci.16, Dynamical Systems7, Springer Verlag.]
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## Citations in EuDML Documents

top- Yuri L. Sachkov, Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
- Ross M. Adams, Rory Biggs, Claudiu C. Remsing, Two-input control systems on the euclidean group SE (2)
- Ugo Boscain, Remco Duits, Francesco Rossi, Yuri Sachkov, Curve cuspless reconstruction via sub-riemannian geometry

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