# Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 4, page 1018-1039
- ISSN: 1292-8119

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topSachkov, Yuri L.. "Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane." ESAIM: Control, Optimisation and Calculus of Variations 16.4 (2010): 1018-1039. <http://eudml.org/doc/250728>.

@article{Sachkov2010,

abstract = {
The left-invariant sub-Riemannian problem on the group of motions
(rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized.
Lower and upper bounds on the first conjugate time are proved.
The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete
symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.
},

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; conjugate time; cut time; optimal control},

language = {eng},

month = {10},

number = {4},

pages = {1018-1039},

publisher = {EDP Sciences},

title = {Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane},

url = {http://eudml.org/doc/250728},

volume = {16},

year = {2010},

}

TY - JOUR

AU - Sachkov, Yuri L.

TI - Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/10//

PB - EDP Sciences

VL - 16

IS - 4

SP - 1018

EP - 1039

AB -
The left-invariant sub-Riemannian problem on the group of motions
(rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized.
Lower and upper bounds on the first conjugate time are proved.
The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete
symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.

LA - eng

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

UR - http://eudml.org/doc/250728

ER -

## References

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## Citations in EuDML Documents

top- Igor Moiseev, Yuri L. Sachkov, Maxwell strata in 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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