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

Yuri L. Sachkov

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

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

Abstract

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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.

How to cite

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Sachkov, 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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