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

Published online by Cambridge University Press:  11 August 2009

Yuri L. Sachkov
Yuri L. Sachkov*
Affiliation:
Program Systems Institute, Pereslavl-Zalessky, Russia. sachkov@sys.botik.ru
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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.

Keywords

Optimal controlsub-Riemannian geometrydifferential-geometric methodsleft-invariant problemgroup of motions of a planerototranslationsconjugate timecut time
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 16 , Issue 4 , October 2010 , pp. 1018 - 1039
Copyright
© EDP Sciences, SMAI, 2009

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