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Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*

Published online by Cambridge University Press:  24 March 2010

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 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.

Keywords

Optimal controlsub-Riemannian geometrydifferential-geometric methodsleft-invariant problemgroup of motions of a planerototranslationscut locusoptimal synthesis
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 2 , April 2011 , pp. 293 - 321
Copyright
© EDP Sciences, SMAI, 2010

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