| Issue |
ESAIM: COCV
Volume 17, Number 2, April-June 2011
|
|
|---|---|---|
| Page(s) | 293 - 321 | |
| DOI | https://doi.org/10.1051/cocv/2010005 | |
| Published online | 24 March 2010 | |
Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*
Program Systems Institute, Pereslavl-Zalessky, Russia. This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
28
May
2009
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.
Mathematics Subject Classification: 49J15 / 93B29 / 93C10 / 53C17 / 22E30
Key words: Optimal control / sub-Riemannian geometry / differential-geometric methods / left-invariant problem / group of motions of a plane / rototranslations / cut locus / optimal synthesis
The author is partially supported by Russian Foundation for Basic Research, Project No. 09-01-00246-a, and by the Program of Presidium of Russian Academy of Sciences “Mathematical control theory”.
© EDP Sciences, SMAI, 2010
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