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

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dc.creatorSachkov, Yu. L.
dc.date2009-03-04
dc.date.accessioned2026-07-07T12:49:01Z
dc.date.available2026-07-07T12:49:01Z
dc.descriptionA solution to the left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is obtained. 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. An explicit global description of the cut locus is obtained. Optimal synthesis is described.
dc.description63 pages, 49 figures, 14 tables
dc.identifierhttps://arxiv.org/abs/0903.0727
dc.identifierhttp://arxiv.org/abs/0903.0727
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/222258
dc.subjectOptimization and Control
dc.subject49J15; 93B29; 93C10; 53C17; 22E30
dc.titleCut time and optimal synthesis in sub-Riemannian problem on the group of motions of a plane
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