Maxwell strata in sub-Riemannian problem on the group of motions of a plane

Maxwell strata in sub-Riemannian problem on the group of motions of a plane

The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized...

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Veröffentlicht in:ESAIM. Control, optimisation and calculus of variations optimisation and calculus of variations, 2010-04, Vol.16 (2), p.380-399
Hauptverfasser: Moiseev, Igor, Sachkov, Yuri L.
Format: Artikel
Sprache:eng
Schlagworte:
22E30
49J15
53C17
93B29
93C10
Control theory
differential-geometric methods
exponential mapping
left-invariant problem
Lie group
Lie groups
Maxwell stratum
Optimal control
Pontryagin Maximum Principle
Robotics
sub-Riemannian geometry
symmetries
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Beschreibung
Zusammenfassung:The left-invariant sub-Riemannian problem on the group of motions of a plane is considered. Sub-Riemannian geodesics are parameterized by Jacobi's functions. Discrete symmetries of the problem generated by reflections of pendulum are described. The corresponding Maxwell points are characterized, on this basis an upper bound on the cut time is obtained.
ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2009004