Geodesic
Conjugate and cut time in the sub-riemannian problem on the group of motions of a plane
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1018-1039

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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.

DOI : 10.1051/cocv/2009031
Classification : 49J15, 93B29, 93C10, 53C17, 22E30
Keywords: optimal control, sub-riemannian geometry, differential-geometric methods, left-invariant problem, group of motions of a plane, rototranslations, conjugate time, cut time 
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     title = {Conjugate and cut time in the sub-riemannian problem on the group of motions of a plane},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1018--1039},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {4},
     year = {2010},
     doi = {10.1051/cocv/2009031},
     mrnumber = {2744160},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009031/}
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Sachkov, Yuri L. Conjugate and cut time in the sub-riemannian problem on the group of motions of a plane. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1018-1039. doi: 10.1051/cocv/2009031

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