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cut time

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
Yuri L. Sachkov
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 16 / Issue 4 / October 2010

Published online by Cambridge University Press:

11 August 2009, pp. 1018-1039

Print publication:

October 2010
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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.