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

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

2009-03-04

arxiv.org/abs/0903.0727v1

Mathematics

Optimization and Control

63 pages, 49 figures, 14 tables

Scientific paper

A 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.

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