Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
Program Systems Institute, Pereslavl-Zalessky, Russia. email@example.com
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.
Mathematics Subject Classification: 49J15 / 93B29 / 93C10 / 53C17 / 22E30
Key words: Optimal control / sub-Riemannian geometry / differential-geometric methods / left-invariant problem / group of motions of a plane / rototranslations / conjugate time / cut time
© EDP Sciences, SMAI, 2009