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Geometrical methods have had a profound impact in the development of modern nonlinear control theory. Fundamental results such as the orbit theorem, feedback linearization, disturbance decoupling or the various controllability tests for non-linear systems are all deeply rooted on a geometric view of control theory. It is perhaps surprising, and possibly(More)
Flat sub-Riemannian structures are local approximations — nilpo-tentizations — of sub-Riemannian structures at regular points. Lie algebras of symmetries of flat maximal growth distributions and sub-Riemannian structures of rank two are computed in dimensions 3, 4, and 5. A sub-Riemannian geometry is a triple (M, ∆, ·, ··), where M is a smooth man-ifold, ∆(More)
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(More)
The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping is described. On this basis an explicit characterization of the cut locus and Maxwell set is obtained. The optimal(More)