Cut time in sub-Riemannian problem on Engel group
Differential Geometry
2014-08-29 v1 Optimization and Control
Abstract
The left-invariant sub-Riemannian problem on the Engel group is considered. The problem gives the nilpotent approximation to generic nonholonomic systems in four-dimensional space with two-dimensional control, for instance to a system which describes motion of mobile robot with a trailer. The global optimality of extremal trajectories is studied via geometric control theory. The global diffeomorphic structure of the exponential mapping is described. As a consequence, the cut time is proved to be equal to the first Maxwell time corresponding to discrete symmetries of the exponential mapping.
Cite
@article{arxiv.1408.6651,
title = {Cut time in sub-Riemannian problem on Engel group},
author = {A. A. Ardentov and Yu. L. Sachkov},
journal= {arXiv preprint arXiv:1408.6651},
year = {2014}
}