Conjugate points in nilpotent sub-Riemannian problem on the Engel group
Optimization and Control
2012-09-14 v1
Abstract
The left-invariant sub-Riemannian problem on the Engel group is considered. This problem is very important as nilpotent approximation of nonholonomic systems in four-dimensional space with two-dimensional control, for instance of a system which describes movement of mobile trailer robot. We study the local optimality of extremal trajectories and estimate conjugate time in this article.
Keywords
Cite
@article{arxiv.1209.2865,
title = {Conjugate points in nilpotent sub-Riemannian problem on the Engel group},
author = {A. A. Ardentov and Yu. L. Sachkov},
journal= {arXiv preprint arXiv:1209.2865},
year = {2012}
}
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19 pages