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arXiv · 1209.2865

Conjugate points in nilpotent sub-Riemannian problem on the Engel group

A. A. Ardentov·Yu. L. Sachkov
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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.

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A. A. Ardentov, Yu. L. Sachkov. 2012-09-13. Conjugate points in nilpotent sub-Riemannian problem on the Engel group. https://arxiv.org/abs/1209.2865

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