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

2012/09/13 by A. A. Ardentov, Ardentov, A. A., Yu. L. Sachkov +1 · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1209.2865

openalex publication_date 2012/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Abelian instances of nonabelian symplectic reduction
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