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arXiv · 1408.6651

Cut time in sub-Riemannian problem on 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. 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.

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A. A. Ardentov, Yu. L. Sachkov. 2014-08-28. Cut time in sub-Riemannian problem on Engel group. https://arxiv.org/abs/1408.6651

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