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

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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 motion of mobile robot with a trailer. We study local optimality of extremal trajectories and estimate conjugate time in this article.

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Authors and Affiliations

  1. Program Systems Institute of RAS, Pereslavl-Zalessky, Russia

    A. A. Ardentov & Yu. L. Sachkov

Authors
  1. A. A. Ardentov
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  2. Yu. L. Sachkov
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Correspondence to A. A. Ardentov.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 82, Nonlinear Control and Singularities, 2012.

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Ardentov, A.A., Sachkov, Y.L. Conjugate points in nilpotent sub-Riemannian problem on the Engel group. J Math Sci 195, 369–390 (2013). https://doi.org/10.1007/s10958-013-1584-2

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  • DOI: https://doi.org/10.1007/s10958-013-1584-2

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