Conjugate points in nilpotent sub-Riemannian problem on the Engel group
By A. Ardentov, Yuri L. Sachkov. 2012
57 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f73cc41b583cef7d2a5693bcc74d4e3d14779c94
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Measure contraction properties of Carnot groups (2015, background): “Checking whether the Engel group satisfies the MCP(0, N ) should be possible, at least in principle, as expressions for the Jacobian determinant are known [6].”