Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Ardentov, A. A."'
Autor:
Ardentov, Andrei, Hakavuori, Eero
We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachkov for the sub-Riemannian Cartan problem. Along the proof, we obtain a
Externí odkaz:
http://arxiv.org/abs/2107.06730
We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose front tracks are either non-inflectional Euler elasticae or straight li
Externí odkaz:
http://arxiv.org/abs/2010.04201
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for arbitrary $\Omeg
Externí odkaz:
http://arxiv.org/abs/2004.10194
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bou
Externí odkaz:
http://arxiv.org/abs/1810.05431
In this paper we study a sub-Finsler geometric problem on the free-nilpotent group of rank 2 and step 3. Such a group is also called Cartan group and has a natural structure of Carnot group, which we metrize considering the $\ell_\infty$ norm on its
Externí odkaz:
http://arxiv.org/abs/1810.03869
Autor:
Ardentov, A. A., Sachkov, Yu. L.
We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kine
Externí odkaz:
http://arxiv.org/abs/1710.00216
Autor:
Ardentov, Andrey A.
The work studies a number of approaches to solving motion planning problem for a mobile robot with a trailer. Different control models of car-like robots are considered from the differential-geometric point of view. The same models can be also used f
Externí odkaz:
http://arxiv.org/abs/1612.01344
In this note we describe a relation between Euler's elasticae and sub-Riemannian geodesics on SE(2). Analyzing the Hamiltonian system of Pontryagin maximum principle we show that these two curves coincide only in the case when they are segments of a
Externí odkaz:
http://arxiv.org/abs/1609.03704
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally maximizing. Secon
Externí odkaz:
http://arxiv.org/abs/1507.07326
Autor:
Ardentov, A. A., Sachkov, Yu. L.
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
Externí odkaz:
http://arxiv.org/abs/1408.6651