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2013
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# Andrei Ardentov

Program Systems Institute of RAS

## Publications:

 Mashtakov A. P., Ardentov A. A., Sachkov Y. L. Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$ 2016, vol. 21, no. 7-8, pp.  832-839 Abstract In this note we describe a relation between Euler’s elasticae and sub-Riemannian geodesics on $SE(2)$. Analyzing the Hamiltonian system of the Pontryagin maximum principle, we show that these two curves coincide only in the case when they are segments of a straight line. Keywords: elastica, sub-Riemannian geodesic, group of rototranslations Citation: Mashtakov A. P., Ardentov A. A., Sachkov Y. L.,  Relation Between Euler’s Elasticae and Sub-Riemannian Geodesics on $SE(2)$, Regular and Chaotic Dynamics, 2016, vol. 21, no. 7-8, pp. 832-839 DOI:10.1134/S1560354716070066
 Ardentov A. A. Controlling of a Mobile Robot with a Trailer and Its Nilpotent Approximation 2016, vol. 21, no. 7-8, pp.  775-791 Abstract This work studies a number of approaches to solving the 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 also be used for controlling a mobile robot with a trailer. However, in cases where the position of the trailer is of importance, i.e., when it is moving backward, a more complex approach should be applied. At the end of the article, such an approach, based on recent works in sub-Riemannian geometry, is described. It is applied to the problem of reparking a trailer and implemented in the algorithm for parking a mobile robot with a trailer. Keywords: mobile robot, trailer, motion planning, sub-Riemannian geometry, nilpotent approximation Citation: Ardentov A. A.,  Controlling of a Mobile Robot with a Trailer and Its Nilpotent Approximation, Regular and Chaotic Dynamics, 2016, vol. 21, no. 7-8, pp. 775-791 DOI:10.1134/S1560354716070017