Program Systems Institute of RAS
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
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.
Ardentov A. A.
Controlling of a Mobile Robot with a Trailer and Its Nilpotent Approximation
2016, vol. 21, no. 7-8, pp. 775-791
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.