Controlling of a mobile robot with a trailer and its nilpotent approximation

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 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.
Comment: 26 pages, 15 figures