Flatness, motion planning and trailer systems

A solution of the motion planning without obstacles for the standard a-trailer system is proposed. This solution relies basically on the fact that the system is flat with the Cartesian coordinates of the last trailer as a linearizing output. The Frenet formulae are used to simplify the calculations and permit to deal with angle constraints. The general 1-trailer system, where the trailer is not directly hitched to the car at the center of the rear axle, is also flat. The geometric construction used for the standard 1-trailer system can be extended to this more realistic system. MATLAB simulations illustrate this method.<>