Modelling of optimal parking for a wheeled robot

We consider a kinematic model for a differential wheeled robot. The corresponding optimal control problem is stated in the general form with an arbitrary domain for the controls and an arbitrary minimized functional. The known specifications of the problem lead to the classical models given by Markov-Dubins problem, Reeds-Shepp problem, Euler’s elastic problem and the sub-Riemannian problem on the rototranslation group. We describe the algorithms for constructing optimal trajectories of the robot for the given boundary conditions. These algorithms are implemented in an interface software developed in Wolfram Mathematica system. Additionally, we allow to equip the robot with a trailer. Trailer trajectories are computed for each model. We assume that the robot stays at the initial and final positions with zero velocities and accelerates to the given maximum linear velocity along the way. The interface program animates the movement of the robot (with a trailer) along the chosen optimal paths.