Modeling of car parking along Markov-Dubins and Reeds-Shepp paths

We examine three classical model problems to describe optimal car parking: the Markov problem, the Dubins problem, the Reeds-Shepp problem. We investigate the kinematic laws for the trailer when the car is moving along the examined optimal paths. An interface is developed as Mathematica software. It constructs the desired optimal paths and the animation of the car (with a trailer) movement.