Abstract:
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.
Key words and phrases:optimal control, time-minimizating problem, Wolfram Mathematica, kinematic.