Geometric Path Planning and Tracking Control with Bounded Steering Angle for the Parking Problem of Automatic Vehicles

In this paper, we deal with the problems of geometric collision-free path planning and feedback steering control for automatic perpendicular reverse parking maneuver of front wheel steering vehicles. An important condition to achieve effective collision-free parking is to determine a convenient start position of the vehicle depending on the widths of the parking aisle and the parking place, as well as, the dimensions and the steering capabilities of the car. Using Dubins strategy, geometric collision-free path planning based on admissible circular arcs within the available spot is proposed, in order to steer the vehicle moving backward with a given velocity profile and bounded steering angle in the direction of the parking place. A constrained feedback control is designed, which achieves quick steering in tiny spots and parks (practical stabilization) the vehicle in the parking place. The stability of the closed-loop system is analyzed using Lyapunov stability theory. Simulation results are presented to illustrate the effectiveness of the proposed approach.