Automated Perpendicular Parking System with Approximated Clothoid-Based Local Path Planning

Abstract

This paper proposes an automated perpendicular parking system using approximated clothoid-based local path planning and a virtual towing method. Clothoid path planning provides smooth maneuvering, but we cannot obtain a closed-form solution. Further, it costs computational overhead. To cope with these problems, we present a novel vehicle control algorithm with approximated clothoid-based local path planning. We show that a parking control system could be presented as a closed-loop system by integrating path planning and control. The closed-loop system is represented as a discrete linear time-varying system and its stability is proved using the Lyapunov stability theorem. In the proposed system, we also see that a numerical singularity problem may incur, which could bring undesirable steering. To avoid numerical singularity, we also propose a virtual towing method. From numerical simulations, we show that the vehicle converges smoothly to the parking spot.