Perfect Parallel Parking Via Pontryagin’s Principle

Abstract

Parallel parking of an automobile can be a frustrating exercise for the driver. A simple, on vehicle control augmentation design for parallel parking is described in the paper. Using a steering control model, parking is cast as an optimal control problem. The minimization of a path length objective function, which was constrained by the bounds on the steering control angle, provided the setting for the problem definition. Pontryagin’s maximum principal was employed to discover a family of optimal trajectories that guaranteed perfect parallel parking. A bang-bang controller logic was shown to result. The design was experimentally tested using a light duty truck outfitted with a drive-by-wire capability.