In this brief, a simple control approach is proposed for the multichain systems based on a switching algorithm of two sets of steering laws. Global exponential convergence to any prescribed norm bound ( -convergence) is guaranteed and the convergence rate is explicitly given. This approach has a distinctive feature that one of the inputs (driving input) is free. This feature plays a key role in achieving realistic parking tasks. For the design of steering laws, a method based on backstepping is proposed and analyzed in detail. Further, this control algorithm is applied to the automatic parking systems. The corresponding system package is developed which is composed of control laws for the steering angle and the driving velocity, algorithms for various kinds of parking tasks under steering angle and parking space limitations. A prototype system is built to validate this package, and the system works well in experiments subject to various parking situations.Index Terms-Automatic parking, chained system, constraint of parking space, exponential -convergence, parking algorithm, piecewise smooth algorithm, steering angle limitation, switching control.

This paper aims at developing a practical automatic parking technology for 4-wheeled cars, which is able to park cars subject to parking space constraint and steering angle saturation. The feedback law is designed based on the switching control method proposed by the authors for chained systems. The focus of this paper is to prove a condition on the state under which the stability is guaranteed even when the steering angle is saturated. The proposed method is validated by numerous parking experiments.

The control of position and orientation angle of 4-wheeled cars is the central part in the development of automatic parking systems which is going to play an important role in ITS. There have been many approaches to this problem from a viewpoint of application of nonholonomic control theory. But there are still some practical problems such as steering angle limitation that need to be addressed. In this paper, a method is proposed to deal with the steering control with a steering angle limitation. The basic idea is to contruct a circle family and let the car approach the circle family that leads to the destination asymptotically. Both theoretical and experimental results are described.

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