An Exponentially $epsilon$ -Convergent Control Algorithm for Chained Systems and Its Application to Automatic Parking Systems

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 (epsi-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