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

Abstract

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.

Development of A Practical Automatic Parking Technology for Automobiles

“…The purpose is to drive the state vector z = (z 0 , z 1 , z 2 ) T to zero. The design is carried out according to the switching control algorithm and the Backstepping based design approach of [3]. That is, 1.…”

“…In [2] a method was proposed by the authors based on the tracking of circle family, but this method has a drawback that the steering angle oscillates when the vehicle approaches the origin. So in this paper, a method is proposed to address the steering angle constraint explicitly, based on the switching control approach of the authors [3]. In particular, a stability condition is revealed under which the vehicle can be parked in face of steering angle saturation.…”

Control of mobile robot by switching traveling direction and control gain

“…Therefore, many controllers for chained systems have been proposed. Such controllers include time-varying functions or non-smooth functions such as a sign function [5][6][7][8][9][10][11][12]. The control design method based on the time-state control form is also one such controller [13].…”

Fuzzy Logic Based Autonomous Parallel Parking System with Kalman Filtering

“…Currently there are two different approaches adapted by investigators, the path planning approach [5] and skill based approaches [6]- [8]. In the path planning approach, a driving path is planned before the vehicle starts moving based on knowledge of the size of the parking space and vehicle dynamics.…”

“…A similar idea was suggested in [7] where supersonic transducers are implemented as distance sensors. Reference [8] proposed a switching algorithm of two sets of steering laws. The control algorithm works very nicely but in the experiment the design needs two LEDs and a camera mounted on the roof to detect the vehicle position.…”