Fan, Z. and Chen, H., "Study on Path Following Control Method for Automatic Parking System Based on LQR," SAE Int. J. Passeng. Cars – Electron. Electr. Syst. 10(1):41-49, 2017, doi:10.4271/2016-01-1881.
The Automatic Parking System (APS) is consisted of environmental perception, path planning and path following. As one of the key technologies in APS, path following module controls the lateral movement of the vehicle during the parking process. A mature path following module should meet all the performance indexes of high precision, fast convergence, convenient tuning and good passenger comfort. However, the current path following control methods can only meet parts of the performance indexes, instead of all. In order to satisfy all the performance indexes above, a path following control method based on Linear Quadratic Regulator (LQR) is proposed in this paper. Firstly, the linearization of the non-linear vehicle kinematic model was done to establish a linear system of the path following error. Secondly, LQR optimal control was used to achieve the closed-loop control of this linear system to guarantee its stability and fast convergence property. In this process, optimal quadratic performance index of LQR can be achieved by balancing the weights of the state variables and inputs through the matrix Q and R. For this reason, the control parameters can be conveniently tuned and calibrated. Thirdly, the feasibility of this method was verified through co-simulation of Simulink and Carsim and field tests of Roewe E50 electric vehicle, and the path following error can be limited within 10 centimeters in both parallel parking and vertical parking.