LPV H2 State Feedback Controller for Automated Parking System

Abstract

In this letter, we propose a linear parameter-varying (LPV) kinematic model for automated parking systems. We also design an LPV $\mathcal {H}{2}$ state feedback controller with the proposed model. The vehicle kinematic model is intrinsically a nonlinear system, but we show that the kinematic model can be represented as an LPV kinematic model. The state feedback control gain is obtained using convex interpolation in the $\mathcal {H}{2}$ sense of a linear matrix inequality approach. We will show that the proposed parking system guarantees the stability of the closed-loop system with disturbances. To validate the proposed method, we conduct parking experiments with a test vehicle for two scenarios. Using the proposed LPV $\mathcal {H}{2}$ state feedback controller, the vehicle tracks paths for all scenarios, reaching the final parking spot and showing smooth steering performance. The results show that the lateral position error and the heading angle error are smaller than 0.05 m and 0.005 rad, respectively.