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Mr. John Smith

Job title



Automated driving is one of the main technologies in which the automotive and transport industry are investing to improve safety on roads and in urban environments. Tracking previously planned paths is a fundamental problem for automated driving systems. Different control techniques have been used to address the problem of path tracking. Model Predictive Control has shown good results [1], [2], although the characteristics of the algorithm mean that control gains have to be calculated online and this may compromise its implementation in real vehicles. Robust H∞ control deals with this problem by calculating the control gains offline, but most studies assume that all vehicle states used for control are known [3], which is not always possible [4]. In addition, the higher the complexity of the systems in the vehicle, the higher the probability of failure in some component. Therefore, it is important to analyze the operation of sensors that provide information to the control system and actuators that execute the control signal and to be able to identify and estimate the magnitude of the failure in order to subsequently take it into account in the control algorithm. This paper deals with the path tracking problem by means of a robust H∞ control with a Static Output-Feedback control law, since not all states are known in the vehicle model. Obtention of the control gains has been carried out using an LMI approach, making use of Lyapunov Functionals to ensure system stability. Since the state space model of the vehicle depends on the time-varying velocity, a polytopic gain scheduling model has been used to deal with the non-linearities in the system’s matrices. In addition, an Unknown Input Observer (UIO) has been used to estimate faults in the system's actuators. The main advantage of the Static Output-Feedback control law is its simplicity for implementation. However, finding a solution for this formulation with available numerical solvers can become challenging [4]. This work proposes a new approach to obtain a feasible solution to the optimization problem for path tracking of an automated vehicle, while estimating actuator faults at the same time. To evaluate the performance of both the proposed controller and the observer, a high-order full vehicle model is used in the vehicle dynamics simulator software CarSim. A previously defined trajectory and a curvature-dependent velocity profile are used as reference for the controller. Additive faults are artificially added to the control signal to simulate a malfunctioning in the steering actuator. Results show that the reference path is tracked with minimum lateral and heading error. At the same time, the observer is able to estimate the faults with acceptable accuracy. For future work, the authors propose to address some of the simplifications made in this paper. Measurement disturbance is not considered in the controller design, as well as delays in the communication between sensors controller and actuators. Uncertainties should be considered as well, as front and rear cornering stiffness are defined constant in this work. An event-triggering condition should be included in future development to avoid network saturation. REFERENCES [1] G. Bai, Y. Meng, L. Liu, W. Luo, Q. Gu, and L. Liu, “Review and Comparison of Path Tracking Based on Model Predictive Control,” Electronics, vol. 8, no. 10, p. 1077, Sep. 2019, doi: 10.3390/electronics8101077. [2] H. Wang, B. Liu, X. Ping, and Q. An, “Path Tracking Control for Autonomous Vehicles Based on an Improved MPC,” IEEE Access, vol. 7, pp. 161064–161073, 2019, doi: 10.1109/ACCESS.2019.2944894. [3] Xiaoyu Huang, Hui Zhang, Guoguang Zhang, and Junmin Wang, “Robust Weighted Gain-Scheduling H Vehicle Lateral Motion Control With Considerations of Steering System Backlash-Type Hysteresis,” IEEE Trans. Control Syst. Technol., vol. 22, no. 5, pp. 1740–1753, Sep. 2014, doi: 10.1109/TCST.2014.2317772. [4] P. Li, A.-T. Nguyen, H. Du, Y. Wang, and H. Zhang, “Polytopic LPV approaches for intelligent automotive systems: State of the art and future challenges,” Mech. Syst. Signal Process., vol. 161, p. 107931, Dec. 2021, doi: 10.1016/j.ymssp.2021.107931.

Ing. Manuel Jiménez-Salas, PhD student, Universidad Carlos III de Madrid

Robust H∞ Static Output-Feedback Control for Path Tracking with Sensor Faults Estimation

FWC2023-SCA-032 • Integrated safety, connected & automated driving


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