Speed Dependent Gain Scheduled LQI based Path Following Control System Design for Automated Vehicles

Abstract

Automated path following is one of the major problem in automated vehicle control. Automated vehicle should follow the desired path to minimize the lateral deviation from the path while traveling at the desired speed. In this paper, LQI control method is proposed to solve this problem. LQI based control system is designed based on speed dependent gain scheduling taking into account the effect of vehicle speed on vehicle dynamic behaviour. The proposed method is tested in a simulation environment with a high degree-of-freedom nonlinear vehicle model including steer-by-wire steering actuator model. The performance of the proposed is compared with PID and LQR based control systems in two different simulation scenarios. Statistical error values are used for numerical comparison of different control methods. Simulation results and error values show that speed dependent gain scheduled LQI control system equipped automated vehicle follows the desired path with less error at constant and variable vehicle speed.

Keywords

• Automated vehicles,Control system design,LQI,LQR,Simulation

Otonom Taşıtlar için Hıza Bağlı Kazanç Uyarlamalı LQI Tabanlı Yol Takip Kontrol Sistemi Tasarımı

Öz

Otonom taşıt yol takibi, otonom taşıt kontrolündeki önemli problemlerden birisidir. Otonom taşıt istenilen hızda yol alırken istenilen yol profilini yoldan yana sapma miktarını en aza indirecek şekilde takip etmelidir. Bu çalışmada bu problemin çözümü için LQI kontrol yöntemi önerilmiştir. LQI tabanlı kontrol sistemi, taşıt hızının taşıt dinamik davranışı üzerindeki etkisi dikkate alınarak hıza bağlı olarak kazanç uyarmalı şekilde tasarlanmıştır. Önerilen yöntem yüksek serbestlik dereceli kablosuz direksiyon eyleyici modeli içeren doğrusal olmayan taşıt dinamiği modeliyle simülasyon ortamında test edilmiştir. Önerilen kontrol sisteminin performansı, PID ve LQR tabanlı kontrol sistemleriyle iki farklı simülasyon senaryosunda karşılaştırılmıştır. Farklı kontrol yöntemlerin sayısal olarak karşılaştırılmasında istatistiksel hata değerleri kullanılmıştır. Simülasyon sonuçları ve hata değerleri göstermektedir ki hıza bağlı kazanç uyarlamalı LQI kontrol sistemi kullanan otonom taşıt, sabit ve değişken taşıt hızında istenilen yolu daha az hatayla takip etmektedir.

Anahtar Kelimeler

• Otonom taşıtlar,Kontrol sistemleri tasarımı,LQI,LQR,Simülasyon

Kaynakça

1. [1] L. Güvenç, B. Aksun Güvenç, M. T. Emirler, Connected and Autonomous Vehicles, In Internet of Things and Data Analytics Handbook, Hwaiyu Geng (Ed.), Wiley, New Jersey, (2016) 581-595.
2. [2] J. Ackermann, W. Sienel, Robust Control for Automatic Steering, IEEE American Control Conference (ACC), San Diego, CA, USA, (1990) 795-800.
3. [3] J. Ackermann, J. Guldner, V. I. Utkin, A Robust Nonlinear Control Approach to Automatic Path Tracking of a Car, IET International Conference on Control (Control’94), Coventry, UK, (1994) 196-201.
4. [4] B. Aksun Güvenç, L. Güvenç, Robust Two Degree-of-Freedom Add-On Controller Design for Automatic Steering, IEEE Transactions on Control Systems Technology, 10:1 (2002) 137-148.
5. [5] J. Y. Choi, Robust Controller for an Autonomous Vehicle with look-ahead and look-down information, Journal of Mechanical Science and Technology, 25:10 (2011) 2467-2474.
6. [6] C. Rathgeber, F. Winkler, D. Odenthal, S. Müller, Lateral Trajectory Tracking Control for Autonomous Vehicles, European Control Conference (ECC), Strasbourg, France (2014) 1024-1029.
7. [7] M. T. Emirler, İ. M. C. Uygan, B. Aksun Güvenç, L. Güvenç, Robust PID Steering Control in Parameter Space for Highly Automated Driving, International Journal of Vehicular Technology, 259465 (2014) 1-8.
8. [8] M. T. Emirler, H. Wang, B. Aksun Güvenç, L. Güvenç, Automated Robust Path Following Control based on Calculation of Lateral Deviation and Yaw Angle Error, ASME Dynamic Systems and Control Conference, Columbus, Ohio, USA (2015) 1-8.

9. [9] M. T. Emirler, H. Wang, B. Aksun Güvenç, Socially Acceptable Collision Avoidance System for Vulnerable Road Users, IFAC-PapersOnLine, 49:3 (2016) 436-441.
10. [10] H. Wang, A. Tota, B. Aksun Güvenç, L. Güvenç, Real Time Implementation of Socially Acceptable Collision Avoidance of a Low Speed Autonomous Shuttle using the Elastic Band Method, Mechatronics, 50 (2018) 341-355.
11. [11] C. Hu, R. Wang, F. Yan, N. Chen, Output Constraint Control on Path Following of Four-Wheel Independently Actuated Autonomous Ground Vehicles, IEEE Transactions on Vehicular Technology, 65:6 (2016) 4033-4043.
12. [12] C. Hu, H. Jing, R. Wang, F. Yan, M. Chadli, Robust H∞ Output-feedback Control for Path Following of Autonomous Ground Vehicles, Mechanical Systems and Signal Processing, 70-71 (2016) 414-427.
13. [13] K. Lee, S. E. Li, D. Kum, Synthesis of Robust Lane Keeping Systems: Impact of Controller and Design Parameters on System Performance, IEEE Transactions on Intelligent Transportation Systems (Early Access) (2018) 1-13.
14. [14] J. Ackermann, P. Blue, T. Bünte, L. Güvenç, D. Kaesbauer, M. Kordt, M. Muhler, D. Odenthal, Robust Control: The Parameter Space Approach, Springer-Verlag, 2002.
15. [15] A. Kozáková, M. Hypiusová, LQG/LTR based Reference Tracking for a Modular Servo, Journal of Electrical Systems and Information Technology, 2 (2015) 347-357.
16. [16] Y. Ebihara, T. Hagiwara, M. Araki, Sequential Tuning Methods of LQ/LQI Controllers for Multivariable Systems and Their Application to Hot Strip Mills, Proceedings of the 38th IEEE Conference on Decision & Control, Phoenix, Arizona, USA (1999) 767-772.
17. [17] E. Esmailzadeh, A. Goodarzi, G. R. Vosoughi, Optimal Yaw Moment Control Law for Improved Vehicle Handling, Mechatronics, 13 (2003) 659-675.
18. [18] D. Luong, T-C Tsao, Linear Quadratic Integral Control of an Organic Rankine Cycle for Waste Heat Recovery in Heavy-Duty Diesel Powertrain, IEEE American Control Conference (ACC), Portland, Oregon, USA (2014) 3147-3152.
19. [19] A. Phillips, F. Şahin, Optimal Control of a Twin Rotor MIMO System using LQR with Integral Action, World Automation Congress (WAC), Waikoloa, Hawaii, USA (2014) 1-6.
20. [20] B. S. Anjali, A. Vivek, J. L. Nandagopal, Simulation and Analysis of Integral LQR Controller for Inner Control Loop Design of a Fixed Wing Micro Aerial Vehicle (MAV), Procedia Technology, 25 (2016) 76-83.
21. [21] J. Smith, J. Su, C. Liu, W-H Chen, Disturbance Observer based Control with Anti-Windup Applied to a Small Fixed Wing UAV for Disturbance Rejection, Journal of Intelligent & Robotic Systems, 88:2-4 (2017) 329-346.
22. [22] V. F. D. Poggetto, A. L. Serpa, Vehicle Rollover Avoidance by Application of Gain-Scheduled LQR Controllers using State Observers, Vehicle System Dynamics, 54:2 (2016) 191-209.
23. [23] A. Owczarkowski, D. Horla, Robust LQR and LQI Control with Actuator Failure of a 2DOF Unmanned Bicycle Robot Stabilized by an Inertial Wheel, International Journal of Mathematics and Computer Science, 26:2 (2016) 325-334.
24. [24] Y. Altun, Çeyrek Taşıt Süspansiyon Sistemi için LQR ve LQI Denetleyiclerinin Karşılaştırılması, Gazi Üniversitesi, Fen Bilimleri Dergisi Part C: Tasarım ve Teknoloji, 5:3 (2017) 61-70.
25. [25] I. Kisszölgyémi, K. Beneda, Z. Faltin, Linear Quadratic Integral (LQI) Control for a Small Scale Turbojet Engine with Variable Exhaust Nozzle, IEEE International Conference on Military Technologies (ICMT), Brno, Czech Republic (2017) 507-513.
26. [26] Z. Wang, U. Montanaro, S. Fallah, A. Sorniotti, B. Lenzo, A Gain Scheduled Robust Linear Quadratic Regulator for Vehicle Direct Yaw Moment Control, Mechatronics, 51 (2018) 31-45.