Trajectory tracking performance comparison of kinematic bicycle model with LQR and Lyapunov-based controllers on a circular trajectory

Year 2022, Volume: 14 Issue: 3, 153 - 162, 31.12.2022

Halit Ege Ceyhun Aytac Goren

https://doi.org/10.55974/utbd.1130198

Abstract

This paper focuses on comparative results of two different controllers applied to kinematic bicycle model with rear wheel contact point to the ground as the reference point. The wide range of representation of different types of robots and vehicles of kinematic bicycle model is the main reason for this model selection. This paper has three main sections. The first section of the paper is mathematical modeling of the model. The second section is describing the utilized control techniques. The last section shares results of the simulations. The simulations have been carried out with pure feedback signals in absence of noise. The compared two controllers are an (Linear Quadratic Regulator)LQR controller and a Lyapunov based controller. The objective in the simulations is to track and complete a given constant radius trajectory. Last section includes comparison of results by analyzing statistical values of a defined error signal.

Keywords

Wheeled mobile robot, LQR, Lyapunov, Kinematic bicycle model, Trajectory tracking

LQR ve Lyapunov temelli iki kontrolcünün kinematik bisiklet tipi model için güzergah izleme performansı karşılaştırması

Abstract

Bu makale farklı kontrol tekniklerinin arka tekerleğinin yere temas noktasını referans alan kinematik bisiklet tipi robot üzerine uygulamasının karşılaştırmalı sonuçlarına odaklanmıştır. Kinematik bisiklet tipi modelin seçilmesinin ardında yatan asıl sebep, bu modelin günümüzde kullanılan birçok robot modelini ve aracı temsil edebilmesidir. Çalışma üç ana bölümden oluşmaktadır. İlk bölüm robotun modellenmesini içermekte. İkinci bölüm uygulanan kontrol teknikleri ile ilgili çalışmaları barındırmakta. Son bölüm ise simülasyon sonuçlarını paylaşmaktadır. Kullanılan sinyaller gürültüsüz ortamda bir geribesleme sinyali için oluşturulmuştur. Karşılaştırılan kontrolcüler (Linear Quadratic Regulator)LQR ve bir Lyapunov temelli kontrolcülerdir. Simülasyonların ana amacı modelin verilen sabit yarıçaplı güzergahı takip ederek tamamlamasıdır. Son bölüm içerisinde tanımlanan hata sinyalinin istatistiksel olarak değerlendirmesini içerir.

Keywords

Mobil robot, LQR, Lyapunov, Kinematik bisiklet modeli, Güzergah takibi

References

• [1] Siegwart RI, Nourbakhsh R, Scaramuzza D. Introduction to Autonomous Mobile Robots, Second Edition. vol. 23, 2011.
• [2] Choset H, Lynch KM, Hutchinson S, Kantor GA, Burgard W. Principles of Robot Motion, 2005.
• [3] Siciliano B, Sciavicco L, Villani L, Oriolo G. Robotics: Modelling, planning and control. no. 9781846286414. doi: 10.5860/choice.46-6226, 2009.
• [4] Dixon W, Dawson DM, Zergeroglu E, Behal A. Nonlinear Control of Wheeled Mobile Robots. Lecture Notes in Control and Information Sciences, vol. 262, 2020.
• [5] Isidori A. Nonlinear Control Systems: An Introduction. 3rd ed. Berlin, Germany: Springer-Verlag, 1995.
• [6] Siciliano B, Khatib O. Springer handbook of robotics. doi: 10.1007/978-3-319-32552-1, 2016.
• [7] Forte MDN, Correia WB, Nogueira FG, Torrico BC. Reference Tracking of a Nonholonomic Mobile Robot using Sensor Fusion Techniques and Linear Control. IFAC-Papers OnLine, vol. 51, no. 4. doi: 10.1016/j.ifacol.2018.06.092, 2018.
• [8] Fareh R, Saad M, Khadraoui S, Rabie T. Lyapunov-Based Tracking Control for Nonholonomic Wheeled Mobile Robot. International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering, vol. 10, no. 8, pp. 1042–1047, 2018.
• [9] Nurmaini S, Dewi K, Tutuko B. Differential-drive mobile robot control design based-on linear feedback control law. International Conference on Electrical Engineering, Computer Science and Informatics (EECSI), vol. 3. doi: 10.1088/1757-899X/190/1/012001, 2016.
• [10] Zidani G, Drid S Larbi, CA, Arar D, Bussy P. Robust nonlinear control of a mobile robot. Journal of Electrical Engineering and Technology, vol. 11, no. 4, doi: 10.5370/JEET.2016.11.4.1014, 2016.
• [11] Bui TH, Nguyen TT, Chung TL, Kim SB. A simple nonlinear control of a two-wheeled welding mobile robot. Int J Control Autom Syst, vol. 1, no. 1, 2003.
• [12] Serralheiro W, Maruyama N, Tannuri EA. Motion Control of an Underactuated Wheeled Mobile Robot: A Kinematic Input-Output Linearization Approach. Proceedings of the 23rd ABCM International Congress of Mechanical Engineering. doi: 10.20906/cps/cob-2015-1291, 2015.
• [13] Snider JM. Automatic Steering Methods for Autonomous Automobile Path Tracking. Work, no. February, 2009.
• [14] Alcala E, Puig V, Quevedo J, Escobet T, Comasolivas R. Autonomous vehicle control using a kinematic Lyapunov-based technique with LQR-LMI tuning. Control Eng Pract, vol. 73, doi: 10.1016/j.conengprac.2017.12.004, 2018.
• [15] Khalaji AK, Jalalnezhad M. Robust forward\backward control of wheeled mobile robots. ISA Trans, vol. 115, doi: 10.1016/j.isatra.2021.01.016, 2021.
• [16] Muir PF, Neuman CP. Kinematic modeling of wheeled mobile robots. J Robot Syst, vol. 4, no. 2, doi: 10.1002/rob.4620040209, 1987.
• [17] Kirk DE. Optimal control theory: An introduction. IEEE Trans Automat Contr, vol. 1, 2004.
• [18] Gamkrelidze RV. Principles of Optimal Control Theory. doi: 10.1007/978-1-4684-7398-8, 1978.
• [19] Soloperto R, Wenzelburger P, Meister D, Scheuble D, Breidohr VSM, Allgöwer F. A control framework for autonomous e-scooters. IFAC-PapersOnLine, vol. 54, no. 2. doi: 10.1016/j.ifacol.2021.06.030, 2021.
• [20] Jiang J, Evangelou SA, Torquil MR, Astolfi A. Robust H Control for Autonomous Scooters. IFAC-PapersOnLine, vol. 50, no. 1. doi: 10.1016/j.ifacol.2017.08.049, 2017.
• [21] Corke P. Robotics, Vision and Control - Fundamental Algorithms. MATLAB® Second, Completely Revised, Extended And Updated Edition, vol. 75, no. 1–2, 2017.
• [22] Divelbiss AW, Wen JT. Trajectory tracking control of a car-trailer system. IEEE Transactions on Control Systems Technology, vol. 5, no. 3, doi: 10.1109/87.572125, 1997.
• [23] Uyar E, Çetin L, Gören A. Navigation and GPS based path control of an autonomous vehicle. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3949 LNAI. doi: 10.1007/11803089_3, 2006.
• [24] Uyar E, Çetin L, Gören A, Ensoner S. Vision based tracking control and obstacle avoidence of a mobile vehicle. IFAC Proceedings Volumes (IFAC-PapersOnline), vol. 37, no. 8, 2004.
• [25] Yıldız B. Object detection and mapping using LIDAR for a mobile robot. M.S. thesis, Dokuz Eylül University, 2016.
• [26] Gören A. Controlling a non-holonomic vehicle via artificial neural networks. Ph.D. dissertation, Dokuz Eylul University, 2007.
• [27] Ergenc AF, Nak H, Akkaya Ş. Design, Analysis and Experimental Verification of a Novel Nonlinear Pi Controller. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 18, no. 4, doi: 10.18038/aubtda.340651, 2017.
• [28] Ortatepe Z, Parlaktuna O. Two Dof Robot Control With Fuzzy Based Neural Networks. Anadolu University Journal Of Science And Technology A - Applied Sciences and Engineering, vol. 18, no. 4, doi: 10.18038/aubtda.340002, 2017.