An Application of Quasi Newton Algorithm and Improvement of Sliding Surface for Robot Control

Chi-Ngon  Nguyen; Thanh Tung  Pham

doi:10.6180/jase.202510_28(10).0018

An Application of Quasi Newton Algorithm and Improvement of Sliding Surface for Robot Control

Chi-Ngon Nguyen¹ and Thanh Tung Pham²This email address is being protected from spambots. You need JavaScript enabled to view it.

¹Vice Chairman of the Board of Trustees, Can Tho University, Vietnam

²Faculty of Electrical and Electronics Engineering Technology, Vinh Long University of Technology Education, Vietnam

Received: November 12, 2024
Accepted: December 21, 2024
Publication Date: February 27, 2025

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202510_28(10).0018

This article describes the use of an enhanced sliding surface and a Quasi-Newton algorithm for mobile robot control. To enhance performance and reduce chattering around a sliding surface, a proportional-integral sliding surface (PI-SS) is used. The objective of the proportional-integral sliding mode control declared in this study is to provide a switching control law that will allow the system’s output to get closer to the references and significantly lessen chattering. Regarded as the most well-liked and effective method for resolving unconstrained optimization issues is the Quasi Newton algorithm. The radial basis function neural network (RBF-NN), which approximates the nonlinear elements in the sliding mode controller, is trained using this approach. According to this proposed controller, the confirmed trajectory of the mobile robot will converge to the request trajectory in f inite time. By using Lyapunov’s theory, the system’s stability is demonstrated. The efficacy of the suggested controller is demonstrated by the MATLAB/Simulink simulation results, which show that the chattering phenomenon was reduced and that the steady-state error converged to zero, the rising time reached 0.2284 s, the settling time was 0.4454 s, the overshoot was 1.9984e-13 % in x-coordinate; 0.2285 s, 0.4456 s, 1.5543e-13 % in y-coordinate, respectively.

Keywords: Quasi Newton; sliding surface; proportional-integral; robot; MATLAB/Simulink

[1] C.Wang,X.Liu,X.Yang,F.Hu,A.Jiang,andC.Yang, (2018) “Trajectory Tracking of an Omni-Directional Wheeled Mobile Robot Using a Model Predictive Con trol Strategy" Applied Sciences 8: 1–15. DOI: 10.3390/app8020231.
[2] H.Taheri and C. Zhao, (2020) “Omnidirectional mobile robots, mechanisms and navigation approaches" Mecha nism and Machine Theory 153: 1–28. DOI: 10.1016/j.mechmachtheory.2020.103958.
[3] A.WIBISANA,B. Dewantara, and D. Pramadihanto, (2022) “Development of an Omni Directional based Mo bile Robot Navigation System using Optimized-Fuzzy So cial Force Model" ELKOMIKA: Jurnal Teknik Energi Elektrik, Teknik Telekomunikasi, Teknik Elektron ika 10: 961–975. DOI: 10.26760/elkomika.v10i4.961.
[4] A.Mehmood,I. Shaikh, and A. Ali, (2021) “Applica tion of Deep Reinforcement Learning for Tracking Control of 3WD Omnidirectional Mobile Robot" Information Technology and Control 50: 507–521. DOI: 10.5755/j01.itc.50.3.25979.
[5] D.Hoa,T. ChuyÍn, L. Lai, and L. Ha, (2024) “Trajec tory Tracking Control for Wheeled Mobile Robot System with Uncertain Nonlinear Model based on Integral Rein forcement Learning Algorithm" International Journal of Engineering Trends and Technology 72: 290–298. DOI: 10.14445/22315381/IJETT-V72I5P130.
[6] M. Albaker Kawtharani, V. Fakhari, and M. Reza Haghjoo. “Tracking Control of an Omni-Directional Mobile Robot”. In: 2020 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA). 2020, 1–8. DOI: 10.1109/HORA49412.2020.9152835.
[7] J. PalacÌn, E. Rubies, E. Clotet, and D. MartÌnez, (2021) “Evaluation of the Path-Tracking Accuracy of a Three-Wheeled Omnidirectional Mobile Robot Designed as a Personal Assistant" Sensors 21: 1–19. DOI: 10.3390/s21217216.
[8] A. Andreev and O. Peregudova, (2020) “On Global Trajectory Tracking Control for an Omnidirectional Mo bile Robot with a Displaced Center of Mass" Nelineinaya Dinamika 16: 115–131. DOI: 10.20537/nd200110.
[9] F. Pang, M.Luo, X. Xu, and Z. Tan, (2021) “Path Track ing Control of an Omni-Directional Service Robot Based on Model Predictive Control of Adaptive Neural-Fuzzy Inference System" Applied Sciences 11: 1–8. DOI: 10.3390/app11020838.
[10] D. Trujillo, L. Morales, G. Chavez Garcia, and D. Pozo, (2023) “Trajectory Tracking Control of a Mobile Robot using Neural Networks" Emerging Science Jour nal 7: 1843–1862. DOI: 10.28991/ESJ-2023-07-06-01.
[11] J. Xu and G. Zhang, (2023) “Tracking Control of Wheeled Mobile Robot Based on MMPC" Academic Journal of Science and Technology: 137ñ145.
[12] P. Anggraeni, N. Ramadhan, and M. Huda. “Trajec tory Tracking Control of Three Wheeled Omnidirec tional Mobile Robot Using Proportional Controller”. In: 2024, 548–563. DOI: 10.2991/978-94-6463-364 1_51.
[13] T. Tolossa, M. Gunasekaran, K. Halder, H. Verma, S. Parswal, N. Jorwal, F. Orlando, and Y. Hote, (2024) “Trajectory tracking control of a mobile robot using fuzzy logic controller with optimal parameters" Robotica 42: 1–24. DOI: 10.1017/S0263574724001140.
[14] N.Th·i, (2024) “DESIGN NEURAL NETWORK-PID CONTROLLERFORTRAJECTORYTRACKINGOF DIFFERENTIAL DRIVE MOBILEROBOT"Vietnam Journal of Science and Technology 62: 374ñ386. DOI: 10.15625/2525-2518/18066.
[15] W.Xue,B. Zhou, F. Chen, E. Ghaderpour, and A. Mo hammadzadeh, (2024) “Design of a robust intelligent controller based neural network for trajectory tracking of high-speed wheeled robots" Physica Scripta 99: 1–18. DOI: 10.1088/1402-4896/ad8486.
[16] Z. Aminifard, S. Babaie-Kafaki, and S. Ghafoori, (2021) “An augmented memoryless BFGS method based on a modified secant equation with application to com pressed sensing" Applied Numerical Mathematics 167: 187ñ201. DOI: 10.1016/j.apnum.2021.05.002.
[17] M.Bai, J. Zhao, and Z. Zhang, (2020) “A descent cau tious BFGS method for computing US-eigenvalues of sym metric complex tensors" J Glob Optim 76: 889ñ911. DOI: https://doi.org/10.1007/s10898-019-00843-5.
[18] K. K. Lai, S. Mishra, R. Sharma, M. Sharma, and B. Ram, (2023) “Citation: mathematics A Modified q-BFGS Algorithm for Unconstrained Optimization" Mathemat ics 11: 1–24. DOI: 10.3390/math11061420.
[19] D. Goldfarb, Y. Ren, and A. Bahamou, (2020) “Prac tical Quasi-Newton Methods for Training Deep Neural Networks": 1–11. DOI: 10.48550/arXiv.2006.08877.
[20] B. A. H. I. A. R. Moghrabi and A. Askar, (2022) “New Self-scaling Quasi-Newton methods for unconstrained optimization" International Journal of Mathematics and Computer Science 17: 1061ñ1077.
[21] C.-H.LinandF.-Y.Hsiao,(2020)“Proportional-Integral Sliding Mode Control with an Application in the Balance Control of a Two-Wheel Vehicle System" Applied Sci ences 10: 1–27. DOI: 10.3390/app10155087.
[22] J.LiuandX.Wang.“AdvancedSlidingModeControl for Mechanical Systems”. In: 2011.
[23] J. Xia, Rusli, and A. Kumta, (2010) “Feedforward Neu ral Network Trained by BFGS Algorithm for Modeling Plasma Etching of Silicon Carbide" Plasma Science, IEEE Transactions on 38: 142–148. DOI: 10.1109/TPS.2009.2037151.
[24] T. Pham, M.-T. Le, and C.-N. Nguyen, (2021) “Omni directional Mobile Robot Trajectory Tracking Control with Diversity of Inputs" International Journal of Mechan ical Engineering and Robotics Research 10: 639–644. DOI: 10.18178/ijmerr.10.11.639-644.
[25] T.PhamandC.-N.Nguyen,(2023) “Adaptive PID slid ing mode control based on new Quasi-sliding mode and radial basis function neural network for Omni-directional mobile robot" AIMS Electronics and Electrical Engi neering 7: 121–134. DOI: 10.3934/electreng.2023007.
[26] I. Mukherjee and S. Routroy, (2012) “Comparing the performance of neural networks developed by using Levenberg-Marquardt and Quasi-Newton with the gradi ent descent algorithm for modelling a multiple response grinding process" Expert Syst. Appl. 39: 2397–2407. DOI: 10.1016/j.eswa.2011.08.087.