Development of an Adaptive Trajectory Tracking Control of Wheeled Mobile Robot

Abstract

Classical modeling and control methods applied to differential locomotion mobile robots generate mathematical equations that approximate the dynamics of the system and work relatively well when the system is linear in a specific range. However, they may have low accuracy when there are many variations of the dynamics over time or disturbances occur. To solve this problem, we used a recursive least squares (RLS) method that uses a discrete-time structure first-order autoregressive model with exogenous variable (ARX). We design and modify PID adaptive self-adjusting controllers in phase margin and pole allocation. The main contribution of this methodology is that it allows the permanent and online update of the robot model and the parameters of the adaptive self-adjusting PID controllers. In addition, a Lyapunov stability analysis technique was implemented for path and trajectory tracking control, this makes the errors generated in the positioning and orientation of the robot when performing a given task tend asymptotically to zero.  The performance of the PID adaptive self-adjusting controllers is measured through the implementation of the criteria of the integral of the error, which allows to determine the controller of best performance, being in this case, the PID adaptive self-adjusting type in pole assignment, allowing the mobile robot greater precision in tracking the trajectories and paths assigned, as well as less mechanical and energy wear, due to its smooth and precise movements.

Keywords

telerobotics, Lyapunov stability, Matlab, mobile robots, parametric model, simulation

Author Biography

Guiovanny Suarez-Rivera

Rol: Conceptualization, Investigation, Methodology, Writing – Original draft.

Nelson David Muñoz-Ceballos, M.Sc.

Rol: Methodology, Writing – Review & Editing.

Henry Mauricio Vásquez-Carvajal, M.Sc.

Rol: Methodology, Writing – Review & Editing.

References

[1] G. Cook, F. Zhang, "Kinematic Models for Mobile Robots," in Mobile Robots: Navigation, Control and Sensing, Surface Robots and AUVs, 2019, pp. 5-12. https://doi.org/10.1002/9781119534839.ch1

[2] M. Ben-Ari, F. Mondada, Elements of Robotics, Springer, Switzerland, 2018.

[3] R. Bibi, B. S. Chowdhry, R. A. Shah, "PSO based localization of multiple mobile robots employing LEGO EV3," in International Conference on Computing, Mathematics and Engineering Technologies, Sukkur, 2018, pp. 1-5. https://doi.org/10.1109/icomet.2018.8346452

[4] T. G. Alves, W. F. Lages, R. V. Henriques, “Parametric Identification and Controller Design for a Differential-Drive Mobile Robot,” IFAC-PapersOnLine, vol. 51, no. 15, pp. 437-442, 2018. https://doi.org/10.1016/j.ifacol.2018.09.184

[5] J. G. N. D. Carvalho Filho, E. Á. N. Carvalho, L. Molina, E. O. Freire, "The Impact of Parametric Uncertainties on Mobile Robots Velocities and Pose Estimation," IEEE Access, vol. 7, pp. 69070-69086, 2019. https://doi.org/10.1109/access.2019.2919335

[6] M. Abdelwahab, V. Parque, A. M. R. Fath Elbab, A. A. Abouelsoud, S. Sugano, "Trajectory Tracking of Wheeled Mobile Robots Using Z-Number Based Fuzzy Logic," IEEE Access, vol. 8, pp. 18426-18441, 2020. https://doi.org/10.1109/ACCESS.2020.2968421

[7] L. Fan, Y. Zhang, S. Zhang, "Dynamic Trajectory Tracking Control of Mobile Robot," in 5th International Conference on Information Science and Control Engineering, Zhengzhou, 2018, pp. 728-732. https://doi.org/10.1109/icisce.2018.00156

[8] D. Dobriborsci, A. Kapitonov, N. Nikolaev, "The basics of the identification, localization and navigation for mobile robots," in International Conference on Information and Digital Technologies, Zilina, 2017, pp. 100-105. https://doi.org/10.1109/dt.2017.8024279

[9] A. Kapitonov, E. Antonov, K. Artemov, D. Dobriborsci, E. Zamotaev, A. Karavaev, R. Al-Naim, O. Souzdalev, "Lego Mindstorms EV3 for teaching the basics of trajectory control problems," in IEEE Frontiers in Education Conference, United States, 2018, pp. 1-4. https://doi.org/10.1109/fie.2018.8659322

[10] S. Mokhlis, S. Sadki, B. Bensassi, "System Identification of a DC Servo Motor Using ARX and ARMAX Models," in International Conference on Systems of Collaboration Big Data, Internet of Things & Security, Morocco, 2019, pp. 1-4. https://doi.org/10.1109/syscobiots48768.2019.9028015

[11] B. Raafiu, P. A. Darwito, "Identification of Four-Wheel Mobile Robot based on Parametric Modelling," in International Seminar on Intelligent Technology and Its Applications, Indonesia, 2018, pp. 397-401. https://doi.org/10.1109/isitia.2018.8710761

[12] M. A. Akmal, N. F. Jamin, N. M. A. Ghani, "Fuzzy logic controller for two wheeled EV3 LEGO robot," in IEEE Conference on Systems, Process and Control, Malacca, 2017, pp. 134-139. https://doi.org/10.1109/spc.2017.8313035

[13] A. Saradagi, V. Muralidharan, V. Krishnan, S. Menta, A. D. Mahindrakar, "Formation Control and Trajectory Tracking of Nonholonomic Mobile Robots," IEEE Transactions on Control Systems Technology, vol. 26, no. 6, pp. 2250-2258, Nov. 2018. https://doi.org/10.1109/tcst.2017.2749563

[14] A. Ashe, K. M. Krishna, "Dynamic Target Tracking & Collision Avoidance Behaviour of Person Following Robot Using Model Predictive Control," in 24th International Conference on System Theory, Control and Computing, Romania, 2020, pp. 660-666. https://doi.org/10.1109/icstcc50638.2020.9259720

[15] R. C. Dorf, Modern Control Systems, 13th Edition, Prentice Hall. 2017.

[16] F. Correa. J. Gallardo. N. Muñoz. R. Perez, “Estudio comparativo basado en métricas para diferentes arquitecturas de navegación reactiva,” Ingeniare, vol. 24, no. 1, pp. 46-54, Jan. 2016. https://doi.org/10.4067/s0718-33052016000100005