Synthesis of Active Disturbance Rejection Controller via Extended State Observer Combined with LQR Controller for Two-Wheeled Line Tracking Robot
DOI:
https://doi.org/10.18196/jrc.v6i2.24754Keywords:
LQR Controller, ADRC Method, ESO, Mobile Robot, Track FollowingAbstract
This paper presents a method of synthesizing control laws based on the LQR controller and ADRC method for a two-wheel differential line-following robot when the robot dynamics have uncertain factors. First, the mathematical model includes line-following kinematic and dynamic models. LQR controller is designed based on the linear model of the robot when coincident with the line. When the robot has uncertain factors such as model parameter uncertainty and impact noise, the LQR controller will not ensure the control quality of the system. To overcome this, two observers are designed to observe the linear velocity and angular velocity states of the robot. This ensures more complete and accurate information of the model states in the LQR control law. The effectiveness of the control law is demonstrated through numerical simulation results and compared with the LQR controller.
References
S. G. Tzafestas. Introduction to mobile robot control. Elsevier, 2013.
G. Klančar, A. Zdešar, S. Blažič, and I. Škrjanc. Wheeled Mobile Robotics. Butterworth-Heinemann, 2017.
L. Jaulin. Wheeled Mobile Robotics. ISTE Press – Elsevier, 2017.
A. V. Savkin, A. S. Matveev, M. Hoy, and C. Wang. Safe robot navigation among moving and steady obstacles. Butterworth-Heinemann, 2015, doi: 10.1016/C2014-0-04743-0.
C. C. De Wit, “Quasicontinuous stabilizing controllers for nonholonomic systems: Design and robustness considerations,” in Proc. of 3rd European Control Conference, pp. 2630-2635, 1995.
J. Guldner and V. I. Utkin, "Stabilization of non-holonomic mobile robots using Lyapunov functions for navigation and sliding mode control," Proceedings of 1994 33rd IEEE Conference on Decision and Control, pp. 2967-2972, 1994, doi: 10.1109/CDC.1994.411340.
F. Demirbaş and M. Kalyoncu, “Differential drive mobile robot trajectory tracking with using pid and kinematic based backstepping controller,” Selçuk Üniversitesi Mühendislik, Bilim ve Teknoloji Dergisi, vol. 5, no. 1, pp. 1-15, 2017.
R. R. Carmona, H. G. Sung, Y. S. Kim, and H. A. Vazquez, "Stable PID Control for Mobile Robots," 2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV), pp. 1891-1896, 2018, doi: 10.1109/ICARCV.2018.8581132.
A. Barsan, “Position control of a mobile robot through PID controller,” Acta Universitatis Cibiniensis. Technical Series, vol. 71, no. 1, pp. 14-20, 2019, doi: 10.2478/aucts-2019-0004.
C. S. Shijin and K. Udayakumar, "Speed control of wheeled mobile robots using PID with dynamic and kinematic modelling," 2017 International Conference on Innovations in Information, Embedded and Communication Systems (ICIIECS), pp. 1-7, 2017, doi: 10.1109/ICIIECS.2017.8275962.
T. P. Nascimento, C. E. T. Dórea, and L. M. G. Gonçalves, "Nonlinear model predictive control for trajectory tracking of nonholonomic mobile robots: A modified approach," International Journal of Advanced Robotic Systems, vol. 15, no. 1, 2018.
F. Lin, Z. Lin, and X. Qiu, "LQR controller for car-like robot," 2016 35th Chinese Control Conference (CCC), pp. 2515-2518, 2016, doi: 10.1109/ChiCC.2016.7553742.
J. Fang, “The LQR Controller Design of Two‐Wheeled Self‐Balancing Robot Based on the Particle Swarm Optimization Algorithm,” Mathematical Problems in Engineering, vol. 2014, no. 1, p. 729095, 2014, doi: 10.1155/2014/729095.
C. Samson, P. Morin, and R. Lenain, “Modeling and control of wheeled mobile robots,” Springer handbook of robotics, pp. 1235-1266, 2016.
I. Reguii, I. Hassani, and C. Rekik, “Mobile robot navigation using planning algorithm and sliding mode control in a cluttered environment,” Journal of Robotics and Control (JRC), vol. 3, no. 2, pp. 166-175, 2022, doi: 10.18196/jrc.v3i2.13765.
I. A. Hassan, I. A. Abed, and W. A. Al-Hussaibi, “Path planning and trajectory tracking control for two-wheel mobile robot,” Journal of Robotics and Control (JRC), vol. 5, no. 1, pp. 1-15, 2024, doi: 10.18196/jrc.v5i1.20489.
C. E. Martínez-Ochoa, I. O. Benítez-González, A. O. Cepero-Díaz, J. R. Nuñez-Alvarez, C. G. Miguélez-Machado, and Y. E. Llosas-Albuerne, “Active disturbance rejection control for robot manipulator,” Journal of Robotics and Control (JRC), vol. 3, no. 5, pp. 622-632, 2022.
N. A. Alawad, A. J. Humaidi, and A. S. Alaraji, “Observer sliding mode control design for lower exoskeleton system: Rehabilitation case,” Journal of Robotics and Control (JRC), vol. 3, no. 4, pp. 476-482, 2022.
P. Victerpaul, D. Saravanan, S. Janakiraman, and J. Pradeep, “Path planning of autonomous mobile robots: A survey and comparison,” Journal of Advanced Research in Dynamical and Control Systems, vol. 9, no. 12, pp. 1535-1565, 2017.
D. Liu, Q. Gao, Z. Chen, and Z. Liu, “Linear Active Disturbance Rejection Control of a Two‐Degrees‐of‐Freedom Manipulator,” Mathematical Problems in Engineering, vol. 2020, no. 1, 2020.
M. A. Faraj, B. Maalej, and N. Derbel, “Optimal sliding mode controller for lower limb rehabilitation exoskeleton in constrained environments,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 30, no. 3, pp. 1458-1469, 2023.
S. B. Messaoud, M. Belkhiri, A. Belkhiri, and A. Rabhi, “Active disturbance rejection control of flexible industrial manipulator: A MIMO benchmark problem,” European Journal of Control, vol. 77, p. 100965, 2024.
M. Khamar and M. Edrisi, “Designing a backstepping sliding mode controller for an assistant human knee exoskeleton based on nonlinear disturbance observer,” Mechatronics, vol. 54, pp. 121-132, 2018.
A. A. Sneineh and W. A. Salah, “Development of a Sensor-Based Glove-Controlled Mobile Robot for Firefighting and Rescue Operations,” International Journal of Robotics and Control Systems, vol. 4, no. 4, pp. 1641-1655, 2024.
I. Hassani and C. Rekik, “Backstepping controller for mobile robot in presence of disturbances and uncertainties,” International Journal of Robotics and Control Systems, vol. 3, no. 4, pp. 934-954, 2023.
I. Hassani, I. Ergui, and C. Rekik, “Turning Point and Free Segments Strategies for Navigation of Wheeled Mobile Robot,” International Journal of Robotics and Control Systems, vol. 2, no. 1, pp. 172-186, 2022.
R. Rajamani. Vehicle Dynamics and Control. Springer, 2006.
W. E. Dixon, D. M. Dawson, E. Zergeroglu, and A. Behal. Nonlinear Controlof Wheeled Mobile Robots. Springer, 2001.
N. X. Chiem, “Synthesis of LQR Controller Based on BAT Algorithm for Furuta Pendulum Stabilization,” Journal of Robotics and Control (JRC), vol. 4, no. 5, pp. 662-669, 2023, doi: 10.18196/jrc.v4i5.19661.
R. S. Ali, A. A. Aldair, and A. K. Almousawi, “Design an Optimal PID Controller using Artificial Bee Colony and Genetic Algorithm for Autonomous Mobile Robot,” International Journal of Computer Applications, vol. 100, no. 1, pp. 8-16, 2014.
Dhaouadi, R., Hatab, A. A., 2013, ‚Dynamic Modelling of Differential-Drive Mobile Robots using Lagrange and Newton-Euler Methodologies: A Unified Framework‛, Research Article, Advances in Robotics & AutomationTechnology, Vol. 2 (2), pp. 1-7.
A. E. Cabrera. Rapid Prototyping of Mobile Robot Control Algorithms, Degree of Master of Science in Faculty of Electrical Engineering, Department of Control Engineering, Czech Technical University In Prague, 2014.
R. Fierro and F. L. Lewis, “Control of A Nonholonomic Mobile Robot: Backstepping Kinematics Into Dynamics,” in Proceedings of 34th IEEE Conference on Decision and Control, pp. 3805-3810, 1995.
E. J. Hwang, H. S. Kang, C. H. Hyun, and M. Park, “Robust backstepping control based on a Lyapunov redesign for skid-steered wheeled mobile robots,” International Journal of Advanced Robotic Systems, vol. 10, no. 1, p. 26, 2013.
Y. Kanayama, Y. Kimura, F. Miyazaki and T. Noguchi, "A stable tracking control method for an autonomous mobile robot," Proceedings., IEEE International Conference on Robotics and Automation, pp. 384-389, 1990, doi: 10.1109/ROBOT.1990.126006.
M. Oubbati, M. Schanz and P. Levi, "Kinematic and dynamic adaptive control of a nonholonomic mobile robot using a RNN," 2005 International Symposium on Computational Intelligence in Robotics and Automation, pp. 27-33, 2005, doi: 10.1109/CIRA.2005.1554250.
R. Solea, A. Filipescu, A. Filipescu, E. Minca and S. Filipescu, "Wheelchair control and navigation based on kinematic model and iris movement," 2015 IEEE 7th International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), pp. 78-83, 2015, doi: 10.1109/ICCIS.2015.7274600.
E.-J. Hwang, H.-S. Kang, C.-H. Hyun, and M. Park, “Robust Backstepping Control Based on a Lyapunov Redesign for Skid-Steered Wheeled Mobile Robots,” International Journal of Advanced Robotic Systems, vol. 10, 2013, doi: 10.5772/55059.
S. M. Swadi, M. A. Tawfik, E. N. Abdulwahab, and H. A. Kadhim, "Fuzzy-Backstepping Controller Based on Optimization Method for Trajectory Tracking of Wheeled Mobile Robot," 2016 UKSim-AMSS 18th International Conference on Computer Modelling and Simulation (UKSim), pp. 147-152, 2016, doi: 10.1109/UKSim.2016.52.
R. Martínez, O. Castillo, and L. T. Aguilar, “Optimization of Interval Type‐2 Fuzzy Logic Controllers for a Perturbed Autonomous Wheeled Mobile Robot Using Genetic Algorithms,” Inf. Sci., vol. 13, pp. 2158‐2174.
T. T. Mac, C. Copot, R. De Keyser, T. D. Tran, and T. Vu, « MIMO Fuzzy Control for Autonomous Mobile Robot,” Journal of Automation and Control Engineering, vol. 4, no. 1, pp. 65-70, 2016.
N. X. Chiem, N. D. Anh, A. D. Lukianov, P. D. Tung, H. D. Long, and N. D. Linh, “Design real-time embedded optimal PD fuzzy controller by PSO algorithm for autonomous vehicle mounted camera,” AIP Conference Proceedings, vol. 2188, p. 030008, 2019, doi: 10.1063/1.5138401.
R. D. Puriyanto and A. K. Mustofa, “Design and implementation of fuzzy logic for obstacle avoidance in differential drive mobile robot,” Journal of Robotics and Control (JRC), vol. 5, no. 1, pp. 132-141, 2024, doi: 10.18196/jrc.v5i1.20524.
K. Lee, D. Y. Im, B. Kwak, and Y. J. Ryoo, “Design of fuzzy-PID controller for path tracking of mobile robot with differential drive,” International Journal of Fuzzy Logic and Intelligent Systems, vol. 18, no. 3, pp. 220-228, 2018, doi: 10.5391/IJFIS.2018.18.3.220.
N. Van Tinh, “Neural network-based adaptive tracking control for a nonholonomic wheeled mobile robot subject to unknown wheel slips,” Journal of Computer Science and Cybernetics, vol. 33, no. 1, pp. 70-85, 2017, doi: 10.15625/1813-9663/33/1/8914.
S. A. Ahmed and M. G. Petrov, “Trajectory control of mobile robots using type-2 fuzzy-neural PID controller,” IFAC-PapersOnLine, vol. 48, no. 24, pp. 138-143, 2015.
X. Hai et al., "Mobile Robot ADRC With an Automatic Parameter Tuning Mechanism via Modified Pigeon-Inspired Optimization," in IEEE/ASME Transactions on Mechatronics, vol. 24, no. 6, pp. 2616-2626, Dec. 2019, doi: 10.1109/TMECH.2019.2953239.
J. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, pp. 900–906, 2009.
B.-Z. Guo and Z.-L. Zhao, “Active disturbance rejection control: theoretical perspectives,” Communications in Information and Systems, vol. 15, no. 3, pp. 361–421, 2015.
L. Guo and S. Cao. Anti-disturbance control theory for systems with multiple disturbances: a survey,” ISA Transactions, vol. 53, no. 4, pp. 846–849, 2014.
S. Li, J. Yang, W.-H. Chen, and X. Chen. Disturbance observerbased control: methods and applications. CRC Press, 2014.
M. Makarov et al., “Modeling and preview H control design for motion control of elastic-joint robots with uncertainties,” IEEE Trans. Ind. Electron., vol. 63, no. 10, pp. 6429–6438, Oct. 2016.
L. H. Wang, “Adaptive control of robot manipulators with uncertain kinematics and dynamics,” IEEE Trans. Autom. Control, vol. 62, no. 2, pp. 948–954, Feb. 2017.
B. Brahmi et al., “Adaptive tracking control of an exoskeleton robot with uncertain dynamics based on estimated time-delay control,” IEEE/ASME Trans. Mechatronics, vol. 23, no. 2, pp. 575–585, Apr. 2018.
M. Van, M. Mavrovouniotis, and S. Ge, “An adaptive backstepping nonsingular fast terminal sliding mode control for robust fault tolerant control of robot manipulators,” IEEE Trans. Syst., Man, Cybern., vol. 49, no. 7, pp. 1448–1458, Jul. 2019.
J. Mukherjee, S. Mukherjee, and I. N. Kar, “Sliding mode control of planar snake robot with uncertainty using virtual holonomic constraints,” IEEE Robot. Autom. Lett, vol. 2, no. 2, pp. 1077–1084, 2017.
N. Martínez-Fonseca et al., “Robust disturbance rejection control of a bipedrobotic system using high-order extended state observer,” ISA Trans., vol. 62, pp. 276–286, May 2016.
B. Ahi and A. Nobakhti, “Hardware implementation of an ADRC controller on a gimbal mechanism,” IEEE Trans. Control Syst. Technol., vol. 26, no. 6, pp. 2268–2275, Nov. 2018.
G. Herbs. A Simulative Study on Active Disturbance Rejection Control as a Control Tool for Practitioners. In Siemens AG, Clemens-Winkler-Strabe 3, Germany. 2013.
Z. Chu, Y. Sun, C. Wu, and N. Sepehri, “Active disturbance rejection control applied to automated steering for lane keeping in autonomous vehicles,” Control Eng. Pract., vol. 74, pp. 13–21, 2018.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Nguyen Xuan Chiem

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
This journal is based on the work at https://journal.umy.ac.id/index.php/jrc under license from Creative Commons Attribution-ShareAlike 4.0 International License. You are free to:
- Share – copy and redistribute the material in any medium or format.
- Adapt – remix, transform, and build upon the material for any purpose, even comercially.
The licensor cannot revoke these freedoms as long as you follow the license terms, which include the following:
- Attribution. You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- ShareAlike. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions. You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
• Creative Commons Attribution-ShareAlike (CC BY-SA)
JRC is licensed under an International License