Fractional Order Extended State Observer Enhances the Accuracy of Estimation for Flexible Joint Single-link Robot

Hakam Marwan; Amjad J. Humaidi; Huthaifa Al-Khazraji

doi:10.18196/jrc.v6i3.26318

Authors

Hakam Marwan Ninevah University
Amjad J. Humaidi University of Technology
Huthaifa Al-Khazraji University of Technology

DOI:

https://doi.org/10.18196/jrc.v6i3.26318

Keywords:

Flexible Joint System, Extended State Observer, RMSE, Disturbance Rejection, Active Disturbance Rejection Control

Abstract

This study focuses on analyzing and evaluating the performance of three types of Extended State Observers (ESOs)—Linear ESO (LESO), Nonlinear ESO (NESO), and Fractional-Order ESO (FOESO)—within a flexible joint robotic system. ESOs are a key component of Active Disturbance Rejection Control (ADRC) due to their ability to estimate system states and internal and external disturbances without requiring an accurate system model, making them particularly suitable for nonlinear and complex systems. This research aims to provide a quantitative comparison among the three observer types under parameter uncertainties and external disturbances using MATLAB/SIMULINK simulations. By reducing the RMSE, a Genetic Algorithm (GA) finds the optimal observer parameters. The results indicate that FOESO significantly outperforms the other observers in terms of estimation accuracy, achieving a remarkably low RMSE of 1.06×10⁻¹⁶ for position estimation, compared to 9.16×10⁻¹³ for NESO and 2.17×10⁻¹¹ for LESO. These findings highlight FOESO's superior robustness in managing nonlinearities and disturbances, making it a promising solution for high-precision robotic applications.

References

S. A. Ajwad and J. Iqbal, "Emerging trends in robotics—A review from applications perspective," in Proc. Int. Conf. Eng. Emerg. Technol. (ICEET), pp. 1–6, 2015.

J. Iqbal et al., "ARM solutions for text, audio and image data processing for ultra low power applications," in Proc. IEEE Int. Multitopic Conf., pp. 32–35, 2004.

M. F. Khan, R. U. Islam, and J. Iqbal, "Control strategies for robotic manipulators," in Proc. IEEE Int. Conf. Robot. Artif. Intell. (ICRAI), pp. 26–33, 2012.

M. I. Ullah et al., "Modeling and computed torque control of a 6 degree of freedom robotic arm," in Proc. IEEE Int. Conf. Robot. Emerg. Allied Technol. Eng., pp. 133–138, 2014.

A. Meddahi et al., "API based graphical simulation of robotized sites," in Proc. 14th IASTED Int. Conf. Robot. Appl., pp. 485–492, 2009.

K. Naveed and J. Iqbal, "Brain controlled human robot interface," in Proc. IEEE Int. Conf. Robot. Artif. Intell., pp. 55–60, 2012.

M. M. Azeem et al., "Emotions in robots," in Emerging Trends Appl. Inf. Commun. Technol., vol. 281, pp. 144–153, 2012.

J. Iqbal et al., "Automating industrial tasks through mechatronic systems—A review of robotics in industrial perspective," Tech. Gaz., vol. 23, no. 3, pp. 917–924, 2016.

J. Iqbal and K. Baizid, "Stroke rehabilitation using exoskeleton-based robotic exercisers: Mini review," Biomed. Res., vol. 26, no. 2, pp. 197–201, 2015.

J. Iqbal, N. Tsagarakis, and D. Caldwell, "Four-fingered lightweight exoskeleton robotic device accommodating different hand sizes," Electron. Lett., vol. 51, no. 12, pp. 888–890, 2015.

J. Iqbal, O. Ahmad, and A. Malik, "HEXOSYS II—Towards realization of light mass robotics for the hand," in Proc. 14th IEEE Int. Multitopic Conf., pp. 115–119, 2011.

J. Iqbal and A. M. Tahir, "Robotics for nuclear power plants—Challenges and future perspectives," in Proc. 2nd IEEE Int. Conf. Appl. Robot. Power Ind., pp. 151–156, 2012.

J. Iqbal et al., "State estimation technique for a planetary robotic rover," Rev. Fac. Ing. Univ. Antioquia, no. 70, pp. 58–68, 2014.

J. Iqbal, S. Heikkilä, and A. Halme, "Tether tracking and control of ROSA robotic rover," in Proc. 10th IEEE Int. Conf. Control, Autom., Robot. Vis., pp. 689–693, 2008.

J. Iqbal et al., "A novel track-drive mobile robotic framework for conducting projects on robotics and control systems," Life Sci. J., vol. 10, no. 2, pp. 130–137, 2013.

K. Baizid et al., "Modelling of robotized site and simulation of robots' optimum placement and orientation zone," in Proc. 21st IASTED Int. Conf. Model. Simul., pp. 9–16, 2010.

K. Baizid et al., "Time scheduling and optimization of industrial robotized tasks based on genetic algorithms," Robot. Comput.-Integr. Manuf., vol. 34, pp. 140–150, 2015.

K. Baizid et al., "Robotized task time scheduling and optimization based on Genetic Algorithms for non redundant industrial manipulators," in Proc. IEEE Int. Symp. Robot. Sens. Environ., pp. 112–117, 2014.

A. M. Tahir and J. Iqbal, "Underwater robotic vehicles: Latest development trends and potential challenges," Sci. Int., vol. 26, no. 1, pp. 1–5, 2014.

J. Iqbal et al., "Real-time target detection and tracking: A comparative in-depth review of strategies," Life Sci. J., vol. 10, no. 3, pp. 804–813, 2013.

J. Iqbal et al., "Computer vision inspired real-time autonomous moving target detection, tracking and locking," Life Sci. J., vol. 10, no. 4, pp. 3338–3345, 2013.

S. A. Ajwad and J. Iqbal, "Recent advances and applications of tethered robotic systems," Sci. Int., vol. 26, no. 4, pp. 2045–2051, 2014.

J. Iqbal, N. Tsagarakis, and D. Caldwell, "Design optimization of a hand exoskeleton rehabilitation device," in Proc. RSS Workshop Understand. Hum. Hand Adv. Robot. Manip., pp. 44–45, 2009.

J. Iqbal, N. Tsagarakis, and D. Caldwell, "Human hand compatible underactuated exoskeleton robotic system," Electron. Lett., vol. 50, no. 7, pp. 494–496, 2014.

J. Iqbal et al., "Design requirements of a hand exoskeleton robotic device," in Proc. 14th IASTED Int. Conf. Robot. Appl., pp. 44–51, 2009.

I. Muhammad et al., "Regulation of hypnosis in Propofol anesthesia administration based on non-linear control strategy," Braz. J. Anesthesiol., vol. 66, no. 4, pp. 367–375, 2016.

A. A. Khan, R. U. Nabi, and J. Iqbal, "Surface estimation of a pedestrian walk for outdoor use of power wheel chair based robot," Life Sci. J., vol. 10, no. 4, pp. 1697–1704, 2013.

M. I. Ullah et al., "Non-linear control law for articulated serial manipulators: Simulation augmented with hardware implementation," Electron. Electr. Eng., vol. 22, no. 2, pp. 3–7, 2016.

O. Ahmad, I. Ullah, and J. Iqbal, "A multi-robot educational and research framework," Int. J. Acad. Res., vol. 6, no. 1, pp. 217–222, 2014.

M. Zohaib et al., "An improved algorithm for collision avoidance in environments having U and H shaped obstacles," Stud. Inform. Control, vol. 23, no. 1, pp. 97–106, 2014.

M. Zohaib et al., "Addressing collision avoidance and nonholonomic constraints of a wheeled robot: Modeling and simulation," in Proc. IEEE Int. Conf. Robot. Emerg. Allied Technol. Eng., pp. 306–311, 2014.

R. U. Nabi et al., "A unified SLAM solution using partial 3D structure," Electron. Electr. Eng., vol. 20, no. 2, pp. 3–8, 2014.

M. Zohaib et al., "IBA: Intelligent Bug Algorithm—A novel strategy to navigate mobile robots autonomously," in Emerging Trends Appl. Inf. Commun. Technol., vol. 281, pp. 291–299, 2013.

A. H. Arif et al., "A hybrid humanoid-wheeled mobile robotic educational platform—Design and prototyping," Indian J. Sci. Technol., vol. 7, no. 10, pp. 2140–2148, 2015.

H. Khan et al., "Longitudinal and lateral slip control of autonomous wheeled mobile robot for trajectory tracking," Front. Inf. Technol. Electron. Eng., vol. 16, no. 2, pp. 166–172, 2015.

S. A. Ajwad, U. Iqbal, and J. Iqbal, "Hardware realization and PID control of multi-degree of freedom articulated robotic arm," Mehran Univ. Res. J. Eng. Technol., vol. 34, no. 1, pp. 1–12, 2015.

U. Iqbal et al., "Embedded control system for AUTAREP—A novel AUTonomous Articulated Robotic Educational Platform," Tech. Gaz., vol. 21, no. 6, pp. 1255–1261, 2014.

J. Iqbal et al., "Towards sophisticated control of robotic manipulators: An experimental study on a pseudo-industrial arm," Stroj. Vestn.-J. Mech. Eng., vol. 61, no. 7–8, pp. 465–470, 2015.

S. A. Ajwad et al., "Disturbance-observer-based robust control of a serial-link robotic manipulator using SMC and PBC techniques," Stud. Inform. Control, vol. 24, no. 4, pp. 401–408, 2015.

F. Xi and R. G. Fenton, "Coupling effect of a flexible link and a flexible joint," Int. J. Robot. Res., vol. 13, no. 5, pp. 443–453, 1994.

S. Ulrich, J. Z. Sasiadek, and I. Barkana, "Nonlinear adaptive output feedback control of flexible-joint space manipulators with joint stiffness uncertainties," J. Guid., Control, Dyn., vol. 37, no. 6, pp. 1961–1975, 2014.

L. Qiao and W. Zhang, "Adaptive non-singular integral terminal sliding mode tracking control for autonomous underwater vehicles," IET Control Theory Appl., vol. 11, no. 8, pp. 1293–1306, 2017.

A. Suprem, N. Mahalik, and K. Kim, "A review on application of technology systems, standards and interfaces for agriculture and food sector," Comput. Stand. Interfaces, vol. 35, no. 4, pp. 355–364, 2013.

C. Yang et al., "Global adaptive tracking control of robot manipulators using neural networks with finite-time learning convergence," Int. J. Control Autom. Syst., vol. 15, no. 5, pp. 1916–1924, 2017.

C. Yang et al., "Haptic identification by ELM-controlled uncertain manipulator," IEEE Trans. Syst., Man, Cybern., Syst., vol. 47, no. 8, pp. 2394–2409, 2017.

M. Mosayebi, M. Ghayour, and M. J. Sadigh, "A nonlinear high gain observer based input–output control of flexible link manipulator," Mech. Res. Commun., vol. 86, pp. 4–12, 2017.

H. Rahimi and M. Nazemizadeh, "Dynamic analysis and intelligent control techniques for flexible manipulators: A review," Adv. Robot., vol. 28, no. 2, pp. 63–76, 2014.

Z. Chen, M. Wang, and Y. Zou, "Dynamic learning from adaptive neural control for flexible joint robot with tracking error constraints using high-gain observer," Syst. Sci. Control Eng., vol. 6, no. 2, pp. 177–190, 2018.

S. K. Dwivedy and P. Eberhard, "Dynamic analysis of flexible manipulators, a literature review," Mech. Mach. Theory, vol. 41, no. 7, pp. 749–777, 2006.

D. Feliu-Talegon et al., "Stable force control and contact transition of a single link flexible robot using a fractional-order controller," ISA Trans., vol. 89, pp. 139–157, 2019.

K. Wei and B. Ren, “A method on dynamic path planning for robotic manipulator autonomous obstacle avoidance based on an improved RRT algorithm,” Sensors, vol. 18, no. 571, 2018.

N. A. Alawad, A. J. Humaidi, and A. S. Alaraji, "Sliding mode-based active disturbance rejection control of assistive exoskeleton device for rehabilitation of disabled lower limbs," An. Acad. Bras. Cienc., vol. 95, no. 2, p. e20220680, Jun. 2023.

A. Q. Al-Dujaili, A. F. Hasan, A. J. Humaidi, and A. Al-Jodah, "Anti-disturbance control design of exoskeleton knee robotic system for rehabilitative care," Heliyon, vol. 10, no. 9, p. e28911, 2024.

N. A. Alawad, A. J. Humaidi, A. S. M. Al-Obaidi, and A. S. Alaraji, "Active disturbance rejection control of wearable lower-limb system based on reduced ESO," Indones. J. Sci. Technol., vol. 7, no. 2, pp. 203–218, 2022.

N. A. Alawad, A. J. Humaidi, and A. S. Al-Araji, "Improved active disturbance rejection control for the knee joint motion model," Math. Model. Eng. Probl., vol. 9, no. 2, pp. 477–483, 2022.

E. E. Mitchell and E. Harrison, “Design of a Hardware Observer for Active Machine Tool Control,” Journal of Dynamic Systems Measurement and Control-transactions of The Asme, vol. 99, pp. 227-232, 1977.

N. Léchevin and P. Sicard, “Observer design for flexible joint manipulators with parameter uncertainties,” Proceedings of International Conference on Robotics and Automation, vol. 3, pp. 2547-2552, 1997.

F. Abdollahi, H. A. Talebi, and R. V. Patel, “A stable neural network-based observer with application to flexible-joint manipulators,” IEEE transactions on neural networks, vol. 17, no. 1, pp. 118–129, 2006.

H. Ullah, F. M. Malik, A. Raza, N. Mazhar, R. Khan, A. Saeed, and I. Ahmad, "Robust Output Feedback Control of Single-Link Flexible-Joint Robot Manipulator with Matched Disturbances Using High Gain Observer," Sensors, vol. 21, no. 9, p. 3252, 2021.

H. Ma, H. Ren, Q. Zhou, H. Li, and Z. Wang, "Observer-Based Neural Control of N-Link Flexible-Joint Robots," IEEE Transactions on Neural Networks and Learning Systems, vol. 35, no. 4, pp. 5295–5305, 2024.

S. E. Talole, J. P. Kolhe, and S. B. Phadke, "Extended-State-Observer-Based Control of Flexible-Joint System with Experimental Validation," IEEE Trans. Ind. Electron., vol. 57, pp. 1411–1419, 2009.

S. A. Bortoff, J. Y. Hung, and M. Spong, "A Discrete-Time Observer for Flexible-Joint Manipulators," in Proc. of the 28th IEEE Conference on Decision and Control, vol. 3, pp. 2078-2082, 1989.

M. W. Spong and M. Vidyasagar, Robot Dynamics and Control, New York, USA: Wiley, 1989.

W. Wang and Z. Gao, "A Comparison Study of Advanced State Observer Design Techniques," in Proc. of the American Control Conference, pp. 4754–4759, Jun. 2003.

A. J. Humaidi and I. K. Ibraheem, "Speed control of permanent magnet DC motor with friction and measurement noise using novel nonlinear extended state observer-based anti-disturbance control," Energies, vol. 12, no. 9, p. 1651, 2019.

W. R. Abdul-Adheem, A. T. Azar, I. K. Ibraheem, and A. J. Humaidi, "Novel active disturbance rejection control based on nested linear extended state observers," Appl. Sci., vol. 10, no. 12, p. 4069, 2020.

M. Y. Hassan, A. J. Humaidi, and M. K. Hamza, "On the design of backstepping controller for acrobot system based on adaptive observer," Int. Rev. Electr. Eng., vol. 15, no. 4, pp. 328–335, 2020.

A. Ma’Bdeh, N. Tawalbeh, and R. El-Khazali, "Sensorless Speed Control of a PMSM Using Fractional-Order Extended State Observer," in 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), pp. 1-5, 2023.

A. F. Hasan, A. J. Humaidi, A. S. M. Al-Obaidi, A. K. Al-Mhdawi, and F. A. Abdulmajeed, "Fractional order extended state observer enhances the performance of controlled tri-copter UAV based on active disturbance rejection control," Stud. Comput. Intell., vol. 1090, pp. 439–487, 2023.

A. H. Hameed, S. A. Al-Samarraie, and A. J. Humaidi, "Backstepping-based nonlinear disturbance observer for speed control of DC motor," AIP Conf. Proc., vol. 3232, no. 1, p. 030007, 2024.

I. Toumi, B. Meghni, O. Hachana, G. Fusco, and N. K. Bahgaat, "Robust variable-step perturb-and-observe sliding mode controller for grid-connected wind-energy-conversion systems," Entropy, vol. 24, no. 5, p. 731, 2022.

A. J. Humaidi, A. A. Mohammed, A. H. Hameed, A. T. Azar, and A. Q. Al-Dujaili, "State estimation of rotary inverted pendulum: A comparative study of observers performance," 2020 IEEE Congreso Bienal de Argentina, ARGENCON 2020, pp. 9505507, 2020.

A. J. Humaidi, E. N. Tala'at, A. Q. Al-Dujaili, D. A. Pereira, and I. K. Ibraheem, "Design of backstepping control based on adaptive observer for underactuated system," 7th Int. Conf. Control, Decis. Inf. Technol., CoDIT 2020, pp. 288–293, 9263929, 2020.