Hybrid PID-feedforward control for trajectory tracking in 2-DOF Robotic Systems
Article Sidebar
Main Article Content
Abstract
This paper presents a hybrid control strategy combining proportional-integral-derivative (PID) feedback with model-based feedforward compensation for precise trajectory tracking in two-degree-of-freedom (2-DOF) robotic manipulators. The approach addresses nonlinear dynamics, including inertial coupling, Coriolis effects, and gravity, by deriving the Euler-Lagrange equations for a planar arm and implementing a computed torque feedforward term augmented by PID correction. Theoretical stability is analyzed using Lyapunov methods, ensuring asymptotic convergence of tracking errors. Simulations demonstrate superior performance compared to standalone PID, with root-mean-square errors reduced to 0.5751° for the first joint and 1.4416° for the second under sinusoidal references. Results include phase portraits, torque decompositions, and sensitivity analysis to parameter variations, validating the method's robustness for industrial applications.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
[1] H. T. T. Ngo, C. C. Nguyen, T. T. C. Duong, and T. T. Nguyen, "Trends in control strategies of parallel robot manipulators for robot-assisted rehabilitation", Engineering, Vol. 7(1), p. 44, https://doi.org/10.3390/eng7010044, (2026)
[2] E. A. Aner, O. M. Shehata, M. I. Awad, and N. E. ElHady, "A decade of soft robotic manipulators: Advances in design, modeling, control, and emerging challenges", Journal of Bionic Engineering, Vol. 23(1), pp. 55–98, https://doi.org/10.1007/s42235-025-00819-0, (2026)
[3] C. L. Nkwocha, A. Adewumi, S. O. Folorunsho, C. Eze, P. Jjagwe, J. Kemeshi, and N. Wang, "A comprehensive review of sensing, control, and networking in agricultural robots: From perception to coordination", Robotics, Vol. 14(11), p. 159, https://doi.org/10.3390/robotics14110159, (2025)
[4] C. D. Santina, R. K. Katzschmann, A. Bicchi, and D. Rus, "Model-based dynamic feedback control of a planar soft robot: Trajectory tracking and interaction with the environment", The International Journal of Robotics Research, Vol. 39(4), pp. 490–506, https://doi.org/10.1177/0278364919897292, (2020)
[5] A. M. Tusset, J. J. De Lima, F. C. Janzen, P. L. P. Filho, J. A. G. Luz Junior, J. M. Balthazar, and A. Kossoski, "A hybrid PID-LQR control applied in positioning control of robotic manipulators subject to excitation from non-ideal sources", Nonlinear Vibrations Excited by Limited Power Sources, Mechanisms and Machine Science, Vol. 116, pp. 321–328, https://doi.org/10.1007/978-3-030-96603-4_21, (2022)
[6] M. Wan, J. Dai, W. H. Zhang, Q.-B. Xiao, and X.-B. Qin, "Adaptive feed-forward friction compensation through developing an asymmetrical dynamic friction model", Mechanism and Machine Theory, Vol. 170, p. 104691, https://doi.org/10.1016/j.mechmachtheory.2021.104691, (2022)
[7] L. Zhang, J. Li, Y. Cui, M. Dong, B. Fang, and P. Zhang, "Design and performance analysis of a parallel wrist rehabilitation robot (PWRR)", Robotics and Autonomous Systems, Vol. 125, p. 103390, https://doi.org/10.1016/j.robot.2019.103390, (2020).
[8] Q. Xie, Q. Meng, Q. Zheng, Y. Fan, Y. Dai, and H. Yu, "Human-exoskeleton coupling dynamics of a multi-mode therapeutic exoskeleton for upper limb rehabilitation training", IEEE Access, Vol. 9, pp. 61998-62007, https://doi.org/10.1109/ACCESS.2021.3072781, (2021)
[9] V. Falkenhahn, A. Hildebrandt, R. Neumann, and O. Sawodny, "Dynamic control of the bionic handling assistant", IEEE/ASME Transactions on Mechatronics, Vol. 22(1), pp. 6–17, https://doi.org/10.1109/TMECH.2016.2605820, (2017)
[10] G. Grioli, W. Sebastian, M. Garabini, et al., "Variable stiffness actuators: The user's point of view", The International Journal of Robotics Research, Vol. 34(6), pp. 727–743, https://doi.org/10.1177/0278364914566515, (2015).
[11] W. S. Rone and P. Ben-Tzvi, "Continuum manipulator statics based on the principle of virtual work", Proceedings of the ASME 2012 International Mechanical Engineering Congress and Exposition. Vol. 4: Dynamics, Control and Uncertainty, Parts A and B, Houston, Texas (USA), pp. 321–328, https://doi.org/10.1115/IMECE2012-87675, (2012)
[12] P. Hyatt, D. Wingate, and M. D. Killpack, "Model-based control of soft actuators using learned non-linear discrete-time models", Frontiers in Robotics and AI, Vol. 6(22), https://doi.org/10.3389/frobt.2019.00022, (2019)
[13] T. G. Thuruthel, Y. Ansari, E. Falotico, and C. Laschi, "Control strategies for soft robotic manipulators: A survey", Soft Robotics, Vol. 5(2), pp. 149–163, https://doi.org/10.1089/soro.2017.0007, (2018)
[14] D. Rus and M. T. Tolley, "Design, fabrication and control of soft robots", Nature, Vol. 521, pp. 467–475, https://doi.org/10.1038/nature14543, (2015)
[15] N. Kellaris, V. G. Venkata, G. M. Smith, S. K. Mitchell, and C. Keplinger, "Peano-HASEL actuators: Muscle-mimetic, electrohydraulic transducers that linearly contract on activation", Science Robotics, Vol. 3(14), p. eaar3276, https://doi.org/10.1126/scirobotics.aar3276, (2018)