Design Of Robotic Leg Using Proportional Integral Deferential Controller with Computed Torque Control Method
DOI:
https://doi.org/10.31272/jeasd.2493Keywords:
Computed torque control, Dynamic control, Five-bar mechanism, Mobile legged robotAbstract
Mobile robots are now crucial elements in manufacturing sectors. A five-link robot leg is fundamental for understanding robotic leg principles, modelled by a nonlinear differential equation. Numerical solutions are used when closed-form solutions become difficult for systems with higher degrees of freedom. This study focused on controlling the robot leg to reach the desired position by combining computed torque control with a PID (Proportional Integral Derivative) controller based on the motion equation derivation. The numerical solution implemented using MATLAB includes simulation and modelling, where Simulink tools are used for simulating dynamic systems and then evaluated against the computed torque control approach. Position errors for motor 1 and motor 4 were observed for 1 second and 10 seconds. Stability was achieved in the first motor after approximately 0.75 seconds. The second motor's movement stabilized after around 0.9 seconds, with the error value between input and output for 10 seconds starting at 0.06 and 6.1, stabilizing at zero within 1 second at motors 1 and 4, respectively. The system reached stability after approximately 0.3 seconds using computed torque with PID control, with gains (Kp, Kd, and Ki) set to (9500:10:20). Numerical simulation outcomes validate the controller's effectiveness in accurately tracking diverse trajectories.
References
A. A. Khalate, Gopinathan Leena, and G. Ray, “An Adaptive Fuzzy Controller for Trajectory Tracking of Robot Manipulator,” Intelligent Control and Automation, vol. 02, no. 04, pp. 364–370, Jan. 2011, doi: https://doi.org/10.4236/ica.2011.24041
SK Mahmood, SH Bakhy, MA Tawfik. “Motion Analysis and Trajectory Tracking Control of Propeller-Type Climbing Robot”. 2nd Annual International Conference on Information and Sciences (AiCIS), Fallujah, Iraq. Nov, 2020. https://doi.org/10.1109/AiCIS51645.2020.00016
G. Nandy, B. Chatterjee, and A. Mukherjee, “Dynamic Analysis of Two-Link Robot Manipulator for Control Design,” Lecture Notes in Electrical Engineering, pp. 767–775, 2018, doi: https://doi.org/10.1007/978-981-10-7901-6_83.
E. Khanbabayi and M.-R. S. Noorani, “Design Computed Torque Control for Stewart Platform with Uncertainty to the Rehabilitation of Patients with Leg Disabilities,” Computer Methods In Biomechanics And Biomedical Engineering, vol. 27, no. 8, pp. 1028–1041, Jun. 2024, doi: https://doi.org/10.1080/10255842.2023.2222863.
P. Chotikunnan and R. Chotikunnan, “Dual Design PID Controller for Robotic Manipulator Application,” Journal of Robotics and Control (JRC), vol. 4, no. 1, pp. 23–34, Feb. 2023, doi: https://doi.org/10.18196/jrc.v4i1.16990
K. Ba et al., “Dynamics Compensation of impedance-based Motion Control for LHDS of Legged Robot,” Robotics and Autonomous Systems, vol. 139, pp. 103704–103704, Nov. 2020, doi: https://doi.org/10.1016/j.robot.2020.103704.
T. Zhou et al., “Adaptive Control for Manipulators with Unknown Virtual Control Coefficients and Input Nonlinearities,” IET Control Theory and Applications, vol. 16, no. 11, pp. 1063–1074, Apr. 2022, doi: https://doi.org/10.1049/cth2.12285
L. Shi, H. Yao, M. Shan, Q. Gao, and X. Jin, “Robust Control of a Space Robot Based on an Optimized Adaptive Variable Structure Control Method,” Aerospace Science and Technology, vol. 120, pp. 107267–107267, Dec. 2021, doi: https://doi.org/10.1016/j.ast.2021.107267.
K. V. Sancak and Z. Y. Bayraktaroglu, “Nonlinear Computed Torque Control of 6-Dof Parallel Manipulators,” International Journal of Control Automation and Systems, vol. 20, no. 7, pp. 2297–2311, Jun. 2022, doi: https://doi.org/10.1007/s12555-021-0198-6
F. Sedghi, S Neisarian, M. M. Arefi, M. H. Asemani, and Navid Vafamand, “Practical finite-time Adaptive Sliding Mode Control for 5-link Biped Robot in the Presence of Uncertainty,” International Journal of Control, vol. 96, no. 8, pp. 1989–2002, May 2022, doi: https://doi.org/10.1080/00207179.2022.2079564
A. M. El-Dalatony, T. Attia, H. Ragheb, and A. M. Sharaf, “Cascaded PID Trajectory Tracking Control for Quadruped Robotic Leg,” International Journal of Mechanical Engineering and Robotics Research, vol. 12, no. 1, pp. 40–47, Jan. 2023, doi: https://doi.org/10.18178/ijmerr.12.1.40-47
C. Feng, Z. Chen, W. Jin, and W. Guo, “Motion Control and Simulation Analysis of a Manipulator Based on Computed Torque Control Method,” Lecture notes in computer science, pp. 10–22, Jan. 2023, doi: https://doi.org/10.1007/978-981-99-6483-3_2.
A. Adnan and E. H. Karam, “Optimal Improved PID Controller with Goa Algorithm for Single Link Human Leg Robot,” Journal of Engineering and Sustainable Development, vol. 26, no. 2, pp. 103–110, Mar. 2022, doi: https://doi.org/10.31272/jeasd.26.2.10.
M. Ahmadizadeh, A. M. Shafei, and M. Fooladi, “Dynamic Modeling of closed-chain Robotic Manipulators in the Presence of Frictional Dynamic forces: a Planar Case,” Mechanics Based Design of Structures and Machines, vol. 51, no. 8, pp. 4347–4367, Aug. 2021, doi: https://doi.org/10.1080/15397734.2021.1966304
Q. He, G. Zhao, X. Shui, and K. Xu, “Kinematic Analysis and Simulation Study of 5R Robotic Arm,” In Ninth International Symposium on Sensors, Mechatronics, and Automation System, China (ISSMAS 2023), pp. 222–222, Mar. 2024, doi: https://doi.org/10.1117/12.3015018
A.-A. Ayazbay, G. Balabyev, S. Orazaliyeva, K. Gromaszek, and A. Zhauyt, “Trajectory Planning, Kinematics, and Experimental Validation of a 3D-Printed Delta Robot Manipulator,” International Journal of Mechanical Engineering and Robotics Research, vol. 13, no. 1, pp. 113–125, 2024, doi: https://doi.org/10.18178/ijmerr.13.1.113-125
C. E. Ponce and D. A. Ponce, “A Didactic Approach to Energy-Based Dynamic Modeling: Least Action, D’Alembert Principle and Euler-Lagrange Formalism,” Lecture notes in networks and systems, pp. 91–102, Jan. 2024, doi: https://doi.org/10.1007/978-3-031-47269-5_11
Y. Li, J. Gao, W. Chen, Y. Zhou, and Z. Yin, “Simulation and Trajectory Optimization of Articulated Robots via Spectral Variational Integrators,” Communications in Nonlinear Science and Numerical Simulation, vol. 131, pp. 107877–107877, Feb. 2024, doi: https://doi.org/10.1016/j.cnsns.2024.107877
P. K. Khosla and Takeo Kanade, “Real-time Implementation and Evaluation of the computed-torque Scheme,” IEEE Transactions on Robotics and Automation, vol. 5, no. 2, pp. 245–253, Apr. 1989, doi: https://doi.org/10.1109/70.88047.
H. Badkoobehhezaveh, R. Fotouhi, and Q. Zhang, “Particle Swarm Optimization / PID-Computed Torque Control for a Manipulator,” Volume 7: 46th Mechanisms and Robotics Conference (MR), Aug. 2022, doi: https://doi.org/10.1115/detc2022-89769
A. Ibrahim Majeed, “Mobile Robot Motion Control Based On Chaotic Trajectory Generation,” Journal of Engineering and Sustainable Development, vol. 24, no. 4, pp. 48–55, Jul. 2020, doi: https://doi.org/10.31272/jeasd.24.4.6.
Downloads
Key Dates
Received
Revised
Accepted
Published Online First
Published
Issue
Section
License
Copyright (c) 2025 Zaineb Wared Matteb, Sadeq Hussein Bakhy, Nabil Hassan Hadi (Author)

This work is licensed under a Creative Commons Attribution 4.0 International License.










