Abstract—This article presents a hybrid model and control strategy for a knee joint actuated by antagonistic McKibben pneumatic artificial muscles. The approach integrates a static force model, which captures the relationship between muscle contraction ratio and internal pressure, and a dynamic model that accounts for friction effects. A compressible flow model describes how pressure is established within each muscle during inflation and released during deflation. By unifying these elements with a differential equation for the knee joint's motion, a comprehensive representation of the system is developed. The accuracy of the model was validated against published experimental data for two different McKibben muscles, achieving Normalized Root Mean Square Errors (NRMSE) between 3.39% and 6.46% under various validation scenarios. A Proportional–Integral–Derivative (PID) controller manages the discrepancy between the reference trajectory and the actual knee angle, adjusting the valve orifice area to regulate airflow accordingly. The system's closed-loop performance is evaluated using multiple trajectories—including square wave, triangular, sine wave, and a human gait cycle—quantified through root mean square of the tracking error, the highest absolute deviation recorded, and the normalized error expressed as a percentage of the total motion span. Findings indicate that this methodology provides a robust basis for future advancements in pneumatic actuation for robotics applications.

Keywords—pneumatic artificial muscles, bipedal robot, knee joint, hybrid modelling, antagonistic actuation, dynamic system simulation, Proportional–Integral–Derivative (PID) controller, trajectory tracking

Cite: Jessica Magdy, Omar M. Shehata, Hamdy A. Kandil, and ElSayed I. Morgan, "Hybrid Modelling, Control and Simulation of Knee Joint Actuated by Antagonistic Pneumatic Artificial Muscles," International Journal of Mechanical Engineering and Robotics Research, Vol. 14, No. 4, pp. 445-453, 2025. doi: 10.18178/ijmerr.14.4.445-453

Copyright © 2025 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).