Viscoelasticity-Based Mechanistic Modeling and Control of Bending Pneumatic Muscles

Abstract

Predicting the kinematics of bending pneumatic muscles (BPMs) remains challenging due to the necessity for models that effectively address the pronounced hysteresis and creep inherent in soft materials. While prior research has predominantly focused on phenomenological and data-driven modeling approaches, this study introduces a viscoelasticity-based mechanistic model (VBMM) and a feedforward- feedback hybrid control system tailored for BPMs. First, the VBMM is developed by leveraging the principles of viscoelasticity—a common property of soft materials and a mechanistic driver of hysteresis and creep. Second, we address the computational challenge arising from the history-dependent viscoelastic response of BPMs, where the current state depends on the cumulative stress-strain history. Conventional methods incur escalating computational costs over time, rendering real-time control impractical. To resolve this, we propose a sliding window-based long-term prediction mechanism (long-term VBMM) that maintains model accuracy while significantly reducing computational overhead. Finally, a hybrid control system integrating the long-term VBMM as a feedforward compensator with feedback correction is designed to achieve BPM motion tracking. Experimental validation confirms the VBMM's superior predictive accuracy (error <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&lt; $</tex-math></inline-formula> 3.69%) and demonstrates the control system's effectiveness.