Improved Static Model for Pneumatic Artificial Muscle Based on Virtual Work and Bladder Radial Deformation Work Losses

Existing pneumatic artificial muscle (PAM) static geometrical models based on the principle of virtual work provide only approximate force predictions since they neglect the effects of volume change and radial bladder deformation work loss. In this study, we propose an improved geometrical static model called the Accurate Volume and Bladder Deformation Loss (AVBDL) model. This model introduces a physically consistent calculation of muscle volume at different contractions and pressures and incorporates a new way of describing work losses due to radial deformation of the bladder. The hyperelastic properties of the bladder were experimentally characterized and modeled using the Mooney–Rivlin formulation. The AVBDL model was validated against experimental data from four types of pneumatic muscles and compared with three established analytical models. Results show that the AVBDL model significantly improves force prediction accuracy, achieving a normalized root mean square (NRMS) error of 6.7–16.4%, compared to 20–68% for existing models. Due to its analytical transparency, reduced error, and broad applicability, the AVBDL model provides a robust basis for accurate simulation and control of pneumatic artificial muscles.