Nonlinear analysis of quasi-static response of pneumatic artificial muscles for agonistic and antagonistic actuation modes

Pneumatic artificial muscles (PAMs) are actuators known for their light weight, high specific force, and natural compliance. Employed in antagonistic schemes, these actuators closely mimic biological muscle pairs, which has led to their use in humanoid and other bio-inspired robotics applications. Such systems require precise actuator modeling and control in order to achieve high performance. In the present study, refinements are introduced to an existing model of pneumatic artificial muscle force-contraction behavior. The force balance modeling approach is modified to include the effects of non-constant bladder thickness and up to a fourth-order polynomial stress-strain relationship is adopted in order to more accurately capture nonlinear PAM force behavior in both contraction and extension. Moreover, the polynomial coefficients of the stress-strain relationship are constrained to vary linearly with pressure, improving the ability to predict behavior at untested pressure levels while preserving model accuracy at tested pressure levels. Additionally, a detailed geometric model is applied to improve force predictions, particularly during PAM extension. By modeling bladder end effects as sections of an elliptic toroid, PAM force predictions as a function of strain are improved. These modeling improvements combine to enable enhanced model-based control in PAM actuator applications.