Quasi-static nonlinear response of pneumatic artificial muscles for both agonistic and antagonistic actuation modes

Pneumatic artificial muscles are actuators known for their low weight, high specific force, and natural compliance. Employed in antagonistic schemes, these actuators closely mimic biological muscle pairs, resulting in applications for humanoid and other bio-inspired robotic systems. 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 accurately capture nonlinear pneumatic artificial muscle force behavior in 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. Lastly, a detailed geometric model is applied to improve force predictions, particularly during pneumatic artificial muscle extension. By modeling the deformation shape of the actuator ends as sections of an elliptic toroid, pneumatic artificial muscle force predictions as a function of strain are improved. These modeling improvements combine to enable enhanced model-based control in pneumatic artificial muscle actuator applications.