Theoretical Dynamic Modeling and Validation of Braided Pneumatic Artificial Muscles

Abstract

The high force-to-weight ratios of braided fluidic artificial muscles (AMs) are ideal for human scale and mobile robot applications. Prior modeling efforts focus on the theoretical static characteristics or empirical dynamic models of these actuators when pressurized. This paper develops a comprehensive high fidelity theoretical dynamic model based on first principles for braided pneumatic AMs and presents experimental validation. A novel theoretical model for the nonlinear stiffness is derived to describe the pressure–displacement behavior. The stiffness model, together with friction, damping, and inertia models, forms an equation of motion (EOM) for braided pneumatic AMs. The EOM is coupled with first-order servopneumatic pressure dynamics, resulting in a third-order system model. System model simulations are compared to experimental results of prototypes with nine different geometries. On average, the system model is able to predict the quasi-static displacement within 7% and the dynamic response within 11%. The theoretical model is also benchmarked against a high fidelity curve fit method, with the empirical method showing a 2% improvement in only quasi-static scenarios. The model promises to be useful for mechanical system and model-based control designs.