Pressurization of gas within embedded channels and cavities is a popular method for actuating soft robots. Various previous works examined the effects of internal fluid mechanics on this actuation approach, as well as on leveraging viscous effects to extend the capabilities of soft robots. However, no existing works studied the combined effects of fluid viscosity and compressibility, relevant to miniaturized configurations, which is the aim of the current work. We derive a general model for compressible viscous flow in an elastic media representing a simplified miniaturized soft robot. We illustrate applying this model to periodic configurations, simplifying it via a long-wave approximation. Steady, and time-dependent solutions are obtained, allowing to model the flow and to provide insight into the actuation dynamics of miniaturized pneumatic soft robots.
Keywords: actuation; approximation; compressible flow; elastic beams; long-wave; viscous peeling.