A Generalized Modeling Approach to Liquid-driven Ballooning Membranes

Soft robotics is advancing the use of flexible materials for adaptable robotic systems. Membrane-actuated soft robots address the limitations of traditional soft robots by using pressurized, extensible membranes to achieve stable, large deformations, yet control and state estimation remain challenging due to their complex deformation dynamics. This paper presents a novel modeling approach for liquid-driven ballooning membranes, employing an ellipsoid approximation to model shape and stretch under planar deformation. Relying solely on intrinsic feedback from pressure data and controlled liquid volume, this approach enables accurate membrane state estimation. We demonstrate the effectiveness of the proposed model for ballooning membrane-based actuators by experimental validation, obtaining the indentation depth error of $RMS{E_{{h_2}}} = 0.80\;{\text{mm}}$, which is 23% of the indentation range and 6.67% of the unindented actuator height range. For the force estimation, the error range is obtained to be RMSE<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</inf> = 0.15 N which is 10% of the measured force range.