A Generalized Modeling Approach to Liquid-driven Ballooning Membranes

TL;DR

The paper tackles the challenge of estimating the shape and stretch of liquid-driven ballooning membranes in soft robotics using only intrinsic feedback. It introduces a generalized ellipsoid-based, quasi-static modeling framework that links injected liquid volume and internal pressure to ellipsoidal membrane geometry and principal stretches, employing a Yeoh hyperelastic energy model within a minimum potential energy formulation. The approach defines state variables $(h_1,h_2,F)$ and derives closed-form geometric relations for the ellipsoid axes, enabling full state estimation during planar contact without external sensing beyond $p$ and $V_f$; experimental validation on Ecoflex membranes demonstrates accurate indentation depth and force estimation with quantifiable RMSEs. This work provides a foundation for observers and controllers for ballooned-membrane actuators and advances robust soft-robot control in contact-rich tasks, while identifying limitations related to initial inflation and material hysteresis that warrant future enhancements.

Abstract

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 $RMSE_{h_2}=0.80\;$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 $RMSE_{F}=0.15\;$N which is $10\%$ of the measured force range.

Figures (9)

• Figure 1: Overview of Ballooning Membrane Actuator (BMA) with (a) pre-ballooned membrane, (b) ballooned membrane, (c) membrane with point contact and (d) deformed membrane.
• Figure 2: Flow diagram: intrinsic quasi-static modeling, the state variables are indicated in red color.
• Figure 3: Modeling of BMA: (a) Pre-ballooned configuration of the membrane (non-contact phase). (b) Interaction forces during external contact. (c) Shape estimation of BMA under contact. (d) Regions of ellipsoid components define the estimated stretch of the membrane.
• Figure 4: Experimental setup for model validation
• Figure 5: Trajectory sequencing on the ballooning membrane: (a) The formed geometry with selected volume trajectory (non-contact phase), (b) Interaction of the formed membrane with point contact assuming no force or indentation applied, and (c) The first indentation trajectory point for a given volume trajectory. (d) The second indentation trajectory point for the same volume.