Nonlinear Modeling for Soft Pneumatic Actuators via Data-Driven Parameter Estimation

TL;DR

The paper tackles the challenge of modeling soft pneumatic actuators by adopting a nonlinear data-driven framework built on Ludwick's Law, where the stress-strain relation $\sigma = E \e^{n}$ uses a fractional power $n$ estimated from material properties. A least-squares approach links $n$ to predictors like Young's modulus $E$, tensile strength $TS$, and mixed viscosity $MV$, enabling a predictive model for the material nonlinearity. This nonlinear constitutive model is embedded into a cantilever-beam dynamic formulation, yielding a governing equation $M \, tot{ heta} + C_n \, ot{ heta} + K_n \, heta^{n} = F$ with $F$ capturing actuator input; a parameter-varying extension switches to the linear law at small deformations via a threshold $\eta$. The method is validated experimentally on two Ecoflex-based actuators, estimating $n$ values (e.g., $n \\approx 2.365$ for Dragon Skin 20 and $n \\approx 1.727$ for Dragon Skin FX-Pro) and showing RMS errors under 3° for the nonlinear model, outperforming the linear model especially at larger deflections. Overall, the study provides a material-property-driven pathway to accurately model nonlinear soft actuators and suggests avenues for robustness via perturbations in $n$ and a hybrid, parameter-varying framework.

Abstract

Precise modeling soft robots remains a challenge due to their infinite-dimensional nature governed by partial differential equations. This paper introduces an innovative approach for modeling soft pneumatic actuators, employing a nonlinear framework through data-driven parameter estimation. The research begins by introducing Ludwick's Law, providing a accurate representation of the large deflections exhibited by soft materials. Three key material properties, namely Young's modulus, tensile stress, and mixed viscosity, are utilized to estimate the parameters inside the nonlinear model using the least squares method. Subsequently, a nonlinear dynamic model for soft actuators is constructed by applying Ludwick's Law. To validate the accuracy and effectiveness of the proposed method, several experiments are performed demonstrating the model's capabilities in predicting the dynamic behavior of soft pneumatic actuators. In conclusion, this work contributes to the advancement of soft pneumatic actuator modeling that represents their nonlinear behavior.

Figures (8)

• Figure 1: Stress-strain curve of soft materials (solid lines) c25 versus predicted stress-strain curve of Ludwick's Law c22 (dashed lines).
• Figure 2: The stress-strain curve of commonly used soft materials are nonlinear c25.
• Figure 3: Selected material properties correlate to the fractional power $n$.
• Figure 4: The irregular geometric structure of the soft pneumatic actuator is approximated by a cantilever beam.
• Figure 5: The bending geometric of the soft actuator when it is pressurized.