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.

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