Accurately modeling soft robots remains a challenge due to their inherent nonlinear behavior and parameter variations. This paper presents a novel approach to modeling soft pneumatic actuators using a nonlinear parameter-varying framework. The research begins by introducing Ludwick's Law, providing a more accurate representation of the complex mechanical behavior exhibited by soft materials. Three key material properties, namely Young's modulus, tensile stress, and mixed viscosity, are utilized to estimate the parameter 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, experimental validations are performed. We perform several experiments, demonstrating the model's capabilities in predicting the dynamical behavior of soft pneumatic actuators. In conclusion, this work contributes to the advancement of soft pneumatic actuator modeling that represents their nonlinear behavior.

翻译：准确建模软体机器人仍是一项挑战，因其固有的非线性行为和参数变化。本文提出了一种基于非线性参数变化框架的软体气动执行器建模新方法。研究首先引入卢德威克定律（Ludwick's Law），更精确地描述了软材料展现的复杂力学行为。利用三个关键材料属性——杨氏模量、拉伸应力和混合粘度——通过最小二乘法估计非线性模型中的参数。随后，基于卢德威克定律构建了软体执行器的非线性动力学模型。为验证所提方法的准确性和有效性，进行了实验验证。通过多项实验，展示了该模型预测软体气动执行器动力学行为的能力。总之，本研究推动了能够表征其非线性行为的软体气动执行器建模方法的发展。