Integrating Physics-Based and Data-Driven Approaches for Accurate Bending Prediction in Soft Pneumatic Actuators

Soft pneumatic actuators (SPAs) are gaining attention in the field of soft robotics due to their lightweight, highly flexible, and safer interaction while operated under an unstructured environment. They are easy to fabricate, produce high output force, and are relatively very inexpensive compared to other soft actuators. However, accurate prediction of their nonlinear bending behavior is one of the main challenges, which is mainly due to the complex material properties and high deformation patterns. Therefore, this study focused on a hybrid approach that accurately captures the bending behavior of a single-chambered SPAs. This approach integrates physics-based modeling (finite element analysis (FEA) and analytical modeling) with a data-driven (polynomial regression modeling) approach to analyze the bending of single-chambered SPAs. Initially, four different hyperelastic material models (Neo-Hookean, Yeoh, Arruda–Boyce, and Ogden) were tested using FEA to analyze how material selection affects the SPA response. It is found that the Arruda–Boyce model generates the highest bending of 101° at 30 kPa pressure, while the other models consistently underestimated deformation at higher pressures. Further, an enhanced mathematical or analytical model was developed using Euler and Timoshenko beam theory with certain assumptions, such as neutral axis shifting, chamber ballooning, and shear deformation. These assumptions significantly improve the prediction accuracy and generate a bending angle of 99°at 30 kPa, which closely matches FEA bending. Further, a polynomial regression-based machine learning (ML) model was trained using analytical or mathematical bending data for faster output prediction. This data-driven approach achieves very high accuracy in the validation range, with an average absolute percentage deviation of only 0.002%. Additionally, comparison with the analytical results showed a mean absolute error (MAE) of 0.00180°, root mean squared error (RMSE) of 0.00205°, and coefficient of determination (R2) value of 0.999999808. Overall, integrating physics-based modeling with a data-driven approach provides a reliable and scalable method for SPA design. It provides practical information on material selection, analytical correction, and ML modeling, which will reduce the need for time-consuming prototyping. Finally, this hybrid approach can help to accelerate the development of soft robotic grippers, rehabilitation tools, and other bio-inspired actuation systems.