Physics-Guided Deep Learning Enabled Surrogate Modeling for Pneumatic Soft Robots

Soft robots, formulated by soft and compliant materials, have grown significantly in recent years toward safe and adaptable operations and interactions with dynamic environments. Modeling the complex, nonlinear behaviors and controlling the deformable structures of soft robots present challenges. This study aims to establish a physics-guided deep learning (PGDL) computational framework that integrates physical models into deep learning framework as surrogate models for soft robots. Once trained, these models can replace computationally expensive numerical simulations to shorten the computation time and enable real-time control. This PGDL framework is among the first to integrate first principle physics of soft robots into deep learning toward highly accurate yet computationally affordable models for soft robot modeling and control. The proposed framework has been implemented and validated using three different pneumatic soft fingers with different behaviors and geometries, along with two training and testing approaches, to demonstrate its effectiveness and generalizability. The results showed that the mean square error (MSE) of predicted deformed curvature and the maximum and minimum deformation at various loading conditions were as low as $10^{-4}$ mm $^{2}$ . The proposed PGDL framework is constructed from first principle physics and intrinsically can be applicable to various conditions by carefully considering the governing equations, auxiliary equations, and the corresponding boundary and initial conditions.