PINN-Ray: A Physics-Informed Neural Network to Model Soft Robotic Fin Ray Fingers

TL;DR

PINN-Ray tackles the challenge of accurately modelling large-deformation soft robotic fingers under limited data by embedding elastic-mechanics laws into a physics-informed neural network and augmenting training with real-world measurements. It uses two neural nets to predict the displacement components $u$ and $v$ over a 2D Fin Ray finger domain, routing through a total energy objective $\Pi(u,v) = U + W$ and enforcing boundary conditions and data assimilation via a Monte Carlo PDE loss. The approach yields a sim-to-real bridge, with data assimilation reducing displacement MAE to $\$0.03$ (from around $1.46$) using only 9 assimilated points, and provides improved stress/strain estimates compared to FEM and non-assimilated PINN variants. This framework enables faster prototyping and more robust deformation prediction for soft robots while maintaining physical consistency through continuum-elastic theory.

Abstract

Modelling complex deformation for soft robotics provides a guideline to understand their behaviour, leading to safe interaction with the environment. However, building a surrogate model with high accuracy and fast inference speed can be challenging for soft robotics due to the nonlinearity from complex geometry, large deformation, material nonlinearity etc. The reality gap from surrogate models also prevents their further deployment in the soft robotics domain. In this study, we proposed a physics-informed Neural Networks (PINNs) named PINN-Ray to model complex deformation for a Fin Ray soft robotic gripper, which embeds the minimum potential energy principle from elastic mechanics and additional high-fidelity experimental data into the loss function of neural network for training. This method is significant in terms of its generalisation to complex geometry and robust to data scarcity as compared to other data-driven neural networks. Furthermore, it has been extensively evaluated to model the deformation of the Fin Ray finger under external actuation. PINN-Ray demonstrates improved accuracy as compared with Finite element modelling (FEM) after applying the data assimilation scheme to treat the sim-to-real gap. Additionally, we introduced our automated framework to design, fabricate soft robotic fingers, and characterise their deformation by visual tracking, which provides a guideline for the fast prototype of soft robotics.

Figures (10)

• Figure 1: The framework of PINN-Ray to model the deformation of soft robotic finger with sim-to-real treatment.
• Figure 2: PINN-Ray architecture: two artificial neural networks are used to predict u and v respectively. The minimum potential energy method is implemented in the loss function
• Figure 3: (a) Design space of the proposed soft robotics fingers, which is determined by 9 parameters, (b) Uniform sampling point discretization of the design space, while the design uses parameter values of [90 mm, 30 mm, 20 mm, 20 mm, 20$^0$, 4, 2 mm, 2 mm, 2 mm]
• Figure 4: Left: Fin Ray finger under testing in the Jimstron test rig. Upper right: Fin Ray finger with no load. Lower right: Fin Ray finger under load. The markers are printed with robotic finger using a multi-material 3D printing step
• Figure 5: Marker positions in pixel coordinates which are acquired by an image processing algorithm applied to images captured by a calibrated camera. Top: initial state; Bottom: actuated state