Physics-informed learning for modelling of continuum robots

This paper proposes a spatiotemporal modeling framework for continuum robots based on Cosserat theory and physics-informed neural networks. First, we derive the governing equations for the central backbone of the continuum robot, modeling it as a slender rod. Using Cosserat theory, we account for bending, twisting, stretching, and shearing, extending the Kirchhoff assumptions and deriving the partial differential equations that describe the robot’s dynamics. To solve these equations, we propose a physics-informed spatiotemporal modeling method that combines physical modeling and data-driven approaches. We built a simulation platform using the open-source library Elastica and generated training data through simulation experiments. The model was trained using physics-informed neural networks, which leverage observational data and physical laws to improve accuracy. Compared to an improved finite difference method, our modeling approach reduces computation time by a factor of 30. The experimental results demonstrate that the proposed method effectively captures the dynamic characteristics of the continuum robot, providing a robust solution for real-time modeling in robotic applications.