Physics Informed Neural Pose Estimation for Real-Time Shape Reconstruction of Soft Continuum Robots

Soft continuum robots are increasingly valued for their remarkable flexibility, but accurate shape reconstruction remains challenging due to their infinite degrees of freedom and high nonlinearity. Existing approaches often rely on either simplified-curvature statics equations for physical derivation or large labeled datasets for imitation learning, both of which limit accuracy. We propose PINPE (Physics Informed Neural Pose Estimation), a deep learning algorithm for high-accuracy, real-time shape reconstruction. It reformulates this task as an open-loop, continuous-time optimal control problem, integrating an exact-curvature statics equation (as transition dynamics) and a small amount of labeled data (as expert demonstrations) into a unified framework. A neural network controller, also named deformation policy, is trained offline to both satisfy transition dynamics and align with expert demonstrations. During online application, the robot shape is efficiently reconstructed by integrating the trained deformation policy from zero to the total length of robot centerline. Experiments show that our method outperforms online optimization and imitation learning approaches in reconstruction accuracy, with a position error of less than 5 mm for a 180 mm robot and an angle error of less than 3$^\circ$. Furthermore, our single-step computation time consistently remains below 1ms, demonstrating real-time feasibility.