Few-Shot Physics-Informed Neural Network for Shape Reconstruction of Concentric-Tube Robots

2026-05-12

AI Summary

This work addresses the limitations of existing approaches for concentric tube robot (CTR) modeling—namely, insufficient accuracy in purely physics-based models and the data-driven methods’ neglect of mechanical principles coupled with high data demands—by proposing a few-shot physics-informed neural network (PINN). For the first time, the Cosserat rod differential equations are embedded directly into the network architecture, enabling joint estimation of the full state—including shape, twist angle, torsional strain, bending moments, and pose—for a 6-degree-of-freedom CTR with three precurved tubes. By integrating physical priors with limited observational data, the method achieves sub-1% shape error relative to robot length while preserving mechanical consistency, outperforming pure physics-based models. It also demonstrates high computational efficiency and robustness, making it suitable for real-time control applications.

Abstract

Modeling concentric tube robots (CTRs) involves complex nonlinear continuum mechanics, and despite recent progress, physics-based models often lack an accurate representation of the experimental setups. To overcome these limitations, deep neural network-based models have been explored as alternatives with superior accuracy; however, they often overlook known mechanics, require large training datasets, and typically discard shape estimation of the robot. We present a physics-informed neural network (PINN) for kinematic modeling of a 6-DoF CTR with three pre-curved tubes that embeds the Cosserat rod differential equations and learns from few-shot observational data, balancing physics priors with data-driven fitting. PINN enables full-state estimation of shape, twist angle, torsional strain, bending moment, and orientation. Benchmark tests show a mean shape error below 1% of the robot length and accurately recovered other kinematic states, outperforming a purely physics-based Cosserat rod model baseline while using a minimal training set. The resulting model is also computationally efficient and robust, making it well-suited for real-time control applications.

Problem

• Concentric-Tube Robots
• Shape Reconstruction
• Physics-Informed Neural Network
• Few-Shot Learning
• Kinematic Modeling

Innovation

• Physics-Informed Neural Network
• Few-Shot Learning
• Concentric-Tube Robot
• Cosserat Rod Theory
• Shape Reconstruction