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

TL;DR

This paper introduces a physics-informed neural network for accurately modeling and reconstructing the shape of concentric-tube robots using minimal observational data, integrating physics equations with data-driven learning.

Contribution

The novel PINN model combines Cosserat rod equations with few-shot learning to improve shape estimation and kinematic modeling of CTRs over existing methods.

Findings

Mean shape error below 1% of robot length

Accurately recovers shape, twist, and bending moment

Outperforms purely physics-based models with minimal data

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.