Few-Shot Physics-Informed Neural Network for Shape Reconstruction of Concentric-Tube Robots
Navid Feizi, Filipe Pedrosa, Rajnikant V. Patel, Jagadeesan Jayender
AI summary
Problem
Physics-based models for concentric-tube robots are computationally heavy and inaccurate due to unmodeled effects, while standard deep learning models require massive datasets and ignore underlying mechanics, hindering accurate, efficient full-shape estimation.
Approach
The method embeds Cosserat rod differential equations directly into the neural network's training loss, balancing physical laws with a small set of observational data to learn forward kinematics and full-state estimation.
Key results
- Mean shape error below 1% of robot length
- Recovery of full 3D backbone shape without external shape-sensing hardware
- Reduction of required training data from tens of thousands to a few hundred samples
- Accurate estimation of latent kinematic states like twist angle and torsional strain
Why it matters
Provides a computationally efficient and data-efficient modeling framework for safe, real-time navigation and control of continuum robots in minimally invasive surgery.
Abstract
Modeling concentric tube robots (CTRs) involves complex nonlinear continuum mechanics, and despite recent progress, physics-based models often lack an accurate represen- tation of the experimental setups. To overcome these limitations, deep neural network-based models have been explored as al- ternatives 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 embed 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 recovers 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.