用少量数据训练出高精度的机器人形变预测模型
Few-Shot Physics-Informed Neural Network for Shape Reconstruction of Concentric-Tube Robots
- 将连续体力学方程嵌入神经网络，融合物理规律与观测数据
- 仅用少量样本即实现低于机器人长度1%的形变误差
- 适合需要实时控制的柔性机器人系统
建模同心管机器人（CTRs）涉及复杂的非线性连续体力学问题。尽管已有进展，基于物理的模型常无法准确反映实验条件。深度神经网络虽具更高精度，但常忽略已知力学规律，需大量训练数据，且通常不输出机器人形变信息。本文提出一种少样本物理信息神经网络（PINN），用于六自由度三管预弯同心管机器人的运动学建模，其嵌入柯西罗德微分方程，并从少量观测数据中学习，平衡物理先验与数据拟合。该模型可实现全状态估计：形状、扭转角、扭转变形、弯曲力矩和姿态。基准测试显示，平均形变误差低于机器人长度的1%，并准确恢复其他运动学状态，优于纯物理的柯西罗德模型基线，且仅需极小训练集。模型计算高效、鲁棒，适用于实时控制。
原文摘要 · Abstract (English)
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.
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