Learning-Based Tip Contact Force Estimation for FBG-Embedded Continuum Robots

Knowledge of the tip contact force in continuum robots, which are often used as medical instruments, is critical for clinical applications. It enhances the interventionalist's decision-making, navigation efficiency, and procedural safety. However, accurately determining the tip contact force in conventionally sized instruments remains challenging. This study introduces a learning-based method for estimating the external contact force at the tip of a continuum robot. By leveraging curvature and bending angle data from a multi-core fiber equipped with fiber Bragg gratings (FBGs) embedded inside the Nitinol tube, the method maps these inputs to the corresponding tip force in 3D. Experiments conducted on an FBG-embedded Nitinol rod validate the feasibility of the proposed method, yielding Mean Squared Error (MSE), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE) values of 20.9 $\left(m N^{2}\right), 2.7(m N)$, and $4.6(m N)$, respectively, which represent a 26 % improvement compared to the learning-based vision methodology.