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.

Concentric tube robots (CTRs) hold great potential for minimally invasive surgery, offering flexibility, small diameters, and the ability to navigate within complex anatomical structures. While machine learning models have been increasingly used to predict the kinematics of CTRs, there is a lack of an established framework for evaluating generative inverse kinematic models, which are able to solve the inverse kinematic problem by providing various joint solutions for a desired end position. In this study, we introduce a workspace-based measure to assess the diversity of solutions produced by three generative models: an invertible neural network (INN), a conditional invertible neural network (cINN), and a conditional variational autoencoder (cVAE). We find that all three models record similar end position errors (3-6 mm) on dexterous subsets of the workspace, but that a cINN outperforms the others in generating diverse solutions using a workspace-based 1-Wasserstein distance by at least 2.38 standard deviations. To further test the applicability of these models, we integrate the best-performing cINN into a CTR controller and demonstrate the first use of a generative CTR model with real-time teleoperation under task-based constraints.