Evaluating Generative Models for Inverse Kinematics of Concentric Tube Robots

Abstract

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.