Learning-Based Kinematic Modeling for Concentric Tube Robot: Addressing its Nonlinearity and Snapping Behavior

The Concentric Tube Robot (CTR) has great promise for minimally invasive surgery. However, accurately modeling nonlinear and history-dependent behaviors remains a significant challenge. This letter proposes a learning-based forward and inverse kinematics model that accounts for the history dependence and nonlinearities of CTR, including the snapping behavior. A lightweight LSTM-MLP hybrid neural network with an input buffer and directional parameters was used to train forward and inverse kinematics models for 4-degree-of-freedom (DOF) CTR. The model was validated by comparing its predictions with actual values and results from a conventional torsional-compliant model (TCM) across random points, rotational trajectories, and arbitrary paths. This validation successfully demonstrated the model's ability to capture snapping behavior. For forward kinematics, the model achieved a Root Mean Square Error (RMSE) of 0.69 mm and 0.16° with a computation time of 0.831 ± 0.200 ms. The inverse kinematics model achieved an RMSE of 1.22 mm and 2.46° with a computation time of 0.816 ± 0.200 ms. The proposed method improves the accuracy and speed of kinematic modeling by capturing nonlinear behaviors, such as snapping and hysteresis. The lightweight system ensures accurate real-time control and offers a safer and more reliable solution for microsurgical applications.