Inverse Kinematic Modeling of the Tendon-Actuated Medical Continuum Manipulator Based on a Lightweight Timing Input Neural Network

Continuum manipulators can manipulate objects in complex environments and conform to curvilinear paths, which makes it emerging to be applied in minimally invasive surgery. However, due to their critical nonlinearities and distinct time-sequential characteristics of motion states, the modeling of inverse kinematics remains challenging. This work proposes a model-free method based on a timing input neural network (TINN) model to obtain the inverse kinematics mapping relationship of tendon-actuated medical continuum manipulators. The new TINN model improves the traditional fully connected neural network (FNN) model's ability to process time-sequential information through a sampling layer consisting of a modified window function positioned in front of the core layers. The lightweight fully connected structure of TINN's core layers can be trained effectively with fewer epochs or less time compared with the long short-term memory (LSTM) model. Furthermore, this lightweight structure maintains the robustness and accuracy of the TINN model when the training data volume decreases. Through experimental validation on two kinds of tendon-actuated continuum manipulators, this TINN-based model-free method shows high accuracy and strong robustness against the decrease of training data volume, as well as high transferability. Meanwhile, the TINN model's effective utilization of feedback data results in higher precision in closed-loop control compared to traditional model-based PID controllers in free space and under various payload conditions.