Fast Real-Time Neural Network-Based Kinematics Solving of the Cosserat Rod Model for a Parallel Continuum Surgical Manipulator

The parallel continuum mechanism offers distinct advantages in the design of surgical manipulators, including enhanced stiffness, improved precision, and a simplified structure compared to traditional Tendon-driven systems. Conventional kinematic models based on constant-curvature assumptions are often inadequate for accurately capturing the complex bending behaviors of this mechanism. In contrast, the Cosserat rod theory provides a rigorous framework for precise kinematic modeling of flexible structures. However, its computational complexity results in slow solving speeds, particularly when dealing with spatial points that are widely separated. This paper focuses on a miniaturized parallel continuum manipulator and employs the Cosserat rod model for kinematic modeling, combined with a neural network-based inverse kinematics solver to achieve rapid real-time computation. To expedite inverse kinematics, a multilayer perceptron is trained on 5,000 samples generated from the Cosserat rod model, yielding the average absolute error of 0.046mm and the average relative error of 0.41% in predicting rod lengths. Experimental validation demonstrates that the neural network solver reduces computation time to about 0.16ms compared to 700-3100ms for conventional numerical methods, underscoring its potential for enhancing the precision and responsiveness of surgical systems in minimally invasive procedures.