Koopman‐based 3‐dimensional path following control for robotic flexible needles

Robotic flexible needles have gained significant attention in minimally invasive medical procedures due to their ability to navigate complex anatomical structures and reach targets with high precision. Addressing the complex control problem in a 3‐dimensional environment, a Koopman‐based data‐driven control strategy is proposed in this paper. First, a 3‐dimensional (3D) path tracking problem is modeled using the simplified high‐dimensional bicycle model with the puncture kinematic. Then, with the Koopman operator theory, a finite linear approximation is designed and trained to simplify the nonlinear system of flexible needles. Finally, based on the linear approximation, a Koopman‐based model predictive control (MPC) scheme is proposed to realize 3‐dimensional path tracking for flexible needles. Based on simulations, the linear approximation and data‐driven control strategy are validated.