A Kinematics Constrained Convex Optimal Trajectory Generation Method for Robotic-assisted Flexible Needle

Abstract

Needle puncture is a fundamental technique in minimally invasive surgical procedures. However, the limited flexibility of flexible needles and their complex interactions with tissues make it challenging to avoid critical organs along the puncture path. Preoperative path planning, which generates feasible collision-free trajectories, can effectively reduce repeated punctures and mitigate patient discomfort. To address this challenge, a flexible needle with increased maximum curvature is designed, which introduces more complex kinematic characteristics and poses greater challenges for trajectory planning under kinematic constraints. Then, for the first time, a convex feasible set (CFS)-based flexible needle trajectory planning method is developed to tackle the non-convex optimization problem posed by obstacle avoidance in unstructured surgical environments. Specifically, our method explicitly incorporates kinematic and curvature constraints, enabling direct generation of feasible trajectories without additional post-processing. Finally, comparative experiments on a self-developed robotic-assisted flexible needle system demonstrate the superior performance of the proposed algorithm. In particular, the proposed trajectory generation method allows the flexible needle to effectively avoid obstacles and accurately reach the target.