Optimal path planning for inserting a steerable needle into tissue

Bevel-tip steerable needles are widely used in modern minimally invasive percutaneous procedures to reach specific positions inside the body. In this paper, we design a shortest path with the least control effort for such a steerable needle, giving the start and the goal positions with or without obstacles. We assume that the environment is static and the motion of the needle is counted based on the state of the needle tip. Due to flexibility of the needle, the moving path is a curve instead of a straight line. We design the path in such a way that the path is within two parallel lines, and the optimal distance between the two lines is determined such that the length of the moving path of the needle is the shortest with the least control effort. Upon choosing the optimal distance between the parallel lines, we then proposed an algorithm to generate the needle path. Simulation is performed to demonstrate the effectiveness of the proposed approach.