3D motion planning for steerable needles using path sets

Abstract

Bevel-tipped flexible needles can be steered in soft tissue to clinical targets along curved paths in 3D while avoiding critical structures. Duty-cycled rotation [1] during insertion allows for control of the curvature of the needle. These capabilities of 3D steerable needles make it potentially suitable for applications such as deep brain stimulation (DBS) and drug delivery to brain tumors [2]. Manually guiding a steerable needle is unintuitive due to the high-dimensional nature of the problem. Planning algorithms can help provide a feasible motion plan for steering the needle between the start and target locations while avoiding critical structures in the tissue. Imaging feedback is incorporated to control the needle along the pre-planned path.

In this paper, we present an algorithm for path planning of steerable needles based on A* graph search on path sets in 3D. Path sets have been utilized extensively, in the past, for motion planning of mobile robots with nonholonomic constraints [3]. The formulation using path sets allows the planner to ouput paths that respect the differential or nonholonomic constraints associated with needle steering. Compared to more commonly used sampling-based approaches such as RRT [4,5,6], an A* search-based approach can guarantee optimality of the path with respect to a predefined cost function. Since safety is of paramount importance in our application, we consider two factors in our path cost that influence safety: a) path length and b) curvature. Critical structures are avoided by treating them as obstacles.