Insertion planning for steerable flexible needles reaching multiple planar targets

In this paper, we propose a new insertion plan for steerable flexible needles with which we can target multiple locations in the plane with a single entry point (i.e. port). The method is developed based on the observation that multiple locations can be reached by a flexible needle through insertion, partial retraction, rotation, and re-insertion of the needle. We show that in 2D space this problem can be solved using a geometric relationship between multiple tangent circles. Specifically we find a needle insertion point, a corresponding insertion direction and lengths for insertion and retraction with which we can generate the optimal needle trajectory that reaches two or three planar targets with the minimum tissue damage. This minimization problem is solved using exhaustive search of a cost function on the 1D bounded domain. We build a prototype of a needle insertion system and develop C#-based software to compute the optimal needle paths and perform the planned insertion as an open-loop controller. Finally, actual insertion examples are presented.