Abstract
Steerable needles are medical devices with the ability to follow curvilinear paths to reach targets while circumventing obstacles. In the deployment process, a human operator typically places the steerable needle at its start position on a tissue surface and then hands off control to the automation that steers the needle to the target. Due to uncertainty in the placement of the needle by the human operator, choosing a start position that is robust to deviations is crucial since some start positions may make it impossible for the steerable needle to safely reach the target. We introduce a method to efficiently evaluate steerable needle motion plans such that they are safe to variation in the start position. This method can be applied to many steerable needle planners and requires that the needle's orientation angle at insertion can be robotically controlled. Specifically, we introduce a method that builds a funnel around a given plan to determine a safe insertion surface corresponding to insertion points from which it is guaranteed that a collision-free motion plan to the goal can be computed. We use this technique to evaluate multiple feasible plans and select the one that maximizes the size of the safe insertion surface. We evaluate our method through simulation in a lung biopsy scenario and show that the method is able to quickly find needle plans with a large safe insertion surface.