  Medical steerable needles can move along 3D curvilinear trajectories to avoid
anatomical obstacles and reach clinically significant targets inside the human
body. Automating steerable needle procedures can enable physicians and patients
to harness the full potential of steerable needles by maximally leveraging
their steerability to safely and accurately reach targets for medical
procedures such as biopsies and localized therapy delivery for cancer. For the
automation of medical procedures to be clinically accepted, it is critical from
a patient care, safety, and regulatory perspective to certify the correctness
and effectiveness of the motion planning algorithms involved in procedure
automation. In this paper, we take an important step toward creating a
certifiable motion planner for steerable needles. We introduce the first motion
planner for steerable needles that offers a guarantee, under clinically
appropriate assumptions, that it will, in finite time, compute an exact,
obstacle-avoiding motion plan to a specified target, or notify the user that no
such plan exists. We present an efficient, resolution-complete motion planner
for steerable needles based on a novel adaptation of multi-resolution planning.
Compared to state-of-the-art steerable needle motion planners (none of which
provide any completeness guarantees), we demonstrate that our new
resolution-complete motion planner computes plans faster and with a higher
success rate.
