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Medical steerable needles can follow 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. 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 planning algorithms involved in procedure automation. In this paper, we take an important step toward creating a certifiable optimal planner for steerable needles. We present an efficient, resolution-complete motion planner for steerable needles based on a novel adaptation of multi-resolution planning. This is the first motion planner for steerable needles that guarantees to compute in finite time an obstacle-avoiding plan (or notify the user that no such plan exists), under clinically appropriate assumptions. Based on this planner, we then develop the first resolution-optimal motion planner for steerable needles that further provides theoretical guarantees on the quality of the computed motion plan, that is, global optimality, in finite time. Compared to state-of-the-art steerable needle motion planners, we demonstrate with clinically realistic simulations that our planners not only provide theoretical guarantees but also have higher success rates, have lower computation times, and result in higher quality plans. [ABSTRACT FROM AUTHOR]

Inspection planning, the task of planning motions for a robot that enable it to inspect a set of points of interest, has applications in domains such as industrial, field, and medical robotics. Inspection planning can be computationally challenging, as the search space over motion plans grows exponentially with the number of points of interest to inspect. We propose a novel method, Incremental Random Inspection-roadmap Search (IRIS), that computes inspection plans whose length and set of successfully inspected points asymptotically converge to those of an optimal inspection plan. IRIS incrementally densifies a motion-planning roadmap using a sampling-based algorithm and performs efficient near-optimal graph search over the resulting roadmap as it is generated. We prove the resulting algorithm is asymptotically optimal under very general assumptions about the robot and the environment. We demonstrate IRIS's efficacy on a simulated inspection task with a planar five DOF manipulator, on a simulated bridge inspection task with an Unmanned Aerial Vehicle (UAV), and on a medical endoscopic inspection task for a continuum parallel surgical robot in cluttered human anatomy. In all these systems IRIS computes higher-quality inspection plans orders of magnitudes faster than a prior state-of-the-art method. [ABSTRACT FROM AUTHOR]