Abstract This paper presents a technique for planning and controlling bevel-tip steerable needles towards a target location in 3-D anatomy under the guidance of partial, noisy sensor feedback. Our approach minimizes the probability that the needle intersects obstacles such as bones and sensitive organs by (1) explicitly taking into account motion uncertainty and sensor types, and (2) allowing for efficient optimization of sensor placement. We allow for needle trajectories of arbitrary curvature through duty-cycled spinning of the needle, which is believed to make a needle path small-time locally “trackable ” [13]. This enables us to use LQG control to guide the needle along the path. For a given path and sensor placement, we show that a priori probability distributions of the needle state can be estimated in advance. Our approach then plans a set of candidate paths and sensor placements and selects the pair for which the estimated uncertainty is least likely to cause intersections with obstacles. We demonstrate the performance of our approach in a modeled prostate cancer treatment environment. 1

Abstract — An active cannula is a medical device composed of thin, pre-curved, telescoping tubes that may enable many new surgical procedures. Planning optimal motions for these devices is challenging due to their kinematics, which involve both beam mechanics and space curves. In this paper, we propose an optimization-based motion planning algorithm that computes actions to guide the device to a target point while avoiding obstacles in the environment. The planner uses a simplified active cannula kinematic model that neglects beam mechanics, and focuses on planning for the (piecewise circular) space curves. The method is intended for use in image-guided procedures where the target and obstacles can be segmented from preprocedure images. Given the target location, the start position and orientation, and a geometric representation of obstacles, the algorithm computes the insertion length and orientation angle for each tube of the active cannula such that the device follows a collision-free path to the target. We formulate the planning problem as a constrained nonlinear optimization problem and use a penalty method to convert this formulation into a sequence of more easily solvable unconstrained optimization problems. Simulations demonstrate optimal paths for a 3-tube active cannula with spherical obstacles. The algorithm typically computes plans in less than 1 minute on a standard PC. I.

Abstract — Accurate needle insertion in 3D environment is always a grand challenge. When multiple targets are located in the tissue, a procedure of inserting multiple needles from a single small region on the patient’s skin, so called “fireworks” insertion as shown in Fig. 1, can be executed to further reduce trauma on the patient. In this paper, we explore motion planning for “fireworks ” needle insertion in 3D environments by developing an algorithm based on the Forest of Rapidlyexploring Random Trees (RRTs). Given a set of targets, we propose an algorithm to quickly explore the configuration space by building a forest of RRTs and find feasible plans for multiple steerable needles from a single entry region. With different optimality considerations, we present two path selection algorithms to optimize the final plan among all feasible outputs. Finally, we implement the algorithm in an approximate prostate cancer treatment environment and simulation results demonstrate the performance of the proposed algorithm. I.

Abstract — Medical procedures such as lung biopsy and brachytherapy require maneuvering through tubular structures such as the trachea and bronchi to reach clinical targets. We introduce a new method to plan configurations for active cannulas, medical devices composed of thin, pre-curved, telescoping lumens that are capable of following controlled, curved paths through open or liquid-filled cavities. Planning optimal configurations for these devices is challenging due to their complex kinematics, which involve both beam mechanics and space curves. In this paper, we propose an optimization-based planning algorithm that computes active cannula configurations through tubular structures that reach specified targets. Given the target location, the start position and orientation, and a geometric representation of the physical environment extracted from pre-procedure medical images, the planner optimizes insertion length and orientation angle of each lumen of the active cannula. The planner models active cannula kinematics using a physically-based simulation that incorporates beam mechanics and minimizes energy. The algorithm typically computes plans in less than 2 minutes on a standard PC. We apply the method in simulation to anatomy extracted from a human CT scan and demonstrate configurations for a 5-lumen active cannula that maneuver it through the bronchi to targets in the lung. I.

Abstract. Many surgical procedures could benefit from guiding a bevel-tip needle along circular arcs to multiple treatment points in a patient. At each treatment point, the needle can inject a radioactive pellet into a cancerous region or extract a tissue sample. Our main result is an algorithm to steer a bevel-tip needle through a sequence of treatment points in the plane while minimizing the number of times that the needle must be reoriented. This algorithm is related to [6] and takes quadratic time when consecutive points in the sequence are sufficiently separated. We can also guide a needle through an arbitrary sequence of points in the plane by accounting for a lack of optimal substructure.

This paper presents the minimum-time sequences of rotations and translations that connect two configurations of a rigid body in the plane. The configuration of the body is its position and orientation, given by(x,y,θ) coordinates, and the rotations and translations are velocities (˙x, ˙y, ˙ θ) that are constant in the frame of the robot. There are no obstacles in the plane. We completely describes the structure of the fastest trajectories, and present a polynomialtime algorithm that, given a set of rotation and translation controls, enumerates a finite set of structures of optimal trajectories. These trajectories are a generalization of the well-known Dubins and Reeds-Shepp curves, which describe the shortest paths for steered cars in the plane. 1

We develop a new motion planning algorithm for a variant of a Dubins car with binary left/right steering and apply it to steerable needles, a new class of flexible bevel-tip medical needle that physicians can steer through soft tissue to reach clinical targets inaccessible to traditional stiff needles. Our method explicitly considers uncertainty in needle motion due to patient differences and the difficulty in predicting needle/tissue interaction. The planner computes optimal steering actions to maximize the probability that the needle will reach the desired target. Given a medical image with segmented obstacles and target, our method formulates the planning problem as a Markov decision process based on an efficient discretization of the state space, models motion uncertainty using probability distributions and computes optimal steering actions using dynamic programming. This approach only requires parameters that can be directly extracted from

Many surgical procedures could benefit from guiding a bevel-tip needle through a sequence of treatment points in a patient. For example, brachytherapy procedures implant radioactive seeds to treat cancer, and biopsy

Abstract:—Steerable needles can be used in medical applications to reach targets behind sensitive or impenetrable areas. The kinematics of a steerable needle are nonholonomic and, in 2D, equivalent to a Dubins car with constant radius of curvature. In 3D, the needle can be interpreted as an airplane with constant speed and pitch rate, zero yaw, and controllable roll angle. We present a constant-time motion planning algorithm for steerable needles based on explicit geometric inverse kinematics similar to the classic Paden-Kahan subproblems. Reachability and path competitivity are analyzed using analytic comparisons with shortest path solutions for the Dubins car (for 2D) and numerical simulations (for 3D). We also present an algorithm for local path adaptation using null-space results from redundant manipulator theory. Finally, we discuss several ways to use and extend the inverse kinematics solution to generate needle paths that avoid obstacles. I.

Robotic motion planning aspires to match the ease and efficiency with which humans move through and interact with their environment. Yet state of the art robotic planners fall short of human abilities; they are slower in computation, and the results are often of lower quality. One stumbling block in traditional motion planning is that points and paths are often considered in isolation. Many planners fail to recognize that substantial shared information exists among path alternatives. Exploitation of the geometric and topological relationships among path alternatives can therefore lead to increased efficiency and competency. These benefits include: better-informed path sampling, dramatically faster collision checking, and a deeper understanding of the trade-offs in path selection. In path sampling, the principle of locality is introduced as a basis for constructing an adaptive, probabilistic, geometric model to influence the selection of paths for collision test. Recognizing that collision testing consumes a sizable majority of planning time and that only collision-free paths provide value in selecting a path to execute on the robot, this model provides a significant increase in efficiency by