Abstract — Flexible, tip-steerable needles promise to enhance physicians ’ abilities to accurately reach targets and maneuver inside the human body while minimizing patient trauma. Here, we present a functional needle steering system that integrates two components: (1) a patient-specific 2D pre- and intraoperative planner that finds an achievable route to a target within a planar slice of tissue (Stochastic Motion Roadmap), and (2) a low-level image-guided feedback controller that keeps the needle tip within that slice. The planner generates a sequence of circular arcs that can be realized by interleaving pure insertions with 180 ◦ rotations of the needle shaft. This preplanned sequence is updated in realtime at regular intervals. Concurrently, the low-level image-based controller servos the needle to remain close to the desired plane between plan updates. Both planner and controller are predicated on a previously developed kinematic nonholonomic model of beveltip needle steering. We use slighly different needles here that have a small bend near the tip, so we extend the model to account for discontinuities of the tip position caused by 180 ◦ rotations. Further, during large rotations of the needle base, we maintain the desired tip angle by compensating for torsional compliance in the needle shaft, neglected in previous needle steering work. By integrating planning, control, and torsion compensation, we demonstrate both accurate targeting and obstacle avoidance. I.

We present algorithms for simulating and visualizing the insertion and steering of needles through deformable tissues for surgical training and planning. Needle insertion is an essential component of many clinical procedures such as biopsies, injections, neurosurgery, and brachytherapy cancer treatment. The success of these procedures depends on accurate guidance of the needle tip to a clinical target while avoiding vital tissues. Needle insertion deforms body tissues, making accurate placement difficult. Our interactive needle insertion simulator models the coupling between a steerable needle and deformable tissue. We introduce (1) a novel algorithm for local remeshing that quickly enforces the conformity of a tetrahedral mesh to a curvilinear needle path, enabling accurate computation of contact forces, (2) an efficient method for coupling a 3D finite element simulation with a 1D inextensible rod with stick-slip friction, and (3) optimizations that reduce the computation time for physically based simulations. We can realistically and interactively simulate needle insertion into a prostate mesh of 13,375 tetrahedra and 2,763 vertices at a 25 Hz frame rate on an 8-core 3.0 GHz Intel Xeon PC. The simulation models prostate brachytherapy with needles of varying stiffness, steering needles around obstacles, and supports motion planning for robotic needle insertion. We evaluate the accuracy of the simulation by comparing against real-world experiments in which flexible, steerable needles were inserted into gel tissue phantoms.

Abstract—Steerable needles composed of a highly flexible material and with a bevel tip offer greater mobility compared to rigid needles for minimally invasive medical procedures. In this paper, we apply sampling-based motion planning technique to explore motion planning for the steerable bevel-tip needle in 3D environments with obstacles. Based on the Rapidly-exploring Random Trees (RRTs) method, we develop a motion planner to quickly build a tree to search the configuration space using a new exploring strategy, which generates new states using randomly sampled control space instead of the deterministically sampled one used in classic RRTs. Notice the fact that feasible paths might not be found for any given entry point and target configuration, we also address the feasible entry point planning problem to find feasible entry points in a specified entry zone for any given target configuration. To solve this problem, we developed a motion planning algorithm based on RRTs with backchaining, which grow backward from the target to explore the configuration space. Finally, simulation results with a approximated realistic prostate needle insertion environment demonstrate the performance of the proposed motion planner. I.

Abstract Partially observable Markov decision processes (POMDPs) are a principled mathematical framework for planning under uncertainty, a crucial capability for reliable operation of autonomous robots. By using probabilistic sampling, pointbased POMDP solvers have drastically improved the speed of POMDP planning, enabling POMDPs to handle moderately complex robotic tasks. However, robot motion planning tasks with long time horizons remain a severe obstacle for even the fastest point-based POMDP solvers today. This paper proposes Milestone Guided Sampling (MiGS), a new point-based POMDP solver, which exploits state space information to reduce the effective planning horizon. MiGS samples a set of points, called milestones, from a robot’s state space, uses them to construct a compact, sampled representation of the state space, and then uses this representation of the state space to guide sampling in the belief space. This strategy reduces the effective planning horizon, while still capturing the essential features of the belief space with a small number of sampled points. Preliminary results are very promising. We tested MiGS in simulation on several difficult POMDPs modeling distinct robotic tasks with long time horizons; they are impossible with the fastest point-based POMDP solvers today. MiGS solved them in a few minutes. 1

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

This paper presents LQG-MP (linear-quadratic Gaussian motion planning), a new approach to robot motion planning that takes into account the sensors and the controller that will be used during execution of the robot’s path. LQG-MP is based on the linear-quadratic controller with Gaussian models of uncertainty, and explicitly characterizes in advance (i.e., before execution) the a-priori probability distributions of the state of the robot along its path. These distributions canbeusedtoassessthequalityofthepath, forinstancebycomputingtheprobability of avoiding collisions. Many methods can be used to generate the needed ensemble of candidate paths from which the best path is selected; in this paper we report results using Rapidly-Exploring Random Trees (RRT). We study the performance of LQG-MP with simulation experiments in three scenarios: A) a kinodynamic car-like robot, B) multi-robot planning with differential-drive robots, and C) a 6-DOF serial manipulator. We also apply Kalman Smoothing to make paths Ck-continuous while avoiding obstacles and apply LQG-MP to precomputed roadmaps using a variant of Dijkstra’s algorithm to efficiently find near-optimal paths. 1 1

Abstract. Motion planning under uncertainty is an important problem in robotics. Although probabilistic sampling is highly successful for motion planning of robots with many degrees of freedom, sampling-based algorithms typically ignore uncertainty during planning. We introduce the notion of a bounded uncertainty roadmap (BURM) and use it to extend samplingbased algorithms for planning under uncertainty in environment maps. The key idea of our approach is to evaluate uncertainty, represented by collision probability bounds, at multiple resolutions in different regions of the configuration space, depending on their relevance for finding a best path. Preliminary experimental results show that our approach is highly effective: our BURM algorithm is at least 40 times faster than an algorithm that tries to evaluate collision probabilities exactly, and it is not much slower than classic probabilistic roadmap planning algorithms, which ignore uncertainty in environment maps. 1

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. The inverse kinematics algorithm can be used as a fast local planner for global motion planning in environments with obstacles, either fully autonomously or in a computer-assisted setting. 1

Abstract: We describe a simple approach for executing manipulation programs in the presence of significant, but bounded, uncertainty. The key idea is to maintain a belief-state (a probability distribution over world states) and to execute fixed trajectories relative to the most-likely state of the world. These world-relative trajectories, as well as the transition and observation models needed for belief update, are all constructed off-line, so the approach does not require any on-line motion planning. 1

Abstract: We present a sample-based replanning strategy for driving partiallyobservable, high-dimensional robotic systems to a desired goal. At each time step, it uses forward simulation of randomly-sampled open-loop controls to construct a belief-space search tree rooted at its current belief state. Then, it executes the action at the root that leads to the best node in the tree. As a node quality metric we use Monte Carlo simulation to estimate the likelihood of success under the QMDP beliefspace feedback policy, which encourages the robot to take information-gathering actions as needed to reach the goal. The technique is demonstrated on target-finding and localization examples in up to 5D state spacess. 1