Diffusion-Based Motion Planning for a Nonholonomic Flexible Needle Model (original) (raw)
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Flexible needle steering and optimal trajectory planning for percutaneous therapies
2004
Flexible needle insertion into viscoelastic tissue is modeled in this paper with a linear beam supported by virtual springs. Using this simplified model, the forward and inverse kinematics of the needle is solved analytically, providing a way for simulation and path planning in real-time. Using the inverse kinematics, the required needle basis trajectory can be computed for any desired needle tip path. It is shown that the needle base trajectory is not unique and can be optimized to minimize lateral pressure of the needle body on the tissue. Experimental results are provided of robotically assisted insertion of flexible needle while avoiding "obstacle".
Springer Tracts in Advanced Robotics, 2008
We consider a variant of nonholonomic motion planning for a Dubins car with no reversals, binary left/right steering, and uncertainty in motion direction. We apply our new motion planner to steerable needles, a new class of flexible bevel-tip medical needles that clinicians can steer through soft tissue to reach 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 turning points 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 (MDP) based on an efficient discretization of the state space, models motion uncertainty using probability distributions, and computes turning points to maximize the probability of success using infinite horizon Dynamic Programming (DP). This approach has three features particularly beneficial for medical planning problems. First, the planning formulation only requires parameters that can be directly extracted from images. Second, we can compute the optimal needle insertion point by examining the DP look-up table of optimal controls for every needle state. Third, intra-operative medical imaging can be combined with the pre-computed DP look-up table to permit optimal control of the needle in the operating room without requiring time-consuming intra-operative re-planning. We apply the method to generate motion plans for steerable needles to reach targets inaccessible to stiff needles and illustrate the importance of considering uncertainty during motion plan optimization.
Motion Planning Under Uncertainty for Image-guided Medical Needle Steering
The International Journal of Robotics Research, 2008
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 images, allows fast computation of the optimal needle entry point and enables intra-operative optimal steering of the needle using the precomputed dynamic programming look-up table. We apply the method to generate motion plans for steerable needles to reach targets inaccessible to stiff needles, and we illustrate the importance of considering uncertainty during motion plan optimization.
Path Planning for Flexible Needles Using Second Order Error Propagation
Springer Tracts in Advanced Robotics, 2009
In this paper we propose a computationally efficient method for the steering of flexible needles with a bevel tip in the presence of uncertainties for the case when there are no obstacles in the environment. Based on the stochastic model for the needles, we develop a new framework for path planning of a flexible needle with a bevel tip. This consists of three parts: (a) approximation of probability density functions for the needle tip pose; (b) application of a second order error propagation algorithm on the Euclidean motion group; and (c) application of the path-of-probability (POP) algorithm. The probability density functions are approximated as Gaussians under the assumption that the uncertainty in the needle insertion is fairly small. The means and the covariances for the probability density functions are estimated using the error propagation algorithm that has second order accuracy. The POP algorithm is adapted to the path planning for the flexible needles so as to give the appropriate steering plan. Combining these components and considering 5 degree-of-freedom targets, the new method gives the path of the flexible needle that hits the target point with the desired hitting direction. A number of recent works have been reported on the topic of the steerable flexible needles with bevel tips that are inserted into soft tissue for minimally invasive
Nonholonomic Modeling of Needle Steering
The International Journal of Robotics Research, 2006
As a flexible needle with a bevel tip is pushed through soft tissue, the asymmetry of the tip causes the needle to bend. We propose that, by using nonholonomic kinematics, control, and path planning, an appropriately designed needle can be steered through tissue to reach a specified 3D target. Such steering capability could enhance targeting accuracy and may improve outcomes for percutaneous therapies, facilitate research on therapy effectiveness, and eventually enable new minimally invasive techniques. In this paper, we consider a first step toward active needle steering: design and experimental validation of a nonholonomic model for steering flexible needles with bevel tips. The model generalizes the standard three degree-of-freedom (DOF) nonholonomic unicycle and bicycle models to 6 DOF using Lie group theory. Model parameters are fit using experimental data, acquired via a robotic device designed for the specific purpose of inserting and steering a flexible needle. The experiments quantitatively validate the bevel-tip needle steering model, enabling future research in flexible needle path planning, control, and simulation.
Needle Steering and Motion Planning in Soft Tissues
IEEE Transactions on Biomedical Engineering, 2005
In this work, needle insertion into deformable tissue is formulated as a trajectory planning and control problem. A new concept of needle steering has been developed and a needle manipulation Jacobian defined using numerical needle insertion models that include needle deflection and soft tissue deformation. This concept is used in conjunction with a potential-field-based path planning technique to demonstrate needle tip placement and obstacle avoidance. Results from open loop insertion experiments are provided.
3D Motion Planning for Robot-Assisted Active Flexible Needle Based on Rapidly-Exploring Random Trees
Journal of Automation and Control Engineering, 2015
An active flexible needle is a self-actuating needle that can bend in the tissue and reach the clinical targets while avoiding anatomic obstacles. In robot-assisted needlebased medical procedures, motion planning is a vital aspect to operations. However, it is challenging with regard to time consumption and searching for a robust solution. This is due to the nonholonomic motion of the needle and the presence of anatomic obstacles and sensitive organs that must be avoided. We propose a novel and fast motion planning algorithm for the robot-assisted active flexible needle. The algorithm is based on Rapidly-Exploring Random Trees combined with greedy-heuristic strategy and reachabilityguided strategy. Linear segment and relaxation of insertion orientation are taken into consideration to the paths. Results show that the proposed algorithm yields superior results as compared to the commonly used algorithm in terms of computational speed, form of path and robustness of searching ability, which potentially make it suitable for the real-time intraoperative planning in clinical operations.
Reverse Path Planning for Flexible Needle in 2D Soft Tissue with Obstacles
In clinic it is of very practical significance to optimize the entry point and pose in path planning. We proposed a reverse path planning algorithm adopting multiform combined paths based on the improved kinematic model of flexible needle, and the objective function is established. Utilizing the reversibility of the path, we started from the target to optimize the whole path including the entry point and pose. Then we optimally calculated and simulated in the environment with obstacles. Results show that this algorithm effectively makes the needle steer clear of obstacles to reach the target precisely, and gains the entry point and pose at the same time, guaranteeing the optimal path.
2015
An active flexible needle is a self-actuating needle that can bend in the tissue and reach the clinical targets while avoiding anatomic obstacles. In robot-assisted needlebased medical procedures, motion planning is a vital aspect of operations. It is challenging due to the nonholonomic motion of the needle and the presence of anatomic obstacles and sensitive organs that must be avoided. We propose a novel and fast motion planning algorithm for the robotassisted active flexible needle. The algorithm is based on Rapidly-Exploring Random Trees combined with greedyheuristic strategy and reachability-guided strategy. Linear segment and relaxation of insertion orientation are taken into consideration to the paths. Results show that the proposed algorithm yields superior results as compared to the commonly used algorithm in terms of computational speed, form of path and robustness of searching ability, which potentially make it suitable for the real-time intraoperative planning in clinical operations.
Optimal Feedback Control of a Flexible Needle under Anatomical Motion Uncertainty
Bevel-tip flexible needles allow for reaching remote/inaccessible organs while avoiding the obstacles (sensitive organs, bones, etc.). Motion planning and control of such systems is a challenging problem due to the uncertainty induced by needle-tissue interactions, anatomical motions (respiratory and cardiac induced motions), imperfect actuation, etc. In this paper, we use an analogy where steering the needle in a soft tissue subject to the uncertain anatomical motions is compared to the Dubins vehicle traveling in the stochastic wind field. Achieving the optimal feedback control policy requires solution of a dynamic programming problem that is often computationally demanding. Efficiency is not central to many optimal control algorithms that often need to be computed only once for a given system/noise statistics. However, intraoperative policy updates may be required for adaptive or patient-specific models. We use the method of approximating Markov chain to approximate the continuous (and controlled) process with its discrete and locally consistent counterpart. We examine the linear programming method of solving the imposed dynamic programming problem that significantly improves the computational efficiency in comparison to the state-of-the-art approaches. In addition, the probability of success and failure are simply the variables of the linear optimization problem and can be directly used for different objective definitions. A numerical example of the 2D needle steering problem is considered to investigate the