3D Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics.
3D Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics.
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DOI：
10.1007/978-3-642-00312-7_33
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发表时间：
2009
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可操纵针头可用于医疗应用，以达到敏感或难以穿透的区域后面的目标。可操纵针的运动学是非完整的，在二维中相当于曲率半径恒定的杜宾车。在3D中，针可以解释为一架飞机恒定的速度和俯仰率，零偏航和可控的滚转角。提出了一种基于显式几何逆运动学的可操纵针的常时运动规划算法，该算法与经典的Paden-Kahan子问题类似。通过与杜宾斯汽车的最短路径解（2D）和数值模拟（3D）的分析比较，分析了可达性和路径竞争力。我们还提出了一种利用冗余机械手理论的零空间结果进行局部路径自适应的算法。最后，我们讨论了几种使用和扩展逆运动学解来生成避开障碍物的针路径的方法。
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.