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.

中文翻译：

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使用反向运动学的可转向针的 3D 运动规划算法。

可转向针可用于医疗应用，以到达敏感或不可穿透区域后面的目标。可操纵针的运动学是非完整的，并且在 2D 中相当于具有恒定曲率半径的 Dubins 汽车。在 3D 中，指针可以解释为具有恒定速度和俯仰率、零偏航和可控滚转角的飞机。卡汉子问题。可达性和路径竞争性通过与 Dubins 汽车（2D）和数值模拟（3D）最短路径解决方案的分析比较进行分析。我们还提出了一种使用冗余操纵器理论的零空间结果进行局部路径自适应的算法。最后，