We present an analytic solution to the 3D Dubins path problem for paths composed of an initial circular arc, a straight component, and a final circular arc. These are commonly called CSC paths. By modeling the start and goal configurations of the path as the base frame and final frame of an RRPRR manipulator, we treat this as an inverse kinematics problem. The kinematic features of the 3D Dubins path are built into the constraints of our manipulator model. Furthermore, we show that the number of solutions is not constant, with up to seven valid CSC path solutions even in non-singular regions. An implementation of solution is available at https://github.com/aabecker/dubins3D.

翻译：针对由初始圆弧、直线段和最终圆弧构成的3D杜宾斯路径问题，本文提出了一种解析解，这类路径通常被称为CSC路径。通过将路径的起点和终点构型建模为RRPRR机械臂的基坐标系与末端坐标系，我们将该问题转化为逆运动学问题。在机械臂模型的约束中嵌入了3D杜宾斯路径的运动学特征。进一步研究表明，解的数量并非恒定不变，即使在非奇异区域也存在多达七个有效CSC路径解。相关算法实现已开源发布于 https://github.com/aabecker/dubins3D。