While Product of Exponentials (POE) formula has been gaining increasing popularity in modeling the kinematics of a serial-link robot, the Denavit-Hartenberg (D-H) notation is still the most widely used due to its intuitive and concise geometric interpretation of the robot. This paper has developed an analytical solution to automatically convert a POE model into a D-H model for a robot with revolute, prismatic, and helical joints, which are the complete set of three basic one degree of freedom lower pair joints for constructing a serial-link robot. The conversion algorithm developed can be used in applications such as calibration where it is necessary to convert the D-H model to the POE model for identification and then back to the D-H model for compensation. The equivalence of the two models proved in this paper also benefits the analysis of the identifiability of the kinematic parameters. It is found that the maximum number of identifiable parameters in a general POE model is 5h+4r +2t +n+6 where h, r, t, and n stand for the number of helical, revolute, prismatic, and general joints, respectively. It is also suggested that the identifiability of the base frame and the tool frame in the D-H model is restricted rather than the arbitrary six parameters as assumed previously.

翻译：尽管指数积公式（POE）在串联机器人运动学建模中日益流行，但Denavit-Hartenberg（D-H）符号因其对机器人直观简洁的几何解释，仍是最广泛使用的方法。本文针对构成串联机器人的三种基本单自由度低副关节（旋转关节、移动关节和螺旋关节）的完整集合，提出了将POE模型自动转换为D-H模型的解析解。所开发的转换算法可用于标定等应用场景——即需先将D-H模型转换为POE模型进行辨识，再转换回D-H模型进行补偿。本文证明的两种模型等价性也有助于运动学参数的可辨识性分析。研究发现，通用POE模型中可辨识参数的最大数量为5h+4r+2t+n+6，其中h、r、t、n分别表示螺旋关节、旋转关节、移动关节和通用关节的数量。同时指出，D-H模型中基坐标系和工具坐标系的辨识能力存在限制，而非先前假设的任意六个参数均成立。