Problem

While the 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.

Method

This study outlines the development of 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 seriallink 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 study also benefits the analysis of the identifiability of the kinematic parameters.

Fig. 2. Standard D-H parameters for three basic 1-DOF lower pair joints.

Result

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.

Publications & Code

[1] Liao Wu, Ross Crawford, Jonathan Roberts. Geometric interpretation of the general POE model for a serial-link robot via conversion into D-H parameterization. In: Proceedings of IEEE International Conference on Robotics and Automation (ICRA 2019). Montreal, Canada, 2019: 7360-7366 . [pdf][code][poster][pub]

[2] Liao Wu, Ross Crawford, Jonathan Roberts. An analytic approach to converting POE parameters into D-H parameters for serial-link robots. IEEE Robotics and Automation Letters. 2017, 2(4): 2174-2179. (presented at IROS 2017) [pdf][code][pub]