A Minimal POE-Based Model for Robotic Kinematic Calibration With Only Position Measurements

This paper proposes an algorithm for robotic kinematic calibration based on a minimal product of exponentials (POE)-based model for the applications where only position measurements are required. Both joint zero-offset errors and initial frame twist error can be involved in this model. Analysis of the identifiability of these errors shows that at most six elements of these parameters can be identified. It also suggests that at least three noncollinear points on the end-effector should be measured to maximize the identifiability. Compared with the traditional POE-based model with full pose (position and orientation) measurements, the minimal model with only position measurements outperforms in terms of convenience, efficiency, and accuracy. Note to Practitioners-Kinematic calibration is pivotal to improve the position accuracy of a robot. To avoid the disadvantages of measuring the orientation of the end-effector during calibration, an algorithm using only position measurements is presented, with which one needs only position measurements of several points fixed on the end-effector without orientation information during the whole calibration process. This will greatly facilitate the scheme design as well as the practical operations. The identifiability of the parameters is then analyzed with two conclusions: 1) at most six elements of the joint zero-offsets and the initial frame twist in total can be identified simultaneously and 2) at least three points on the end-effector which are not collinear should be measured so as to make the identifiability maximum. According to these conclusions, one should carefully select parameters to formulate the error model and measure sufficient points on the end-effector during the calibration procedure.