Error Analysis on Closed-Form Solutions for Kinematic Calibration

Sheng-Wen Shih, Yi-Ping Hung and Wei-Song Lin

TR-IIS-96-014 (Fulltext)


Keywords:
Error Analysis, Kinematic Calibration, Rotation Axis Estimation

Abstract

Many closed-form solutions have been developed for calibrating robot kinematic parameters. The existing closed-form solutions for kinematic calibration can be classfied into two categories according to the information they used. Methods estimating kinematic parameters by using pose measurements are referred to as the pose methods. While there is only one closed-form solution referred to as the point method using 3D point measurements for calibrating robot kinematic parameters. Relatively less work has been devoted to the error analysis on the calibration methods. Error analysis results are very useful to serve as a guideline for selecting calibration techniques, for determining the calibration condition and even for designing a robot head or a robot arm when considering the calibration task. In this paper, we derived the expressions of variances of the kinematic parameters estimated by using the point method or the pose method, respectively. The derived error variances for the point method are functions of the calibration range, number of measurements, amount of measurement noise and amount of joint value noise. Furthermore, if the joint under calibration is revolute, then the error variances are also functions of the distance between the calibration point and the revolute joint axis and length of the link corresponding to the joint under calibration. The derived error variances for a pose method are functions of the calibration range, number of measurements, amount of measurement noise, amount of the joint value noise and length of the link corresponding to the joint under calibration.