Journal of Intelligent & Robotic Systems

, Volume 94, Issue 2, pp 339–348 | Cite as

Application of Universal Kriging for Calibrating Offline-Programming Industrial Robots

  • Ying Cai
  • Peijiang YuanEmail author
  • Zhenyun Shi
  • Dongdong Chen
  • Shuangqian Cao


The requirement for absolute positioning accuracy has also increased with the increasing use of industrial robots in offline programming. The present study proposed Universal Kriging (UK) for calibrating offline-programming industrial robots. This method was based on the similarities in positional errors. In addition, the method represented the positional errors as a deterministic drift and a residual part, which considered both geometric and non-geometric errors. The semivariogram was designed and the drift was determined to implement UK. Then, the method was applied for predicting positional errors and realizing error compensations. In addition, contrast experiments were performed to verify the practicality and superiority of UK compared with Ordinary Kriging (OK). Experimental results showed that after calibration by UK, the maximum of the original spatial positional errors reduced from 1.3073 mm to 0.2110 mm, that is, by 83.86%. Moreover, the maximum of the spatial positional errors reduced from 1.3073 mm to 0.3148 mm by only 75.92% after calibration using OK. An evident increase was reported in the maximum of the spatial positional errors from 0.3148 mm to 0.2110 mm, with an improvement rate of 32.97%. This is of great significance when accuracy is less than 0.5 mm. Overall, the experimental results proved the effectiveness of UK.


Universal Kriging Drift Semivariogram Error prediction Error compensation 


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This research is supported by the National Nature Science Foundation of China(No.61375085).


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationBeihang UniversityBeijingChina

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