Hand-Eye Calibration: 4-D Procrustes Analysis Approach

Jin Wu, Yuxiang Sun, Miaomiao Wang, Ming Liu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

56 Citations (Scopus)


We give a universal analytical solution to the hand-eye calibration problem {AX} = {XB} with known matrices {A} and {B} and unknown variable {X} , all in the set of special Euclidean group SE(3). The developed method relies on the 4-D Procrustes analysis. A unit-octonion representation is proposed for the first time to solve such a Procrustes problem through which an optimal closed-form eigendecomposition solution is derived. By virtue of such a solution, the uncertainty description of {X} , being a sophisticated problem previously, can be solved in a simpler manner. The proposed approach is then verified using simulations and real-world experimentations on an industrial robotic arm. The results indicate that it owns better accuracy and better description of uncertainty and consumes much less computation time.

Original languageEnglish
Article number8788685
Pages (from-to)2966-2981
Number of pages16
JournalIEEE Transactions on Instrumentation and Measurement
Issue number6
Publication statusPublished - Jun 2020
Externally publishedYes


  • Hand-eye calibration
  • homogenous transformation
  • least squares
  • octonions
  • quaternions

ASJC Scopus subject areas

  • Instrumentation
  • Electrical and Electronic Engineering


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