A solution to the hand-eye calibration in the manner of the absolute orientation problem

Abstract

Purpose

This paper aims to introduce a simple hand-eye calibration method that can be easily applied with different objective functions.

Design/methodology/approach

The hand-eye calibration is solved by using the closed form absolute orientation equations. Instead of processing all samples together, the proposed method goes through all minimal solution sets. Final result is chosen after evaluating the solution set for arbitrary objectives. In this stage, outliers can be excluded optionally if more accuracy is desired.

Findings

The proposed method is very flexible and gives more accurate and convenient results than the existing solutions. The mathematical error expression defined by the calibration equations may not be valid in practice, where especially systematic distortions are present. It is shown in the simulations that the solution which results the least mathematical error in systems may have incorrect, incompatible results in the presence of practical demands.

Research limitations/implications

The performance of the calibration performed with the proposed method is compared with the reference methods in the literature. When the back-projection error is benchmarked, which corresponds to the point repeatability, the proposed approach is considered as the most successful method among all others. Due to its robustness, it is decided to make tooling-sensor calibrations by the recommended method, in the robotic non-destructive testing station in Ford-OTOSAN Kocaeli Plant Body Shop Department.

Originality/value

Arranging the well-known AX = XB calibration equation in quaternion representation as Q_A = Q_x × Q_B × Q_x reveals another common spatial rotation equation. In this way, absolute orientation solution satisfies the hand-eye calibration equations. The proposed solution is not presented in the literature as a standalone hand-eye calibration method, although some researchers drop a hint to the relative formulations.

Citation

Deniz, C. and Cakir, M. (2018), "A solution to the hand-eye calibration in the manner of the absolute orientation problem", Industrial Robot, Vol. 45 No. 1, pp. 64-77. https://doi.org/10.1108/IR-08-2017-0152