<title>Robot-based surface inspection system with estimation of spatial uncertainties</title>

Abstract

This paper presents a robot based surface inspection application for measuring mould surface in foundries. The surface measuring its performed using a robot with six degrees of freedom equipped with a laser-triangulation-based distance sensor. The measuring process is divided into four phases: sensor calibration, calibration of the mould location, surface inspection measurements and measurement analysis. In the sensor calibration phase, tool correction is calculated by using algorithms based on least square estimation with Newton iteration. Equations derived for calibration uncertainty estimation are verified using Monte Carlo simulations. The real covariance of sensor tool correction has been obtained with test measurements. Calibration of the mould location is based on the same estimation principle as was used in sensor calibration. Total uncertainty of the measuring system is obtained by transforming all separate uncertainties into one total uncertainty covariance. Spatial uncertainties are expressed and manipulated in the form of covariance matrices. The volume of the uncertainty ellipsoid in 3D space is calculated for each sensor calibration and mould location calibration. For comparison, the goodness of the measurement model is evaluated also by the condition number of the Jacobian matrix.