Optimized Design and Characterization of a Non-Linear 3D Misalignment Measurement System

Abstract

This work proposes a framework for the optimization of the metrological performances of a system that measures the relative position and orientation between two surfaces. The method is based on the creation of a non-linear measurement model of the instrument. The method uses the Monte Carlo method and the Design of Experiments techniques for determining the instrument uncertainty and the uncertainty sensitivity versus the geometrical and metrological instrument characteristics. The result of the proposed approach is a nonlinear simplified numerical model of the measurement uncertainty and of the bias error components, that is used for the instrument design and compensation. A case-study related to a misalignment measurement system based on a universal joint is presented. The measurement uncertainty computed with the proposed method has been compared with the one obtained in fit-to-purpose experiments performed with a robotic manipulator. An optimal calibration procedure is then used in order to identify the parameters of the system minimizing the overall uncertainty.

Statistical Techniques in Precision Metrology, Applications and Best Practices

“…Multiple linear regression extends simple linear regression to model the relationship between multiple independent variables and a single dependent variable. In metrology, multiple linear regression is applied to characterize complex measurement systems with multiple influencing factors (Fabris et al, 2022). Metrologists use multiple linear regression to develop predictive models for estimating measurement outcomes based on multiple input variables (Jacob, 2021).…”

Metrological Characterization of a Laser-Camera 3d Vision System Through Perspective-N-Point Pose Computation and Monte Carlo Simulations

“…The measurement uncertainty of the deriving system can be evaluated by applying the Monte Carlo Method (MCM) as it is prescribed by the ISO GUM Supplement 1 (Joint Committee for Guides in Metrology (JCGM) 2008) and Supplement 2 (Joint Committee for Guides in Metrology (JCGM) 2011). This method exploits the MCM for estimating the uncertainty deriving from the Probability Distribution Functions (PDF) of the input variables and has been applied in several works and studies (Cox and Siebert 2006;Fabris et al 2022;Ghiani, Locci, and Muscas 2004;Moschioni et al 2013;Nuccio and Spataro 2008). Section 2 describes the method used for the projection of the laser point clouds to the image plane and for the estimation of its uncertainty starting from the most influencing input parameters.…”