Uncertainty evaluation of distributed Large-Scale-Metrology systems by a Monte Carlo approach Maurizio Galetto *, Luca Mastrogiacomo, Domenico Maisano, Fiorenzo Franceschini DIGEP – Department of Management and Production Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy Submitted by Raffaello Levi (1), Torino, Italy 1. Introduction In the field of Large Scale Metrology (LSM), distributed systems are more and more diffused [1]. Industrial applications generally concern assembly and dimensional verification of large-sized mechanical components, in which levels of accuracy of several tenths of millimetre are tolerated [2]. The typical configuration of a distributed LSM system includes [3]: (i) a network of sensors, distributed around the measured object, (ii) some targets to be localized, generally in contact with the measured object’s surface, or mounted on a hand-held probe, and (iii) a centralized data processing unit (DPU), which receives and processes data from sensors, in order to localize targets. The scientific literature encompasses three possible approaches for target localization [4]: (i) multiangulation, using the angles subtended by targets, with respect to sensors; (ii) multilateration, using the distances between targets and sensors; (iii) hybrid techniques, based on the combined use of distances and angles. The relative positioning of sensors with respect to targets and their technical features strongly affect the system performance, both from the metrological and the operational point of view. When designing a network of sensors for a distributed LSM system, one of the most important features to be considered is the uncertainty in target localization; in general, the more technologi- cally advanced and expensive the sensors, the lower their uncertainty in distance/angular measurements and, hence, that in target localization. Despite this importance, the scientific literature on the subject is relatively scarce and fragmented [4,5]. The aim of this paper is to introduce a new methodology to evaluate the overall measurement uncertainty in the localization of targets by LSM systems based on distance and angular measurements. The proposed approach relies on the General Least Square (GLS) method and makes it possible to obtain the covariance matrix of the 3D coordinates of targets, using the uncertainties in the distance/angular measurements by network sensors and those of the sensors’ parameters resulting from their calibration process [6]. The remainder of the paper is structured as follows. Section 2 defines a mathematical model for the 3D target localization of a general LSM system. Section 3 describes the new methodology for evaluating the uncertainty in target localization. Section 4 presents an experimental test of the methodology, using a distributed LSM system, which integrates one laser tracker and three photogram- metric cameras. 2. Target localization model A general distributed LSM system includes a number of network sensors positioned around the measurement volume [3]. It is assumed that (i) O-XYZ is a global Cartesian coordinate system and (ii) each ith sensor (D i ) has a local coordinate system, o i -x i y i z i , roto- translated with respect to O-XYZ, reflecting its spatial position/ orientation. The (six) position/orientation parameters related to each ith sensor (i.e., X 0 i ; Y 0 i ; Z 0 i and v i , f i , k i ) are treated as known parameters, since as they are measured in an initial calibration phase. The calibration process generally includes multiple measure- ments of calibrated artefacts, within the measurement volume [3]. Assuming that P is the point to be localized in the 3D space (e.g., the centre of a spherical target), associated with vector X, the positioning problem may be decomposed according to the following linearized model [1,4]: MXB  M dis: M ang:   X B dis: B ang:   ¼ 0; (1) where X = [X, Y, Z] T is the position vector of P in the global coordinate system O-XYZ; M dis. , M ang. and B dis. , B ang. are the design CIRP Annals - Manufacturing Technology 65 (2016) 491–494 A R T I C L E I N F O Keywords: Uncertainty Sensor Large Scale Metrology A B S T R A C T Distributed systems for Large-Scale-Metrology applications generally include a set of angular and/or distance sensors, distributed around the measurement volume, and some targets to be localized, in contact with the measured object’s surface. For these systems, estimating the uncertainty in target localization is far from trivial, as it may be affected by several factors: uncertainty in sensor calibration and angular/distance measurements, relative position between targets and sensors, etc. This paper proposes a novel approach based on the combined use of the Multivariate Law of Propagation of Uncertainty and Monte Carlo method. Preliminary results and experimental tests are presented and discussed. ß 2016 CIRP. * Corresponding author. E-mail address: maurizio.galetto@polito.it (M. Galetto). Contents lists available at ScienceDirect CIRP Annals - Manufacturing Technology journal homepage: http://ees.elsevier.com/cirp/default.asp http://dx.doi.org/10.1016/j.cirp.2016.04.017 0007-8506/ß 2016 CIRP.