Statistical inferences for two-dimensional workpiece localisation

In this paper, we study Workpiece Localisation (WL) which can be described as follows. Before machining, a rigid workpiece is fixed to a work table approximately at its nominal location after minimal calibration. With data measured on the fixed workpiece using a Coordinate Measuring Machine (CMM), we aim to determine the Euclidean transformation of the workpiece Computer-Aided Design (CAD) model frame relative to some known world reference frame. Recently the WL problems have been formulated as Least Squares Problems (LSP). Although various algorithms have been proposed to solve the LSP, they involve an iterative process to update the Euclidian transformation and the home points of the measured data. In this paper we propose a new formulation of the WL problems, which can be solved using standard nonlinear least squares method where updating the home points is unnecessary. Additionally, the new formulation enables constructing confidence intervals for the Euclidean transformation parameters.