Kinematic calibration of a laser tracker based on nonlinear optimization of a refined geometric error model

大型飞机装配中的高精度测量技术研究进展

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Analyses of Key Variables to Industrialize a Multi-Camera System to Guide Robotic Arms

Laser trackers (LTs) are indispensable instruments in large-scale dimensional metrology. Nevertheless, geometric errors are prone to increase in site environments due to the occurrence of mechanical and optical misalignments, which deteriorates the measurement accuracy of the LT. The geometric error parameters are difficult to determine by traditional measuring or calibrating approaches. In this article, a classification calibration method is proposed without any other etalons or instruments that accurately estimate the geometric error parameters in a site environment. First, to determine the environmental sensitivity error parameters, a refractive index correction model in a variable temperature environment is constructed, which performs well in reducing the interference of environmental temperature fluctuations. Subsequently, a spatial measurement network is established to determine two-face sensitivity error parameters using the difference between the frontsight and backsight measurements of the targets. Finally, the two-face nonsensitivity error parameters are solved by minimizing the residuals of the coordinate transformation from each LT station to the reference frame. Indeed, the effects of temperature fluctuation and geometrical misalignments on the measurement accuracy are deeply analyzed, which provide meaningful guidance for calibration and compensation of the geometric errors of the LT. The effectiveness of the proposed method is validated by a series of site experiments. The results show that the length error is reduced to 0.030 mm on average, which is 44% lower than that of the network method.

Calibration of the Geometric Error Parameters of Laser Trackers in Site Environments

Laser trackers (LTs) are indispensable instruments in large-scale dimensional metrology. Nevertheless, geometric errors are prone to increase in site environments due to the occurrence of mechanical and optical misalignments, which deteriorates the measurement accuracy of the LT. The geometric error parameters are difficult to determine by traditional measuring or calibrating approaches. In this paper, a classification calibration method is proposed without any other etalons or instruments that accurately estimate the geometric error parameters in a site environment. First, to determine the environmental sensitivity error parameters, a refractive index correction model in a variable temperature environment is constructed, which performs well in reducing the interference of environmental temperature fluctuations. Subsequently, a spatial measurement network is established to determine two-face sensitivity error parameters using the difference between the frontsight and backsight measurements of the targets. Finally, the two-face non-sensitivity error parameters are solved by minimizing the residuals of the coordinate transformation from each LT station to the reference frame. Indeed, the effects of temperature fluctuation and geometrical misalignments on the measurement accuracy are deeply analyzed, which provide meaningful guidance for calibration and compensation of the geometric errors of the LT. The effectiveness of the proposed method is validated by a series of site experiments. The results show that the length error is reduced to 0.030mm on average, which is 44% lower than that of the network method. 

Five National Metrology Institutes (NMIs) worked together to validate the assessment of laser tracker's (LT) uncertainty for large scale dimensional metrology in subsequent measurements using the network method. The LT uncertainty is assessed by measuring a set of a fixed network of targets from different LT positions. Afterward, we must perform a “bundled adjustment” of all the measurements to determine the transformations of the LT positions that minimize the residuals (differences) between a computed “virtual” group of targets, called composite points, and the redundant targets coming from the LT positions transformed to a unique LT position. Each residual is weighted with the LT's Maximum Permissible Error (MPE) specified by the LT manufacturer. The standard deviation of the weighted residuals becomes LT uncertainty. Afterward, with Monte-Carlo simulation, we propagate the LT uncertainty to the position of every target in the network and 3D distances between them. LT uncertainty is valid if 3D distance's uncertainties computed with composite points is greater than the error computed with these distances minus the same distances calibrated with the line of sight method (LOS) or if the absolute normalized error is less or equal to one. LOS method uses only the LT's interferometer for calibration, which dispense the use of a calibrated scale bar. Based on the network method, the NMIs developed two methods to improve LT geometry error parameters. The first improves the LT geometry error parameters by fitting the composite points to the LT geometry error model. The second evaluates the parameters placing the LT geometry error model in the minimization of the bundled adjustment's residual. LT geometry error parameters are valid if the parameter's uncertainties are negligent compared to its value.

Validation of the network method for evaluating uncertainty and improvement of geometry error parameters of a laser tracker

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Validation of the network method for evaluating uncertainty and improvement of geometry error parameters of a laser tracker