A multilateral laser-tracking three-dimensional coordinate measuring system based on plane constraint

Abstract

In a multilateral laser-tracking three-dimensional (3D) coordinate measuring system, the error caused by the laser tracker angle measurement is not an issue, while the 3D coordinates of space points are determined using only distance measurement data. Thus in order to improve the accuracy of the whole system it is crucial to calibrate the parameters of the multilateral system with precision. To this end, a parameter-calculating method based on plane constraint is proposed in this paper. A standard plane constraint is used to provide optimal system equations without increasing the number of unknowns. Moreover, while a traditional multilateral system requires at least four stations of laser-tracking measurement, a system based on plane constraint produces more equations, reducing the number of required stations to three. A method for obtaining the required standard plane at the measurement site is also presented in this paper, thus making the above-mentioned scheme feasible. In order to highlight the advantages of a multilateral system over a long distance, an experiment is set up where three scale bars are placed within the range of 25–38 m. The experiment shows that the measurement error of scale bars using a four-station plane constraint model is distributed within the range from 10 to 49 µm, with an average value of 29 µm, while the error using the three-station model is distributed within the range from 31 to 55 µm, with an average value of 39 µm. Using traditional four-station multilateral method the error is distributed from 33 to 79 µm, with an average of 56 µm. The accuracy of the system based on plane constraint appears to be improved compared with single-station measurement and traditional multilateral systems.