Significance Because the distance measurement error of the laser tracker is much smaller than the angle measurement error, a high-precision coordinate measurement system composed of multiple laser trackers is widely used in large-scale space measurement. The system requires self-calibration before measurements, which is a process that determines the distance between centers of different laser trackers. Although the method based on common points can achieve higher accuracy, it has high requirements for the measurement environment and has a high workload. Although the method based on sphere fitting is simple to operate, its self-calibration accuracy is low. In general, it is difficult to balance measurement efficiency and measurement accuracy with current methods.
Progress To overcome the shortcomings of current methods, we propose a self-calibration method based on triangular structure. Firstly, error analysis for the method based on circle fitting is conducted in two-dimensional space. For simplification, laser tracker A is assumed to measure the target ball on laser tracker B at a distance of 5 m. The angle measurement error of A will make the measurement error of points on the circle more than 30 μm through the amplification effect of length, and reduce the self-calibration accuracy further. Second, we notice that the laser tracker B also has angle observations, and propose a new method that uses angle observations from B coupled with distance observations from A, which can avoid the big error from laser tracker A. The function model based on the triangular structure is established, and the self-calibration results are obtained through iterative optimization. Compared with the method based on circle fitting, the advantages of the new method are analyzed quantitatively. Finally, our method is easily applicable to three-dimension measurement.
Results We verify the superiority of this algorithm through simulated and actual measurements. In the two-dimensional simulated experiment, the true value of self-calibration is set to 5 m. In 100 repeated experiments, most of the absolute deviations based on sphere fitting were greater than 20 μm, while the absolute deviations of the proposed method were less than 10 μm. The root mean square error (RMSE) of the proposed algorithm in this article was 20.98% of RMSE for the sphere fitting method. Moreover, the number of points that the algorithm in this paper needs to measure was significantly less than the method based on spherical fitting. The measurement was implemented in the alignment laboratory of the National Synchrotron Radiation Laboratory (NSRL). Two Leica AT930 laser trackers were used and their true distance was 7 231.548 8 mm. We tested the proposed method and the method based on sphere fitting ten times. The mean absolute bias and standard deviation for the former method were only 6.21 μm and 2.44 μm respectively, while the bias and standard deviation for the latter one was 21.30 μm and 7.37 μm. The proposed method, which had better repeatability, showed the superiority of accuracy in real measurement.
Conclusions and Prospects We analyze that the reason for the decrease in accuracy of the self-calibration method based on sphere center fitting is the low accuracy of the angle observation values of the aiming laser tracker. The self-calibration method based on a triangular structure is proposed. This method uses the angle on the target laser tracker to match the distance observation with high accuracy. The accuracy advantages of this algorithm are verified through quantitative analysis and two experiments. The algorithm in this paper can complete self-calibration between laser trackers without common points and improves measurement efficiency while ensuring accuracy.
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