In this work, we examine the accuracy of the geometric error calibration of machine tools using a laser tracer, via the multilateration or sequential multilateration principle. An uncertainty analysis of geometric errors or target point coordinates, based on the Monte-Carlo method, is often adopted to assess the accuracy of measurement results. However, this approach is not comprehensive, and can be time-consuming. This paper adopts the average volumetric localization accuracy to assess the quality of geometric error calibration, where the accuracy is evaluated approximately by means of a formulaic method, based on the multivariate law of propagation of uncertainty. Using this method, the accuracy of measurement results can be denoted quantitatively with a single indicator, and the influence of measurement strategy on measurement accuracy can be analyzed more intuitively. To further improve the average volumetric localization accuracy, we employ an optimization method for the measurement path, based on the greedy algorithm. Simulations and experiment are then conducted to verify the proposed method; the results show that both the laser tracer setup and measurement path have a great deal of influence on the measurement accuracy of geometric errors.

在这项工作中，我们通过多边或顺序多边原理，研究了使用激光示踪仪对机床进行几何误差校准的准确性。通常采用基于蒙特卡洛方法的几何误差或目标点坐标的不确定性分析来评估测量结果的准确性。但是，这种方法并不全面，并且可能很耗时。本文采用平均体积定位精度来评估几何误差校准的质量，在此基础上，基于不确定性传播的多变量定律，采用公式化方法对精度进行了近似评估。使用这种方法，可以用一个指标定量表示测量结果的准确性，可以更直观地分析测量策略对测量精度的影响。为了进一步提高平均体积定位精度，我们基于贪婪算法对测量路径采用了一种优化方法。然后进行仿真和实验以验证所提出的方法。结果表明，激光示踪剂的设置和测量路径对几何误差的测量精度有很大的影响。