为了提高超精密级二维工作台的运动定位精度, 提出了一种实现工作台系统误差分离的二维自标定算法。基于工作台测量误差模型, 该算法利用辅助标记板的5个不同测量位姿, 分别得到迭代模型和迭代初始值, 最终建立完整的迭代二维自标定模型。应用该算法对系统误差为0.2 μm的二维工作台进行仿真, 结果显示: 当不存在随机测量噪声时, 标定精度为0.33 nm; 引入随机测量噪声时, 标定精度与噪声同一量级。对x、y向给定测量精度分别为2.98 μm和3.22 μm的二维工作台进行自标定, 得到x、y向测量精度分别为2.59 μm和3.14 μm。提出的自标定算法对随机测量噪声有很好的鲁棒性, 能够用于精密或超精密级二维工作台自标定。

A two-dimensional self-calibration algorithm was developed to extract the stage systematic measurement error from a stage position measurement error. On the basis of the stage measurement error model, the algorithm got the iterative self-calibration model and the initial value by measuring five different views of an artifact on the stage, and then it established a complete iterative 2D self-calibration model. The algorithm was used to simulate a 2D stage with an accuracy of 0.2 μm. The results show that the calibration error is 0.33 nm without random measurement noises and is the same order of magnitude with random measurement noises. The actual self-calibration experiment on a stage with the given measuring accuracies of 2.98 μm and 3.22 μm in x and y directions was performed, and obtained measuring accuracies are 2.59 μm and 3.14 μm in x and y directions, respectively. All results demonstrate that the proposed algorithm has a good robustness for the random measurement noises, and it is suitable for the calibrations for precision stages or ultra-precision stages.