中文摘要：

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0.2μm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0.33nm;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2.98μm和3.22μm的二维工作台进行自标定,得到x、y向测量精度分别为2.59μm和3.14μm。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。

英文摘要：

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-cali- bration model. The algorithm was used to simulate a 2D stage with an accuracy of 0.2 ~m. The re- sults 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 per- formed, and obtained measuring accuracies are 2.59 /μm and 3.14 /μm in x and y directions, respec- tively. 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 sta- ges.