测角误差的自适应分段多项式补偿方法研究

Research on Adaptive Piecewise Polynomial Compensation Method for Angular Measurement Error

针对圆光栅制造工艺和安装误差引起的圆光栅测角误差标定问题,提出了一种基于最小二乘法的自适应分段多项式拟合方法。通过设计区间自适应增长策略,在限制各拟合点最大拟合误差的条件下,将整个拟合区间分段,针对不同拟合区间采取不同阶数多项式进行拟合。通过实验采集了某转台圆光栅的测角误差,用提出的拟合方法进行了实验验证。结果表明该拟合方法具有更高的拟合精度,拟合过程简单,易于软硬件实现。

A piecewise polynomial fitting method based on least square method was proposed to calibrate the angular error of circular grating caused by manufacturing process and installation error.By designing the interval growth strategy,the whole fitting interval was segmented adaptively under the condition of limiting the maximum fitting error of each fitting point,and different order polynomials were adopted for fitting on different fitting intervals.The angle measurement error of a rotary’s grating was collected by experiment,and the fitting method proposed in this paper was verified by experiment.The results show that this fitting method has the advantages of higher fitting accuracy,simple fitting process,and easy implementation of software and hardware.