为了实现高次回转对称非球面的全口径超光滑加工，对磨头的运动控制算法进行了研究。介绍了超光滑加工的基本原理以及相应数控机床的机构，并对其光学表面的创成方式进行了描述。为了精确控制磨头的运动轨迹，提出了非球面驻留点的等误差递推求解算法进而分析了轨迹误差。计算了磨头位于不同位置时去除率的分布情况，并建立了驻留时间数学求解模型。在自研设备上对口径为150 mm，非球面度为116 μm的样件进行了超光滑加工。表面粗糙度方均根值由1.523±0.045 nm降低至0.399±0.0238 nm且分布均匀。实验结果表明，利用该算法可以精确控制磨头的运动轨迹，从而保证表面粗糙度的均匀一致。

In order to realize full aperture ultra-smooth polishing on the high order rotary symmetrical aspheric surface, the polishing head controlling algorithm is studied. The basic theory of ultra-smooth polishing technology and the computer numerical control machine mechanism are introduced. And the optical surface generating method is also descripted. Then, a kind of equal error recurrence algorithm is proposed which is used in solving dwell points and controlling polishing head path. And the path error is also analyzed. The polishing removal rate distribution of different positions is calculated and the dwell time mathematical solving model is established. Finally, an experiment for polishing an aspheric lens with a aperture of 150 mm and a asphericity of 116 μm is carried out on the self-research machine. The root-mean-square of surface roughness is reduced from 1.523±0.045 nm to 0.399±0.0238 nm. The result indicates that the algorithm described in this paper could improve the precision of asphere polishing path and the uniformity of the roughness distribution.