## 1 Introduction  
The applications of aspheric surfaces in optical systems not only improve performance but also significantly reduce the number of optical components, therefore reducing the manufacturing cost of optical systems [1]. These advantages mean that large-aperture aspherical surfaces are widely used in high-power laser systems, remote-sensing satellites, and space-based astronomical telescopes [2]. However, increasing the size and accuracy requirements of aspheric optical components often increases the processing difficulty. Taking the Hubble Space Telescope as an example, the main lens with a diameter of 2.4 m had a surface form error of 2 \(\upmu\)m, which shortened the observation distance from the expected value of 14 billion light years to 4 billion light years [3]. The James Webb Space Telescope, originally scheduled to launch in 2018, was also delayed because of the demanding design and manufacturing requirements for the optical components. Therefore, the fabrication of large-aperture aspherical surfaces with high efficiency and accuracy is an important issue in the optical manufacturing industry. Various ultra-precision polishing processes are available for polishing aspheric surfaces and off-axis segments, including computer-controlled optical surfacing (CCOS) [4], bonnet polishing [5], magnetorheological finishing [6], stress lap polishing [7], and ion figuring [8]. Because each polishing process has its own merits and limitations, the most suitable method for a specific function must be selected in the process chain. For example, [PERSON] et al. [9] performed the super-smooth finishing of diamond-turned hard X-ray molding dies by combined fluid jet polishing and bonnet polishing. [PERSON] et al. [10] used a combined polishing technique, including stress lap polishing and rigid conformal polishing, to achieve the ultra-precision machining of large-aperture off-axis mirrors. By choosing reasonable polishing parameters, the proposed polishing method could improve the surface roughness RMS value of the polished surface to below 1 nm [11]. The computer-controlled optical surfacing (CCOS) technique is an enabling technology that actively controls the position, orientation, and dwell time of a small rotating tool as it sweeps through the polished surface to construct the desired optical contour in an iterative process [12]. CCOS can provide a solution for the low-cost mass production of large-aperture optical surfaces because of its advantages of high polishing efficiency and shape accuracy [13]. [PERSON] and [PERSON] [6] reported that the form error of the large optic (up to four meters in size) was reduced from 24 \(\upmu\)m to 1.9 \(\upmu\)m, and a surface texture with a 1.6 nm RMS value could be achieved for a 1 m diameter optic [14]. In the polishing process, the convergence accuracy and efficiency of the surface form achieved by CCOS mainly depend on the influence function, the dwell time algorithm, and the tool path planning. Hence, much research has been conducted on improving the polishing process [15], edge control [16], dwell time calculation [17], and polishing path generation [18]. During the polishing process of aspherical surfaces, the normal error of the polishing tool relative to the workpiece affects the pressure and velocity distribution in the contact area, resulting in the distortion of the removal function and the deterioration of the polishing efficiency and accuracy. However, research on the theoretical modeling and influence mechanism of the motion accuracy of polishing equipment on surface topography during the polishing process is still limited. Given these considerations, a novel material removal model considering the normal error of the polishing tool was developed based on contact mechanics, kinematic theory, and the abrasion mechanism. In combination with the polishing trajectory, the surface morphology and form accuracy after polishing were predicted under different normal-error conditions.