High-efficiency smooth pseudo-random path planning for restraining the path ripple of robotic polishing

Computer-controlled subaperture polishing technology is limited by its propensity to introduce midspatial frequency (MSF) error (ripple error), which significantly inhibits the performance improvement of optical systems. The pseudo-random polishing path is an important method for suppressing MSF error. However, a pseudo-random path that ensures both path smoothness and planning efficiency is difficult to generate. This paper proposes a novel, to the best of our knowledge, pseudo-random path planning method employing a reconstructive points algorithm that efficiently achieves full coverage of the workpiece under massive sampling points at once. Moreover, the generation time for millions of path points is reduced to less than 3 minutes. Additionally, a path modification method is proposed that achieves smooth processing on a machine tool with few additional path points; the vibration magnitude under the proposed smooth path can be reduced to 0.749 g (gravity acceleration), which is the same as that of a raster path. A precise speed management method is also proposed to ensure precise surface error corrections. Overall, the experimental results show that the peak valley of the form error can be converted to 0.115 λ using the proposed algorithm without introducing a periodic MSF error.