This paper aims to improve the precision and efficiency of precision polishing technology for large-scale free-form surface optical devices. By constructing a robotic polishing center as a polishing platform

the travelling salesman problem is solved in a planar mapping domain including unit circle domain

unit square domain and free boundary domain. For the quotient problem

the circularity value is calculated by projection

the mapping area is classified

and the obtained planar trajectory is mapped to the curved surface to obtain the polishing path for the ultra-precision optical device with large-scale freedom. The algorithm in this paper takes into account the calculation efficiency and boundary coverage quality. When the circularity of the projection area exceeds 0.9

the unit circle domain is used as the mapping plane domain. when the circularity value of the projection area is relatively small

between 0.8 and 0.9

the unit square domain is used as the mapping plane domain. When the circularity value is less than 0.8

the free boundary mapping domain is adopted. Simulation and experimental verification of polishing results show that this method can obtain an efficient non-crossing path

effectively reduce the intermediate frequency and high frequency errors caused by a single direction operation

meet the actual polishing processing requirements of changing direction of the polishing path

effectively eliminate the polishing texture

and significantly improve the polishing accuracy and efficiency.