Abstract: Configuration design of spacecraft formations is the first problem to be faced in the study of spacecraft formation design. Based on a review of three typical triangular formation design scheme of space-based gravitational-wave detection mission， this paper extends the triangular formation design scheme to polygon formation design scheme， and gives a polygonal formation optical path design method for laser link path transit of gravitational-wave detectors. On this basis， a polygonal formation design method based on the combination of the Clohessy-Wiltshire equation and the cycle matching principle is given in this paper， including two new formation types： polygonal frame formation and polygonal grid formation. The results of the study can provide a theoretical basis for the design of formation configurations for a variety of space missions， including gravitational wave detection in the space. Simulations and analysis show that the change rate of formation arm length in this paper is stable enough， which shows that the proposed formation configuration design method is effective and has a good potential for engineering application.

Key words: space-based gravitational-wave detection, spacecraft formation, relative dynamics, triangular formations, polygonal formation, framework-type formation, grid-type formation