Abstract: Space-based gravitational-wave observatory requires that the spacecraft fly in a triangular formation in which the configuration initialization and keeping problems should be solved carefully. This paper classifies the three kinds of triangular formations and makes some comparison and analysis. The dynamics mechanism of this triangular formation is summarized and the long-term propagation characteristics under kinds of perturbations are discussed The control methods for initialization, keeping and reconfiguration are designed. The results will provide a fundamental theory for space-based gravitational-wave observatory missions.