Orbital Configuration Control for Space-based Gravitational Wave Observatory Based on the Output Regulation Theory

This paper presents an analysis of the formation of an equilateral triangle for a space-based gravitational wave observatory (GWO) near a collinear libration point in the circular-restricted three-body problem. To achieve continuous observation of gravitational waves, stable triangle configurations are required. However, the motion near the collinear libration points is highly unstable. This problem is examined by employing a two-layer design. In an inner-layer loop, the tracking problem is solved by using the output regulation theory to establish equilateral triangle formation in two periods. As for the outer-layer loop, the radius, frequency, and direction angle of the formation are examined. These parameters play a crucial role in establishing a stable and efficient triangle formation configuration for the GWO. Finally, when the radius, frequency and direction angle are changed, the fuel consumption that required to initialize and maintain the desired formation is calculated.