Formation flight design for a LISA-like gravitational wave observatory via Cascade optimization

Laser Interferometer Space Antenna (LISA) is a project to detect and measure gravitational waves. The project has three spacecraft flying in a formation of near equilateral triangle in a heliocentric orbit trailing Earth. Many sources of perturbations cause the configuration to deviate from the nominal. This paper studies the formation design problem for a LISA-like mission by considering ephemeris-based dynamics. This type of mission is well-known for addressing several strict mission requirements under the realistic dynamics. The problem is formulated as optimizing multiple mission performance indices. It is observed that some indices are correlated with each other, whereas some indices have different sensitivities with respect to the semi-major axis. Therefore, the problem is transformed into a two-step cascade single-objective optimization, in which the optimal solution of the first optimization problem is fed to the second optimization as initial value. In addition, the major perturbing celestial bodies are picked up to make a simplified but accurate enough dynamics to speed up the optimization. Numerical examples verify the analysis and show the effectiveness of the optimization procedure. The influences of mission lifetime and spatial scales on the optimal solutions are also presented.