Design and optimization of stable initial heliocentric formation on the example of LISA

Space-based gravitational wave (GW) detector such as the LISA (Laser Interferometer Space Antenna) mission requires high-precision and stability of the triangular formation. The dynamic environment of the detectors is complex, the science requirements for the formation are tight, and consequently, design and optimization of this high-standard formation with essentially many decision variables are very challenging. This paper studies the design and optimization of the stable initial formation of the heliocentric GW detector by taking the LISA as an example. The linearization method based on relative orbital elements is used for formation design in the two-body system. Three constraints are presented to reduce the number of decision variables to fourteen. The geometric features of the arm length and breathing angle of the triangular formation and the relative position of LISA to the Earth are analyzed and numerically verified in a high-fidelity dynamic model, from which the relationships of multiple requirements of LISA are studied, and a single index is summarized to simplify the optimization. Sobol sensitivity analysis is used to quantitatively evaluate the sensitivities of the decision variables to the cost function, with which a self-adaptive adjustment algorithm of the region of the variables is presented to improve the computational efficiency. The availability of the method to quickly and precisely find a stable initial formation in an extensive neighborhood of the nominal formation is verified by numerical simulation, where the best solution decreases about 47.54% of the arm length change from the requirement. This study shows that the initial formation should be deployed appropriately away from the Earth, and the gravitations of Venus and Jupiter should be utilized to maintain the formation stability.