The ESA/NASA joint LISA (laser interferometer space antenna) mission is designed to detect gravitational waves to perform gravitational astronomy. A key mission requirement is the maintenance of a three-spacecraft constellation in a near-equilateral triangular configuration with a prescribed inter-spacecraft separation. Existing approaches have addressed this problem using simplified dynamical models to enhance tractability; however, the resulting solutions are generally suboptimal with respect to the true system dynamics. In this paper, a precise nonlinear model based on exact nonlinear Keplerian orbit equations is developed. The orbit design problem is consequently formulated as a nonlinear, nonconvex optimization problem. An efficient arc-search interior-point method is employed to address the challenging optimization problem. Numerical results demonstrate that the obtained optimal solution enforces strict agreement between the mean formation distance and the prescribed value. Moreover, the proposed methodology is readily extensible to other optimal orbit design problems formulated using higher-fidelity dynamical models.
Citation
The Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering