A Dynamical System Approach to Orbit Down-Selection of Earth-Moon Autonomous Navigation Constellations

The article develops a method for the exploration of a concept of autonomous navigation constellations in the Earth-Moon system. This concept consists of using autonomous GPS-like beacons on three-body periodic orbits to provide navigation services to an end-user in the larger Earth-Moon neighborhood. The autonomy of the constellation spacecraft would be achieved using LiAISON navigation as introduced by Hill, Born, and Lo. The article focuses on the problem of orbit down-selection for such a concept, which is approached by formulating an optimization problem. The discussion of potential cost functions and the resulting simplifications of the problem are addressed. A continuation based method that leverages the structure of periodic orbits in the circular restricted three-body problem is then proposed to analyze the problem. The method allows notably for a succinct representation of the solution space as a one-dimensional graph that highlights local and global extrema of the optimization problem. Illustration of the method using a simplified down-selection metric is discussed to balance the strengths and limitations of the approach.