Optimal Planner for Spacecraft Formations in Elliptical Orbits

An optimal planner for spacecraft formations in elliptical reference orbits is presented. A fast solution to an individual spacecraft minimum time or fuel maneuver using the Hamilton-Jacobi-Bellman formulation is developed using spline approximations to evaluate thrust effect integrals. The individual optimal spacecraft maneuvers use realistic low-thrust, bounded inputs similar to future electric propulsion systems. A formation optimal planner is then formulated using the individual spacecraft maneuvers as a basis. The formulation is easily scalable to larger clusters, provably optimal over the formation, and numerically robust; it also requires minimal communication between fleet members. An example is presented of a tetrahedron formation in a highly elliptical reference orbit (e = 0.8), with solutions to both formation minimum-time and minimum-fuel problems given. Comparison with linear programming techniques show a distinct savings in fuel usage for high-eccentricity examples.