Capture of near-Earth objects with low-thrust propulsion and invariant manifolds

In this paper, a mission incorporating low-thrust propulsion and invariant manifolds to capture near-Earth objects (NEOs) is investigated. The initial condition has the spacecraft rendezvousing with the NEO. The mission terminates once it is inserted into a libration point orbit (LPO). The spacecraft takes advantage of stable invariant manifolds for low-energy ballistic capture. Low-thrust propulsion is employed to retrieve the joint spacecraft-asteroid system. Global optimization methods are proposed for the preliminary design. Local direct and indirect methods are applied to optimize the two-impulse transfers. Indirect methods are implemented to optimize the low-thrust trajectory and estimate the largest retrievable mass. To overcome the difficulty that arises from bang-bang control, a homotopic approach is applied to find an approximate solution. By detecting the switching moments of the bang-bang control the efficiency and accuracy of numerical integration are guaranteed. By using the homotopic approach as the initial guess the shooting function is easy to solve. The relationship between the maximum thrust and the retrieval mass is investigated. We find that both numerically and theoretically a larger thrust is preferred.