Feul optimal, low thruster, earth escape/moon capture trajectories design

Abstract

A homotopy approach is studied for fuel optimal low thrust Earth-Moon trajectory, by solving two point boundary value problem(TPBVP). Recently, maneuvers using low thrust propulsion system have been identified as emerging technologies. So , the low thruster is considered as the main actuator for the maneuver. In this thesis, the low thruster is not assumed as a constant magnitude. So, the thruster can be variable thruster or variable specific impulse. The TPBVP, optimal trajectories using low thruster from earth to moon, is solved using the NPSOL(Nonlinear programming Solver). The cost function is related with a fuel consumption function, and constraints are the position vector and the velocity vector at each escape/capture end point. The necessary conditions for the first variation of the augmented cost function, to be zero include the costate differential equations, necessary conditions and optimality condition. However, the costate equations are highly nonlinear and unstable. So, it is not easy to find initial value of the costates. To solve this difficulty, we adopt the homotopy analysis. And to apply the minimum energy/fuel problem, the final time is estimated by using the previous optimal fuel solution. The solution of the minimum energy is more regular and it can be solved more easier. The minimum fuel problem should be solved based on the minimum energy problem. The set of the solution between min. energy and fuel is called as zero path. The zero path following techniques are investigated. Using these techniques, we can solve the problem effectively.