Earth-To-Halo Low-Thrust Minimum Fuel Optimization with Optimized Launch Conditions

Transfer time and fuel consumption are two major performance indexes in trajectory optimization. In this paper, low-thrust propulsion is applied after an impulsive maneuver. Both phases are optimized, and trajectory optimization with optimized launch conditions in the Earth Moon restricted three-body model is performed. The total fuel consumption is minimized, and the first-order necessary condition for optimality as well as their analytic Jacobians are derived. Homotopy method is used to link the related and easier minimum-energy problem to the corresponding minimum-fuel problem. The combination of these methods stated above are applied to minimum-fuel Earth Halo transfer. Simulation show that this method can afford various combinations of time of flight and total mass consumption, which gives a great flexibility in mission design.