Preliminary design of low-energy, low-thrust transfers to halo orbits using feedback control

Calculating low-thrust trajectories that connect geocentric orbits to Earth-moon halo orbits involves designing the many-revolution thrust arc required to depart Earth vicinity. Existing methods are based on solving the corresponding optimal control problem and hence are computationally expensive, involve providing hard-to-obtain initial guesses, and do not lend themselves well to quick parametric trade studies. In this paper, a stochastic optimization algorithm is coupled with a Lyapunov feedback control law to explore the solution space for designing Earth-to-halo low-energy, low-thrust trajectories. While the objective is to minimize the fuel consumed for the transfer, the time of flight is constrained so as to optimally distribute the coast time between the low-thrust escape spiral and the low-energy arc. Engines are assumed to have a constant specific impulse and provide constant thrust throughout the transfer. The results obtained from this method are then compared with other available reference solutions in order to quantify its effectiveness in designing such transfers. Favorable comparisons thus obtained demonstrate the utility of the proposed method in achieving near-optimal solutions, combined with a large improvement in computation time.