Optimal Gravity-Assist Low-Thrust Trajectory Using a Robust Homotopic Approach

Using Gravity-Assist with low-thrust propulsion system can significantly improve interplanetary mission payload mass. In this paper, an optimization algorithm combined with the indirect and direct methods is revisited to determine fuel-optimal hang-hang control problem. Accordingly, the GA time-fixed low-thrust scenario with complicated constraints is investigated in an efficient computational algorithm. This paper applies a set of effective techniques, such as a homotopic approach, proper normalization approach, and modified switching detection, to improve the optimal convergence and overcome the difficulties of GA low-thrust model. In addition, this paper implements the modified objective functions for both indirect and direct methods. The modified constraints control the discontinuities of the GA trajectory along the MPBVP with a high-accuracy. An advanced application of the algorithm to an interplanetary mission from Earth to Jupiter with intermediate Earth-GA scenario is established. Such challenging mission requirements demonstrate that the GA hang-hang optimal-control problem tends to numerical treatment via exploiting the practical techniques. The complete numerical results are accessible in the provided figures and tables so that some significant attributes of the algorithm are analyzed and compared with two existing solutions. The results show that the proposed algorithm achieves a more efficient solution than existing solutions, in terms of computational process and fuel-consumption of the spacecraft.