Optimization of Space Trajectories Including Multiple Gravity Assists and Deep Space Maneuvers

Abstract

The optimization of high-thrust interplanetary trajectories continues to draw attention. Especially when both Multiple Gravity Assists (MGA) as well as Deep Space Maneuvers (DSMs) are included, the optimization is typically very difficult. The search space may be characterized by a large number of minima and is furthermore very sensitive to small deviations in the decision vector. Various options are available to model these high-thrust trajectories. The trajectory may be modeled using a simple MGA trajectory model as well as using models including DSMs. Both a position and a velocity formulation variant may be adopted and also unpowered or powered swing-bys may be used. These trajectory models were implemented to study the effect of both DSM as well as powered swing-bys. Especially the option to perform DSMs proved to be vital for obtaining good trajectories. Also powered swing-bys may improve the efficiency of the trajectory. The velocity formulation variant proved to be much easier to optimize than the position formulation model. By analyzing the sensitivity and dependency of the various parameters in both models, a proposal for an even better trajectory model is suggested. Also regarding the optimization of these trajectories many options are available. Especially metaheuristics have proven to be very successful in optimizing these trajectories. Various studies have shown the importance of proper tuning of the basic versions of these metaheuristics, which is however often overlooked. This study applied a very rigorous tuning scheme to find the optimal settings for DE, GA and PSO. The results clearly reveal the superiority of DE above other methods. The tuned variants of DE outperformed other settings by one or multiple orders of magnitude, revealing the importance of this tuning scheme. The tuned variants of DE helped to improve a large number of instances in the Global Optimization Trajectory Problem (GTOP) database of ESA. Also the efficiency of these DE variants was shown to be competitive with, and sometimes better than, the best algorithms encountered in literature.