Hybrid optimization of low-thrust many-revolution trajectories with coasting arcs and longitude targeting for propellant minimization

Despite the ongoing advancements in low-thrust propulsion technology and the rise of all-electric satellite platforms, low-thrust spacecraft trajectory optimization remains a complex field of research. Shape-based approximations are predominant in interplanetary applications, but they are generally unsuitable for many-revolution trajectories, common in terrestrial applications. Indirect optimization methods allow for global optimization of many-revolution trajectories, but their mathematical complexity generally requires significant simplifications of the dynamical model, and they must be re-derived for any modification to the system dynamics or constraints. Conversely, direct optimization methods exhibit larger convergence radii and are flexible for application in different problems yet suffer from impractical computational times due to large design vectors. This paper presents a methodology for the optimization of low-thrust many-revolution trajectories, employing a hybrid combination of indirect and direct optimization methods. Similar hybrid approaches have been shown to be highly reliable for minimum-time trajectories. This methodology preserves similar performance while additionally enabling minimum-propellant optimization, through a mechanism that allows for coasting (non-thrusting) arcs, as well as targeting of the final geodetic-longitude. To reduce the propagation load of the methodology, we combine an orbital averaging scheme with a differential evolution algorithm, leading to a global optimization process with a practical computational effort. The analytical nature of the methodology reduces the number of optimization variables and its computational counterpart provides unmatchable flexibility for a configurable force and perturbation model as well as operational constraints fulfilment. The approach is applied to an unperturbed and a J₂-perturbed GTO-GEO transfer, revealing a 0.03% and a 0.4% error, for time- and propellant-minimization respectively, relative to the reference optimal trajectories. This proves that the method can match the performance of former hybrid approaches while additionally allowing for engine on/off switching. Moreover, the inclusion of the J₂ perturbation shows that, in contrast to indirect methods, it can accommodate modifications to the system dynamics without the need to re-derive the optimal control laws. Furthermore, a superior convergence radius of the optimization problem is demonstrated for the hybrid method, with respect to a reference indirect method, through the simultaneous optimization for minimum-propellant expenditure and final geodetic-longitude targeting. This research constitutes a significant advancement for space mission design and satellite operations, because it simultaneously harnesses the advantages of indirect and direct methods with broader flexibility than the popular indirect approaches and enhanced functionality than the former hybrid methods published in literature.