Hybrid Optimization of Low-Thrust Many-Revolution Trajectories with Coasting Arcs and Longitude Targeting for Propellant Minimization

Abstract

Electric Propulsion (EP) has become one of the most efficient technologies for spacecraft propulsion. In contrast to conventional chemical propulsion, the low thrust force generated by EP thrusters can deliver a momentum transfer to the spacecraft that is up to twenty times greater, for an equivalent propellant expenditure. Despite decades of heritage, the topic of low-thrust spacecraft trajectory optimization remains an active field of research, with many approaches available yet much room for improvement. This MSc thesis presents the development of a novel methodology for low-thrust many-revolution trajectory optimization. It employs the state-of-the-art hybrid technique to harness the strengths of both indirect and direct optimization methods. Its indirect nature efficiently reduces the number of optimization variables and its direct counterpart provides an unmatchable flexibility in terms of a configurable force and perturbation model as well as operational constraints handling. This methodology was already shown in literature to be highly reliable for minimum-time trajectories. The research hereby presented maintains these results while enabling it to optimize minimum-propellant trajectories through a mechanism that allows for coasting (non-thrusting) arcs. This approach is additionally combined with an orbital averaging scheme to reduce the propagation load at the expense of accuracy for the rapidly changing variables. Nonetheless, it retains the continuous integration scheme to enable final geodetic longitude targeting in combination with propellant-minimization, which the former hybrid methodologies were incapable of solving for. The trajectory simulator is coupled with an enhanced objective function that reduces the user fine-tuning effort, and with a differential evolution algorithm that leads to a flexible global optimization process with a practical computational effort.

This research is the outcome of the cooperation between the author, Delft University of Technology, and GMV Innovating Solutions, a technology business group with a strong leadership in space engineering. The specific interest of application of this research lies in many-revolution planetocentric trajectories, such as an orbital transfer to Geostationary Earth Orbit, where there are growing market opportunities for all-electric satellite platforms. The resulting software, integrated as part of GMV's Flight Dynamics solution, allows the user to include orbital perturbations and perform a multi-objective optimization with respect to time-of-flight, propellant expenditure, and final geodetic longitude. This research constitutes a quantum leap for the hybrid optimization method because it shows that its accuracy in propellant-minimization is comparable to the analytical global optima despite the simplified co-state dynamics. Furthermore, it is a significant advancement for space mission design and satellite operations because it demonstrates the superior convergence performance of the hybrid methodology relative to GMV's implementation of the indirect approach, particularly in complex problems that combine multiple optimization objectives with varied orbital perturbations and operational constraints fulfillment.