Interplanetary trajectory optimization with swing-bys using evolutionary multi-objective optimization

Interplanetary trajectory optimization studies mostly considered a single objective of minimizing travel time between two planets or launch velocity of spacecraft at the departure planet or maximizing delivered payload at the destination planet. Despite a few studies, in this paper, we have considered a simultaneous minimization study of both launch velocity and time of travel between two specified planets with and without the use of gravitational advantage (swing-by) of some intermediate planets. Using careful consideration of a Lambert's approach with the Newton-Raphson based root finding procedure of developing a trajectory dictated by a set of variables, a number of derived parameters, such as time of flight between arrival and destination planet, date of arrival, and launch velocity, are computed. A commonly-used evolutionary multi-objective optimization algorithm (NSGA-II) is then employed to find a set of trade-off solutions. The accuracy of the developed software (we called GOSpel) is demonstrated by matching the trajectories with known missions

Multiobjective design of gravity-assist trajectories via graph transcription and dynamic programming

Multiple gravity-assist (MGA) trajectory design requires the solution of a mixed-integer programming problem to find the best sequence among all possible combinations of candidate planets and dates for spacecraft maneuvers. Current approaches require computing times rising steeply with the number of control parameters, and they strongly rely on narrow search spaces. Moreover, the challenging multiobjective optimization needs to be tackled to appropriately inform the mission design with full extent of launch opportunities. This paper describes a methodology based upon a trajectory model to transcribe the mixed-integer space into a discrete graph made by grids of interconnected nodes. The model is based on Lambert arc grids obtained for a range of departure dates and flight times between two planets. A Tisserand-based criterion selects planets to pass by. Dynamic programming is extended to multiobjective optimization of MGA trajectories and used to explore the graph, guaranteeing Pareto optimality with only moderate computational effort. Robustness is ensured by evaluating the relationship between graph and mixed-integer spaces. Missions to Jupiter and Saturn alongside challenging comet sample return transfers involving long MGA sequences are discussed. These examples illustrate the robustness and efficiency of the proposed approach in capturing globally optimal solutions and wide Pareto fronts on complex search spaces.Airbus