Trajectory design of multi-target missions via graph transcription and dynamic programming. - Bellome, Andrea (Cranfield University, 2022)
Missions that can visit multiple orbital targets represent the next cornerstone for space travels, be it for science, exploration or even exploitation. The trajectory design of such missions requires to solve a mixed-integer programming problem, on which the selection of a proper sequence of targets depends upon the quality of the trajectory that links them, where quality usually refers to propellant consumption or mission duration. Two aspects are important when addressing these problems. The first one is to identify optimal solutions with respect to critical mission parameters. Current approaches to solve these problems require computing time that rises with the number of control parameters, as the visiting objects sequence length, as well as rely on a-priori knowledge to define a manageable design space (i.e., departing dates, presence of deep space manoeuvres, etc.). Moreover, the more challenging multi-objective optimization needs to be tackled to ap- propriately inform the mission design with full extent of launch opportunities. The second aspect is that beyond the obvious complexity of such problems formulation, preliminary mission design requires not only to locate the global optimum solutions but, also, to map the ensemble of solutions that leads to feasible transfers. This thesis describes a pipeline to transcribe the mixed-integer space into a discrete graph made by grids of interconnected nodes for missions that visit multiple celestial objects, like planets, asteroids, comets, or a combination thereof, by means of one single space- craft. This allows to exploit optimal substructure of such problems, opening dynamic programming to be conveniently applied. Dynamic programming principles are thus ex- tended to multi-objective optimization of such trajectories and used to explore the tran- scribed graph, guaranteeing Pareto optimality with efficient computational effort. A mod- ified dynamic programming approach is also derived that allows to retain more and diverse solutions in the final set compared to known standard approaches, while guaranteeing global optimality on the transcribed space. Numerous applications are presented where such pipeline is successfully applied. Tra- jectories towards Jupiter and Saturn alongside novel transfers for comet sample return missions are discussed, as well as trajectories that visit multiple asteroids in the main belt. Such scenarios prove robustness and efficiency of proposed approaches in capturing optimal solutions and wide Pareto fronts on search spaces of complex configuration.
Keywords: Mission analysis; combinatorial optimization; dynamic programming; multiple gravity assist; main asteroids belt; mixed-integer programming problem