Low-thrust trajectory design as a constrained global optimization problem

Abstract

The design of a spacecraft trajectory can be formulated as a global optimization task. The complexity of the resulting problem depends greatly on the final target planet, the chosen spacecraft intermediate route, and the type of engine and power system available on-board. Few attempts have been made to directly use a global optimization framework to design trajectories that make use of low-thrust propulsion because of the large scale and extreme complexity of the resulting non-linear programming problem. The presence of non-convex constraints, in particular, requires the use of solvers able to deal with such an added complexity. Here, the Sims–Flanagan transcription method is proposed to model the low-thrust trajectory design as a constrained global optimization problem. Then, two different solvers are applied: basin hopping and simulated annealing with adaptive neighbourhood. Both algorithms are hybridized with a local search. Two different interplanetary trajectories are considered: an Earth–Earth–Jupiter transfer with a nuclear electric propulsion spacecraft inspired by the Jupiter Icy Moons Orbiter and a transfer to Mercury inspired by the BepiColombo mission. For both problems, the proposed approach proves to be able to explore automatically the vast solution space, producing a large number of trajectories in a large range of final mass and flight times, proving the possibility to apply global optimization techniques directly to the low-thrust problem.