Constrained global optimization of low-thrust interplanetary trajectories

The optimization of spacecraft trajectories can be formulated as a global optimization task. The complexity of the problem depends greatly on the problem formulation, on the spacecraft route to its final target planet, and on the type of engine and power system that is available on-board the spacecraft. Few attempts have been made to use a global optimization framework to design trajectories that make use of electric propulsion to propel the spacecraft between planets because of the large scale and extreme complexity of the resulting nonlinear programming problem. The presence of a high number of nonlinear constraints, in particular, requires a special attention with respect to the global optimization technique adopted. Here we use the Sims-Flanagan transcription method to produce the nonlinear programming problem and we make use of two global optimization algorithms, basin hopping and simulated annealing with adaptive neighborhood to attempt exploring efficiently the solution space. Both algorithms are hybridized with a local search. We consider two different interplanetary trajectories, an Earth-Earth-Jupiter transfer and an Earth-Earth-Earth-Jupiter transfer with a nuclear electric propulsion spacecraft inspired by the Jupiter Icy Moons Orbiter. For both problems, our approach is able to explore automatically the vast solution space producing a large number of trajectories in a large range of final mass and flight times.