An incremental algorithm for fast optimisation of multiple gravity assist trajectories

Multiple gravity assist (MGA) trajectories are essential to reach high gravity targets with low propellant consumption. In mathematical terms, the problem of finding a good first guess solution for the design of a MGA trajectory can be seen as a global optimisation problem. The dimension of the search space, and of the possible alternative solutions, increases exponentially with the number of swing-bys, and the problem is even more complex if deep space manoeuvres are considered. This makes the search for a globally optimal transfer quite difficult. The proposed approach aims at decomposing the main problem into smaller sub-problems, solved incrementally. In fact, starting from the departure planet and flying to the first swing-by planet, only a limited set of transfers are feasible, for example with respect to the maximum achievable. Therefore, when a second leg is added to the trajectory, only the feasible set for the first leg is considered and the search space is reduced. The process iterates by adding one leg at a time and pruning the unfeasible portion of the solution space. The algorithm has been applied to two test cases - an E-E-M transfer and an E-E-V-V-Me transfer - to investigate the efficiency of the exploration of each sub-problem, and the reliability of the space pruning. A comparison to the direct global optimisation of the whole trajectory is shown.