Gravity-assisted maneuvers applied in the multi-objective optimization of interplanetary trajectories

In this work, the problem of optimization of interplanetary trajectories with minimum fuel consumption, but with a time limit is studied. It was used a methodology known as the Patched Conics, where the trajectory is divided into three parts: (1) departure phase, inside of the sphere of influence of the departure planet; (2) heliocentric phase, during the journey between the planets; and (3) arrival phase, inside of the sphere of influence of the arrival planet. Furthermore, the possibility of gravitational assisted maneuvers (swing-by) was considered to reduce fuel consumption. In this case the full trajectory would be divided into more parts, depending on the number of maneuvers. Therefore, the goal of this work is to find a combination of conical trajectories, using gravitational assisted maneuvers, which perform the transfer close to the departure planet to the vicinity of the arrival planet, spending minimal fuel with minimal time for the journey. Considering the minimization of time, the solution cannot be the solution of minimum fuel consumption, because the minimization of time and the minimization of fuel are conflicting objectives. Thus, a multi-objective problem must be solved. Hence, a methodology based on the Non Inferiority Criterion (Pareto, 1909 [2]) and the Smallest Loss Criterion (Rocco et al., 2002 [6]) was used, capable of considering multiple objectives simultaneously, without reducing the problem to the case of optimizing a single objective as occur in most methods found in the literature. A mission to Pluto, similar to NASA’s New Horizons Mission, was studied considering gravitational assisted maneuvers in Mars, Jupiter and Saturn. Simulating the trajectories and the maneuvers using the Transfer Trajectory Design Programs (Sukhanov, 2004 [13]), several possibilities were analyzed for many combinations of fuel consumption, time of departure, time of arrival and planet used for the swing-by. Then, using the Multi-objective Optimization Program (Rocco et al., 2002 [6]) the problem was solved seeking the best combination. The results can provide good assistance for mission analysis reducing the cost and time.