Modified tisserand map exploration for preliminary multiple gravity assist trajectory design

Abstract

Multiple-gravity assist (MGA) trajectories are used in interplanetary missions to change the spacecraft orbital energy by exploiting the gravity of celestial bodies. This allows the spacecraft to reach regions in the Solar System that otherwise would be extremely demanding in terms of propellant. However, if a trajectory seeks to benefit from a long MGA sequence, it is necessary to solve a complex mixed integer programming problem in order to find the best swing-by sequence among all combinations of encountered planets and dates for the various spacecraft manoeuvres. Tisserand graphs provide an efficient way to tackle the combinatorial part of the MGA problem, by allowing a simple computation of the effect of different sequences of gravity assists, based only on energy considerations. Typically, the exploration of Tisserand graphs is performed via a comprehensive Tree Search of possible sequences that reach a specific orbital energy and eccentricity (e.g. Langouski et al.). However, this approach is generally directed by heuristic techniques aimed at finding duration limited, low Δv transfers without formal optimization or time constraint. This results in not having information from Tisserand graphs associated to the trajectory shape, namely the planetary phasing and mission durations. This paper presents a more comprehensive strategy involving the solution of the phasing problem to automatically generate viable ballistic planetary sequences. This approach has proven to be effective in representing trajectory shape already from the Tisserand map exploration step. All the solutions identified by the modified Tisserand map exploration are validated by re-optimizing the complete MGA trajectories as sequences of swing-bys, DSMs and Lambert Arc transfers intersecting the real positions of the planets involved. Different mission scenarios towards Jupiter are used as test cases to validate and demonstrate the accuracy of the Tisserand-based first-guess solutions