Search-based method optimization applied to bi-impulsive orbital transfer

In this paper optimal bi-impulse orbital transfer between coplanar and non-coplanar elliptical orbits has been considered. First, an efficient algorithm based on grid search method has been developed to find the global solution of the impulsive orbital transfer. There are three independent parameters in this algorithm: i) the angular position of the point on the initial orbit where the first impulse is applied to, ii) the angular position of the point on the final orbit where the second impulse is applied to and, iii) the argument of periapsis of the transfer orbit. The other parameters can be obtained from these three parameters in both coplanar and non-coplanar cases. The algorithm is able to obtain the global optimal solution for any arbitrary initial and final elliptical orbits. Second, the algorithm is employed to solve an extensive set of numerical examples, including coplanar and non-coplanar, co-axial and non-co-axial orbits of different shape and energy. This comprehensive set of examples allows disentangling the roles of each relevant orbital parameter in the evaluation of the optimal transfer. Finally, the numerical results are employed to achieve a very precise fitting function which is helpful onboard calculation and mission design.