Incremental solution of LTMGA transfers transcribed with an advanced shaping approach

In the last decade the global optimisation of low-thrust multi-gravity assist transfers (LTMGA) has been tackled with different approaches. Some authors proposed to generate a first guess solution by building a multi-gravity assist transfer with impulsive manoeuvres and then using a direct or an indirect method to transcribe the multi-impulse arcs into low-thrust arcs. Other authors, notably Petropoulos et al. (2002), De Pascale et al. (2006), Wall et al. (2008) and Schütze et al. (2009), proposed the use of several forms of trajectory shaping to model low-thrust arcs. The disadvantage in all these studies is that the swingbys are powered and therefore suggest the use of high thrust propulsion along with the low thrust propulsion on board the spacecraft. The problem generally resides in the lack of flexibility of the low thrust trajectory models to satisfy a variety of boundary conditions. In this paper, a spherical shaping model is used whereby all encountered types of boundary constraints are satisfied analytically. Furthermore, a special incremental pruning of the search space is performed before employing a global optimiser. The process is conceptually equivalent to the approach proposed by Becerra et al. for the search space pruning of multi-gravity assist trajectories and exploits the decoupling of pairs of transfer arcs. Such decoupling removes the dependency of one arc from all those that are two or more before, and allows for pruning the search space in polynomial time. Numerical examples are presented for LTMGA transfers from Earth to asteroid Apollo and Earth to Jupiter