A graph-based framework of low-energy transfer design

Exploring the solution space of low-energy transfer trajectories in the multi-body gravitational environment is a challenging task. The highly nonlinear dynamics and many degrees of freedom of control inputs lead to avast variety and number of possible solutions. This paper develops a graph-based framework for computing low- energy transfer trajectories in a multi-objective fashion. The graph nodes are represented by the periapsis states and their connectivity is evaluated by the fixed-time-of-arrival method. This paper introduces special apsis conditions, with which pivotal dynamical objects in the low-energy regime such as the zero-velocity surface, the recently identified barrier surface, and symmetric periodic orbits associate, to generate the periapsis states in a practical manner. Initial guess solutions are obtained as shortest paths in the graphs that are optimized to minimize the fuel cost. The framework is shown to be effectively applicable to distinct phase-space regions in a unified manner demonstrating its versatility in the complex dynamical environment. This paper finds new Pareto solutions in the halo-to-halo transfer problem as well as the high-energy excursion technique that enhances the flyby effect in the multi-flyby transfer problem as by-products of the applications.