Sparse optimal trajectory design in three-body problem

A structure of the optimal trajectory for minimizing fuel consumption in an unstable dynamical environment such as the three-body problem is not well studied. Recently, it has been found that a sparse solution structure appears in the optimal control of a dynamical system. The concept of sparsity explains the property that the minimum fuel trajectory corresponds to the trajectory which minimizes the total thrusting time. In this paper, we propose a numerical method to obtain the minimum fuel sparse optimal trajectory in the unstable dynamical system. As an example, proposed methods are applied to the transfer in the Sun-Earth system.