Sparse Optimal Trajectory Design in Three-Body Problem

This paper proposes the sparse optimal control in the circular restricted three-body problem to exploit the dynamical structure of the linearized motion around equilibrium points or periodic orbits. First, optimal transfer problem is formulated for a linearized system where the objective function and constraints are given by convex sets. For a long time transfer problem in the vicinity of periodic orbits, the Floquet-Lyapunov transformation and a normal form are introduced to enable numerical calculations. Then, the proposed method is applied to several transfer problems around an equilibrium point or periodic orbits and a parameter analysis is performed to understand the optimal transfer by changing the maximum thrust acceleration and time of flight. Finally, a new station-keeping strategy is proposed to implement the sparse optimal solution in a nonlinear dynamics.