Sparse Optimal Trajectory Design in Three-Body Problem

• Published in: The Journal of the astronautical sciences Vol. 69; no. 3; pp. 829 - 856
• Main Authors: Kayama, Yuki, Bando, Mai, Hokamoto, Shinji
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Aerospace Technology and Astronautics; Canonical forms; Convexity; Dynamical systems; Engineering; Linearization; Mathematical Applications in the Physical Sciences; Nonlinear dynamics; Optimal control; Orbits; Original Article; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Three body problem; Trajectory optimization; Circular restricted three-body problem; Dynamical systems theory; Linear quadratic regulator; Sparse optimal control
• ISSN: 2195-0571; 0021-9142; 2195-0571
• DOI: 10.1007/s40295-022-00315-1

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.