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Sparse Optimal Trajectory Design in Three-Body Problem

Abstract

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.

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Funding

The work of the first author was partially supported by JSPS KAKENHI Grant Number JP19J11762. The work of the second author was partially supported by JSPS KAKENHI Grant Number JP21K18781.

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Correspondence to Yuki Kayama.

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Kayama, Y., Bando, M. & Hokamoto, S. Sparse Optimal Trajectory Design in Three-Body Problem. J Astronaut Sci (2022). https://doi.org/10.1007/s40295-022-00315-1

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  • DOI: https://doi.org/10.1007/s40295-022-00315-1

Keywords

  • Sparse optimal control
  • Circular restricted three-body problem
  • Dynamical systems theory
  • Linear quadratic regulator