Areostationary Satellite Station Keeping Via a Natural Motion Trajectory and Predictive Control

Abstract

Areostationary Mars orbit (AMO) satellites will play an important role in future expeditions to the Martian surface due to their strength as navigation and communication satellites. Perturbative forces experienced by an AMOR satellite will cause it to drift from its nominal orbit, necessitating station keeping. This note presents a novel approach to AMO station keeping that bridges the gap seen in prior predictive control methods between fuel-efficiency and computational-efficiency. The method proposed in this notes involves the discovery and use of a fuel-free natural motion trajectory that maintains the satellite within one degree of longitude from a areostationary orbit. Two of these natural motion trajectories exist as limit cycles about Mars' stable equilibrium longitudes. They are the resulting motion in the presence of Mars' non-homogeneous gravitational field, accounting for Keplerian and higher-order gravitational perturbations. The proposed MPC policy uses a linear time-varying (LTV) dynamic model that is derived by linearizing the satellite's dynamics relative to the appropriate natural motion trajectory. The result is a station keeping policy that minimizes the fuel consumed, maintains thrust and station-keeping constraints, and is computationally tractable for on-board implementation as a quadratic program.

Figures (3)

• Figure 1: The natural motion trajectory caused by spherical harmonic perturbations about $17.92^\circ$ West.
• Figure 2: Simulated year of the proposed station-keeping policy tracking the natural motion trajectory.
• Figure 3: Control inputs during a simulated year of the proposed station-keeping policy tracking the natural motion trajectory.