Robust model predictive control for satellite formation keeping with eccentricity/inclination vector separation

Abstract

Satellite formation flying is one of the most important research subjects in space engineering. It offers benefits compared to a large single satellite, such as

simpler design procedure, low development cost, short development time, and higher redundancy. However, these favorable aspects do not fully account for why satellite formation is garnering a great deal of attention. Its importance grows rapidly as the number of small satellites increases and distributed system concepts such as synthetic aperture radar or optical stellar interferometers are under consideration. These new concepts contribute to transforming satellite formation from a challenging future technology to a real mission operational issue. For complex mission objectives, proximity operation based on relative states is essential to achieve the required formation between more than two satellites. There are several approaches to express relative satellite motions. One of the popular methods is to assume the chief orbit as a perfect circular and linearize dynamics, and more general version with elliptic chief orbit exists also. These approaches linearize the dynamics and there is drawback that the states are not directly related to the absolute orbital states. Using orbit elements as the states is another option for representing relative motions between two satellites. It offers benefits even for the relative dynamics, not only intuitiveness. For example, large distance separation can be replaced by differences in small orbital elements. This approach can be extended to other state representations, including relative eccentricity/inclination vectors. Eccentricity/inclination vector separation has been generally adopted for geostationary satellites with small inclination angles, and extended to low earth orbit satellites applications. Using eccentricity/inclination vectors, an alternative collision avoidance strategy can be implemented by maintaining two vectors in a parallel configuration. The dissertation presents a model predictive controller (MPC) based on a relative eccentricity/inclination vector separation strategy. To maximize the strength of this state representation, a relevant collision avoidance approach is considered and included in the goal function of the MPC controller. To produce real-time control input, the proposed goal function for MPC is convexified. For control input, low thrusters such as ion thrusters are assumed since they have a higher specific impulse than chemical propellants, and therefore are more advantageous for small satellites. Continuous dynamics are extended for eccentricity/inclination vectors from orbit elements’ dynamics using state conversion. The proposed controller is further extended to a robust MPC to consider oscillating terms and possible disturbances as well, because the dynamics usually consider mean-orbital elements only. Constraint tightening approach is each to adopt because of the simplicity, since it requires only the maximum bound of disturbance is given. Using this approach, the robust MPC is applicable to control satellite formations within given constraints even under external disturbances. The robust MPC will guarantee collision avoidance under disturbances, while reconfiguring the formation within the given constraints.