Stable Model Predictive Strategy for Rendezvous Hovering Phases Allowing for Control Saturation

Abstract

This paper presents a model predictive control strategy for the spacecraft rendezvous hovering phases. Using a sequence of impulsive velocity changes, the spacecraft is controlled to reach and remain on a periodic trajectory inside a given box-type hover zone, while minimizing the fuel consumption. The path constraints (box type and periodicity) are satisfied continuously in time based on a particular parameterization of the linearized relative spacecraft trajectories. The control saturation constraint is enforced by replanning. First, a sequence of saturated impulsive controls is selected, such that the spacecraft gets on a periodic trajectory. Second, a fixed-length sequence of saturated impulses brings the spacecraft closer to the hover zone. The convergence of this approach is proved. Numerical methods are proposed to solve the required constrained optimization problems. Finally, hardware-in-the-loop simulations, using a synthesized LEON3 microprocessor, are performed to assess the efficiency and robustness of the proposed approach.