Multi-rate Cascade Spacecraft Attitude-Orbit Integrated State Estimation and Control Framework based on MHE and PWA-MPC

This paper develops a unified multi-rate control framework based on piecewise affine model predictive control (PWA-MPC) and moving horizon estimator (MHE) to address the nonlinear attitude and orbit integrated control problem of spacecraft with multiple measurement sampling and control rates. The most notable advantage of this control framework lies in its systematic design method and its ability to effectively suppress attitude disturbances acting orbital dynamics, thereby improving orbital control performance. The reason for the impact is the coupling effect between attitude and orbit, where the source of the coupling effect is the real-time attitude of the spacecraft, which affects the direction of the thrust vector during orbital motion. To account for the interactions between the inner attitude control and outer orbit control, a six-degree-of-freedom spacecraft dynamic model is established, consisting of relative orbital dynamics based on the line-of-sight frame and attitude dynamics described by the Modified Rodrigues Parameters, which is more suited to the actual measurement environment. To estimate states that are not within the measurement period or lack direct measurement, a state estimator based on Moving Horizon Estimation (MHE) is developed. While Kalman estimator requires tuning of the covariance matrix, MHE uses a simpler adjustment of the estimation window size as tuning parameter. It turns out that MHE is easier to tune than Kalman estimator. In addition, simulation results demonstrate that different measurement and control ratio could lead to different control outcomes. The proposed framework provides a convenient means to evaluate this design dimension.