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This paper investigates the asteroid hovering problem using the Multiple-Overlapping-Horizon Multiple-Model Predictive Control method. The effectiveness of the predictive controllers in satisfying control constraints and minimizing the required control effort is making Model Predictive Control a desirable control method for asteroid exploration missions which consist of the asteroid hovering phase. However, the computational burden of Model Predictive Control is an obstacle to employing the asteroid's complex gravitational field model. As an alternative option, the Multiple Horizon Multiple-Model Predictive Control method has been introduced previously, which could provide a solution with the less computational burden with respect to the nonlinear Model Predictive Control. It was shown that it is not necessary to deduce the exact dynamics model to predict the system's behavior during a long period using this approach. However, the calculated control acceleration was not smooth enough because of the crisp borders of consecutive horizons, which may cause an image motion and degrades the geometric accuracy of high-resolution images in asteroid hovering missions. In this paper, the Multiple-Overlapping-Horizon Multiple-Model Predictive Control method is introduced instead to solve the problem of controlling acceleration fluctuations by overlapping consecutive horizons. Numerical simulation results are presented to validate the effectiveness of the proposed control method, and its advantage is demonstrated accordingly for the asteroid hovering problem in achieving the hovering position and velocity. [ABSTRACT FROM AUTHOR]

Hovering over an asteroid is challenging due to both the large gravitational uncertainty and the strong external disturbance. When a spacecraft is not equipped with velocity sensors to simplify the navigation system and reduce the mass and costs, or the velocity sensors malfunction, the situation may be worse. In this paper, an extended state observer (ESO) is devised to estimate the velocity and the lumped disturbance simultaneously. The estimate errors are proved to be uniformly ultimately bounded with the assumption that the change rate of the lumped disturbance is bounded. To cope with control input saturation, a backstepping controller in conjunction with an auxiliary system is proposed for the hovering. Combining the controller with the ESO, we develop a disturbance rejection control scheme without velocity feedback. The stability of the whole closed-loop system is analyzed via the Lyapunov theory, showing that the control scheme can drive a spacecraft to the neighborhood of the desired hovering state. The numerical simulations of both body-fixed hovering and inertial hovering are conducted to demonstrate the effectiveness of the proposed scheme.