Tube-based robust output feedback model predictive control for autonomous rendezvous and docking with a tumbling target

Abstract

In this paper, a tube-based robust output feedback model predictive control method (TRMPC) is proposed for controlling chaser spacecraft docking with a tumbling target in near-circular orbit. The controller contains a simple, stable, Luenberger state estimator and a tube-based robust model predictive controller. Several practical challenges are also considered under dock-enabling conditions, such as the control saturation, velocity constraint, approach corridor constraint, and collision avoidance constraint. Meanwhile, uncertainties are carefully analyzed when designing the controller, including dynamics uncertainty, measurement error, and control deviation. The TRMPC ensures that all possible state trajectories with uncertainties lie in the minimum robust positively invariant set (mRPI, i.e., the so-called tube in this paper). The tube center is the solution of a nominal (without uncertainties) system. Another important contribution of this paper is to propose a technique where it is unnecessary to calculate the mRPI explicitly. Thereby, the ‘curse of dimensionality’ can be avoided for a six-dimensional system. To verify the feasibility of the proposed TRMPC strategy in the presence of uncertainties, two scenarios of autonomous rendezvous and docking (AR&D) are simulated. The simulation results show that the TRMPC method is more efficient in minimizing the uncertainties, fuel consumption, and computational cost, compared to the classic model predictive control (MPC) method.