Predictive control algorithm for spacecraft rendezvous hovering phases

The paper proposes a predictive control law for orbital rendezvous hovering phases. The proposed algorithm provides an impulsive control that steer the vehicle to a set of the periodic relative orbits enclosed in a hovering zone. The control law is computed by determining a point lying in the intersection between a semi-algebraic set and a hyperplane using an alternating projections algorithm. The present work proposes several improvement compare to previous published works based on a two-impulse strategy: the control consists of one impulse instead of two, the periodic and admissible orbit that the chaser is steered to is not defined a priori, and the budget and saturation conditions are taken into account. The efficiency of the proposed predictive control algorithm is bench tested on a nonlinear simulator.