Relative and absolute on-board optimal formation acquisition and keeping for scientific activities in high-drag low-orbit environment

In this paper, a novel Model Predictive Control (MPC) technique for multi-satellite formation flying geometry acquisition and maintenance in high-drag environment is presented. The proposed MPC relies on a linearized and convexified quasi-nonsingular Relative Orbital Elements (ROE) model based on state transition matrices propagation, allowing to include the effect of perturbations in the prediction to optimize fuel efficiency and tracking accuracy. The formation is controlled with respect to a non-decaying orbiting point to perform absolute and relative station keeping simultaneously. For this purpose, a new dedicated plant matrix to include drag effects on ROE in the propagation is derived and validated with respect to numerical results. In all simulations, the satellites are assumed to be equipped with a single low-thrust propulsion unit, therefore, specific constraints are included in the controller to obtain a feasible solution in a real operational scenario. Moreover, a collision avoidance constraint is added in case of close proximity operations exploiting a linear mapping between the set of ROE and cartesian coordinates expressed in the Local-Vertical-Local-Horizontal (LVLH) reference frame. The controller response is simulated in several realistic mission contexts with a high-fidelity orbital propagator and the results are validated for fuel efficiency by comparing them to similar approaches available in literature and to optimal solutions obtained respectively with a direct single shooting algorithm and with a closed-form impulsive formulation.