Drag-based analytical optimal de-orbiting guidance from low earth orbit via Deep Neural Networks

Controlled de-orbiting is crucial for a low earth orbiting (LEO) satellite or capsule intending to land in a desired location and to prevent damage to people and property on the ground caused by debris. Drag modulation is one possible mechanism to control de-orbiting, exploiting atmospheric drag variation to reduce the necessary orbital energy from the initial conditions to the re-entry interface. In this context, this paper proposes a novel targeted de-orbiting Artificial Neural Network (ANN) and drag-based guidance algorithm for a LEO artificial satellite. It relies on the combination of empirical and analytical relations with Deep Neural Networks (DNNs) to estimate the main parameters of the optimal control law in real time. The training set is composed of several optimal control solutions generated with a previously developed optimal control algorithm, exploiting the formulation in equinoctial modified orbital parameters to manage the large time scale of the problem and the computational cost. An innovative procedure for the training set generation led to the achievement of general results with a limited number of samples. The successful outcome of the guidance algorithm on over 1000 cases demonstrates its robustness and generalization of results. To conclude, a Linear Quadratic Regulator (LQR) feedback control is applied to one case to deal with a more realistic and uncertain density model.