Optimal real-time landing using deep networks

Optimal trajectories for spacecraft guidance, be it during orbital transfers or landing sequences are often pre-computed on ground and used as nominal desired solutions later tracked by a secondary control system. Linearization of the dynamics around such nominal profiles allows to cancel the error during the actual navigation phase when the trajectory is executed. In this study, instead, we assess the possibility of having the optimal guidance profile be represented on-board by a deep artificial neural network trained, using supervised learning, to represent the optimal control structure. We show how the deep network is able to learn the structure of the optimal state-feedback outside of the training data and with great precision. We apply our method to different interesting optimal control problems, a multicopter time and power optimal pinpoint landing control problem and two different mass optimal spacecraft landing problems. In all cases, the deep network is able to safely learn the optimal state-feedback, also outside of the training data, making it a viable candidate for the implementation of a reactive real-time optimal control architecture.