Real-Time Optimal Guidance and Control for Interplanetary Transfers Using Deep Networks

Abstract

We consider the Earth-Venus mass-optimal interplanetary transfer of a low-thrust spacecraft and show how the optimal guidance can be represented by deep networks in a large portion of the state space and to a high degree of accuracy. Imitation (supervised) learning of optimal examples is used as a network training paradigm. The resulting models are suitable for an on-board, real-time, implementation of the optimal guidance and control system of the spacecraft and are called G&CNETs.A new general methodology called "Backward Generation of Optimal Examples" is introduced and shown to be able to efficiently create all the optimal state action pairs necessary to train G&CNETs without solving optimal control problems. With respect to previous works, we are able to produce datasets containing a few orders of magnitude more optimal trajectories and obtain network performances compatible with real missions requirements. Several schemes able to train representations of either the optimal policy (thrust profile) or the value function (optimal mass) are proposed and tested. We find that both policy learning and value function learning successfully and accurately learn the optimal thrust and that a spacecraft employing the learned thrust is able to reach the target conditions orbit spending only 2 more propellant than in the corresponding mathematically optimal transfer. Moreover, the optimal propellant mass can be predicted (in case of value function learning) within an error well within 1%. All G&CNETs produced are tested during simulations of interplanetary transfers with respect to their ability to reach the target conditions optimally starting from nominal and off-nominal conditions.

Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks

“…To cite some examples, it was employed in [17] to derive low−thrust fuel−optimal trajectories, in [18] to calculate fuel−optimal low−thrust Earth−orbit transfers, accounting for shadow eclipses, and in [19] to study fuel optimal soft landing trajectories on asteroids. As an example of the logarithmic perturbing function, it is exploited by Izzo and Öztürk [20] to obtain the fuel−optimal trajectories required to build a dataset and train a Deep Neural Network (DNN) in a supervised fashion. The resulting model appears to hold promise for the potential real−time onboard implementation of an optimal guidance and control system for a spacecraft.…”