Neural representation of a time optimal, constant acceleration rendezvous

Abstract

We train two neural models to represent, respectively, the optimal policy (i.e. the optimal thrust direction) and the value function (i.e. the time of flight) for a time optimal, constant acceleration, low-thrust rendezvous. In both cases we develop and make use of the data augmentation technique we call backward generation of optimal examples. We are thus able to produce and work with large dataset and to fully exploit the benefit of employing a deep learning framework. We achieve, in all cases, accuracies resulting in successful rendezvous (simulated following the learned optimal policy) and time of flight predictions (using the learned value function). We find that residuals as small as a few m/s, thus well within the possibility of a spacecraft navigation ΔV budget, are achievable for the velocity at rendezvous. We also find that, on average, the absolute error to predict the optimal time of flight to rendezvous from any orbit in the asteroid belt to an Earth-like orbit is small (less than 4%) and thus also of interest for practical uses, for example, during preliminary mission design phases.