  Precise soft landings on asteroids are central to many deep space missions
for surface exploration and resource exploitation. To improve the autonomy and
intelligence of landing control, a real-time optimal control approach is
proposed using deep neural networks (DNN) for asteroid landing problems wherein
the developed DNN-based landing controller is capable of steering the lander to
a preselected landing site with high robustness to initial conditions. First,
to significantly reduce the time consumption of gravity calculation, DNNs are
used to approximate the irregular gravitational field of the asteroid based on
the samples from a polyhedral method. Then, an approximate indirect method is
presented to solve the time-optimal landing problems with high computational
efficiency by taking advantage of the designed gravity approximation method and
a homotopy technique. Furthermore, five DNNs are developed to learn the
functional relationship between the state and optimal actions obtained by the
approximate indirect method, and the resulting DNNs can generate the optimal
control instructions in real time because there is no longer need to solve the
optimal landing problems onboard. Finally, a DNN-based landing controller
composed of these five DNNs is devised to achieve the real-time optimal control
for asteroid landings. Simulation results of the time-optimal landing for Eros
are given to substantiate the effectiveness of these techniques and illustrate
the real-time performance, control optimality, and robustness of the developed
DNN-based optimal landing controller.
