# Real-Time Optimal Control for Irregular Asteroid Landings Using Deep Neural Networks

## TL;DR

This paper introduces a deep neural network-based control system for real-time, precise asteroid landings, significantly improving computational efficiency and robustness compared to traditional methods.

## Contribution

It develops a novel DNN-based approach that approximates asteroid gravity fields and learns optimal control actions, enabling real-time, robust asteroid landing control.

## Key findings

- DNNs accurately approximate irregular asteroid gravity fields
- The control system achieves real-time optimal landings in simulations
- The approach demonstrates high robustness to initial conditions

## Abstract

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.