Application of Neural Ordinary Differential Equations to Trajectory Control Laws for Lunar Landing

This paper proposes a new methodology that applies neural ordinary differential equations (ODEs) to spacecraft trajectory control laws. Neural ODEs are deep learning algorithms that represent the solutions to a system of ODEs in the form of deep neural networks, utilizing the derivatives of the hidden state instead of specifying a discrete sequence of hidden layers in neural networks. Neural ODEs have such notable features as the ability to learn continuous dynamics and the flexibility to incorporate data that may appear at any time, unlike recurrent neural networks, which require discretization of observation and emission intervals and high memory efficiency. This study extended this mechanism to design control laws for trajectory control, particularly aiming at applying neural ODEs to lunar landing. The proposed method offers various advantages over conventional control methods, including developing robust control laws that achieve the objective in any state without relying on a reference trajectory. In contrast, conventional control methods require the spacecraft to follow a reference trajectory, making it difficult to recover from deviations. Similarities are found between the processes of deriving control laws by neural ODEs and of solving optimal control problems by indirect methods. Such features make neural ODEs particularly suitable and interesting for various navigation guidance control and optimization problems, warranting future development.