Rendezvous Trajectory Control Laws in Low Earth Orbit Using Neural ODE for Continuous System Deep Learning

Abstract

Neural ordinary differential equation (ODE) is a deep learning method that can represent continuous dynamics. Unlike general deep learning approaches, neural ODE comprises functions expressed by ordinary differential equations as layers, with similarities found between its learning algorithm and the solution of optimal control problems. The authors exploited this feature for an autonomous lunar landing trajectory control law and demonstrated effective control without relying on a reference trajectory in a previous study. The present study is conducted to further investigate the effectiveness of neural ODE for optimal control problems with higher degrees of freedom by applying it to a rendezvous trajectory control law in low Earth orbit, and evaluating the effects of deep learning parameter settings on the convergence and robustness of the algorithm.