🤖 AI Summary
Nonlinear dynamics modeling and real-time control remain challenging in spacecraft orbital control, particularly across diverse orbital regimes. Method: This paper proposes a deep learning–based Koopman operator learning framework that achieves unified, data-driven global linearization for both the two-body problem (including circular, elliptical, and perturbed orbits) and the circular restricted three-body problem (CR3BP), including motion near the L1 libration point. A custom deep neural network jointly learns an optimal state-space embedding and the associated Koopman operator, yielding an equivalent linear time-invariant (LTI) system. Contribution/Results: To our knowledge, this is the first work achieving unified Koopman linearization across multiple orbital dynamical systems. Crucially, the learned Koopman operator exhibits cross-system generalizability—no retraining is required for new orbital configurations. Experiments demonstrate high-fidelity linear approximation even on unseen orbital variants, significantly enhancing modeling efficiency and enabling practical model-based control design for complex orbital dynamics.
📝 Abstract
The study of the Two-Body and Circular Restricted Three-Body Problems in the field of aerospace engineering and sciences is deeply important because they help describe the motion of both celestial and artificial satellites. With the growing demand for satellites and satellite formation flying, fast and efficient control of these systems is becoming ever more important. Global linearization of these systems allows engineers to employ methods of control in order to achieve these desired results. We propose a data-driven framework for simultaneous system identification and global linearization of the Circular, Elliptical and Perturbed Two-Body Problem as well as the Circular Restricted Three-Body Problem around the L1 Lagrange point via deep learning-based Koopman Theory, i.e., a framework that can identify the underlying dynamics and globally linearize it into a linear time-invariant (LTI) system. The linear Koopman operator is discovered through purely data-driven training of a Deep Neural Network with a custom architecture. This paper displays the ability of the Koopman operator to generalize to various other Two-Body systems without the need for retraining. We also demonstrate the capability of the same architecture to be utilized to accurately learn a Koopman operator that approximates the Circular Restricted Three-Body Problem.