A NEURAL KOOPMAN FRAMEWORK FOR CUBESAT ATTITUDE CONTROL USING QUATERNION REPRESENTATION

Abstract

CubeSats have gained significant attention due to their lowcost and versatile applications. However, their low inertia makes them highly susceptible to disturbances, such as magnetic torques and residual atmospheric drag, and introduces significant nonlinearity into their rotational dynamics. Attitude Determination and Control Systems (ADCS) are critical in addressing these challenges as they continuously monitor and adjust the CubeSat's orientation to ensure that communication antennas, sensors, and solar panels remain properly aligned. Traditional control approaches have either resorted to computationally intensive nonlinear controllers or employed linearization techniques that fail to capture the underlying nonlinear dynamics, especially during non-unit quaternion, which may happen due to numerical errors or sensor noise. In this work, we present a framework that leverages the Koopman operator theory to map the nonlinear dynamics of CubeSat attitude determination and control into a higher-dimensional linear space. By employing deep neural networks as lifting functions, our method is designed to automatically extract rich feature representations of the CubeSat's state. While a control-aware loss function, integrating prediction, reconstruction, linearity, and infinity losses, ensures accurate state reconstruction and robust dynamic modeling. Simulation data, generated using diverse initial conditions and multiple excitation inputs, such as multi-sine signals, pseudorandom binary sequences and Gaussian white noise, underpin our training process, enabling the model to capture a broad operational domain. The resulting Koopman-based model not only achieves high fidelity in predicting state evolution but also facilitates the design of efficient linear controllers. We demonstrate the practical efficacy of our approach by implementing a Linear Quadratic Regulator (LQR) in the lifted space, which successfully stabilizes the CubeSat's quaternion states even under conditions where traditional linearization fails. Our results suggest that the integration of Koopman operator theory with deep learning presents a promising pathway toward overcoming the limitations of conventional control strategies for CubeSats. Furthermore, it paves the way for future extensions, such as incorporating advanced control schemes like Model Predictive Control (MPC). Overall, this work contributes a robust, data-driven framework for CubeSat attitude control that offers both theoretical insights and practical improvements, potentially transforming control system design for next-generation small satellites.