Learning Robust Satellite Attitude Dynamics with Physics-Informed Normalising Flow

TL;DR

The paper tackles robust satellite attitude control by marrying physics-informed learning with expressive normalizing-flow networks. It introduces a Real NVP-based architecture enhanced with self-attention and trained with a physics-informed loss, integrated into a nonlinear MPC framework. Empirical results show substantial improvements in mean relative error and closed-loop control robustness, including faster settling times—up to about 62% faster than traditional MPC—and strong resilience to observation noise and actuator friction. The approach is validated on Basilisk-simulated data and demonstrates feasible edge-device inference, highlighting practical applicability for autonomous space systems.

Abstract

Attitude control is a fundamental aspect of spacecraft operations. Model Predictive Control (MPC) has emerged as a powerful strategy for these tasks, relying on accurate models of the system dynamics to optimize control actions over a prediction horizon. In scenarios where physics models are incomplete, difficult to derive, or computationally expensive, machine learning offers a flexible alternative by learning the system behavior directly from data. However, purely data-driven models often struggle with generalization and stability, especially when applied to inputs outside their training domain. To address these limitations, we investigate the benefits of incorporating Physics-Informed Neural Networks (PINNs) into the learning of spacecraft attitude dynamics, comparing their performance with that of purely data-driven approaches. Using a Real-valued Non-Volume Preserving (Real NVP) neural network architecture with a self-attention mechanism, we trained several models on simulated data generated with the Basilisk simulator. Two training strategies were considered: a purely data-driven baseline and a physics-informed variant to improve robustness and stability. Our results demonstrate that the inclusion of physics-based information significantly enhances the performance in terms of the mean relative error with the best architectures found by 27.08%. These advantages are particularly evident when the learned models are integrated into an MPC framework, where PINN-based models consistently outperform their purely data-driven counterparts in terms of control accuracy and robustness, and achieve improved settling times when compared to traditional MPC approaches, yielding improvements of up to 62%, when subject to observation noise and RWs friction.

Figures (6)

• Figure 1: A schematic description of the proposed PINN for satellite dynamics learning and attitude control. The PINN models, trained using a weighted sum of the data-driven and physics-informed losses, is used as dynamics model in a non-linear MPC.
• Figure 2: Neural Network architecture diagrams. NVPSA1 (violet flow) uses the output of the Real NVP model to weigh the delta state predicted through a self-attention approach. NVPSA2 (green flow) instead uses the input torque and the inertia matrices of the spacecraft and of the RWs as input of the Query and Key layers. S is the length of the predicted trajectory, in our case $S=10$.
• Figure 3: Attitude MPC with learned dynamics, a schematic of the complete framework.
• Figure 4: Distribution of the results obtained during the experiments to evaluate the effect of different relative weights $\alpha$ and $\beta$ in the loss. We show the results for various ratio of fixed weights ($\alpha / \beta$) and for the Lagrangian dual approach LD.
• Figure 5: 300 MC simulation with parameter estimation errors, state estimation noise and RWs friction for NVPSA2-DD (upper left), NVPSA2-LD (upper right), traditional MPC with linear (lower left) and non-linear (lower right) dynamics.