Energy-based Regularization for Learning Residual Dynamics in Neural MPC for Omnidirectional Aerial Robots

arXiv cs.RO / 4/17/2026

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Key Points

The paper proposes an energy-based regularization loss for Neural MPC, targeting residual dynamics learning in an omnidirectional aerial robot where physical properties are otherwise hard for neural models to capture.
By encouraging control corrections that stabilize the system’s energy, the method improves how residual dynamics are integrated into the MPC optimization loop.
Experiments on real-world flights show a 23% improvement in positional mean absolute error (MAE) versus an analytical MPC baseline, and up to 15% lower MAE versus a standard neural MPC without regularization.
The authors report that flight stability is also improved, largely as an implicit benefit of the energy regularization during training.
The implementation code is made available on GitHub, enabling reproducibility and further experimentation.

Abstract

Data-driven Model Predictive Control (MPC) has lately been the core research subject in the field of control theory. The combination of an optimal control framework with deep learning paradigms opens up the possibility to accurately track control tasks without the need for complex analytical models. However, the system dynamics are often nuanced and the neural model lacks the potential to understand physical properties such as inertia and conservation of energy. In this work, we propose a novel energy-based regularization loss function which is applied to the training of a neural model that learns the residual dynamics of an omnidirectional aerial robot. Our energy-based regularization encourages the neural network to cause control corrections that stabilize the energy of the system. The residual dynamics are integrated into the MPC framework and improve the positional mean absolute error (MAE) over three real-world experiments by 23% compared to an analytical MPC. We also compare our method to a standard neural MPC implementation without regularization and primarily achieve a significantly increased flight stability implicitly due to the energy regularization and up to 15% lower MAE. Our code is available under: https://github.com/johanneskbl/jsk_aerial_robot/tree/develop/neural_MPC.