RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network (2209.09025v3)

Abstract: Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional constraints, increasing the hardness of the problem. The problem exacerbates in performance-critical applications, when more compute is required in lesser time. Data-driven regression methods such as Neural Networks have been proposed in the past to approximate system dynamics. However, such models rely on high volumes of labeled data, in the absence of symbolic analytical priors. This incurs non-trivial training overheads. Physics-informed Neural Networks (PINNs) have gained traction for approximating non-linear system of ordinary differential equations (ODEs), with reasonable accuracy. In this work, we propose a Robust Adaptive MPC framework via PINNs (RAMP-Net), which uses a neural network trained partly from simple ODEs and partly from data. A physics loss is used to learn simple ODEs representing ideal dynamics. Having access to analytical functions inside the loss function acts as a regularizer, enforcing robust behavior for parametric uncertainties. On the other hand, a regular data loss is used for adapting to residual disturbances (non-parametric uncertainties), unaccounted during mathematical modelling. Experiments are performed in a simulated environment for trajectory tracking of a quadrotor. We report 7.8% to 43.2% and 8.04% to 61.5% reduction in tracking errors for speeds ranging from 0.5 to 1.75 m/s compared to two SOTA regression based MPC methods.

• The paper introduces RAMP-Net, a novel MPC framework that combines physics-informed neural networks with data-driven techniques to enhance quadrotor control.
• It demonstrates a reduction in tracking errors by up to 43.2% and faster convergence, validating its robustness against dynamic uncertainties.
• The method balances physics-based and data-driven losses, improving training efficiency and generalizing well to diverse flight trajectories.

Robust Adaptive MPC for Quadrotors via Physics-informed Neural Networks: An Insightful Overview

The paper "RAMP-Net: A Robust Adaptive MPC for Quadrotors via Physics-informed Neural Network" presents a novel approach in the application of Model Predictive Control (MPC) techniques to the control of quadrotors. Traditional MPC methods, while effective, face challenges when addressing uncertain dynamic disturbances, which are prevalent in high-speed, performance-critical applications like drone navigation.

In this work, RAMP-Net is proposed, a Robust Adaptive MPC framework that leverages Physics-informed Neural Networks (PINNs) to incorporate both data-driven and analytical modeling for controlling quadrotors. This method aims to overcome the limitations of classical MPC techniques, which struggle with computational demands and robustness in the presence of dynamic uncertainties.

Key Contributions

1. Combined Physics and Data-driven Modeling: The paper introduces a novel PINN-based approach where the neural network is trained using both simple ordinary differential equations (ODEs) representing the ideal system dynamics and data gathered from simulated environments infused with uncertainties. This dual training methodology ensures that the network learns robust behavior from the physical model while adapting to real-world disturbances not fully captured by the analytical model.
2. Reduction in Tracking Errors: Experimental results demonstrate significant improvements in tracking accuracy. The RAMP-Net method reports a 7.8% to 43.2% reduction in tracking errors for speeds ranging from 0.5 to 1.75 m/s compared to two state-of-the-art (SOTA) regression-based MPC methods. This reduction highlights the effectiveness of the proposed method in maintaining accuracy under varying conditions.
3. Training Efficiency: The paper addresses the training overhead by balancing the use of physics-based losses with data-driven losses. The experiments show that a careful tuning of the ratio of data points to collocation points (data-skewness) can significantly enhance the training efficiency and accuracy of the neural network, achieving around 60% lesser training error and 11% faster convergence.

Theoretical and Practical Implications

The integration of Physics-informed Neural Networks into the MPC framework for quadrotors offers several critical theoretical and practical advantages:

• Enhanced Robustness: By coupling physical models with data-driven techniques, the proposed approach achieves higher robustness and generalizes better across different flight conditions compared to purely data-driven or purely model-based methods.
• Computational Efficiency: The PINN-based approach demonstrates an order of magnitude lower latency in forward propagation times compared to standard numerical integration methods, making it highly suitable for real-time control applications.
• Scalability and Generalization: The method's ability to generalize to unseen flight trajectories (like lemniscate paths) beyond the training conditions reinforces its potential applicability in diverse and dynamic operational environments.

Future Developments

Looking forward, this research opens several avenues for further exploration:

• Scalability to Complex Environments: Extending the framework to more complex and real-world environments, potentially integrating more sophisticated physics models and data from heterogeneous sources.
• Adaptive Learning Schemes: Developing adaptive learning schemes that can continuously update the neural network model in real-time, based on incoming flight data, improving the system's adaptability to evolving environmental conditions.
• Enhanced Model Interpretability: Increasing the interpretability of the neural network outputs by incorporating more sophisticated explainability techniques, which could facilitate better trust and adoption in critical applications.

Conclusion

The "RAMP-Net" framework represents a significant advancement in the field of control systems for quadrotors, merging the strengths of physical modeling and data-driven learning. This integration not only enhances the robustness and efficiency of the MPC but also sets a foundation for future research in applying hybrid modeling techniques to other complex, real-world control problems. The promising results and the potential for scalability mark this work as an essential step towards more adaptive and resilient AI-driven control systems.