Physics-informed Neural Network for Quadrotor Dynamical Modeling

The explosive growth of civil applications of Unmanned Aerial Vehicles (UAVs) calls for control algorithms that enable safe and trustworthy operations, especially in complex environments to facilitate real-world deployment. Although Model-Based Control (MBC) has found great applicability in the last decades, it relies heavily on the accuracy of the underlying mathematical models. Thanks to their powerful approximation capability, datadriven approaches such as Artificial Neural Networks (ANNs) have raised a great interest in UAV dynamical modeling in recent years. Despite the promising results achieved in learning either full or partial dynamics such as aerodynamic effects, prior studies merely pay little to no attention to the black-box nature of ANNs, yielding poorly interpretable learning processes and implying a lack of generalization capability due to undesirably learned spurious relationships among features and labels. While nowadays practitioners and society are far from being concerned just with performance, such risk evidently reduces the overall trustworthiness of the control system with ANNs as control-oriented models. With the goal of both accurate and interpretable neural modeling of nonlinear dynamics, we propose a novel modeling approach that utilizes Physics-Informed Neural Networks (PINN), designed to seamlessly embed physical laws into Deep Neural Networks (DNN). To further enhance model interpretability, we adopt the Covariance Confidence Ellipse (CCE) as post-hoc visualization to help understand the model behavior. We also set up a visual and physical simulator based on AirSim with custom implementation on quadrotor ground effect, which is made publicly available to facilitate further experiments for the community. An extensive simulation campaign validates our approach on data sets including aerodynamics and periodic wind, highlighting advantages regarding the accuracy and physical consistency, pointing to further insight on the development of learning-based control-oriented models for quadrotors, and facilitating flight controller design with performance guarantees.