Online Trajectory Regeneration for Multirotors via a Proportional-Derivative Physics-Informed Neural Network

Abstract

This paper presents a novel framework based on a Proportional-Derivative Physics-Informed Neural Network (PD-PINN) for real-time trajectory regeneration. Unlike conventional methods that rely on static, precomputed paths, the proposed approach dynamically adapts the reference trajectory using real-time sensor feedback and the system's physical model. The PD-PINN incorporates proportional-derivative error terms into a physics-informed learning process, where the loss function explicitly embeds the system's governing equations into the backpropagation algorithm. This integration enables physically consistent, control-aware weight updates that preserve dynamic feasibility. The framework is evaluated on a multirotor UAV model under realistic simulation conditions, including sensor noise, wind disturbances, and parametric uncertainty. Results show that PD-PINN reduces the total three-dimensional root mean square error from 0.7178 meters to 0.1352 meters, an 81.2% improvement over classical methods. The normalized control effort also decreases from 82,600 to 78,200, representing a 5.3% reduction. These findings indicate that the proposed method holds strong potential for online operation in autonomous flight scenarios characterized by uncertainty and dynamic environmental changes. The results confirm that PD-PINN enhances trajectory guidance accuracy, robustness, and computational efficiency in multirotor UAVs, making it well-suited for practical applications such as aerial mapping, environmental monitoring, and package delivery in complex and evolving conditions.