Advancements in Quadrotor UAVs: Trajectory Tracking and Energy Optimal Control Using PINN and HJ Formalism for Quadrotor UAV Dynamics

This paper presents a comprehensive dynamic analysis of Quadrotor unmanned aerial vehicles (UAVs) using the Hamilton–Jacobi (HJ) formalism for energy-efficient trajectory tracking and stabilization of quadrotor UAVs by unifying Hamilton–Jacobi–Bellman equation (HJBE) with physics-informed neural networks (PINNs). We introduce a Generating Function, approximated by PINNs that solve the HJBE while incorporating non-conservative forces through canonical transformations. The proposed method enforces Hamiltonian directly into the network’s loss function, ensuring rigorous adherence to energy conservation principles. Numerical simulations demonstrate precise trajectory tracking with improved energy efficiency. This research enhances the understanding of UAV dynamics and provides a foundation for advanced autonomous control systems with high stability and adaptability.