Energy-Efficient Trajectory Planning for Multirotor UAVs With Time-Varying Mass: Mass-Augmented A* and Hybrid DP\u2013NLP Speed Optim

The large-scale deployment of multirotor delivery UAVs is fundamentally constrained by limited battery endurance. In practical logistics missions, discrete payload changes during parcel delivery result in time-varying vehicle mass, which in turn affects both vehicle dynamics and power consumption. However, most existing planners assume constant mass, leading to trajectories that are energy-inefficient and difficult for low-level controllers to track accurately. This paper presents a payload-aware trajectory planning and energy optimization framework for multirotor UAVs. The proposed method employs a hierarchical architecture: the front-end utilizes a mass-augmented A* algorithm to search a four-dimensional position\u2013mass state space, using energy consumption as the edge cost to obtain a globally optimal geometric path. The back-end features a hybrid dynamic programming (DP) and nonlinear programming (NLP) trajectory generator that optimizes the speed profile along the path under strict thrust-sphere constraints. This formulation accounts for gravity, inertial forces, and aerodynamic drag, producing smooth and dynamically feasible space\u2013time trajectories. High-fidelity software-in-the-loop (SITL) simulations based on PX4 and RflySim demonstrate that, compared to conventional geometric shortest-path methods, the proposed framework reduces total mission energy by 9.4%\u20139.6% in urban and mountainous delivery scenarios. Additionally, it reduces the mean tracking error to approximately 0.8 m (sub-meter level), showing significant improvements in both energy efficiency and operational safety for UAV logistics operations.