3D Trajectory and Pickup/Drop-Off Strategy for UAV-Enabled Delivery: Trade-Off Between Time and Energy Minimization

In this paper, we explore the rigorous mathematical modeling of an unmanned aerial vehicle (UAV)-enabled parcel delivery to optimize a three-dimensional (3D) trajectory and pickup/drop-off strategy. Taking into account practical considerations including the avoidance of no-fly zones (NFZs) and the weight restrictions of the UAV, our goal is to jointly optimize the pickup and drop-off indicators, lengths of time slots, and horizontal and vertical trajectories, with the objective of minimizing the weighted-sum of completion time and energy consumption. To address the nonconvexity of the formulated problem, which involves mixed-integer nonlinear programming, we first apply a successive convex approximation to transform the nonconvex problem into a convex one for optimization variables. Moreover, we utilize a penalty convex-concave procedure to maintain the binary nature of integer variables. Finally, for the relaxed convex problem, we propose a low-complexity algorithm that derives the suboptimal UAV strategy iteratively. The simulation results demonstrate the effectiveness of the proposed strategy in establishing 3D trajectories for specific objectives and completely avoiding NFZs while maintaining the binary nature of the pickup and drop-off indicators. Furthermore, the comparative study provides insight into the trade-offs between time-minimization and energy-minimization strategies, offering the flexibility to choose the most suitable approach based on the specific service requirements and objectives.