On Correcting Errors in Existing Mathematical Approaches for UAV Trajectory Design Considering No-Fly-Zones

Motivated by the fact that current mathematical methods for the trajectory design of an unmanned aerial vehicle (UAV) considering no-fly-zones (NFZs) cannot perfectly avoid NFZs throughout the entire continuous trajectory, this study introduces a new constraint that ensures the complete avoidance of NFZs. Moreover, we provide mathematical proof demonstrating that a UAV operating within the proposed constraints will never violate NFZs. Under the proposed constraint on NFZs, we aim to optimize the scheduling, transmit power, length of the time slot, and the trajectory of the UAV to maximize the minimum throughput among ground nodes without violating NFZs. To find the optimal UAV strategy from the non-convex optimization problem formulated here, we use various optimization techniques, in this case quadratic transform, successive convex approximation, and the block coordinate descent algorithm. Simulation results confirm that the proposed constraint prevents NFZs from being violated over the entire trajectory in any scenario. Furthermore, the proposed scheme shows significantly higher throughput than the baseline scheme using the traditional NFZ constraint by achieving a zero outage probability due to NFZ violations.