Optimal 1D Trajectory Design for UAV-Enabled Multiuser Wireless Power Transfer

In this paper, we study an unmanned aerial vehicle (UAV)-enabled wireless power transfer (WPT) network, where a UAV flies at a constant altitude in the sky to provide wireless energy supply for a set of ground nodes with a linear topology. Our objective is to maximize the minimum received energy among all ground nodes by optimizing the UAV's one-dimensional (1D) trajectory, subject to the maximum UAV flying speed constraint. Different from previous works that only provided heuristic and locally optimal solutions, this paper is the first work to present the globally optimal 1D UAV trajectory solution to the considered min-energy maximization problem. Towards this end, we first show that for any given speed-constrained UAV trajectory, we can always construct a maximum-speed trajectory and a speed-free trajectory, such that their combination can achieve the same received energy at all these ground nodes. Next, we transform the original UAV-speed-constrained trajectory optimization problem into an equivalent UAV-speed-free problem, which is then optimally solved via the Lagrange dual method. The obtained optimal 1D UAV trajectory solution follows the so-called successive hover-and-fly (SHF) structure, i.e., the UAV successively hovers at a finite number of hovering points each for an optimized hovering duration, and flies among these hovering points at the maximum speed. Numerical results show that our proposed optimal solution significantly outperforms the benchmark schemes in prior works under different scenarios.