  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.
