Trajectory Design for UAV-Enabled Multiuser Wireless Power Transfer With Nonlinear Energy Harvesting

In this paper, we study an unmanned aerial vehicle (UAV)-enabled multiuser wireless power transfer (WPT) network, where a UAV is responsible for providing wireless energy for a set of ground devices (GDs) deployed in an area. We focus on the design of UAV trajectory subject to the maximum flight speed limit, in order to maximize the minimum harvested energy among GDs over a particular charging duration. Different from prior works that considered simplified linear energy harvesting models, this paper for the first time takes into account the realistic nonlinear energy harvesting model for the UAV trajectory design. However, the formulated trajectory design problem is highly non-convex and has infinite number of variables, thus making it be challenging to be solved optimally. To tackle this difficulty, we adopt the following three-step approach to obtain an efficient solution. First, we rigorously characterize that the optimal trajectory follows a new successive-hover-and-fly (SHF) structure, where the UAV hovers at a certain set of points for efficiently transferring energy, and flies among these hovering points with the maximum speed following certain arcs (not necessarily straight lines). Next, based on this SHF structure, we transform the original problem to a new one for finding a set of turning point variables during the maximum-speed flight, at which the UAV changes the flight direction without hovering. Finally, we use the techniques of convex approximation to solve the transformed problem. According to the convexity of the nonlinear energy harvesting model, we iteratively solve a series of convex optimization problems to update the UAV trajectory towards a high-quality solution. Numerical results show the convergence of the proposed approach, and validate its performance gain over conventional designs.