Several recent works have studied mobile charging under the “one-to-many” charging pattern where a single charger can charge multiple devices simultaneously. However, most of them focus on path planning and charging time allocation, but overlook the underlying dependence of the charging efficiency on initial deployment positions of chargers. This paper studies the problem ofPlacing directional wIreless chargers withLimited mObiliTy (PILOT), that is, maximize the overall charging utility for a set of static rechargeable devices on a 2D plane by determining deployment positions, stop positions and orientations, and portions of time for all deployed chargers that can move in a limited area after their deployment. To the best of our knowledge, we are the first to study placement of mobile directional chargers under the “one-to-many” pattern. To address PILOT, we propose a$(\frac{1}{2}-\epsilon)$-approximation algorithm. First, we present a method to approximate nonlinear charging power of chargers, and further propose an approach to construct Maximal Covered Set uniform subareas to reduce the infinite continuous search space for stop positions and orientations to a finite discrete one. Second, we present geometrical techniques to further reduce the infinite solution space for candidate deployment positions to a finite one without performance loss, and transform PILOT to a mixed integer nonlinear programming problem. Finally, we propose a linear programming based greedy algorithm to address it. Simulation and experimental results show that our algorithm outperforms six comparison algorithms by$19.74 \% \sim 500.01 \%$.

Unmanned aerial vehicle (UAV) has attracted much attention due to its excellent ability to collect visual information of surroundings. In this paper, we investigate a new monitoring model to focus on sizes and shapes of objects, and occlusion between objects, and then study the placement of a set of UAVs to monitor polygonal sizable objects. Our aim is to maximize the overall monitoring utility of all objects by determining the positions and orientations of UAVs, given a set of polygonal sizable objects with fixed coordinates and shapes on a$2\mathbf{D}$plane. We study two typical scenarios of the problem: the former stipulates that a line segment is effectively monitored only when it is completely monitored by a single UAV, and the latter allows multiple UAVs to cooperatively monitor a line segment and then integrate their image information. The problem is proved to be NP-hard with infinite continuous solution space. For the first scenario, we propose a$(1-1/e)$-approximation algorithm. For the second one, we first propose a 1/2-approximation algorithm to address its simple version, and then propose a heuristic solution. Numerical evaluations validate the effectiveness of our proposed algorithms.