Unmanned Aerial Vehicles (UAVs) have recently been widely used in various fields. However, both cooperative charging scheduling and insufficient charging facility problems in UAV charging scenarios have been rarely studied. This paper studies parallel cooperative charging scheduling of UAVs. We adopt cooperative charging to reduce the total cost and parallel scheduling to enable UAVs can be charged even if the number of UAVs is more than the number of charging facilities. We formulate the Parallel Cooperative Charging Scheduling for UAVs Problem (PCCSUP) for optimizing the total cost of whole charging system. We first investigate the special case of PCCSUP with single charging station, and use the approximation algorithm for Uniform Parallel Machines Scheduling Problem (UPMSP) to solve the special case. Then, a greedy approach based approximation algorithm is proposed to solve the PCCSUP, where we use the approximation algorithm for UPMSP to obtain the charging arrangements and the Set Covering Problem (SCP) optimization framework to obtain the charging groups. The results of extensive simulations demonstrate that our algorithm can reduce up to 59.81% total cost compared with the benchmark algorithms. Finally, we discuss and design the algorithms for three related problems: PCCSUP with different arrival times, PCCSUP withK-anonymity, and charging arrangements for excluded UAVs.

Wireless Power Transfer (WPT) technology has been developed rapidly in recent years. The cooperative charging model and corresponding scheduling methods have been proposed to save the charging cost in paid charging service. However, the state-of-the-art methods ignore the spatial occupation issue of rechargeable devices. Moreover, the cooperative charging scheduling in directional wireless charging has not been studied yet. This paper studies the cooperative scheduling for directional wireless charging with spatial occupation. We formulate the Cooperative Charging Scheduling with Spatial occupation (CCSS) problem of Mobile Rechargeable Sensor Devices (MRSDs) for optimizing the total cost of whole charging system. We first investigate the properties of optimal arrangement of MRSDs in charging group and calculate the tight intervals of charging angles of MRSDs. We show that it is sufficient to bound the error by conducting angle discretization for only two MRSDs in each charging group. Then, a$(\ln n+1)(1+\varepsilon)$-approximation algorithm of the CCSS problem is proposed based on greedy approach, where$n$is the number of MRSDs, and$\varepsilon$is the discretization error. The results of extensive simulations and field experiments demonstrate that our algorithm can reduce at most 42.5% total cost comparing with the benchmark algorithms.

Wireless Power Transmission (WPT) has been widely used to replenish energy for wireless rechargeable sensor networks. This paper concerns the fundamental issue of robust fault-tolerant placement of wireless chargers for directional charging. Following the general directional charging model, we formulate theCharger Placement for Robust Coverage (CPRC)problem, which has continuous and infinite constraints, for resisting the wireless charger failure. We transform the problem to the equivalent integer program problem without performance loss by area partition and dominating strategy extraction. We show that the greedy algorithm achieves the logarithmic approximation ratio. We further formulate theCharger Placement for Robust Utility (CPRU)problem for resisting the sensor node failure. This problem also has continuous and infinite constraints. We transform the problem to the combinational optimization problem with finite strategy space through the techniques of charging power approximation, area discretization and dominating strategy extraction. We present the algorithm, which utilizes the combination of binary search and greedy algorithm, to solve theCPRUproblem. We conduct both simulations and field experiments to validate our theoretical results. The simulation results show that the proposed algorithms forCPRCandCPRUcan outperform comparison algorithms by at least 17.48% and 21.15%, respectively.

The multi-hop wireless charging technology can largely extend the charging service range of chargers, thus has promising prospect in sustainable energy replenishment for wireless rechargeable sensor network. This paper proposes a new cost criterion, termed comprehensive cost consisting of energy cost and deployment cost, to measure the actual expenditure of wireless charging. We present a multi-hop wireless charging model and formulate the problem of minimizing the comprehensive cost such that the energy demand of all sensor nodes can be fulfilled by the energy capacitated chargers. We propose a (ln n+1)-approximation algorithm for the optimization problem, where n is the number of sensor nodes. Then, we propose a straightforward cost sharing mechanism, which ensures that no subset of sensor nodes can benefit by breaking away from the current charging tree for any fixed charger position, to realize the paid charging service of multi-hop wireless charging. Furthermore, to keep the magnetic fields of transmitters from the interfering, the conflict avoidance schemes are proposed in both central and distributed situations. Finally, we discuss the distributed scheme for minimizing the comprehensive cost without support of central server. Through extensive simulations, we demonstrate the significant superiority of the proposed algorithms in terms of comprehensive cost.

The multi-hop wireless charging technology has attracted a lot of attention, as it largely extends the charging range of chargers. Different from the existing work with single cost optimization, the objective of this article is to optimize the comprehensive cost, which is the combination of energy cost and deployment cost. We decompose the target problem into two sub-problems. The first sub-problem aims to minimize the deployment cost with energy capacity constraints. The proposed algorithm follows the greedy strategy, where the subset of sensor nodes for any charger is determined by finding the capacitated minimum spanning tree. The second sub-problem, which aims to maximize the reduction of comprehensive cost by adding chargers to the solution of the first sub-problem, is proved to be an unconstrained submodular set function maximization problem and can be solved by a 1/2-approximation randomized linear time algorithm for its equivalent problem. Through extensive simulations, we demonstrate that the proposed solution can reduce the comprehensive cost by 57.55% comparing with the benchmark algorithms.

Wireless Power Transmission (WPT) has been widely used to replenish energy for Wireless Rechargeable Sensor Networks. However, the charging service model, which is of the essence to commercial WPT, has not emerged so far. In this paper, we present a wireless charging service model from the perspective of cooperative charging economics, and formulate the Cooperative Charging Scheduling (CCS) problem for joint optimization of rechargeable devices' charging cost and moving cost. We first propose two intragroup cost sharing schemes to sustain the cooperation among devices. Then, the approximation algorithm CCSA of the CCS problem is proposed based on greedy approach and submodular function minimization. Furthermore, we model the large-scale CCS problem as a coalition formation game and present a game theoretic algorithm CCSGA. We show that CCSGA finally converges to a pure Nash Equilibrium. We conduct simulations, and field experiments on a testbed consisting of 5 chargers and 8 rechargeable sensor nodes. The results show that the average comprehensive cost of CCSA is 27.3% lower than the noncooperation algorithm and is only 7.3% higher than the optimal solution on average. In field experiments, CCSA outperforms the noncooperation algorithm by 42.9% in terms of comprehensive cost on average. Moreover, CCSGA is much faster than the approximation algorithm and is more suitable for large-scale cooperative charging scheduling.

The development of Electric Vehicle (EV) helps to ease energy crises and deduce vehicle exhaust emissions. However, it also brings a great impact on both transportation networks and power grids. There are some serious impediments in terms of energy charging to the popularization of EV, such as high deployment cost of charging stations, low charging efficiency, and voltage deviation of power grid. To address these issues, we design a new EV charging system, which levers the bus network in urban areas through the integration of OnLine Electric Vehicle (OLEV) system and Microwave Power Transfer (MPT) system. We formulate the EV route scheduling problem based on this new charging system to maximize the total residual energy subject to all EVs can arrive to their destinations before deadlines. Then, we propose an approximation algorithm, RSA, to solve the route scheduling problem. To relieve the traffic congestion, we further formulate the conflict-free EV route scheduling problem, and use the matching based algorithm, FRSA, to find the EV route schedules with the maximal residual energy. Through the extensive simulations, we demonstrate that RSA and FRSA can increase the average residual energy by 67.66% and 50.36% compared with the solution without the designed wireless charging system, respectively. Moreover, RSA reduces 22.22% of travel time and outputs 77.23% of residual energy, and FRSA can obtain 83.51% residual energy with 3.62% of extra travel time of the corresponding optimal solutions on average, respectively.