| Wireless Power Transfer(WPT)is an innovative technology,offering a potential solution to the energy provisioning issues often encountered in sensor networks.This challenge has been at the forefront of research into Wireless Sensor Networks(WSNs)in recent years.One significant advantage of WPT is its ability to power devices wirelessly,eliminating the need for manual intervention.This feature not only saves time but also reduces maintenance costs,making it an attractive option for sensor networks where establishing power lines may be challenging or impractical.Furthermore,WPT technology can also be harnessed to charge devices in locations where conventional wired power is unsuitable or dangerous,such as in hazardous or remote environments.Thus,WPT provides an efficient and safe power solution for diverse and challenging conditions.One feasible approach involves the deployment of Mobile Charger Vehicles(MCVs),such as robots or drones.These MCVs are equipped with a high-capacity battery and a WPT transmitter,which enables them to charge the sensor nodes within the network wirelessly.Several challenges must be addressed in order to maximize the utilization of MCVs in delivering energy to the nodes within sensor networks.Among these challenges is the development of efficient charging path planning and scheduling algorithms.Hamiltonian paths are usually regarded as good charging path.However,finding a Hamiltonian path is an NP-complete problem and remains challenging even for special cases such as grid graphs.Scheduling and path planning algorithms are critical in optimizing the power transfer process.By implementing such strategies,it is possible to guarantee an efficient and timely energy supply to nodes and ensure that power is delivered prior to their deadlines.While previous research has attempted to address these challenges,the collective impact of network topology,charging path planning,scheduling,node importance,and energy threshold distribution within WRSNs remains largely unexplored.Further,existing scheduling policies have predominantly focused on the scheduling of charging tasks,often overlooking the significance of network topology and the importance of the nodes.Additionally,the schedulability tests presented in existing studies lack feasibility,and their applicability to a larger set of tasks remains unproven.This shortcoming renders them unsuitable for real-world WRSNs.In order to address the previously mentioned issues,this work introduces innovative heuristic solutions for both scheduling and path planning.Initially,our research proposes an approach of hexagonal cluster-based node deployment,aimed at improving network performance and optimizing resource allocation.Following this,we divide each cluster into several sectors.For these sectors,we propose a heuristic charging path planning algorithm to find a Hamiltonian path—a strategy that’s viable in this topology.The intent here is to augment the efficiency of Mobile Charging Vehicles(MCVs)and elevate charging throughput.To maintain this path,we propose an energy-threshold dynamic assignment algorithm in each sector.Additionally,our research presents an efficient online algorithm to calculate node" importance:—a key metric in determining priorities and preemptively evaluating node workload.Next,we incorporate an analytical charging model to assess network performance,focusing on energy efficiency and queuing analysis.Subsequently,we introduce a non-preemptive dynamic priority scheduling algorithm for the assignment and scheduling of charging tasks.Finally,extensive simulations have been conducted,revealing the significant advantages of our proposed algorithms in terms of energy efficiency,response time,dead nodes’ density,and queuing processing. |