Edge Computing-Aided Dynamic Wireless Charging and Trip Planning of UAVs

Abstract

In today’s era of rapid technological advancement, unmanned aerial vehicles (UAVs) are transforming sectors such as remote delivery, surveillance, and disaster response. However, challenges related to energy consumption and operational efficiency continue to hinder their broader adoption. To address these issues, this study proposes an integrated system design combining dynamic wireless charging (DWC), intelligent trip planning, and intelligent edge computing (IEC). The proposed system leverages IEC for local data processing to reduce latency and optimize energy management, 6G networks for real-time vehicle-to-infrastructure (V2I) communication, and DWC to enable efficient, on-the-go energy replenishment. Additionally, a dynamic arrival management algorithm is introduced to minimize UAV wait times to enhance operational efficiency. Simulations of this system demonstrated significant improvements: larger UAVs achieved an average charging efficiency of 91.2%, while smaller UAVs achieved 92.75%, with dynamic arrival management reducing wait times by an average of 1.5 min for smaller UAVs and 5.0 min for larger UAVs. These findings underscore the system’s effectiveness in optimizing UAV operations and charging efficiency. This integrated approach offers a scalable framework to enhance UAV capabilities and sets a benchmark for future advancements in operational efficiency and charging technology for urban and environmental applications.

1. Introduction

1.1. Background

In our current era of continuous and rapid technological advancements, unmanned aerial vehicles (UAVs) [1,2], commonly known as drones, emerged as a transformative technology with wide-ranging applications across various sectors, including logistics [3], surveillance [4], agriculture [5], and emergency response [6]. UAVs offer significant advantages such as reduced operational costs, enhanced accessibility to remote areas, and the ability to perform tasks that are hazardous for humans. For instance, UAVs can deliver medical supplies to hard-to-reach locations [7], extend cellular communications in remote areas [8], monitor crop health in vast agricultural fields [9], and provide real-time data during disaster relief operations [10]. These capabilities demonstrate the potential of UAVs to revolutionize numerous industries.

Equipped with state-of-the-art sensors, such as cameras, lidar, radar, and infrared sensors, UAVs enhance their perception capabilities. They can capture high-resolution images, create detailed maps, and detect obstacles with precision. These sensors enable UAVs to navigate complex environments autonomously, perform precise maneuvers, and gather critical data for analysis [11]. For instance, in urban environments, UAVs can monitor traffic conditions [12] and the environment [13], inspect infrastructure [14], and assist in emergency response by providing real-time situational awareness [15].

However, one of the most significant challenges associated with UAVs is energy consumption. UAVs, particularly those used for commercial purposes, require longer battery life to maintain flight, which can limit their operational efficiency and sustainability. The high energy consumption of UAVs not only impacts their range and payload capacity, but also raises concerns about their environmental footprint, especially when powered by non-renewable energy sources. Imagine a UAV deployed for real-time traffic monitoring in a busy city, helping to adjust traffic signals and respond to incidents. If the UAV experiences energy inefficiencies, its coverage may become intermittent, delaying responses to traffic disruptions. This could lead to increased congestion, longer delays, and higher risk of accidents. This scenario highlights the need to manage UAV energy consumption for consistent and reliable operation within intelligent transportation systems (ITS), ensuring safer and more efficient traffic management.

The evolution of telecommunication and networking technologies, specifically the advent of 6G networks [16], promises to revolutionize UAV operation. The 6G networks promise to offer unparalleled connectivity with features such as ultra-low latency, massive device connectivity, high-speed data transfer, and ubiquitous computing to enable seamless vehicle-to-infrastructure (V2I) communications. These features will collectively enhance the efficiency and safety of UAV operations by facilitating real-time data exchange and coordination with ground-based systems.

A UAV monitoring traffic could instantly relay data to traffic management centers, thus allowing for dynamic adjustments to traffic signals and routing recommendations to alleviate congestion. The ultra-low latency of 6G will ensure real-time data transfer while enabling immediate responses to changing traffic conditions [17]. In addition to enhancing adaptability of traffic management systems, the high-speed data transfer capabilities of 6G will allow for the transmission of large volumes of data [18], such as high-resolution video and detailed sensor information to further enhance situational awareness of traffic management systems. Furthermore, 6G connectivity can help ensure UAVs have up-to-date information on battery status and optimal landing zones, thus preventing situations where UAVs run out of power mid-operation. The massive device connectivity feature of 6G will support the integration of numerous UAVs and other IoT devices within a smart city infrastructure, enabling coordinated operations and efficient energy management [19]. This advanced communication infrastructure paves the way for a new era of intelligent and sustainable urban transportation systems.

The integration of Internet of Things (IoT) devices in smart cities establishes a robust framework for monitoring and managing UAV activities to help optimize their energy use and reduce their environmental impact. IoT sensors can continuously monitor UAV performance, environmental conditions, and energy consumption to enable predictive maintenance and efficient energy management strategies [20]. This proactive approach will not only enhance operational efficiency, but also extends the lifespan of UAVs while minimizing their carbon footprint.

Intelligent edge computing (IEC) complements these advancements by bringing data processing closer to the source of data generation that is typically on the UAV itself or nearby ground stations [21]. This reduces latency and conserves bandwidth by minimizing the need to transmit large volumes of data to remote servers for analysis. By leveraging edge computing, UAVs can perform crucial computations locally, enabling rapid decision making and optimizing energy management. This capability proves invaluable for applications requiring immediate responses, such as real-time adjustments to flight paths due to changing weather conditions or swift avoidance of unexpected obstacles. By integrating onboard processing power with edge computing capabilities, UAVs can achieve heightened autonomy to operate more efficiently and reliably in dynamic environments.

In addition to these advancements, dynamic wireless charging (DWC) emerges as a transformative solution for UAVs [1,22]. This technology enables UAVs equipped with wireless charging capabilities to receive power remotely while in flight, typically through electromagnetic induction or microwave transmission from ground-based or aerial charging stations [23]. By eliminating the need for frequent landings or battery swaps, DWC addresses one of the critical limitations of traditional UAV operations—limited flight endurance. The benefits of DWC are substantial. UAVs equipped with DWC capabilities can operate for significantly longer periods, making them ideal for applications that require extended aerial surveillance, continuous monitoring of infrastructure, or rapid response to emergencies. This extended flight capability not only improves operational efficiency, but also reduces downtime, thus allowing UAVs to maintain continuous coverage without interruptions for recharging. Moreover, DWC enhances mission flexibility by enabling UAVs to adapt quickly to evolving operational needs, such as sudden changes in mission duration or location requirements. However, challenges such as the need for infrastructure deployment and potential electromagnetic interference need careful consideration in its implementation.

The synergy among 6G networks, V2I communication, ITS, IoT, and IEC plays a crucial role in tackling the energy consumption challenges faced by UAVs. The 6G networks offer unmatched connectivity with ultra-low latency and robust support for massive device connectivity, enabling seamless V2I communication. This advanced communication infrastructure will guarantee that UAVs receive real-time updates on battery status, optimal flight paths, and environmental conditions, thereby averting operational disruptions caused by power depletion.

Together, these technologies form the cornerstone of a sustainable and efficient urban transportation ecosystem. By integrating IoT, IEC, DWC, and 6G capabilities, cities can optimize UAV utilization, minimize energy consumption, and mitigate environmental impact. This integration fosters smarter, greener urban environments that support innovative and resilient transportation solutions to ultimately pave the way for enhanced urban mobility and environmental sustainability.

1.2. Motivation

This research is driven by the urgent need to overcome critical operational limitations of UAVs in urban environments, where limited flight endurance and frequent recharging disrupt operational continuity and add logistical complexity. Enhancing UAV operation time is essential to optimizing mission efficiency and reducing maintenance costs from battery wear. As UAVs become integral to smart city infrastructures and service delivery, their energy efficiency directly impacts both operational sustainability and environmental footprint. To address these challenges, integrative technologies, such as 6G networks, IEC, and IoT, play necessary roles in optimizing UAV performance, rather than being included merely as trends. IEC specifically enables real-time local data processing, essential for quick adjustments in dynamic environments, such as rerouting for weather changes or avoiding obstacles, without the latency of cloud processing, thus conserving bandwidth and energy. Combined with solutions such as DWC, which allows UAVs to recharge in flight and minimize downtime, IEC and 6G together enhance continuous, reliable UAV operations. This research aims to advance these technologies for improved energy management and charging strategies, ultimately contributing to more sustainable and resilient urban transportation systems.

1.3. Objectives

Several critical challenges must be addressed to ensure the seamless integration of UAVs into urban environments. These include the precision of DWC alignment, which can lead to inefficiencies and energy loss, and the reliance on cloud-based data processing, which introduces latency that is unsuitable for real-time UAV operations in dynamic settings. Existing research often focuses on static wireless charging and individual technologies, neglecting the critical interoperability between them. This paper aims to address these gaps. The objective of this paper is to propose a comprehensive system design for intelligent charging and trip planning of UAVs within the context of IEC. Our approach leverages UAVs as mobile IECs capable of providing charging service while enhancing operational efficiency and sustainability in urban environments. We aim to explore UAV-to-UAV charging capabilities, utilizing an IoT application integrated with 6G-enabled ITS. Specifically, we advocate for the implementation of DWC, with a focus on technologies such as laser beaming charging, to extend UAV flight durations and optimize operational flexibility. The proposed system design will effectively schedule charging activities, utilizing real-time data from IoT sensors and user-defined preferences to optimize UAV operations. Additionally, we will address the challenge of late and early UAV charging arrivals by assessing their implications on system efficiency and transportation network performance, thereby ensuring robust and reliable UAV charging.

1.4. Research Contributions

This paper introduces a novel system design and architecture for intelligent charging and trip planning of UAVs by leveraging them as IEC nodes. It explores UAV-to-UAV and UAV-to-laser beaming station charging scenarios, including an analysis of wireless charging feasibility using visible light communication (VLC) such as laser beaming. The paper proposes a new handshake protocol for secure charging interactions, develops algorithms for reservation management and addressing operational challenges such as late or early UAV arrivals, and ensures safe charging with detection of wireless power transfer (WPT) misalignment issues. Two fair real-time metered billing schemes are presented for secure payments. This work supports ongoing standardization efforts and offers a framework for future-proof and sustainable charging networks that can be easily adopted by government and private agencies.

1.5. Outline

The paper is organized into several sections that systematically explore DWC and intelligent trip planning for UAVs aided by IEC. Section 1 introduces the topic, detailing the background, motivations, objectives, and research contributions. Section 2 reviews related works, focusing on UAV charging methods and the role of IEC. Section 3 addresses the challenges in UAV charge scheduling due to untimely arrivals. Section 4 presents the proposed system design, including the architecture and handshake protocol. Section 5 discusses the modeling and algorithms, covering UAV power consumption, drone placement, charge scheduling, and dynamic arrival handling. Section 6 provides a critical distance analysis for UAV operations. Section 7 outlines the simulation setup and results, focusing on UAV-to-UAV DWC, handling late and early arrivals, and exploring the scalability and computational efficiency of the system, while comparing it with existing literature. Section 8 evaluates the sustainability and feasibility of the UAV charging infrastructure. Finally, Section 9 concludes the paper, summarizing key findings and proposing future research directions to enhance UAV capabilities and urban mobility solutions.

2. Related Works

2.1. Types of UAV Charging Methods

Wired charging methods, where UAVs connect to stationary charging stations through physical cables [24], offer a reliable and stable power supply, ensuring consistent energy transfer without electromagnetic interference. This method is straightforward and well-established, providing a robust solution for powering UAVs [1,22]. However, wired charging requires manual intervention for connection and disconnection, thereby limiting its autonomous charging capabilities. Moreover, the installation of wired infrastructure at fixed locations can be costly and time-consuming, therefore potentially hindering its deployment in dynamic operational environments where flexibility and continuous operation are essential.

Static wireless charging (SWC), as can be seen in Figure 1, operates by typically using electromagnetic fields to transfer power between a wireless charging pad (WCP) and a receiver usually installed underneath the UAV [25,26]. This method automates the charging process, reducing wear on UAV components and eliminating risks associated with physical cables. SWC enhances safety by minimizing physical hazards and potential damage during charging. However, precise alignment between the wireless charging pad and UAV is critical for efficient energy transfer [22,27], which can pose challenges in dynamic operational settings. Despite advancements in alignment technology, SWC systems may face limitations in achieving widespread adoption due to these alignment constraints and operational complexities.

DWC using magnetic resonance technology [22,28] involves transferring power wirelessly to UAVs while they are in motion. This method typically utilizes magnetic resonance between a transmitting coil and a receiving coil installed on the UAV. Further, simulations comparing DWC with magnetic resonance to traditional wired methods show promising results. Reference [29] found that DWC with magnetic resonance achieved an average energy transfer efficiency of around 90% over larger distances that is suitable for UAV applications. This technology allows UAVs to extend their operational ranges and maintain continuous missions without the need for manual intervention or frequent landings. However, DWC with magnetic resonance has its limitations. It requires precise alignment between the transmitting and receiving coils to achieve optimal energy transfer efficiency. This alignment challenge can restrict deployment flexibility, as UAVs must navigate within specific zones where the charging infrastructure is installed. Moreover, magnetic resonance technology may face regulatory hurdles due to concerns over electromagnetic interference and safety implications, thus potentially slowing its widespread adoption in urban and sensitive environments.

In contrast to magnetic resonance technology, laser beaming charging, as seen in Figure 2, represents a significant advancement in DWC for UAVs [24,28]. Laser beaming systems utilize focused laser beams to transfer power to UAVs while they are airborne to enable charging without the constraints of physical contact or alignment issues associated with magnetic resonance. Numerical simulations comparing laser beaming with traditional methods, such as inductive wireless power transfer (IWPT), demonstrate its superiority. Laser beaming charging achieved approximately 16.2919 kWh WPT over 3.52 km, compared to 15.048 kWh from IWPT, therefore showcasing higher energy transfer efficiency and longer charging distances [30].

Laser beaming charging offers several advantages:

• Efficiency: Laser beaming systems achieve higher energy transfer efficiency by minimizing energy loss during charging sessions. This efficiency reduces operational costs and enhances mission duration, making UAV operations more sustainable and economically viable.
• Autonomous capability: Laser beaming supports fully autonomous charging capabilities, allowing UAVs to operate continuously in dynamic environments without the need for frequent landings or halting operations. This autonomy is less feasible with magnetic resonance, which often requires precise alignment and proximity to the charging source.
• Flexibility: Laser beaming enables charging on the move, facilitating seamless integration into various UAV applications, such as autonomous surveillance, delivery services, and emergency response. Traditional charging methods often require stationary charging points, thereby limiting the operational flexibility and efficiency of UAVs.
• Precision and control: Laser beaming allows for precise targeting and control of the energy transfer process, which can be fine-tuned to match the specific power requirements of the UAV. This precision ensures optimal charging efficiency and minimizes energy waste.

Laser beaming charging technology is poised to revolutionize DWC applications for UAVs by overcoming the limitations of magnetic resonance, enhancing operational capabilities, and accelerating the adoption of autonomous UAV systems across diverse sectors. Continued advancements and investments in laser technology and infrastructure development will further drive its integration into future UAV operations, facilitating innovative applications in urban mobility and beyond.

However, laser beaming charging presents several challenges that need addressing. These include the requirement for clear line of sight (LOS) between the transmitter and UAV, sensitivity to adverse weather conditions, and safety concerns related to potential laser beam exposure to humans and animals. Optimizing energy conversion efficiency, managing high initial costs, and developing necessary infrastructure are critical for successful implementation.

Recent advancements in optimizing laser parameters and charging protocols, detailed in [31,32,33], underscore ongoing efforts to address integration challenges and environmental considerations. Research in [31] introduces a laser charging system tailored to extend UAV flight times, emphasizing the importance of optimizing parameters such as wavelength (e.g., 850 nm) for superior transmission efficiencies over distances compared to alternatives such as 1060 nm. Investigations in [32] explore laser-powered drones as airborne base stations (ABSs) for continuous wireless charging in urban settings, highlighting enhanced energy efficiency and coverage reliability through Monte Carlo simulations. Additionally, [33] examines laser-charged UAV relay networks, employing trajectory optimization to minimize power consumption at charging stations while optimizing data transmission efficiency. Together, these studies advocate for laser beaming charging as a promising approach to prolong UAV flight durations and improve mission reliability despite challenges related to system integration and environmental conditions.

In conclusion, while laser beaming charging offers significant advantages for UAV energy management, addressing these challenges is essential to fully realize its potential. By overcoming these obstacles, laser beaming can pave the way for more sustainable, efficient, and innovative UAV operations in urban environments, offering superior efficiency, control, flexibility, and operational autonomy compared to magnetic resonance and traditional charging methods.

2.2. UAV Charging Enhanced by Intelligent Edge Computing

IEC plays a pivotal role in advancing UAV technologies, offering more than just a trending capability; it is essential for optimizing charging strategies, improving response times, and enhancing overall operational efficiency and autonomy. By processing data closer to the UAV and reducing dependency on remote servers, IEC enables real-time decision making and rapid adjustments to dynamic conditions, which are critical for sustaining continuous operations and minimizing energy consumption. This section explores recent advancements in IEC applications for UAV charging by highlighting studies that leverage optimization algorithms, machine learning, and distributed computing to improve energy management and operational reliability.

Reference [34] introduces a pioneering approach to UAV charging with a two-stage solution aimed at urban prosumer-operated drone stations. The first stage employs hierarchical federated learning (HFL) with long short-term memory (LSTM) architecture to predict energy requirements while ensuring data privacy. The second stage utilizes stochastic game-based multi-agent double deep Q-learning (MADDQN) to optimize energy scheduling by achieving a minimal mean squared error (MSE) of 0.015. This approach significantly enhances energy satisfaction and quality of experience (QoE) compared to traditional methods by demonstrating the efficacy of IEC in UAV operations.

In [35], an EC-based strategy is proposed for optimizing UAV swarm path planning and energy management in dynamic environments. The algorithm, designed for scenarios with varying user demands across multiple locations, demonstrates low computational complexity and high scalability. Through rigorous testing with up to 400 demand releases across 100 locations, the algorithm consistently outperforms conventional partitioning methods as the number of UAVs increases. By facilitating planned charging paths and utilizing integer linear programming and iterative algorithms, the approach enhances energy efficiency and operational reliability, thus highlighting the potential of IEC in real-time decision making for UAV systems.

Reference [36] introduces a robust system where UAVs form a flying ad hoc network (FANET) to autonomously provide edge computing services post disaster, supported by a renewable energy generator for continuous battery charging. Managed by a model-based reinforcement learning (RL) approach, the FANET controller optimizes UAV deployment based on real-time edge-computing demands and renewable energy availability. Simulation results demonstrate the effectiveness of the RL policy, showing better performance in balancing service demands and energy constraints compared to simpler strategies, such as the greedy policy. This system highlights the efficacy of IEC in ensuring reliable and efficient edge computing deployment in disaster scenarios, independent of conventional infrastructure vulnerabilities.

Reference [37], explores UAVs as flying edge servers using a priority-based deep reinforcement learning (DRL) approach (PD-TCCT) for optimizing energy consumption and task management. PD-TCCT integrates trajectory planning, communication scheduling, charging scheduling, and task offloading to maximize efficiency. Comparative evaluations against deep deterministic policy gradient (DDPG), deep Q-network (DQN), GREEDY, and RANDOM methods show PD-TCCT achieving improvements of 6.36%, 54.42%, 3.65%, and 42.88%, respectively. This underscores the role of IEC in enhancing decision making and sustainability in UAV operations through optimized charging strategies.

In the context of 6G-era aerial edge networks, reference [38] proposes an intelligent approach using distributed charging services and DRL-based strategies for UAV energy management. By optimizing trajectory planning, battery charging schedules, and edge resource allocation, the framework achieves significant reductions in UAV energy costs compared to traditional benchmarks. This integration of IEC not only enhances UAV endurance, but also supports sustainable and efficient UAV operations in dynamic environments, demonstrating its potential for advancing autonomous UAV technologies.

Reference [39] addresses the optimization of UAV-empowered edge computing in environments with multiple obstacles and dependent tasks represented as directed acyclic graphs (DAGs). Through a DRL-based approach, the study formulates UAV trajectory planning, DAG task scheduling, and service function (SF) deployment as a unified NP-hard problem. Simulation results demonstrate the superiority of the proposed DRL algorithm over three heuristic methods and a Q-learning-based approach across various scenarios. Specifically, the DRL algorithm achieves a remarkable 100% success rate in path finding on all tested maps, outperforming competitors that struggle, particularly in complex obstacle-filled areas. Numerical comparisons reveal that the DRL algorithm not only maximizes the number of executed DAG tasks and minimizes average task response latency, but also optimizes path length effectively under energy constraints. These findings underscore the robustness and efficiency of DRL in managing intricate UAV missions, highlighting its potential for enhancing the reliability and performance of edge computing applications in real-world with obstacle-rich environments.

In conclusion, these studies that are summarized in

Table 1. Comparison of papers with focus on UAV charging aided by IEC.

Ref.	Architecture	Approach	Benefits	Applications
[34]	Urban prosumer-operated drone stations.	Stochastic game-based MADDQN.	Enhanced energy satisfaction, improved QoE, minimal MSE of 0.015.	Urban prosumer-operated drone stations, IEC in UAV operations.
[35]	EC-based strategy, integer linear programming, and iterative algorithms.	Path planning optimization, energy management.	Low computational complexity, high scalability, enhanced energy efficiency, and operational reliability.	Dynamic environments with varying user demands, real-time decision making for UAV systems.
[36]	FANET of UAVs	Model-based RL.	Balancing service demands and renewable energy constraints, effective edge computing deployment.	Post-disaster scenarios, disaster recovery operations, and IEC.
[37]	PD-TCCT	Trajectory planning, communication scheduling, charging scheduling, and task offloading.	Improved energy efficiency by 6.36–54.42% over DDPG, DQN, GREEDY, and RANDOM.	UAV energy management, task optimization, and sustainability in UAV operation.
[38]	Distributed charging services, DRL-based strategies.	Optimizes trajectory planning, battery charging schedules, and edge resource allocation.	Reductions in UAV energy costs, enhanced UAV endurance, and sustainable and efficient operations.	The 6G-era aerial edge networks, autonomous UAV technologies.
[39]	DRL	UAV trajectory planning, DAG task scheduling, and SF deployment optimization.	Superiority over heuristic methods and Q-learning in complex environments, 100% success rate in path finding.	UAV-empowered edge computing, obstacle-rich environments, and task execution efficiency.

underscore the transformative potential of IEC in advancing UAV charging technologies. By leveraging advanced algorithms and distributed computing frameworks, IEC enhances energy efficiency, operational reliability, and autonomy in UAV systems. Future research in this field should continue to explore novel approaches that integrate IEC to address emerging challenges and further optimize UAV performance in diverse applications such as urban mobility, surveillance, and disaster response.

3. Challenges in UAV Charge Scheduling Due to Untimely Arrivals

The scheduling of UAV charging, particularly in the context of DWC, faces a multitude of challenges. Early and late arrivals exacerbate these challenges, leading to significant operational and logistical issues. The specific challenges for UAVs in DWC systems are as follows:

• Operational efficiency: Early and late arrivals can disrupt the planned schedule, leading to inefficient use of charging infrastructure. This disruption increases operational costs as the system may have to accommodate unscheduled charging needs or deal with idle time for early arrivals.
• Cost management: Both early and late arrivals can result in additional expenses. Late arrivals may require extended charging times, thus incurring higher costs. Early arrivals might lead to UAVs waiting for their scheduled slot, causing financial burdens due to idle time. Efficient cost management requires minimizing these disruptions to ensure cost-effective operations.
• Resource balancing: Balancing charging resources among early, late, and on-time UAVs is challenging. Factors such as the number of charging stations, charging rates, and the overall demand for charging services must be considered. A system must be designed to dynamically allocate resources to maintain balance and prevent bottlenecks.
• DWC speed and productivity: The primary advantage of DWC lies in its fast and automated charging process. Deviations from scheduled times disrupt the charging speed and productivity of UAV operations. Delays in charging can cause operational delays, affecting the efficiency and productivity of UAVs, which heavily rely on timely charging for their missions.
• Optimization and fairness: Finding a balance between optimization and fairness in DWC scheduling is complex. Both late and early arrivals might demand preferential treatment, leading to conflicts and inefficiencies in resource allocation. The system needs to allocate resources optimally while ensuring fairness among UAV operators.
• Environmental sustainability: DWC systems are designed to minimize environmental impact. Early arrivals waiting at charging stations can contribute to congestion and increased energy consumption, negatively impacting sustainability. Late arrivals extending their charging sessions also lead to higher energy use, raising concerns about sustainable resource utilization.
• Scheduling complexity: The variability in UAV arrival times necessitates the development of sophisticated, adaptive scheduling algorithms. These algorithms must dynamically adjust to real-time changes, accounting for early and late arrivals while ensuring that other scheduled UAVs are not adversely affected.
• Battery management: Frequent and unscheduled charging cycles, as necessitated by early and late arrivals, can adversely impact the battery health and lifecycle of UAVs. Maintaining optimal battery performance requires carefully managed charging schedules, which are difficult to adhere to with unpredictable arrival times.
• Infrastructure strain: Early arrivals can lead to congestion at charging stations, causing strain on the infrastructure. If multiple UAVs arrive early, the available charging capacity may be exceeded, leading to delays and inefficiencies in the charging process for all UAVs.
• Traffic management: Unscheduled early and late arrivals contribute to airspace congestion around charging stations. This congestion poses safety risks and complicates the management of UAV traffic, requiring more sophisticated traffic management systems to ensure safe and efficient operations.

There is a pressing need to address these challenges summarized in Figure 3 due to the critical role that UAVs are expected to play in future ITS. The efficiency, reliability, and sustainability of UAV operations are directly impacted by how well these charging scheduling challenges are managed. Failure to address these issues can lead to reduced operational efficiency, higher costs, resource imbalances, safety risks, and negative environmental impacts due to increased energy consumption and emissions from inefficient charging practices. Surveyed literature often overlooks the specific challenges posed by early and late arrivals, therefore highlighting the urgent need for robust solutions. Developing and implementing adaptive scheduling systems that can handle these variations is crucial for integrating UAVs effectively into future ITS, ensuring the benefits of advanced, automated, and sustainable transportation systems.

4. Proposed System Design

4.1. System Overview

This section introduces a novel DWC system for UAVs featuring two types of UAVs as seen in Figure 4: Laser-beaming UAVs (LBUAVs), equipped with larger batteries for providing charging to other UAVs, and edge intelligence UAVs (EIUAVs), with smaller batteries offering edge intelligence services to ground users (GUs) and potentially acting as roadside units (RSUs) for 6G services. The LBUAVs strategically plan their routes to provide DWC to EIUAVs without disrupting their operations, thereby extending their operational time. Laser communication facilitates efficient data exchange within the system.

The system proposes a charging scheduling and trip planning IoT application for ITS. LBUAVs utilize predictive analytics to anticipate the energy needs of EIUAVs and plan their routes, accordingly, ensuring timely and efficient DWC without interrupting their mission-critical operations. This proactive approach optimizes energy utilization and enhances overall system reliability.

In addition to drone-to-drone charging, the system includes ground-based laser beaming charging stations. These stations provide backup charging capabilities and can supply larger amounts of energy without disrupting UAV operations. This dual approach ensures flexibility and resilience in meeting varying energy demands across the UAV fleet to enhance operational efficiency and extending mission durations effectively.

4.2. Proposed System Design and Architecture

We propose a novel charging reservation and trip planning architecture tailored for the 6G-ready smart city environment, building upon previous work [25,26,40]. The hybrid mesh–star topology is utilized to distribute charging requests among different types of charging networks through their charging network managers (CNMs) and manage communication resilience. This system adopts an edge computing structure organized into three layers:

• End devices: This layer encompasses UAVs, GUs including other EVs, and electric vehicle supply equipment (EVSE). These devices engage in vehicle-to-grid (V2G) and vehicle-to-vehicle (V2V) communications, facilitating both buying and selling of charging services. Due to limited capacity, they forward requests to higher layers for processing.
• EI devices: Positioned along roads and in remote locations, these devices include RSUs, towers, and EIUAVs. They manage network traffic flow, perform tasks such as data collection, computation offloading, and real-time data processing, leveraging V2I communication. While these devices exhibit higher latency than end devices, they reduce load on cloud entities through EI.
• Core cloud: This layer comprises key distribution centers (KDC), banks, energy service providers (ESP), and energy distribution centers (EDC). The KDC ensures secure communications with symmetric encryption, while the bank facilitates transactions using credit points (CPs). ESP manages billing and energy distribution, while EDC coordinates charging reservations, route planning, and energy pricing.

This architecture optimizes system latency and computational efficiency. Edge computing significantly reduces latency compared to traditional cloud computing, enhancing the responsiveness of UAVs serving as edge servers. It minimizes data transfer to the cloud by preprocessing onboard, thereby reducing traffic load, computation costs, and energy consumption—a critical advantage for EIUAVs with limited battery capacity. This scalable design integrates 6G and IoT technologies, enabling real-time data exchange, low-latency communication, and efficient charging management for UAVs. It supports diverse charging methods, including laser beaming charging, thus ensuring robust and sustainable transportation solutions.

This comprehensive system architecture facilitates intelligent management of large-scale charging requests across hybrid communication networks, leveraging 6G capabilities to optimize energy usage and enhance operational efficiency for future mobility solutions.

4.3. Handshake Protocol

The proposed system for UAV charging introduces a handshake protocol designed to accommodate both current and future wireless charging standards. This protocol ensures secure and accurately billed charging sessions, leveraging established payment schemes from prior research [25,26,40]. The key components of the UAV charging protocol are as follows:

• Initiating a Charging Session:
  • Requesting process: UAVs, equipped with edge intelligence capabilities, initiate charging requests by themselves or through other EI devices. These requests include essential parameters such as the current state of charge (SoC), GPS location, and intended destination.
  • Anonymity and tracking: To ensure privacy, EIUAVs append a random ID to the charging request message. This ID facilitates tracking and coordination without compromising UAV operator anonymity.
• Optimizing Route and Charging Network Selection:
  • Coordination with charging network managers: Upon receiving the charging request, EIUAVs communicate with charging network managers to determine the availability of charging stations along the UAV’s planned route.
  • Optimal route planning: The system calculates an optimized route considering factors such as charging station or charging vehicle availability, UAV battery requirements, and operational constraints. This route is communicated back to the UAV along with reservation details.
• Establishing the Charging Session:
  • Authentication and reservation confirmation: Once a suitable route and charging stations are identified, the UAV receives a reservation confirmation message. This message includes details such as the scheduled charging time, location of charging networks, and authentication parameters.
  • Authentication process: at the designated charging station, the UAV authenticates itself using the provided parameters, ensuring that only authorized UAVs access the charging infrastructure.
  • Energy transfer mechanisms: Depending on whether the type of charging network is ground-based laser beaming towers or laser beaming charging networks (LBCNs) or UAV to UAV (U2U) charging, the UAV aligns itself with the charging apparatus. Continuous communication ensures efficient energy transfer while maintaining safety and regulatory compliance.
• Monitoring and Managing Charging Session:
  • Real-time monitoring: Throughout the charging session, the system monitors energy consumption and charging progress. These data are crucial for accurate billing and operational oversight.
  • Payment mechanisms: billing is managed through established payment schemes, such as pay-per-charging or pay-per-energy-unit models, utilizing encrypted virtual currency in the form of CPs to ensure secure and anonymous transactions.
  • End of session: Charging sessions conclude based on predefined criteria, such as reaching a specified energy level or operational time limit. Any discrepancies in billing are addressed promptly through the system’s feedback mechanisms.

This detailed protocol, illustrated in Figure 5, not only addresses the technical aspects of UAV charging, but also emphasizes security, efficiency, and scalability within the evolving landscape of UAV operations. It enables UAVs to seamlessly integrate into smart city infrastructures, supporting sustainable and reliable energy management practices.

5. Modeling and Algorithms

5.1. UAV Power Consumption Model

The adoption of the rotary wing UAV model enhances simulation realism by accurately representing UAV dynamics, including flight control, maneuverability, and power consumption. Leveraging power consumption models derived from single-rotor UAVs [41,42], ensures consistency across multi-rotor configurations [43,44], reflecting established principles while accommodating diverse UAV setups. This process leverages the well-established understanding of single-rotor dynamics, reflecting the behavior of multi-rotor UAVs while maintaining the foundation established by single-rotor models.

Equations (1)–(3) provide models for estimating rotor power consumption in various flight scenarios, which is crucial for analyzing and optimizing UAV performance. These equations detail power consumption during hovering (1), horizontal flight (2), and vertical motion (3), incorporating factors such as UAV weight, rotor characteristics, aerodynamic coefficients, air density, and system inefficiencies.

The power consumed by the i-th rotor of the UAV in hovering flight is given in (1). The equation considers the rotor’s power consumption in hovering, accounting for factors such as the weight of the UAV ($W$), rotor radius ($r$), thrust coefficient ($C$), and additional factors affecting power consumption (${\delta }_s$), along with air density ($\rho$), rotor disk area ($A$), and a constant $k$ representing system inefficiencies. Next, the power consumed by the i-th rotor of the UAV in horizontal flight with a constant speed $V$ is given in (2). It considers factors such as $W, r, C, \rho , V$, additional aerodynamic factors ${\delta }_s$, and a parasitic drag coefficient ($SF{P}_{\left|\right|})$ representing the drag force perpendicular to the direction of motion. Constants $v_2$ and $v_4$ represent aerodynamic characteristics of UAVs. Finally, the power consumed by the i-th rotor of the UAV in vertical ascent and descent is given in (3). This equation includes terms related to the rotor’s power consumption in vertical motion, including $W, r$, thrust in ascent ($T_{ia}$), thrust in descent ($T_{id}$), $V$, and $\rho$.

$$P_{ih}^{ov}=W^{3/2}r\sqrt{{\displaystyle \frac{1}{C}}}-{\displaystyle \frac{3\mathsf{\delta }s}{8\sqrt{\mathsf{\rho }A}}}\sqrt{T}+\left(1+k\right)\sqrt{{\displaystyle \frac{W^{3/2}{r}^2}{\mathsf{\rho }A}}}$$

(1)

$$P_{if}\left(V\right)={\displaystyle \frac{\mathsf{\delta }s}{8\sqrt{\mathsf{\rho }A}}}{\left(\sqrt{{\displaystyle \frac{W}{CT}}}\right)}^{3/2}+{\displaystyle \frac{3\mathsf{\delta }s}{8\sqrt{W\mathsf{\rho }ACT}}}\sqrt{V^2}+\left(1+k\right)\sqrt{{\displaystyle \frac{W^{3/2}{r}^2}{\mathsf{\rho }A}}}{\left(1+\sqrt{{\displaystyle \frac{V^2}{4v_4^2}}-{\displaystyle \frac{V^2}{2v_2^2}}}\right)}^{1/2}+{\displaystyle \frac{1}{2}}SF{P}_{\parallel }\mathsf{\rho }{V}^3$$

(2)

$$P_{\mathrm{ia}}\left(V,T_{\mathrm{ia}}\right)=P_{\mathrm{id}}\left(V,T_{\mathrm{id}}\right)=P_{ih}^{ov}+{\displaystyle \frac{1}{2}}{T}_{\mathrm{ia}}V+{\displaystyle \frac{T_{\mathrm{ia}}^2}{2V^2}}+2T_{\mathrm{ia}}\sqrt{\rho A}\mathrm{ }{P}_{ih}^{ov}+{\displaystyle \frac{1}{2}}{T}_{\mathrm{id}}V+{\displaystyle \frac{T_{\mathrm{id}}^2}{2V^2}}+2T_{\mathrm{id}}\sqrt{\rho A}$$

(3)

5.2. Charging Communication Model

The related works demonstrated that laser beaming charging is an emerging and highly efficient charging method for UAVs, thus the proposed system employs laser beaming for DWC of UAVs. Further, we propose employing laser beaming for optical communication as well. The latter is based on the principle of light fidelity (Li-Fi) [45] and will employ lower power levels for communication and relatively higher power level for DWC of UAVs.

In this setup, LBCNs employ high-power lasers to facilitate efficient charging of UAVs. These towers transmit laser beams to UAVs equipped with solar panels or photovoltaic cells, such as the LBUAVs, which convert the laser energy into electrical power while in motion. This energy is utilized for DWC of EIUAVs, ensuring continuous operation without the need for landing or downtime.

Moreover, the same laser beams used for charging are also employed for data transmission between UAVs. This communication protocol employs Li-Fi technology with on–off keying (OOK) modulation, enabling high-speed data transfer while minimizing interference with other wireless systems. This approach prioritizes charge scheduling and trip planning, ensuring efficient energy management and operational continuity across the UAV network. The power levels of these laser beams are dynamically adjusted based on the operational requirements of the UAVs in the network, prioritizing either charging or communication as needed. This integrated approach not only enhances the efficiency of UAV operations, but also ensures seamless connectivity and energy management across the network of UAVs.

The equations for modeling both charging and communication are derived considering the principles of electromagnetic wave propagation, digital communication, energy transfer efficiency, and environmental conditions. These equations in (4) to (7) are essential for optimizing the performance, efficiency, and reliability of U2U DWC in diverse operational environments.

The power received by a UAV from U2U laser beaming DWC is modeled using (4). It accounts for the efficiency of the receiver (${\eta }_{LRec}),$ the power transmitted by the laser ($P_{LTrans}$), the effective area of the receiver ($A_{LRec}$), the distance between the transmitter and receiver ($d_L$), the line-of-sight factor accounting obstacles ($LOS$), and environmental factors such as atmospheric conditions, obstacles, and interference affecting laser beam propagation ($En{v}_{\lambda }$). Both $LOS$ and $En{v}_{\lambda }$ are a value between 0 and 1.

$$P_{LRec}={\eta }_{LRec}\times P_{LTrans}\times {\displaystyle \frac{A_{LRec}}{d_L^2}}\times LOS\times {Env}_{\lambda }$$

(4)

The total power spent in communication using OOK modulation during DWC is given by (5). It incorporates the principles of digital communication systems, modulation schemes, and energy consumption. The equation accounts for communication transmission efficiency (${\eta }_{CTrans}$), transmitter power ($P_{CTrans}$), receiver area ($A_{CRec}$), distance between transmitter and receiver ($d_C$), $LOS$ and $En{v}_{\lambda }$, energy per bit ($E_b$), and bit duration ($T_b$).

$$P_{comm}={\eta }_{CTrans}\times P_{\mathrm{CTrans}}\times {\displaystyle \frac{A_{CRec}}{d_C^2}}\times LOS\times {Env}_{\lambda }\times {\displaystyle \frac{E_b}{T_b}}$$

(5)

Equation (6) presents a critical charging distance formula aimed at ensuring efficient charging between two drones or a drone and a laser beaming source, leveraging principles of system optimization and power transfer efficiency. It incorporates variables such as transmitter effective area ($A_{LTrans}$), transmitter power ($P_{LTrans}$), receiver efficiency (${\eta }_{LRec}$), and minimum power required by the receiver for successful charging ($P_{LRec}$).

$$d_{\mathrm{crit}}=\sqrt{{\displaystyle \frac{A_{LTrans}\times P_{\mathrm{LTrans}}\times {\eta }_{\mathrm{LRec}}}{P_{LRec}}}\times LOS\times {Env}_{\mathsf{\lambda }}}$$

(6)

Equation (7) focuses on optimizing the alignment between the drone and the laser source to maximize power transfer efficiency, considering factors such as energy required to achieve a desired state of charge ($E_{SoC}$), laser power ($P_L$), charging efficiency (${\eta }_{charge}$), critical distance ($d_{crit}$), and maximum allowable laser power received by the drone ($P_{L_{Max}}$). Additionally, Equation (7) addresses efficient communication, calculating the critical communication distance using receiver effective area ($A_{LRec}$), transmitter power ($P_{LTrans}$), transmission efficiency (${\eta }_{LTrans}$), line of sight ($LOS$), environmental factors (${\mathrm{Env}}_{\lambda }$), and power expended in communication ($P_{comm}$).

$$d_{\mathrm{comm}}=\sqrt{{\displaystyle \frac{A_{\mathrm{CTrans}}\times P_{\mathrm{CTrans}}\times {\eta }_{\mathrm{Trans}}}{P_{\mathrm{comm}}}}\times LOS\times {Env}_{\mathsf{\lambda }}}$$

(7)

The $d_{crit}$ equation defines the optimal distance for effective charging, while $d_{comm}$ determines the critical range for reliable communication. This distinction highlights the different distance requirements for power transfer versus data transmission in the UAV system.

Equation (8) calculates the angle $\theta$ for optimal alignment between a UAV and a laser source to maximize power transfer efficiency. The angle is determined using the arccosine function of a ratio involving several factors: the energy required to achieve the desired state of charge $\left(E_{\mathrm{SoC}}\right)$, the laser power $\left(P_{\mathrm{L}}\right),$ and the charging efficiency $\left({\mathsf{\eta }}_{charge}\right)$. It also incorporates the critical distance for efficient charging $\left(d_{crit}\right)$, the maximum allowable laser power received by the UAV $\left(P_{{\mathrm{L}}_{\mathrm{Max}}}\right)$, the $LOS$ factor accounting for obstacles, and environmental factors affecting laser propagation ($En{v}_{\lambda }$). These variables ensure the calculated angle aligns the UAV for efficient power transfer while accounting for environmental and operational conditions.

$$\theta =\arccos \left({\displaystyle \frac{E_{\mathrm{SoC}}\times P_{\mathrm{L}}\times {\eta }_{charge}}{d_{crit}\times P_{\mathrm{L}\_\mathrm{Max}}}}\times LOS\times {Env}_{\mathsf{\lambda }}\right)$$

(8)

5.3. UAV Placement

Assuming a simplified, even distribution of devices, the deployment strategy for UAVs involves distributing EIUAVs across a grid-based map to ensure thorough coverage of ground units (GUs), including other electric vehicles (EVs). This systematic placement minimizes gaps in surveillance and monitoring capabilities, ensuring comprehensive service delivery and optimal resource utilization by covering the entire area, reducing dead zones, and preventing critical information or events from being missed.

Additionally, a centralized approach places larger, battery-equipped LBUAVs at the grid center to efficiently support EIUAVs with U2U DWC as needed, maximizing operational efficiency and extending mission durations. When the majority of EIUAVs are sufficiently charged (e.g., above 95%), the LBUAVs automatically relocate to a central hub, improving accessibility for maintenance, reducing downtime, and enhancing overall system reliability.

5.4. Charging Scheduling and Trip Planning

Upon receiving a charging request from a UAV, the EDC coordinates with the ESP and CNMs to verify the availability of EVSE. Instead of relying on computationally expensive optimization methods, a heuristic algorithm streamlines the process, balancing simplicity and performance. This approach dynamically prioritizes UAVs based on their urgency, energy levels, and mission requirements, enabling effective resource allocation across aerial vehicle charging networks (AVCN) and ground-based LBCNs.

The algorithm dynamically allocates requests across different charging network (CN) types, prioritizing LBUAVs of part of aerial vehicle charging network (AVCN) and ground-based LBCNs for efficient DWC among UAVs. Specifically, LBUAVs are strategically deployed to provide DWC to EIUAVs, optimizing paths using the A* algorithm extended to 3D space with dynamic obstacle avoidance. Equation (9) outlines the pathfinding algorithm. This algorithm dynamically adjusts flight paths by considering factors such as actual path cost $g\left(n\right),$ heuristic estimates $h\left(n\right)$, altitude impact $c_{alt}\left(n\right)$, and obstacle costs $c_{obs}\left(n\right).$ It should be noted that $n$ is the node index representing each waypoint or location in the UAV’s path. By integrating these elements, LBUAVs can navigate 3D space efficiently, minimizing energy consumption and adapting in real time to obstacles.

$$f\left(n\right)=g\left(n\right)+h\left(n\right)+c_{alt}\left(n\right)+c_{obs}\left(n\right)$$

(9)

For operational scheduling and resource allocation across CNs, the heuristic approach uses (10) to dynamically assess CN suitability based on predefined weights and real-time conditions. The algorithm ranks each CN based on a simplified score. It prioritizes CNs with minimal costs $c_i$, $t_i$, $w_i$, and $b_i$ associated with each CN. Here, $c_i$ refers to the charging costs at a specific CN, $t_i$ denotes the travel time to reach the CN, $w_i$ represents the waiting time at the CN, and $b_i$ signifies battery consumption related to reaching the CN. These terms are scaled using dynamic weights ${\lambda }_1$, ${\lambda }_2$, and ${\lambda }_3$ and ${\lambda }_4$ to adapt real-time needs. These dynamically weighted factors reflect operational priorities, such as minimizing travel for low-energy UAVs or avoiding congested CNs. The heuristic thus efficiently selects CNs, streamlining scheduling while maintaining infrastructure utilization and minimizing downtime.

$${score={\lambda }_{1}c}_i+{\lambda }_2{t}_i+{{\lambda }_{3}w}_i+{{\lambda }_{4}b}_i$$

(10)

Equation (11) ensures UAVs maintain sufficient energy reserves during their missions, providing a dual-check mechanism at charging nodes and during flight. At a charging node, the $i^{th}$ UAV verifies if its state of charge ($So{C}_i$) meets the minimum required threshold in (11) for mission continuation. If $So{C}_i<So{C}_{req}$, the system generates a new charging request to prevent energy deficits. Additionally, UAVs continuously monitor their real-time state of charge ($So{C}_i)$ during flight. If it falls below a critical emergency threshold ($So{C}_{th}$), a charging request is triggered, and the UAV reroutes to the nearest charging facility or LBUAV for immediate replenishment. This comprehensive strategy ensures operational reliability by dynamically addressing energy needs at all stages of the mission.

$$If So{C}_i<\left\{\begin{array}{c}So{C}_{req, } \mathrm{a}\mathrm{t} \mathrm{c}\mathrm{h}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}\\ So{C}_{th} , \mathrm{d}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{m}\mathrm{i}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\end{array}\right.$$

(11)

Equation (12) coordinates reservation times $t_{re{s}_i}$ at CNs, optimizing the scheduling of UAV arrivals, charging sessions, and departures. By synchronizing these times, the algorithm minimizes waiting periods and maximizes the efficient use of charging infrastructure, enhancing overall operational efficiency.

$$t_{ar{r}_i}\le t_{re{s}_i}\le t_{de{p}_i}$$

(12)

To optimize energy efficiency during UAV transit between CNs, (13) imposes a maximum allowable distance $D_{max}$. This constraint ensures that UAVs travel efficiently between charging points, reducing energy consumption and optimizing the use of available resources.

$$d\left(i,j\right)\le D_{max}$$

(13)

Equation (14) addresses the maintenance of adequate energy reserves $E_{rem}$ after visiting CNs. It calculates the remaining energy $E_{rem}$ considering the energy consumed $E_{cons}$ during transit, ensuring UAVs retain sufficient power for subsequent operations and contingencies.

$$E_{rem}-\sum _{i\in \mathcal{N}}{E}_{con{s}_i}\ge E_{min}$$

(14)

Lastly, (15) sets a minimum charging efficiency ${\eta }_i$ requirement at CNs. This optimizes energy transfer efficiency during DWC and ground-based LBCN operations, minimizing delays and ensuring robust charging performance across the UAV network.

$${\eta }_i\ge {\eta }_{min}$$

(15)

5.5. Battery Management and Charging Model

After authentication and synchronization, the EVSE initiates charging within the reserved timeframe aligned with the vehicle’s charging acceptance rate. For accurate simulation, the linear two-stage battery model [46] is recommended over the idealized model (16), which assumes perfect adherence to pilot signals, reflecting real-world lithium-ion battery behavior.

$$\widehat{r}\left(t\right)=\min \left\{r\left(t\right),\overline{r},\widehat{e}\left(t\right)\right\}$$

(16)

The linear two-stage model approximates the charging process with a piecewise linear approach. The charging rate $\widehat{r}\left(t\right)$ in (17) is determined by the pilot signal $r\left(t\right)$, the maximum charging rate $\overline{r}$, the difference between battery capacity and stored energy $\widehat{e}\left(t\right)$, and the state of charge (SoC). This model distinguishes between bulk charging (0% to 70–90% SoC), where current draw is nearly constant, and absorption charging, where current decreases linearly while voltage remains constant. Figure 6 illustrates this realistic charging behavior compared to the idealized model, showing that actual charging rates are lower than pilot signals as the battery approaches full SoC. Environmental factors and charger characteristics influence actual charging rates, making the piecewise linear model a robust approximation of real-world EV charging dynamics.

$$\widehat{r}\left(t\right)=\left\{\begin{array}{c}\min \left\{r\left(t\right),\overline{r},\widehat{e}\left(t\right)\right\} if SoC\le th\hfill \\ \min \{{\displaystyle \frac{\left(1-SoC\right)\overline{r}}{1-th}},r\left(t\right) \} otherwise\hfill \end{array}\right.$$

(17)

5.6. Dynamic Arrival Handling

The management of UAVs at ground-based charging stations involves several strategies to handle early arrivals efficiently. Upon arrival, if a charging station is available, the UAV begins charging immediately. Otherwise, it can enter a queue for subsequent charging slots. This approach ensures that UAVs engaged in tasks such as extending cellular networks or performing edge computing can continue offering services even while waiting. If no queue space is available, the UAV has the option to wait on nearby rooftops or rest areas, or to cancel its reservation and seek another available charging station promptly. This cancellation releases the reserved time slot for immediate rebooking, optimizing the utilization of charging resources.

The proposed system relies on estimating UAV arrival times and pre-emptively communicating with them to adjust their bookings to the earliest available time slot. This involves ultra-fast, reliable communication technologies such as 6G and IoT devices across multiple sensors and devices. The estimated arrival time $t_{arr,Ui}$ for $UA{V}_i$ is calculated using the current time $t_{current},$ the UAV’s distance to the charging station $d_i$, its average velocity $v_i$, and any delays $\Delta t_{delay}$ due to environmental factors. The formula for the arrival time is given in (18).

$$t_{arr,\mathrm{U}i}=t_{current}+{\displaystyle \frac{d_i}{v_i}}+\Delta t_{delay}$$

(18)

This calculation allows the system to predict UAV arrival times and adjust bookings dynamically. If the UAV arrives early and a charging station is available, it begins charging immediately. If the station is not available, the UAV enters a queue for the next available slot. The length of the queue can be updated as in (19), where $q_{length}$ is the current length of the queue.

$$q_{length}=q_{length}+1$$

(19)

If the queue exceeds the maximum capacity $q_{max}$, the UAV is given options to wait nearby or seek another station. This decision is based on the availability and efficiency of other nearby charging stations. The decision-making rule for this case is given in (20), where $statu{s}_i$ determines the UAV’s next action (wait or rebook).

$$statu{s}_i=\left\{\begin{array}{c}Wait if space is avaialble\\ Rebook if space is unavailable \end{array}\right.$$

(20)

For UAVs engaged in DWC, effective coordination is crucial as governed by (21), where $t_{arr,CDV}$ and $t_{arr, CRV}$ are the respective arrival times of the charge-delivering vehicle (CDV) and the charge-receiving vehicle (CRV), and ${\Delta }_{t_{sync}}$ is the maximum allowable time difference for successful coordination.

$$\mid t_{arr,CDV}-t_{arr,CRV}\mid \le {\Delta }_{t_{sync}}$$

(21)

If a charge delivery vehicle arrives early, it can cancel its reservation or wait at a designated area until the charge-receiving UAV arrives. Conversely, late arriving charge-receiving UAVs are offered options to cancel or reschedule. The system aims to optimize charging efficiency and resource utilization by minimizing the total cost in (10), which balances factors such as charging cost, travel time, waiting time, and battery consumption at the chosen station.

For late arrivals, the system adapts by extending booking times if available slots exist. If slots are not available, the UAV may need to rebook at another charging station. This adaptive approach maximizes charging infrastructure efficiency and minimizes waiting times. If the UAV’s delay is predictable, such as due to traffic or environmental conditions, the system can proactively adjust its booking time. The system aims to minimize the likelihood of late arrivals by continuously monitoring progress. This proactive approach allows the system to offer alternative charging stations or adjust booking times accordingly, ensuring that the UAV receives timely charging.

The probability of an on-time arrival is given by (22), where $P_{ontime,i}$ is the probability that $UA{V}_i$ will arrive on time, $F_{delay}(.)$ is the cumulative distribution function of the expected delay, and ${\Delta }_{t_{delay}}$ represents the expected delay.

$$P_{ontime,i}=1-F_{delay}\left({\Delta }_{t_{delay}}\right)$$

(22)

In cases where a UAV’s reservation time needs to be adjusted, the system ensures that the charging slots are used efficiently by updating the departure time $t_{dep,Ui}$ for late arrivals as in (23), where $t_{dep,Ui}$ is the original departure time, and ${\Delta }_{t_{late}}$ is the additional time needed to accommodate a late arrival.

$$t_{dep,\mathrm{U}i}^{\mathrm{\prime }}=t_{dep,\mathrm{U}i}+{\Delta }_{t_{late}}$$

(23)

This adaptive system ensures that each UAV is charged in a timely manner, maximizes infrastructure usage, and minimizes delays or inefficiencies. If reservations are canceled, time slots are freed for other UAVs, ensuring continuous optimization based on real-time conditions.

6. UAV Critical Distance Analysis

An analysis using Equations (4)–(8) evaluates how LOS and environmental factors impact critical charging distances ($d_{crit})$ and communication distances ($d_{comm}$) for both consumer and industrial drones. Industrial drones, being five times more powerful than consumer drones, exhibit greater efficiency across varying transmitter powers when one factor is varied from 0.2 to 1 while keeping the other constant at 1, as illustrated in Figure 7. The study underscores that LOS, and environmental conditions significantly influence $d_{crit}$ and $d_{comm}$, with industrial drones capable of sustaining operations at longer distances due to their larger size and power.

This analysis emphasizes the critical role of robust communication infrastructure and optimal LOS conditions in facilitating seamless UAV operations. It advocates for proactive infrastructure planning that considers these factors to enhance resilience against environmental challenges, thereby optimizing both communication and charging effectiveness for UAVs. Moreover, given our advocacy for laser beaming charging and communication, integrating these technologies into infrastructure planning can further enhance the operational capabilities and efficiency of UAV networks, ensuring reliable performance across diverse environmental conditions.

7. Simulation Setup and Results

The simulator focuses on modeling charging reservations and trip planning for UAVs within a 6G-ITS environment, testing various scenarios to observe the impacts of proposed algorithms. Small-scale experiments ensure correct implementation of system architecture, handshake protocols, and interactions between UAVs.

To evaluate and verify the system setup, performance estimation parameters are computed. These include the average wait time per vehicle $\left(T_Q\right),$ which measures the average time a vehicle spends in the queue of a CN waiting for service. Lastly, the average system wait time $\left(w\right),$ or response time, encompasses the total time a vehicle spends in the system or CN, including both queuing and service times. These parameters collectively assess the efficiency and effectiveness of the charging network’s reservation and scheduling system. All simulations are run on a system equipped with an Intel Core i9-13900HX processor (Intel, Santa Clara, CA, USA), Crucial 32 GB RAM (Micron Technology, Boise, ID, USA), an NVIDIA RTX 4080 GPU (Nvidia, Santa Clara, CA, USA), and Microsoft Windows 11 (Microsoft, Redmund, WA, USA).

7.1. UAV to UAV Dynamic Wireless Charging

In the UAV-centric simulation using Python 3.12, three LBUAVs with 5 kWh batteries and six EIUAVs with 2.5 kWh batteries (industrial drones) are simulated. All UAVs initially hover, with LBUAVs moving towards the EIUAVs to provide UAV-to-UAV charging while hovering. Similarly, LBUAVs fly towards ground-based stations and hover to obtain charging. LBUAVs use a 1 kW laser for charging, while EIUAVs use a 0.5 kW laser for communication. The UAV flight dynamics are governed by the power consumption model in (1) to (3), incorporating key parameters such as weight, rotor characteristics, and aerodynamic factors, to simulate realistic flight modes, speed, trajectory, and altitude. The optimal UAV placement algorithm positions EIUAVs for coverage, while LBUAVs provide DWC to EIUAVs, as shown in Figure 8 and

Table 2. UAV simulation parameters.

Param.	LBUAV	EIUAV	Param.	LBUAV	EIUAV
Weight (kg)	5	2.5	k	0.52	0.52
C	0.95	0.95	v2, v4	0.2, 0.4	0.2, 0.4
δs	50	25	SFC	0.25	0.3
Ρ	1.225	1.225	SFP||	0.156	0.19
A	5.25	5.25	ηreceiver	0.95	0.95
T	200	100	ηtransmitter	0.85	0.85
V	20	15	Areceiver	0.35	0.25
r	0.1	0.1	LOS, Env	0.95, 0.95	0.95, 0.95

.

During the 250 min simulation, EIUAVs request charging, and the algorithm schedules LBUAVs for DWC, illustrated by LBUAV 3’s path planning to service EIUAVs 1, 2, and 3 (Figure 9 and Figure 10). The results, summarized in

Table 3. Mission statistics of LBUAV ID 3 serving EIUAV 1 to 3.

Paths	d (m)	t (min)	Obstacles	SoCreq	SoCdeliv	ηcharge
1	38.78	27.5	1	4.82	4.33	0.898
2	24.50	5.0	1	3.21	2.89	0.900
3	24.50	5.0	0	2.87	2.69	0.937

, show that LBUAVs achieve high operational efficiency with an average charging efficiency of approximately 91.2%. Each EIUAV experiences minimal waiting times, averaging 2.12 min, enhancing mission duration. LBUAVs cover an average distance of approximately 29.26 m per operation.

This experimental validation underscores the system’s effectiveness in optimizing UAV operations and charging efficiency. Integration of laser beaming charging and Li-Fi communication enhances UAV autonomy, enabling extended flight times and reliable data transmission for applications such as surveillance and logistics. Future research will scale these findings to real-world scenarios, further validating the system’s potential to advance UAV capabilities and operational efficiency.

7.2. UAVs: Handling Late and Early Arrivals

The simulation, implemented in Python 3.12 [47] using SUMO with TraCI library 1.19 [48], models the dynamics of CAEV traffic and UAV operations. It features 10 CAEVs generated with a Poisson arrival pattern and strategically positions 3 LBUAVs and 6 EIUAVs in 3D space using a proposed placement algorithm (similar to Table 2 parameters). EIUAVs are statically placed in a grid pattern as RSUs, while LBUAVs are centered among them to optimize coverage. Additionally, the SUMO map includes 2 LBCNs symmetrically positioned on a two-lane highway setup.

During the 550 min simulation, the system manages GUs, such as CAEVs, requesting services from EIUAVs, depleting their batteries. Meanwhile, LBUAVs use an A* extended algorithm with 3D extensions to plan trips for delivering charging to EIUAVs whose battery levels fall below a 40% threshold. Results depicted in Figure 10 show an average charging efficiency of approximately 92.75% for EIUAVs and 96.37% for LBUAVs via LBCN in Figure 11 and Figure 12, respectively. Charging reservations closely align with actual charging received, with discrepancies attributed to system inefficiencies or late arrivals affecting complete charging duration.

A comparison is conducted between a system that does not account for dynamic arrivals (System 1) and a system that incorporates dynamic arrival considerations (System 2) using the proposed dynamic arrival management protocol. This protocol effectively minimizes delays, reducing average wait times by 1.5 min for EIUAVs (Figure 13) and 5.0 min for LBUAVs (Figure 14), with a 95% confidence interval. It should be noted that in Figure 13 and Figure 14, any EIUAV or LBUAV with no bar graph indicates that the vehicle did not experience any waiting time for charging, resulting in a wait time of zero.

The reduction in wait times (1.5 min for EIUAVs and 5.0 min for LBUAVs) may seem minor, but their cumulative effect is substantial in real-world UAV operations. For critical applications such as surveillance, logistics, and search and rescue, even small reductions in wait times can optimize UAV resource utilization, allowing them to maximize flight time, improve coverage, and enhance operational capacity—particularly in real-time scenarios where responsiveness is crucial. In large-scale operations or extended deployments, these small improvements compound, leading to higher system throughput and greater operational flexibility. This reduction also boosts UAV endurance, enabling longer missions with improved performance, which is vital in fields such as emergency response, where every second counts. Moreover, these results address broader UAV challenges, such as operational efficiency, resource balancing, and minimizing downtime in dynamic environments. By improving wait times and optimizing charging, the system ensures UAVs remain operational without delays, helping to integrate them more effectively into complex systems such as ITS. Overall, these cumulative improvements significantly enhance system performance, scalability, and reliability, making UAV missions more effective in dynamic, mission-critical environments.

This approach ensures operational efficiency in managing real-time arrival variations, which is crucial for maintaining service standards and customer satisfaction. Overall, under ideal UAV operational conditions, this experiment highlights the system’s capability to optimize charging reservations and dynamic trip planning for UAVs, showcasing its potential impact in real-world applications.

7.3. Scalability and Computational Efficiency

The proposed trip planning and charging scheduling system employs a heuristic approach that strikes a balance between computational efficiency and real-time performance. For pathfinding, the system uses an A* algorithm extended to 3D space, which considers factors such as energy consumption, obstacles, and altitude. The complexity of this pathfinding, $O(n ·|E| log |V\left|\right)$, represents the computational cost of exploring $n$ waypoints (nodes), evaluating $\left|E\right|$ possible paths (edges) between them, and considering $\left|V\right|$ locations (vertices). It is manageable for small-to-medium-scale systems, but could become computationally expensive as the number of UAVs and waypoints increases. However, the dynamic path adjustments based on real-time data reduce the need for frequent recalculations, ensuring the system remains responsive and efficient.

The charging scheduling system uses a heuristic method to rank and select charging stations based on key parameters such as charging costs, travel time, waiting time, and battery consumption. The complexity of $O(n · m)$, where $n$ is the number of UAVs and $m$ is the number of charging stations, ensures that the system is efficient for smaller fleets. This approach avoids exhaustive optimization, enabling quick resource allocation and real-time decision making. The heuristic algorithm balances performance and computational cost, making it a good solution for small-to-medium-scale applications where cost efficiency is important.

The system architecture is inherently designed to be scalable, ensuring that it can handle larger fleets and charging infrastructure as the system grows. While the current complexity is manageable for small to medium systems, for very large-scale operations, further optimizations will be necessary. Potential enhancements could include parallel processing, distributed computing, or the incorporation of machine learning techniques, which would allow the system to better handle the increased computational load and improve scalability. These improvements would enable the system to maintain performance even as the size of the UAV fleet and the charging network expands.

The proposed system offers a cost-effective solution for UAV trip planning and charging scheduling, particularly for small-to-medium-scale operations, by using a heuristic algorithm that strikes a good balance between computational efficiency and real-time performance. This makes it a viable solution in terms of cost, while key technologies such as IEC and 6G connectivity enable real-time communication and optimization across the fleet. Additionally, the integration of laser-powered DWC between UAVs enhances energy transfer efficiency and minimizes downtime, reducing reliance on physical charging stations. While the system is currently designed to prioritize low operational costs and minimal delays, challenges may arise in larger-scale systems due to computational complexity and infrastructure expansion costs. However, the system architecture is scalable, and future efforts will focus on enhancing algorithmic efficiency, incorporating distributed processing, and utilizing cloud-based infrastructure to address these challenges. These advancements will ensure the system remains effective, cost-efficient, and adaptable to large-scale ITS in the future.

7.4. Comparison with Existing Literature

The proposed UAV system distinguishes itself by integrating DWC, ground-based LBCNs, and IEC, offering an innovative solution to energy constraints through real-time UAV-to-UAV energy transfer and hybrid energy provisioning. Additionally, the integration of 6G further enhances the system’s communication capabilities, enabling more efficient coordination between UAVs and ground stations. Compared to [33], which focuses on laser-powered relay networks with static optimization techniques, our approach introduces a dynamic framework that adapts to changing mission parameters and real-time charging needs, enabling greater operational flexibility and scalability. Unlike their focus on maximizing relay efficiency within fixed laser-powered constraints, our system incorporates diverse energy sources to extend operational endurance.

It is challenging to directly compare our work with existing literature, as it stands unique in its integration of advanced technologies: DWC, LBCNs, and UAV-to-UAV energy transfer, along with IEC and 6G. This innovative combination, tailored to a distinctive application, sets our framework apart from conventional approaches. Additionally, our work is built upon a three-layer architecture and handshake protocol that ensures efficient coordination and communication within the system, further distinguishing it from existing systems. Nevertheless, we sought to draw comparisons with existing works, aiming to highlight areas where our system offers notable advantages and improvements.

Our findings align with the insights from [31], particularly regarding the influence of LOS and environmental factors on charging and communication distances. Both studies emphasize the critical role of these factors in optimizing UAV operational efficiency, with our work focusing on their impact on critical charging distances and communication distances. By incorporating these considerations, our analysis further supports the potential of laser beaming charging to enhance UAV endurance, especially in dynamic mission environments.

While prior studies, such as [33,49], focus on singular charging modalities or static optimization strategies, our system’s hybrid model and real-time adaptability provide greater flexibility and operational robustness. In comparison with [49], which addresses cost-effective trajectory optimization for wireless sensor networks, our hybrid model bridges the gap between efficiency and adaptability. By combining LBCNs and DWC, our work expands on their single-mode charging architecture, particularly in complex, dynamic mission environments. Similarly, [50] optimizes energy usage through predefined recharging paths, whereas our approach dynamically adjusts UAV routes in real time based on mission demands and energy availability, ensuring minimal downtime and enhanced operational coverage.

Finally, compared to [35], which focuses on cooperative path planning with static charging stations, the proposed system enables seamless UAV-to-UAV energy transfer, allowing for unprecedented mission continuity even in the absence of accessible ground infrastructure. While their iterative algorithms improve coverage and service rates, our hybrid charging model ensures greater resilience to environmental and demand variability, offering enhanced adaptability to changing operational conditions. Collectively, these comparisons underscore the uniqueness of our proposed framework in providing dynamic, scalable, and energy-efficient UAV operations, addressing limitations of prior works while enabling sustained mission success in diverse scenarios.

8. Sustainability and Feasibility of UAV Charging Infrastructure

The integration of UAV-to-UAV charging through ground-based laser beaming and DWC systems offers significant potential for enhancing UAV operational efficiency and autonomy. While the initial infrastructure costs for large-scale deployment of laser charging stations are expected to be high due to the complexity of the technology, these challenges are not insurmountable. Emerging technologies, such as fuel cells [51], historically faced similar high upfront costs but have become more affordable over time as technological advancements and economies of scale have been realized. Likewise, the cost of laser charging infrastructure is likely to decrease as the technology matures. Furthermore, the modular and scalable nature of laser charging stations allows for phased deployment, enabling smaller, cost-effective installations that can expand as the technology becomes more widely adopted.

Energy efficiency remains a key consideration, as laser-based energy transfer systems inherently involve some loss. However, ongoing advancements in laser systems and photodiode receivers are addressing these inefficiencies. A feasibility assessment in [52] demonstrated that UAVs can receive up to 73.5 W of net power at a distance of 500 m, with the laser module consuming 600 W of electrical power. This supports that laser charging could extend UAV operating times during flight, improving mission efficiency. Additionally, integrating cooling systems for photovoltaic panels on UAVs could mitigate heat buildup, further enhancing energy conversion and system performance.

Despite the current challenges in cost and efficiency, the long-term benefits of laser-powered UAV charging are substantial. These benefits include extended range, increased operational autonomy, and the elimination of physical charging connections, all of which provide strong justification for investment. Regarding environmental impact, although UAVs are typically manufactured using energy-intensive materials, the industry is shifting towards more sustainable practices, such as using recyclable materials and improving energy efficiency during production. The integration of renewable energy sources, particularly solar or wind power, into UAV charging infrastructure could significantly reduce the carbon footprint of UAV operations. This would align with global goals to cut emissions, such as the European aviation sector’s target of reducing CO₂ emissions by 75% by 2050 through clean technologies [51]. A lifecycle analysis of both UAVs and the laser charging infrastructure would help optimize materials, energy consumption, and system design, further reducing emissions across the entire system lifecycle.

The use of 6G technology and IEC can further optimize the practicality and sustainability of these systems. Real-time data processing enables the optimization of charging schedules, reducing unnecessary energy consumption and ensuring UAVs are charged only when required. This reduces overall energy use, supporting the long-term sustainability and cost-effectiveness of the system.

So, while large-scale deployment of laser-powered UAV charging infrastructure faces challenges in terms of cost and energy efficiency, the combination of laser charging, DWC systems, and advanced technologies such as 6G and IEC offers a promising pathway for reducing UAV operational costs and carbon footprints. The scalability of these systems, along with anticipated cost reductions as the technology advances, makes them a viable solution for future autonomous UAV operations.

9. Conclusions and Future Work

In conclusion, the proposed three-layer system for DWC reservation and UAV trip planning, integrating laser beaming charging and a handshake protocol, represents a significant step forward in managing charging requests and optimizing routes. The system effectively addresses dynamic UAV arrivals, ensuring efficient charging allocation and route optimization.

Discrete-event simulations provided a comprehensive analysis of system interactions, validating key architectural elements—such as the three-layer framework, handshake protocols, and payment schemes—through small-scale experiments. These tests confirmed the system’s ability to handle UAV arrivals, charge scheduling, and trip planning, offering a solid foundation for further development.

Simulations demonstrated high charging efficiency (91.2% for LBUAVs) with minimal wait times (2.12 min) and an average operational distance of 29.26 m. In another scenario, EIUAVs and LBUAVs achieved efficiencies of 92.75% and 96.37%, respectively, with dynamic arrival management reducing wait times by 1.5 min for EIUAVs and 5.0 min for LBUAVs. These results highlight the system’s effectiveness in optimizing UAV operations and charging efficiency.

Given the futuristic nature of the system, no datasets were used, relying instead on simulation. The system’s scalability and flexibility enable potential integration with other charging technologies and vehicle types for comparative studies.

Future research will build on these findings to explore advanced methods for improving system performance, with a focus on optimizing charging processes, enhancing operational efficiency, and adapting to diverse environments and use cases.

Overall, this work provides a strong platform for advancing UAV efficiency and sustainability in DWC environments, supporting reliable operations in complex urban settings.

A list of abbreviations can be found in

Table A1. List of abbreviations.

Acronym	Description
AVCN	Aerial Vehicle Charging Network
CN	Charging Network
CNMs	Charging Network Managers
CP	Credit Point
CDV	Charge Delivering Vehicle
CRV	Charge Receiving Vehicle
DAGs	Directed Acyclic Graphs
DDPG	Deep Deterministic Policy Gradient
DQN	Deep Q-Network
DRL	Deep Reinforcement Learning
DWC	Dynamic Wireless Charging
EDC	Energy Distribution Center
EIUAV	Edge Intelligence Unmanned Aerial Vehicle
ESP	Energy Service Provider
EVSE	Electric Vehicle Supply Equipment
FANET	Flying Ad Hoc Network
GU	Ground User
HFL	Hierarchical Federated Learning
IEC	Intelligent Edge Computing
IoT	Internet of Things
ITS	Intelligent Transportation Systems
IWPT	Inductive Wireless Power Transfer
KDC	Key Distribution Center
LBCN	Laser Beaming Charging Network
LBUAV	Laser-Beaming Unmanned Aerial Vehicle
Li-Fi	Light Fidelity
LOS	Line Of Sight
LSTM	Long Short-Term Memory
MADDQN	Multi-Agent Double Deep Q-Learning
MSE	Mean Squared Error
OOK	On–Off Keying Modulation
QoE	Quality Of Experience
RL	Reinforcement Learning
RSU	Roadside Unit
SF	Service Function
SoC	State Of Charge
SWC	Static Wireless Charging
U2U	UAV to UAV Charging
UAV	Unmanned Aerial Vehicle
V2G	Vehicle-to-Grid Communications
V2I	Vehicle-to-Infrastructure Communications
V2V	Vehicle-to-Vehicle Communications
VLC	Visible Light Communication
WCP	Wireless Charging Pad
WPT	Wireless Power Transfer

, and the list of symbols is presented in

Table A2. List of Symbols.

Symbol	Definition
$A$	rotor disk area (${\mathrm{m}}^2$)
$A_{Trans}$	Transmitter effective area (${\mathrm{m}}^2$)
$A_{Rec}$	Effective area of the receiver (${\mathrm{m}}^2$)
$b_i$	Battery consumption cost related to reaching the CN
$C$	thrust coefficient
$c_{alt}\left(n\right)$	Altitude impact on cost
$c_i$	Charging cost at a specific CN
$c_{obs}\left(n\right)$	Obstacle cost
$d$	Distance between the transmitter and receiver ($\mathrm{m}$)
$D_{max}$	Maximum allowable distance ($\mathrm{m}$)
$d_{crit}$	Critical distance ($\mathrm{m}$)
$\Delta t_{delay}$	UAV delays due to environmental factors
${\Delta }_{t_{sync}}$	Maximum allowable time difference for successful coordination between CDV and CRV
${\Delta }_{t_{delay}}$	Expected UAV delay
$E_{cons}$	Energy consumed during transit
$\widehat{e}\left(t\right)$	Difference between battery capacity and stored energy ($\mathrm{W}\mathrm{h}$)
$E_b$	Energy per bit ($\mathrm{J}$)
$E_{min}$	Minimum energy threshold ($\mathrm{k}\mathrm{W}\mathrm{h}$)
$En{v}_{\lambda }$	Environmental factors such as atmospheric conditions, obstacles, and interference affecting laser beam propagation. It is a value between 0 and 1 with 1 being the best.
$E_{rem}$	Remaining energy of UAVs ($\mathrm{k}\mathrm{W}\mathrm{h}$)
$E_{SoC}$	Energy required to achieve a desired state of charge ($\mathrm{k}\mathrm{W}\mathrm{h}$)
$F_{delay}(.)$	Cumulative distributed function of the expected delay
$g\left(n\right)$	Actual path cost
$h\left(n\right)$	Heuristic estimate of cost
$k$	Constant representing inefficiencies in the system
$LOS$	Line-of-sight factor accounting for obstacles. Line of sight is a value between 0 and 1 with 1 being the best.
$P_{comm}$	Power expended in communication ($\mathrm{W}$)
$P_h$	Power consumed by the i-th rotor of the UAV in hovering flight ($\mathrm{W}$)
$P_{hf}$	Power consumed by the i-th rotor of the UAV in horizontal flight with a constant speed V ($\mathrm{W}$)
$P_L$	Laser power ($\mathrm{W}$)
$P_{Lmax}$	Maximum allowable laser power received by the drone ($\mathrm{W}$)
$P_{LRec}$	Minimum power required by the receiver for successful charging ($\mathrm{W}$)
$P_{LTrans}$	Power transmitted by the laser ($\mathrm{W}$)
$P_{va}$	Power consumed by the i-th rotor of the UAV in vertical ascent ($\mathrm{W}$)
$P_{vd}$	Power consumed by the i-th rotor of the UAV in vertical descent ($\mathrm{W}$)
$P_{ontime,i}$	Probability that $UA{V}_i$ will arrive on time
$q_{length}$	Length of the queue at the charging station
$q_{max}$	Maximum queue capacity at the charging station
$r$	rotor radius ($\mathrm{m}$)
$r\left(t\right)$	Pilot signal controlling the charging rate ($\mathrm{A}$)
$\widehat{r}\left(t\right)$	Charging rate ($\mathrm{A}$)
$\overline{r}$	Maximum charging rate ($\mathrm{A}$)
$SFC$	Specific fuel consumption
$SF{P}_{\parallel }$	Parasitic drag coefficient representing the drag force perpendicular to the direction of motion
$SoC$	State of Charge, indicating the level of charge in the battery ($\%$)
$So{C}_{th}$	Threshold State of Charge ($\%$)
$So{C}_{req}$	Requested State of Charge ($\%$)
$statu{s}_i$	Determines the UAV’s next action
$T$	Thrust ($\mathrm{N}$)
$t_{{arri}_i}$	Arrival time at CNs ($\mathrm{s}$)
$t_{{dep}_i}$	Departure time at CNs ($\mathrm{s}$)
$t_{{resi}_i}$	Reservation time at CNs ($\mathrm{s}$)
$t_{arr,Ui}$	Estimated arrival timefor $UA{V}_i$
$t_{dep,Ui}$	Estimated departure timefor $UA{V}_i$
$t_{current}$	Current time
$t_{arr,CDV}$	Estimated arrival time for CDV
$t_{arr,CRV}$	Estimated arrival time for CRV
$T_b$	Bit duration ($\mathrm{s}$)
$t_i$	Travel cost to reach the CN
$T_{ia}$	Thrust in ascent ($\mathrm{N}$)
$T_{id}$	Thrust in descent ($\mathrm{N}$)
$V$	Constant speed ($\mathrm{m}/\mathrm{s}$)
$v_2,v_4$	Constant representing aerodynamic characteristics of UAVs
$W$	weight of the UAV ($\mathrm{N}$)
$w_i$	Waiting cost at the CN
${\delta }_s$	additional factors affecting power consumption
${\eta }_{Min}$	Minimum charging efficiency requirement at CNs
${\eta }_i$	Charging efficiency at CNs
${\eta }_{charge}$	Charging efficiency
${\eta }_{Rec}$	Efficiency of the receiver
${\eta }_{Trans}$	Efficiency of the transmitter
$\theta$	Angle of alignment between the UAV and the laser source for optimal power transfer ($\mathrm{r}\mathrm{a}\mathrm{d}$)
$\rho$	air density ($\mathrm{k}\mathrm{g}/{\mathrm{m}}^2$)

.