Relay Node Selection Methods for UAV Navigation Route Constructions in Wireless Multi-Hop Network Using Smart Meter Devices

Abstract

Unmanned aerial vehicles (UAVs) offer solutions to issues like traffic congestion and labor shortages. We developed a distributed UAV management system inspired by virtual circuit and datagram methods in packet-switching networks. By installing houses with wireless terminals, UAVs navigate routes in a multi-hop network, communicating with ground nodes. UAVs are treated as network packets, ground devices are treated as routers, and their connections are treated as links. Activating all nodes as relays increases control message traffic and node load. To optimize connectivity, we minimize relay nodes, connecting non-relay nodes to the nearest relay. This study proposes four relay node selection methods: random selection, two adjacency-based methods, and our innovative approach using Multipoint Relay (MPR) from the Optimized Link State Routing Protocol (OLSR). We evaluated these methods according to their route construction success rates, relay node counts, route lengths, and so on. The MPR-based method proved most effective for UAV route construction. However, fewer relay nodes increase link collisions, and we identify the minimum relay density needed to balance efficiency and conflict reduction.

1. Introduction

As the number of parcel deliveries is increasing every year, the logistics industry faces various problems such as traffic congestion and labor shortages, while truck drivers are aging and decreasing in number. Unmanned delivery technology using unmanned aerial vehicles (UAVs) can solve these issues. Valeska E., et al. presented comprehensive review of UAV applications in last-mile logistics, emphasizing their role in alleviating labor shortages and urban traffic challenges [1]. The discussion focuses on the challenges facing delivery systems, such as labor shortages and traffic congestion in urban areas, and the use of unmanned aerial vehicles and autonomous robots in last-mile logistics. Amer J., et al. systematically reviewed the role of UAVs in last-mile delivery and identifies technical and operational challenges [2]. It also discusses multiple delivery strategies and route optimization approaches.

Francesco B. S., et al. systematically reviewed the latest research trends and issues related to UAV-based delivery systems [3]. In particular, it discusses in detail the importance of selecting the power source for UAVs (fuel cells, batteries, solar cells, super capacitors) and energy management systems. Kaneko S., et al. examined the optimization of fleet design for UAVs used for package delivery, taking into account energy consumption [4]. It analyzes the aircraft conceptual design process in detail, from determining typical mission requirements to optimizing design variables. Burke C., et al. studied the ability of UAVs to drop off packages using rotational movements in the air [5]. In particular, it details the design of the basket that holds the package, which is achieved by the UAV performing rapid upside-down aerial maneuvers. Patchou M., et al. analyze the efficiency improvements and communication performance of a hybrid logistics system that combines ground vehicles and UAVs [6]. In particular, they focused on the efficiency improvements of “last-mile” delivery through the coordination of delivery trucks and UAVs.

Currently, any UAV can fly only in the approved airspace. Dissanayaka D., et al. reviewed UAV navigations and proposed a navigation control system for UAVs using visual–LiDAR odometry and mapping (VLOAM) based on real-time processing of video [7]. However, this method has a major problem of the power consumption and the ability to perform a large amount of computation in real time. Therefore, Chen S., et al. divided the map into three layers: awareness, local, and global. Then, they divided the computation process into three parts to optimize the computation process and the power consumption [8]. Rakesh S., et al. discussed a UAV traffic management system that utilizes 6G network technology; their study presents issues and solutions for large-scale UAV operations [9]. In particular, the roles of communication infrastructure and network design are emphasized. Abdeljawed S., et al. discussed methods for optimizing delivery routes using multiple UAVs [10]. They focused on the economic and environmental efficiencies of UAVs. Hao Z., et al. proposed a hybrid differential evolution (HDE) algorithm for UAV route optimization in 3D environments [11].

Yang P., et al. proposed a novel path planning method for UAVs, evolving waypoints separately to optimize route efficiency and adaptability under constraints [12]. Huang C., et al. introduced an improved particle swarm optimization algorithm with a global best path competition mechanism to enhance UAV path planning efficiency [13]. Roberge V., et al. developed a GPU-accelerated genetic algorithm for fast path planning of fixed-wing military UAVs, optimizing computational performance and planning quality [14]. Chen Y., et al. proposed a modified wolf pack search algorithm to efficiently solve 3D path planning problems for UAVs, ensuring obstacle avoidance and energy efficiency [15]. Yu L., et al. introduced a dynamic local path planning method combining laser rangefinder data and extended SVM, which is applicable to outdoor robots and UAVs [16]. Wang G. G., et al. presented an enhanced bat algorithm for 3D path planning of unmanned combat aerial vehicles (UCAVs), focusing on adaptability and obstacle avoidance [17]. Gautam S. A., et al. combined genetic algorithms and artificial neural networks for efficient 3D UAV path planning, enhancing adaptability in complex environments [18]. Goncharenko V. I., et al. proposed a hybrid algorithm integrating multiple methods for efficient UAV route construction under various constraints [19]. Ozlem S. M., et al. discussed methods for optimizing arrival routes to improve flight efficiency in aerial navigation systems [20]. Schouwenaars T., et al. applied mixed-integer programming for efficient multi-vehicle path planning, addressing coordination and collision avoidance [21]. Evdokimenkov V. N., et al. explored pre-flight planning algorithms for UAV groups, focusing on distributed control systems for coordinated missions [22]. Ramesh A., et al. provided a comprehensive review of UAV navigation algorithms, discussing trends, challenges, and advancements [23]. Sivakumar M., et al. surveyed the diverse civil applications of UAVs, highlighting their roles in agriculture, surveillance, and disaster management [24]. Fu Z., et al. proposed a heuristic evolutionary algorithm tailored for UAV path planning, focusing on route efficiency and adaptability [25]. Danancier K., et al. compared various path planning algorithms for UAVs in threat-prone environments, evaluating their performance and robustness [26]. Hodge V. J., et al. explored deep reinforcement learning techniques for UAV navigation, utilizing sensor data to enable intelligent decision making [27].

Aircraft usually flies over an air route, which is called a “route in the air”. Each air route determines the direction and the altitude of an aircraft flight for safe navigation. Normal air routes are published as straight lines connecting air navigation radio facilities (VOR [28] and NDB [29]) to each other. Flight routes are formed by combining several straight lines between the departing and arriving airports. When a large number of UAVs fly over the ground for home delivery, air routes will be necessary for UAVs, like normal aircraft routes.

We have established a distributed management system for UAVs inspired by the virtual circuit and datagram methods of packet switching networks.

In Japan, smart meter networks are becoming popular, in which radio terminals are installed in each house to collect the electricity consumption via wireless multi-hop networks. As of 2020, smart meters have been installed in approximately 80% of homes in the United States. In the EU, smart meters have been introduced in approximately 72% of the electricity market by 2020, and their use is particularly widespread in Western European countries. For example, in the UK, a plan is underway to install smart meters in approximately 27 million homes between 2016 and 2024. China has already installed hundreds of millions of smart meters. Wireless multi-hop networks have been built to communicate power information from smart meters in many countries. This fact indicates that wireless multi-hop routing between all the houses is possible if a radio terminal is installed in every house. Gungor V. C., et al. discussed how wireless networks (including smart meters) enable routing and connectivity [30].

Under these conditions, we have investigated a method to create a route between the source and destination nodes of a parcel delivery on a wireless multi-hop network. The radio terminals installed in each house become the nodes of this network and will be used for navigation radio facilities. The UAVs fly over the nodes on the route as while they were transmitting data packets to UAVs [31]. The control of the packet switching network is applied to the flight route control of UAVs by treating UAVs as packets in the network, wireless devices on the ground as routers, and the connection relationship between wireless devices as links.

If the relay function that constitutes the UAV route is activated on all nodes, the number of control messages for the route construction increases, and the message forwarding load of each node increases. To maintain connectivity for any node pair, the relay functions should be operated in as few nodes as possible. End nodes that have no relay function will connect to the nearest relay node. In this paper, we propose methods for selecting nodes that operate the relay functions called relayed nodes.

The first simple method randomly selects the nodes. Our original second and third methods select them based on the number of adjacent nodes. The fourth method is our innovative idea based on the Multipoint Relay (MPR) of the Optimized Link State Routing Protocol (OLSR). For each method, we evaluate the route construction success rate, the number of selected relay nodes, the total distance of constructed routes, and the distance in population-dense regions. We will find the best method for constructing UAV navigation routes and the minimum relay node density to reduce the number of relay nodes suppressing route conflicts.

The rest of this paper is organized as follows:

Section 2 shows the safe and efficient route construction method for UAV navigation in a wireless multi-hop network.

Section 3 introduces the issue related to the route construction method discussed in this paper.

Section 4 discusses related works on this issue.

Section 5 presents four methods that have been proposed to solve this issue.

Section 6 shows the evaluation results of the proposed methods and discusses their effectiveness and characteristics.

Section 7 concludes the paper with a summary and future works.

2. Safe and Efficient UAV Route Construction Method over Wireless Multi-Hop Network

We have established a distributed management system for UAVs that was inspired by the virtual circuit and datagram methods of packet switching networks [31]. We investigate a method to construct safe and efficient navigation routes for UAVs over a multi-hop network with radio terminal nodes as shown in Figure 1. In this method, UAVs are treated as data packets in a network, ground wireless devices as routers, and the connection between wireless devices as links, and the control of a packet switching network is applied to UAV flight path control.

• (1). Each node exchanges routing protocol packets to construct the UAV flight route.

• (2). Each node creates a routing table for the UAV flight route from the source node to the destination node.

• (3). When the UAV arrives over a relay node on its flight route, it queries the node for information about the next hop node.

• (4). The UAV moves towards the next hop node. Repeating (3) and (4), the UAV follows the relay nodes and arrives at the destination node.

2.1. UAV Navigation Network Topology

Mobile ad hoc networks (MANETs) [32] are typical network topology construction techniques for relaying multiple radio terminals. MANET routing protocols can construct the shortest route between source and destination nodes, as shown on the left side of Figure 2. Among them, Optimized Link State Routing Protocol (OLSR) [33] is known as a typical proactive type, and Ad hoc On-Demand Distance Vector (AODV) Routing [34] is a typical reactive type.

Any route for the UAV navigation must be safe and efficient. Thus, the route requires bypass nodes in population-dense regions as much as possible to ensure safety [31]. For this purpose, we consider two levels for the network configuration. The higher level composes the transmission network with nodes in sparsely populated regions. This level is used as the preferred route because it is safe. The lower level is the access network with nodes in population-dense regions that connect to the transmission network via the shortest route. The right side of Figure 2 shows an example of the network configuration suitable for UAV routing.

The optimal route is a safe route with a short “population-dense regions distance”. In order to avoid the risk of running out of battery power, it is also desirable that the “total distance”, which is the distance from the source node to the destination node, is not too long in terms of efficiency.

Yang Y., et al. propose a method to reliably determine the location of waypoints that construct the routes of UAVs [35]. Yao P., et al. proposed a hybrid differential evolution (HDE) algorithm to generate a high-quality and feasible route for fixed-wing UAVs in complex three-dimensional environments [36]. A multi-objective function is designed, and both the route length and risk are optimized.

We have studied two protocols for UAV navigation. One protocol is based on OLSR, which constructs routes using the Dijkstra method [37]. The link cost is a danger-weighted distance. The other is based on AODV, in which each relay node evaluates the received route request (RREQ) messages in terms of the route safety and the flight time. The relay node selects and forwards the better RREQ message to construct an optimal route [38].

The node which receives i-th RREQ adds the distance in the passage area counter of the RREQ. The node evaluates the i-th received RREQ message with i as the decision variable equivalent of the optimization problem, using the objective function equivalent of Equation (1); then, the node records and sends the best i-th RREQ. The destination node transmits a route reply (RREP) through the best route. By weighting the travel time of each node and taking the minimum value, both the safety and the time perspectives are comprehensively determined. $\alpha (0\leqq \alpha \leqq 1)$ is a balanced value for time and safety perspectives, i.e., a factor to avoid population-dense regions from the viewpoint of safety; $(1-\alpha )$ is a factor to shorten the total travel time. In the route from the source node to the node that receives i-th RREQ, $D_i$ is the sum of the distances between the nodes in the population-dense region and half the sum of the distances between the nodes in the sparsely populated region and the nodes in the population-dense region. $S_i$ is the sum of the distances between nodes in the sparsely populated region and half the sum of the distances between the nodes in the sparsely populated region and the nodes in the population-dense region. $v1$ is the speed of the UAV heading to the node in the population-dense region, and $v2$ is the speed heading to the node in the sparsely populated region. $v1$ and $v2$ are set in all nodes.

(1)$min\{\alpha \times {\displaystyle \frac{D_i}{v1}}+(1-\alpha )\times ({\displaystyle \frac{D_i}{v1}}+{\displaystyle \frac{S_i}{v2}})\}$

Because AODV constructs a route just before the communication request, ADOV is suitable for wireless multi-networks where nodes frequently move. Because OLSR creates the routing table in advance, OLSR is suitable for wireless multi-hop networks with little node movement. In this paper, we use the OLSR-based method among the above two methods for the route construction experiments because the radio terminals in each house do not move. We will describe the details of this in the next section.

2.2. Method for Constructing Optimal Routes in Terms of Distance and Safety Based on OLSR

We have proposed an OLSR-based method, in which each node constructs an optimal route that is a safe route with a short “population-dense regions distance”, and in which the distance from the source node to the destination node, i.e., the “total distance”, is not too long [37].

2.2.1. Optimized Link State Routing Protocol (OLSR)

For OLSR, each node periodically sends HELLO and TC messages to update the routing table. The HELLO message performs the tasks of the link discovery, the neighbor node discovery, and the Multipoint Relay (MPR) set discovery.

TC messages advertise the topology information to the entire network by flooding.

Each node sends TC messages based on its Local Link Information. When each node receives a TC message, it updates the received topology and updates the routing table. MPR is one of the features of OLSR, which provides an efficient method of flooding TC messages to the entire network by specifying the nodes that forward TC messages as an MPR set. Yi Z., et al. enhanced the OLSR protocol by considering mobility and load balancing for UAV ad hoc networks, closely aligning with the described MPR-based method [39].

2.2.2. Dijkstra Method

The Dijkstra method is a popular shortest route algorithm [40]. Each node can determine the minimum cost route between any nodes by inputting the cost of all links into the Dijkstra method. Because OLSR evaluates the routes by the number of hops, it cannot see the actual distance which is important for UAV delivery. The optimal route construction method for UAV delivery uses the Dijkstra method to construct a route that considers the UAV’s travel distance. In addition, by weighting the danger level with the distance of each link, this method can construct the safe and short-distance routes.

2.2.3. Method for Constructing Optimal Routes Based on OLSR

In our protocol, all the nodes are given information about whether they are located in sparsely populated regions or population-dense regions. The OLSR-based method adds several parameters to the HELLO message header. One is the region information of the HELLO message sending node, the others are the region information and the inter-node distances corresponding to each adjacent node: “Neighbor Interface Address”.

In order to search for the optimal route considering the distance and safety, the distance and region information obtained from the HELLO message must be advertised to the entire network. Therefore, the region information of the sending node and the distances between the nodes and the region information corresponding to the “Advertised Neighbor Main Address” are added to the TC message header. When a node receives a HELLO and TC message, it updates the routing table for each node using the Dijkstra method, using the link cost as the danger-weighted distance for each link. Figure 3 shows the method based on OLSR for constructing optimal route. The link where the UAV moves toward the population-dense region is weighted by multiplying the distance by 3.0 to increase the cost because it is dangerous. The link where the UAV moves toward the sparsely populated region is weighted by multiplying the distance by 0.6 to decrease the cost because it is safe.

We define our proposed algorithm in graph-theoretic terms based on Dijkstra’s algorithm [41]. Imagine that a node constructs a graphical representation of the network: here, N denotes the set of nodes in the graph; $d(i,j)$ denotes the distance between nodes i and j in N; $l(i,j)$ denotes the non-negative cost (weight) associated with the link between nodes i and j in N; $l(i,j)$ = ∞ if no link connects i and j. In the following description, we let s in N denote this node; that is, the node executes the algorithm to find the shortest path to all the other nodes in N. Furthermore, the algorithm maintains the following two variables: M denotes the set of nodes incorporated so far by the algorithm, and $C\left(n\right)$ denotes the cost of the path from s to each node n. Given these definitions, the algorithm is defined in Algorithm 1.

Algorithm 1 Algorithm for constructing optimal UAV routes based on OLSR.

1:. $M=\left\{s\right\}$ 2:. for  $each$ n  $in$ $N-\left\{s\right\}$  do 3:.    if $no$$link$$connects$$between$$node$i $and$ j then 4:.      $l(s,n)=\infty$ 5:.    else if $UAV$ $moves$ $toward$ $the$ $population$ $dense$ $region$ then 6:.      $l(s,n)=3.0\times d(s,n)$ {Proposed method original weighting of population-dense region} 7:.    else if  $UAV$ $moves$ $toward$ $the$ $sparsely$ $populated$ $region$ then 8:.      $l(s,n)=0.6\times d(s,n)$ {Proposed method original weighting of sparsely populated region} 9:.    end if 10:.    $C\left(n\right)=l(s,n)$ 11:. end for 12:. while  $(N!=M)$  do 13:.    $M=M+\left\{w\right\}$ $such$ $that$ $C\left(w\right)$ $is$ $the$ $minimum$ $for$ $all$ w $in$ $(N-M)$ 14:.    for $each$ n $in$ $(N-M)$ do 15:.      $C\left(n\right)=MIN\left(C\right(n),C(w)+l(w,n\left)\right)$ 16:.    end for 17:. end while

Basically, the algorithm works as follows. It starts with M containing this node s and then initialize the table of costs (the array $C\left(n\right)$) to other nodes using the known costs to directly connected nodes. We then look for the node that is reachable at the lowest cost $\left(w\right)$ and add it to M. Finally, we update the table of costs by considering the cost of reaching nodes through w. The last line of the algorithm chooses a new route to node n that goes through node w if the total cost of going from the source to w and then following the link from w to n is less than the old route we had to n. This procedure is repeated until all nodes are incorporated in M.

3. Relay Node Selection Issue

If all the wireless terminals in houses are used as relay nodes, there will be a lot of routing protocol signals. Referring to the basic model of relay nodes and end nodes in communication networks, we applied a model in which end nodes are accommodated in relay nodes. In the previous study, we assumed that one cluster consists of about 100 houses wireless terminals and the relay function is operated in one node in each cluster, as shown in Figure 4 which are actual area in Fukushima Prefecture, Japan. This assumption of one node per 100 houses was not logically supported.

If the relay function is operated in all the nodes, the UAV route will become a smooth curve. However, as the number of relay nodes increases, the number of control messages to construct the route increases, and the message forwarding load of each node increases. In the OLSR-based scheme, as the number of relay nodes increases, the processing load on each node increases due to the relay forwarding process for flooding TC messages and the weighted Dijkstra method calculation. In the AODV-based method, the processing load of each node increases in the RREQ message evaluation process and the relay forwarding process due to the increase in the number of received RREQ messages. It is necessary to reduce the number of relay nodes for constructing safe and efficient UAV routes. End nodes with no relay function will be connected to the closest relay node. Figure 5 shows an image of this simplified network.

We will establish a method to select as few relay nodes as possible while keeping the connectivity of all node pairs in the network multi-hop. In the network resulting from the above method, the UAV routes constructed by the optimal route construction method become safe and efficient, with a shorter “population-dense regions distance” and a “total distance” that is not too long. On the other hand, the smaller the number of relay nodes and the simpler the network, the fewer links are available for routes. As UAV home deliveries become popular, the number of overlapping routes (hereafter, “route conflicts”) will increase as more UAVs fly over the same region at the same time and routes, which may cause collisions among UAVs. We evaluate the incidence of “route conflicts” for different relay node densities and numbers of concurrent UAVs flights. From the perspective of a sufficient number of relay nodes to avoid too many “route conflicts”, we clarify the minimum relay node density in the network required to apply the proposed method.

4. Related Works

The cluster-based routing protocol (CBRP) is one of the protocols of MANET for a two-tier network configuration with multi-node clusters and inter-cluster connections [42,43]. Within a cluster, routing is divided into a network layer and an upper layer, and inter-cluster routing is established at the network layer [44]. The clustering can effectively improve the capacity for dealing with node mobility and for reining in the emergence of long route communications by cascading short route communications. The cluster head acts as the gateway (GW) of the cluster, has the relay function, and performs routing. This method uses clustering to accommodate node movements and cascade messages over short routes to reduce the load on long-distance communication. The algorithm selects the node with the “lowest ID” among its adjacent nodes as the cluster head. In other words, CBPR randomly selects nodes that operate the relay function. Therefore, it is not clear whether CBPR is an optimal method for selecting relay nodes.

Heinzelman W. R., et al. proposed Low-Energy Adaptive Clustering Hierarchy (LEACH), a clustering-based protocol in sensor networks [45,46,47]. This protocol randomly rotates local cluster base stations (cluster heads) to distribute the energy load evenly among the sensors in the network.

Mody S., et al. proposed an algorithm for the energy-efficient selection of cluster heads in a sensor network using the k-means method [48]. It applies machine learning to select nodes to build clusters, and to select the cluster heads from the clusters. Baradaran A.et al. proposed the optimal cluster head (CH)-selecting method based on fuzzy logic [49]. Liu X., et al. reviewed atypical hierarchical routing protocols for wireless sensor networks [50]. Abbasi A. A., et al. reviewed various clustering algorithms designed for WSNs, categorizing them based on performance metrics such as scalability, energy efficiency, and fault tolerance [51]. Their study provides a detailed analysis of the advantages and limitations of these algorithms, guiding future research in clustering methodologies. Fujii K., et al. propose a novel relay node selection scheme for WSNs using chaotic neural networks [52]. The method leverages the chaotic dynamics for efficient relay node selection, aiming to enhance communication reliability and reduce energy consumption in the network. Bruckner D., et al. introduced a hierarchical semantic processing architecture designed for smart sensor networks used in surveillance [53]. It integrates semantic reasoning to enable intelligent data interpretation and decision making, improving the functionality and responsiveness of surveillance systems. LoBello L., et al. propose an adaptive topology management strategy tailored for large, dense, real-time WSNs [54]. This approach dynamically adjusts the network topology to optimize performance, enhance reliability, and maintain real-time constraints while minimizing energy consumption. Kim H, et al. explores the application of reinforcement learning to select relay nodes in WSNs [55]. The proposed method aims to optimize network performance by dynamically adapting to changing conditions, reducing energy consumption, and ensuring reliable data transmission.

Menglei J., et al. proposed a mobility-prediction-based virtual routing algorithm to enhance communication reliability in ad hoc UAV networks [56]. Yitao L., et al. developed a relay communication technique for multi-UAV networks, improving data transmission efficiency and network reliability [57]. Ruijin D., et al. explored a multi-agent learning-based approach for packet routing in dynamic multi-hop UAV networks, enhancing adaptability and efficiency [58].

There have been several studies on sensor networks that create clusters of nodes and provide the relay function at the Cluster Head. There has also been a lot of research into controlling the position of UAVs as relay nodes in data transfer networks that use UAVs as relay nodes. They select the relay nodes to distribute the loads among nodes and to be efficient in terms of energy consumption, rather than to optimize the end-to-end route. As a result, these algorithms select relay nodes randomly regardless of whether the route can be reliably constructed or whether it is a safe route.

5. Proposed Method

In this paper, we propose four methods for selecting the relay nodes that operate the relay function for the UAV’s route, from all the nodes in the network. By comparing these methods, we clarify the method for selecting a smaller number of relay nodes that suppress the number of control messages forwarded in the network without splitting the network.

5.1. Method of Randomly Selecting Relay Nodes

Similar to the low-energy adaptive clustering method used in sensor networks [45,46,47,48], the idea of this method is to avoid biasing the relay nodes toward some regions or some types of nodes. We propose a method to randomly select relay nodes to activate the relay function (hereafter, “randomly selecting”). This method controls the number of relay nodes by setting a “relay function activation cut-off value ($RCV$)” as the percentage of relay nodes among all nodes in the network.

• (1). When a node i is activated, a value from 1 to 100 is randomly assigned as the cut-off value $C_i$.

• (2). The relay function is operated for the node whose cut-off value $C_i$ is less than the “relay function activation cut-off value ($RCV$)”. The node i that satisfies the conditions of Equation (2) is selected as the relay node.

  (2)$C_i<RCV$

5.2. Method of Selecting Nodes That Connect to More Adjacent Nodes

If relay nodes are connected to more nodes, many node pairs may be connected with each other in one hop. This may result in an efficient network where each node can be connected with fewer hops. Therefore, we propose a method to select nodes connected to more neighboring nodes (hereafter, “more adjacent nodes”) to operate the relay function.

• (1). In the node i, the number of adjacent nodes $N{a}_i$ can be obtained from the source address of the received HELLO message.

• (2). Each node sends the number of adjacent nodes to the adjacent nodes by the HELLO messages. The M denotes the set of $N{a}_i$s that are received from adjacent nodes.

• (3). As shown in Figure 6, each node selects the nodes among its adjacent nodes that have more adjacent nodes and notifies the selected nodes that they should activate the relay function. Each node is set as “the number of relay nodes (N)” in advance. The node i whose $N{a}_i$ satisfies the conditions of Equation (3) is selected as the relay node.

  (3)$ma{x}_N\left(M\right)$

5.3. Method of Selecting Nodes That Connect to Fewer Adjacent Nodes

Considering the safety of a UAV route, it is desirable to select nodes in the regions with the low relay node density and activate the relay function preferentially. Therefore, we propose a method to activate the relay function of nodes with fewer adjacent nodes (hereafter, “fewer adjacent nodes”).

The procedure for “fewer adjacent nodes” is almost the same as that for “more adjacent nodes”. The only difference is that in (3) “fewer adjacent nodes” selects the nodes with fewer adjacent nodes, while “more adjacent nodes” selects the nodes with more adjacent nodes. Figure 7 shows the “fewer adjacent nodes”. The node i whose $N{a}_i$ satisfies the conditions of Equation (4) is selected as the relay node.

(4)$mi{n}_N\left(M\right)$

5.4. Method Using MPR

OLSR’s MPR selects the minimum number of adjacent nodes that connect to all nodes 2-hops away and eliminates redundant relay nodes, thereby suppressing wasted messages in flooding. We consider MPR as a reference for constructing an efficient and reliable relay network for UAVs. Therefore, we propose a method of selecting relay nodes using the MPR concept (hereafter, “using MPR”).

• (1),(2) 

  are the same as “more adjacent nodes”.

• (3) 

  The node receiving a HELLO message knows which node is two hops away (2-hop neighbors). N is the subset of neighbors in all nodes. $N2$ is the subset of 2-hop neighbors. $N2N\left(i\right)$ is the neighbors of node i. $D\left(i\right)$ is defined as the number of neighbors of node i, M is the MPR set.

• (4) 

  As shown in Algorithm 2 and Figure 8, the node selects the MPR set with the smallest number of neighbors connecting to all nodes two hops away.

• (5) 

  One of the nodes with the lowest number of neighbors is selected as a relay node; then, its MPR set is selected as a relay node; then, the MPR set of the relay node is selected as a relay node, and so on; all relay nodes are selected through sequential propagation.

Algorithm 2 Algorithm for method using MPR.

1:. while  $N2$ $!=$ ∅ do 2:.    $M=M+\left\{i\right\}$ $such$ $that$ $D\left(i\right)$ $is$ $the$ $maximum$ $for$ $all$ i $in$ $(N-M)$ 3:.    for $each$ i $in$ $(N-M)$ do 4:.      $N2=N2-N2N\left(i\right)$ 5:.    end for 6:. end while

Figure 8

Method using MPR.

[Figure omitted. See PDF]

6. Evaluation

6.1. Evaluation Perspectives

We evaluate the performance of the proposed methods by investigating the quality of the obtained network and UAV routes in terms of the following evaluation perspectives.

6.1.1. Parameter Values That Meet Requirements

(Eval. 1) We identify parameter values for each proposed method that meet the requirements that there are no isolated nodes and that clusters are not split (i.e., relay nodes are connected to each other). We observe “cluster split ratio” and “the number of isolated nodes” for each method. “Cluster split ratio” is calculated by (the number of times the cluster split occurred)/(100 times, the total number of simulations runs under the same conditions), and a lower value is better. “The number of isolated nodes” is calculated by (the number of isolated nodes)/(the number of all nodes), and a lower value is better.

6.1.2. Relay Node Ratio

(Eval. 2) We evaluate how much the “relay node ratio” decreases by each method. It is calculated by (the number of relay nodes)/(the number of all nodes), and a lower value is better.

6.1.3. Optimality of the Route

(Eval. 3) We evaluate optimality of the route constructed after the selection of relay nodes by each method, in terms of “total distance” and “population-dense regions distance” of UAV route’ from the source node to the destination node. “population-dense regions distance” had better to be short. “Total distance” should not be too long in order to avoid the risk of running out of battery power.

6.1.4. Route Conflicts Ratio

(Eval. 4) We clarify that the “route conflicts ratio” decreases as the relay node density increases depending on the number of UAVs, and clarify a sufficient relay node density to avoid too many “route conflicts”. It is calculated by (the number of conflicted routes)/(the number of all routes), and a lower value is better.

6.2. Evaluation Method

• In addition to the four proposed methods, we experimented with a method in which all nodes have the relay function enabled (hereafter, “all nodes”).

• For Eval. 1 and Eval. 2, we created a simulator in C++ to experiment on the relay node selection by each method. Eval. 3 and Eval. 4 use the OLSR-based method for route construction. Using the NS-3 network simulator [59] version 3.30, the OLSR simulation software was modified to add OLSR-based signal processing and an information repository, and simulation experiments were conducted.

• Simulation experiments were carried out using the node arrangement model based on a regional city as shown in Figure 9. A population-dense region is located in the center, surrounded by sparsely populated regions. A total of 30 nodes were placed in population-dense region and 20 nodes were placed in each of the 8 blocks in sparsely populated regions.

• The simulation randomly places nodes in each block with the relay node densities shown in Table 1.

• The radio propagation range of each node is 1.5 km, and no nodes are added, deleted, or moved.

• Eval. 3 randomly selects source and destination nodes from sparsely populated regions. Eval. 4 randomly selects source and destination nodes from both population-dense regions and sparsely populated regions.

• We repeat the relay node selection and the route construction 100 times for each method and calculate the mean and standard deviation for each evaluation perspective.

6.3. Evaluation Results

6.3.1. Parameter Values That Meet Requirements, Relay Node Ratio

We show the evaluation results in terms of the evaluation perspectives (Eval. 1) in Section 6.1.1 and (Eval. 2) in Section 6.1.2.

Method of Randomly Selecting Relay Nodes

(Eval. 1) For “randomly selecting”, Figure 10 shows “cluster split ratio” and Figure 11 shows “the number of isolated nodes” for the “relay function activation cut-off value” at each relay node density. The “cluster split ratio” in Figure 10 is the percentage of experiments in which the cluster splitting occurred out of 100 experiments. The red box indicates the regions that meet the requirements. When the “relay function activation cut-off value” was about 50, “the number of isolated nodes” was almost zero. However, even a “relay function activation cut-off value” of 50 was not sufficient to meet the requirement because cluster splitting occurs in models with low relay node density. Since the relay node density has a significant impact on the “cluster splitting ratio”, the “relay function activation cut-off value” should be set to a proper value by the relay node density. If the relay node density is 1.90, the “relay function activation cut-off value” must be greater than 90 to prevent cluster splitting.

(Eval. 2) Figure 12 shows the “relay node ratio” at each “relay function activation cut-off value”. The same characteristics were observed, regardless of the relay node density. The “relay node ratio” becomes close to 90% when the “relay function activation cut-off value” is larger than a 90 cluster, split does not occur even at a relay node density of 1.90, as shown in Figure 10 of Eval. 1. This means that almost all nodes become relay nodes, and that relay nodes are not being selected.

Method of Selecting Nodes That Connect to More Adjacent Nodes

(Eval. 1) In the “more adjacent nodes” and “fewer adjacent nodes”, there are no isolated nodes because each node can select a relay node from its connected neighbors. As shown in Figure 13, as “the number of relay nodes” increases by one, the “cluster split ratio” improves by about 50%. For example, when the relay node density is 1.90 and “the number of relay nodes” increases from 2 to 3, the “cluster split ratio” improves from 30% to 10%. When the relay node density was low, the cluster split ratio was high. Even when the relay node density was the lowest (1.90), the cluster split ratio was kept to 0 if the number of relay nodes was set to more than 4. Regardless of the relay node density, it is expected that the requirements can be satisfied by selecting more than four nodes. Since the relay node density has a significant impact on meeting the requirements, “the number of relay nodes” should also be properly selected to the relay node density.

Figure 10

“Cluster split ratio” for “relay function activation cut-off value” in “randomly selecting”.

[Figure omitted. See PDF]

Figure 11

“The number of isolated nodes” for “relay function activation cut-off value” in “randomly selecting”.

[Figure omitted. See PDF]

(Eval. 2) The red box in Figure 14 indicates the “relay node ratio” to satisfy the requirement in all relay node densities. The “relay node ratio” becomes close to 70% when the “the number of relay nodes” is 4; cluster split does not occur even at a relay node density of 1.90, as shown in Figure 13 of Eval. 1. The “relay node ratio” to satisfy the requirement is lower than that of “randomly selecting”. The results indicate that “more adjacent nodes” is more suitable for selecting relay nodes.

Figure 12

“Relay node ratio” for “relay function activation cut-off value” in “randomly selecting”.

[Figure omitted. See PDF]

Figure 13

“Cluster split ratio” for “the number of relay nodes” in “more adjacent nodes”.

[Figure omitted. See PDF]

Method of Selecting Nodes That Connect to Fewer Adjacent Nodes

(Eval. 1) Compare the size of the red frame that indicates the range where no cluster split occurs (the “cluster split ratio” is 0%) in Figure 10, Figure 13 and Figure 15. In the case of “randomly selecting”, the “relay function activation cut-off value” is 50% or more at a relay node density of 5.27, 60% or more at a relay node density of 3.88, 70% or more at a relay node density of 2.97, and 90% or more at a relay node density of 2.35. There were requirements where no cluster split occurred at any relay node density. In the case of “more adjacent nodes”, cluster split did not occur when “the number of relay nodes” was 2, 3, or 4 at relay node densities of 5.27 and 3.88; it also did not occur when “the number of relay nodes” was 3 or 4 at a relay node density of 2.97, or when “the number of relay nodes” was 4 at a relay node density of 2.35. “Fewer adjacent nodes” did not cause cluster split when “the number of relay nodes” was 3 or 4 at relay node densities of 5.27, 3.88, or 2.97, when “the number of relay nodes” was 4 at a relay node density of 2.35.

Figure 14

“Relay node ratio” for “the number of relay nodes on” in “more adjacent nodes”.

[Figure omitted. See PDF]

Therefore, “fewer adjacent nodes” is more difficult to satisfy as a requirement for not causing cluster split. This is because “fewer adjacent nodes” relays messages to fewer nodes than “more adjacent nodes”, so it is more likely to cause cluster split. On the other hand, “more adjacent nodes” can relay to more nodes than “fewer adjacent nodes”; then, the cluster split is less likely to occur.

Figure 15

“Cluster split ratio” for “the number of relay nodes” in “fewer adjacent nodes”.

[Figure omitted. See PDF]

(Eval. 2) As shown in Figure 16, even when the relay node density is 2.35, which does not cause cluster split, the “relay node ratio” exceeds 70%, which is higher than the “more adjacent nodes” which is less than 70%. “Fewer adjacent node” proved to be a poor method.

Method Using MPR

(Eval. 1) With “using MPR”, any node is not isolated or any cluster is not split, and requirements are always met.

(Eval. 2) Figure 17 shows the evaluation results of “relay node ratio”. Regardless of the relay node density, the “relay node ratio” is about 70%.

Figure 16

“Relay node ratio” for “the number of relay nodes” in “fewer adjacent nodes”.

[Figure omitted. See PDF]

From Figure 12, “relay node ratio” is approximately 90% for “randomly selecting”, regardless of the relay node density, and “using MPR” is always lower. From Figure 14, for “more adjacent nodes”, “using MPR” is better when the relay node density is low at 1.90, with a “relay node ratio” of over 70%, and “more adjacent nodes” is better when the relay node density is 2.35 or higher, with a “relay node ratio” 70%. From Figure 16, “fewer adjacent nodes” does not satisfy the requirements at a relay node density of 1.90, and exceeds 70% at a relay node density of 2.35. “Using MPR” is better when the relay node density is low, and “fewer adjacent nodes” is better when the relay node density is 2.97 or higher and is lower than 70%.

Figure 17

“Relay node ratio” for relay node density in “using MPR”.

[Figure omitted. See PDF]

6.3.2. Optimality of the Route

We show the evaluation results in terms of the evaluation perspective (Eval. 3) in Section 6.1.3.

We selected relay nodes and constructed routes in the high relay node density 5.27 model. This condition could easily meet the requirements. To meet the requirements with this relay node density, we set the “relay function activation cut-off value” at 50 for “randomly selecting”, and set “the number of relay nodes” at 1 for “more adjacent nodes” and at 4 for “fewer adjacent nodes”.

Relay Node Ratio

(Eval. 2) As shown in Figure 18, for each method, the “ratio of activate relay function” is significantly reduced compared to “all nodes”. The result indicates that an efficient network can be constructed.

Total Distance

(Eval. 3) Figure 19 shows the “total distance” of the routes constructed after selecting the relay nodes by each method. This should not be too long to avoid the risk of running out of battery power. In the “more adjacent nodes” and “fewer adjacent nodes”, the “total distance” increased by almost 1 km compared to the “all nodes”, since the “relay node ratio” decreased significantly. For all methods, the “total distance” increased when the number of relay nodes decreased. In particular, “more adjacent nodes” and “fewer adjacent nodes” confirmed that the distance became too large when the number of relay nodes was too small. On the other hand, “using MPR” resulted in a small reduction in the “relay node ratio”, while it did not increase the “total distance” and did not result in worse routing.

Population-Dense Regions Distance

(Eval. 3) Figure 20 shows the “population-dense regions distance” of the constructed routes. The “all nodes” did not construct any route through the population-dense regions. However, the “more adjacent nodes” and “fewer adjacent nodes” constructed routes that go through population-dense regions. Since “more adjacent nodes” gives the priority to the nodes that have more adjacent nodes for the relay nodes, the nodes in population-dense regions are highly selected as the relay nodes. Nodes in sparsely populated regions are less likely to be selected as the relay nodes. As a result, only large circuitous routes or short routes through population-dense regions can be constructed. The reason why the routes in “fewer adjacent nodes” pass through the population-dense regions node is that nodes connected to the relay node in the population-dense regions have been likely selected as source and destination nodes.

Overall, the evaluation found that “using MPR” was the most appropriate method.

6.3.3. Route Conflicts Ratio at Relay Nodes Density

We show the evaluation results in terms of the evaluation perspective (Eval. 4) in Section 6.1.4. The “route conflicts ratio” is calculated by (the number of conflicted routes)/(the number of all routes), and a lower value is better.

(Eval. 4) Figure 21 shows the “route conflicts ratio” at each relay node density. The source and destination nodes are located in sparsely populated regions. The experimental results confirm that the “route conflicts ratio” increases as the relay node density decreases. When the relay node density is low, nodes are sparse and the number of adjacent nodes per node is small. Fewer adjacent nodes mean fewer route candidates. This makes it easier to construct routes that relay certain nodes. As a result, the “route conflicts ratio” is likely to increase.

Figure 22 shows the “route conflicts ratios” at each relay node density when the source and destination nodes are located in population-dense regions. The “route conflicts ratio” was lower than that for route constructions between nodes in sparsely populated regions. Although there were routes that bypassed nodes in population-dense regions, many routes were constructed in small population-dense regions. Therefore, the number of relay links was low in almost routes. There were few cases where multiple routes overlapped at relay links. As a result, the “route conflicts ratio” was low. This suggests that “route conflicts ratio” can be suppressed by constructing short-distance routes in addition to increasing the relay node density.

To suppress the “route conflicts ratio”, the relay node density greater than 5 nodes/km² is desirable, considering both routes between sparsely populated regions nodes and routes between population-dense regions nodes.

“Using MPR” can reduce the number of relay nodes to nearly 70%, but since the relay node density must be greater than 5 nodes/km², it was found that the relay node density to which “using MPR” should be applied is 5/0.7 = 7.12 nodes/km² or greater. This appropriate relay node density value is the result for the node arrangement model based on a regional city (as shown in Figure 9 and Table 1) with a radio propagation range of 1.5 km. The appropriate relay node density will change depending on the evaluation conditions. In particular, it is thought that the value is different in large-scale urban environments, and further simulation experiments are needed.

Routes that pass through sparsely populated regions are prioritized by the route construction algorithm, so more conflicts may occur. Therefore, it is necessary to further study on the appropriate relay node density in population-dense region and sparsely populated regions.

7. Conclusions

We developed a distributed UAV management system inspired by virtual circuit and datagram methods in packet-switching networks. By installing houses with wireless terminals, UAVs navigate routes in a multi-hop network, communicating with ground nodes. UAVs are treated as network packets, ground devices are treated as routers, and their connections are treated as links. In order to construct an efficient network for UAV route constructions, we proposed the four methods for selecting nodes to operate the relay function: “randomly selecting”, “more adjacent nodes”, “fewer adjacent nodes”, and “using MPR”. We evaluated these methods on route construction success rates, relay node counts, route lengths, and so on. Through evaluation experiments, we confirmed that the “using MPR” method is the best way to construct a safer route with the less total distance, while always meeting the requirements, and should be applied when the relay node density is greater than 7.12 nodes/km² to suppress “route conflicts”. In general, the “using MPR” method is the best, but the appropriate relay node density is will change depending on the evaluation conditions. It is necessary to further study on the appropriate relay node density in population-dense region and sparsely populated regions.

We did not evaluate the number of control messages and link crossings, although we did the “relay function activation cut-off value”. Therefore, further evaluations and analysis will be necessary. In addition, to reduce limitations on “route conflicts”, it is desirable to establish a method that selects UAV routes at different altitudes in the airspace, which will be addressed in future study.

Author Contributions

Conceptualization, S.O. and K.U.; methodology, S.O. and K.U.; software, S.O.; validation, S.O., T.Y. and R.Y.; formal analysis, S.O., T.Y. and R.Y.; investigation, S.O., T.Y. and R.Y.; resources, K.U.; data curation, S.O.; writing—original draft preparation, S.O.; writing—review and editing, K.U., T.M., T.Y., R.Y. and N.F.; visualization, S.O.; supervision, K.U., T.M. and N.F.; project administration, K.U.; funding acquisition, K.U. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Data are contained within the article.

Acknowledgments

We would like to thank Haruki Gunji, a former member of our laboratory, for their great efforts.

Conflicts of Interest

All authors declare that the research was conducted in the absence of any commercial or financial relationships that could be constructed as potential conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. UAV navigation route construction by wireless multi-hop network.

Figure 2. Network configuration suitable for UAV routing.

Figure 3. Method for constructing optimal routes based on OLSR.

Figure 4. Models of each node location.

Figure 5. Image of simplified network.

Figure 6. Method of selecting nodes that connect to more adjacent nodes.

Figure 7. Method of selecting nodes that connect to fewer adjacent nodes.

Figure 9. Random node arrangement model.

Figure 18. “Relay node ratio” in each method.

Figure 19. “Total distance” in each method.

Figure 20. “Population-dense regions distance” in each method.

Figure 21. “Route conflicts ratio” for relay node density (between sparsely populated regions nodes).

Figure 22. “Route conflicts ratio” for relay node density (between population-dense regions nodes).

Table 1

Node arrangement models in Eval. 1 to 4.

Relay Node Density[/km2]	Model Size[km2]	Applicable ExperimentsEval. 1 to 4
$1.31$	12 km $\times 12$ km	Eval. 4
$1.57$	11 km $\times 11$ km	Eval. 4
$1.72$	$10.5$ km $\times 10.5$ km	Eval. 4
$1.90$	10 km $\times 10$ km	Eval. 1–4
$2.35$	9 km $\times 9$ km	Eval. 1–4
$2.97$	8 km $\times 8$ km	Eval. 1–3
$3.88$	7 km $\times 7$ km	Eval. 1–3
$5.27$	6 km $\times 6$ km	Eval. 1–4

References

1. Valeska, E.; Evy, R.; Lieselot, V.; Philippe, L. Autonomous Delivery Solutions for Last-Mile Logistics Operations. Sustainability; 2023; 15, 2774. [DOI: https://dx.doi.org/10.3390/su15032774]

2. Amer, J.; Emil, P.; Mazen, B.; Robin, H.; Per, H. Drones in last-mile delivery: A systematic literature review from a logistics management perspective. Int. J. Logist. Manag.; 2024; [DOI: https://dx.doi.org/10.1108/ijlm-04-2023-0149]

3. Francesco, B.S. UAV-Based Delivery Systems: A Systematic Review, Current Trends, and Research Challenges. J. Auton. Transp. Syst.; 2024; 1, pp. 1-40.

4. Kaneko, S.; Martins, J.R. Fleet Design Optimization of Package Delivery UAVs Considering Energy Consumption. Proceedings of the AIAA SCITECH 2022 Forum; San Diego, CA, USA, 3–7 January 2022.

5. Burke, C.; Nguyen, H.; Magilligan, M.; Noorani, R. Study of A Drone’s Payload Delivery Capabilities Utilizing Rotational Movement. Proceedings of the 2019 International Conference on Robotics, Electrical and Signal Processing Techniques (ICREST); Dhaka, Bangladesh, 10–12 January 2019.

6. Patchou, M.; Sliwa, B.; Wietfeld, C. Unmanned Aerial Vehicles in Logistics: Efficiency Gains and Communication Performance of Hybrid Combinations of Ground and Aerial Vehicles. Proceedings of the 2019 IEEE Vehicular Networking Conference (VNC); Los Angeles, CA, USA, 4–6 December 2019.

7. Dissanayaka, D.; Wanasinghe, R.T.; Silva, D.O.; Jayasiri, A.; Mann, K.I.G. Review of Navigation Methods for UAV-Based Parcel Delivery. IEEE Trans. Autom. Sci. Eng.; 2024; 21, pp. 1068-1082.

8. Chen, S.; Chen, H.; Chang, C.W.; Wen, C.Y. Multilayer Mapping Kit for Autonomous UAV Navigation. IEEE Access; 2021; 9, pp. 31493-31503. [DOI: https://dx.doi.org/10.1109/ACCESS.2021.3055066]

9. Rakesh, S.; Rojeena, B.; Shiho, K. 6G Enabled UAV Traffic Management: A Perspective. IEEE Access; 2021; 9, pp. 91119-91136.

10. Abdeljawed, S.; Jalel, E.; Patrick, S. Vehicle Routing with Multiple UAVs for the Last-Mile Logistics Distribution Problem: Hybrid Distributed Optimization; Springer Nature: Berlin/Heidelberg, Germany, 2024.

11. Hao, Z.; Lihua, D.; Chunxiao, C.; Bin, X. Three-Dimensional Unmanned Aerial Vehicle Route Planning Using Hybrid Differential Evolution. J. Adv. Comput. Intell. Intell. Inform.; 2020; 24, pp. 820-828.

12. Yang, P.; Tang, K.; Lozano, J.A.; Cao, X. Path planning for single unmanned aerial vehicle by separately evolving waypoints. IEEE Trans. Robot.; 2015; 31, pp. 1130-1146. [DOI: https://dx.doi.org/10.1109/TRO.2015.2459812]

13. Huang, C.; Fei, J.Y. UAV Path Planning Based on Particle Swarm Optimization with Global Best Path Competition. Int. J. Pattern Recognit. Artif. Intell.; 2018; 32, 6. [DOI: https://dx.doi.org/10.1142/S0218001418590085]

14. Roberge, V.; Tarbouchi, M.; Labonté, G. Fast Genetic Algorithm Path Planner for Fixed-Wing Military UAV Using GPU. IEEE Trans. Aerosp. Electron. Syst.; 2018; 54, pp. 2105-2117. [DOI: https://dx.doi.org/10.1109/TAES.2018.2807558]

15. Chen, Y.; Mei, Y.; Yu, J.; Su, X.; Xu, N. Three-dimensional unmanned aerial vehicle path planning using modified wolf pack search algorithm. Neurocomputing; 2017; 266, pp. 445-457.

16. Yu, L.; Zhou, K. A dynamic local path planning method for outdoor robot based on characteristics extraction of laser rangefinder and extended support vector machine. Int. J. Pattern Recognit. Artif. Intell.; 2016; 30, pp. 1-23. [DOI: https://dx.doi.org/10.1142/S0218001416590047]

17. Wang, G.G.; Chu, H.C.E.; Mirjalili, S. Three-dimensional path planning for UCAV using an improved bat algorithm. Aerosp. Sci. Technol.; 2016; 49, pp. 231-238. [DOI: https://dx.doi.org/10.1016/j.ast.2015.11.040]

18. Gautam, S.A.; Verma, N. Path Planning for Unmanned Aerial Vehicle Based on Genetic Algorithm and Artificial Neural Network in 3D. Proceedings of the 2014 International Conference on Data Mining and Intelligent Computing; Delhi, India, 5–6 September 2014; pp. 1-5.

19. Goncharenko, V.I.; Dzekalo, A.A. The Algorithm for Constructing the UAV Route Based on the Combined Method. Proceedings of the 2023 7th International Conference on Information, Control, and Communication Technologies (ICCT); Astrakhan, Russia, 2–6 October 2023; pp. 2-6.

20. Ozlem, S.M. Optimum Arrival Routes for Flight Efficiency. J. Power Energy Eng.; 2015; 3, pp. 449-452.

21. Schouwenaars, T.; Moor, B.D.; Feron, E.; How, J. Mixed integer programming for multi-vehicle path planning. Proceedings of the 2001 European Control Conference (ECC); Karlsruhe, Germany, 4–7 September 2001; pp. 2603-2608.

22. Evdokimenkov, V.N.; Krasilshchikov, M.N.; Kozorez, D.A. Development of pre-flight planning algorithms for the functional-program prototype of a distributed intellectual control system of unmanned flying vehicle groups. INCAS Bull.; 2019; 11, pp. 75-88. [DOI: https://dx.doi.org/10.13111/2066-8201.2019.11.S.8]

23. Ramesh, A.; Suseendhar, P.; Venugopal, E.; Sivakumar, P. An Overview of Navigation Algorithms for Unmanned Aerial Vehicle. Proceedings of the 2023 International Conference on Intelligent Data Communication Technologies and Internet of Things (IDCIoT); Bengaluru, India, 5–7 January 2023.

24. Sivakumar, M.; Malleswari, N. A Literature Survey of Unmanned Aerial Vehicle Usage for Civil Applications. J. Aerosp. Technol. Manag.; 2021; 13, e4021. [DOI: https://dx.doi.org/10.1590/jatm.v13.1233]

25. Fu, Z.; Yu, J.; Xie, G.; Chen, Y.; Mao, Y. A heuristic evolutionary algorithm of UAV path planning. Wirel. Commun. Mob. Comput.; 2018; 2018, 2851964. [DOI: https://dx.doi.org/10.1155/2018/2851964]

26. Danancier, K.; Ruvio, D.; Sung, I.; Nielsen, P. Comparison of path planning algorithms for an unmanned aerial vehicle deployment under threats. IFAC-PapersOnLine; 2019; 52, pp. 1978-1983. [DOI: https://dx.doi.org/10.1016/j.ifacol.2019.11.493]

27. Hodge, V.J.; Hawkins, R.; Alexander, R. Deep reinforcement learning for drone navigation using sensor data. Neural Comput. Appl.; 2020; 36, pp. 2015-2033. [DOI: https://dx.doi.org/10.1007/s00521-020-05097-x]

28. GBN—Very High Frequency Omni-Directional Range (VOR), Federal Aviation Administration (FAA) United States Department of Transportation. Available online: https://www.faa.gov/about/office_org/headquarters_offices/ato/service_units/techops/navservices/gbng/vor (accessed on 1 January 2025).

29. NAVIGATION AIDS/SYSTEMS, Federal Aviation Administration (FAA) United States Department of Transportation. Available online: https://www.faa.gov/air_traffic/publications/atpubs/aim_html/chap1_section_1.html (accessed on 1 January 2025).

30. Gungor, V.C.; Lu, B.; Hancke, G.P. Opportunities and Challenges of Wireless Sensor Networks in Smart Grid. IEEE Trans. Ind. Electron.; 2010; 57, pp. 3557-3564. [DOI: https://dx.doi.org/10.1109/TIE.2009.2039455]

31. Ueda, K.; Miyoshi, T. Autonomous Navigation Control of UAV Using Radio Smart Meter Devices. J. Telecommun. Inf. Technol.; 2019; 2, pp. 64-72.

32. Corson, S.; Macker, J. Mobile Ad Hoc Networking (MANET): Routing Protocol Performance Issues and Evaluation Considerations, IETF, Network Working Group, RFC2501, January 1999. Available online: https://www.rfc-editor.org/rfc/rfc2501 (accessed on 1 January 2025).

33. Clausen, T.H.; Jacquet, P. Optimized Link State Routing Protocol (OLSR), IETF, Network Working Group, RFC3626, October 2003. Available online: https://datatracker.ietf.org/doc/html/rfc3626 (accessed on 1 January 2025).

34. Perkins, C.E.; B-Royer, E.M.; Das, S.R. Ad Hoc On-Demand Distance Vector (AODV) Routing, IETF, Network Working Group, RFC3561, July 2003. Available online: https://datatracker.ietf.org/doc/html/rfc3561 (accessed on 1 January 2025).

35. Yang, Y.; Khalife, J.; Morales, J.J.; Kassas, Z.M. UAV Waypoint Opportunistic Navigation in GNSS-Denied Environments. IEEE Trans. Aerosp. Electron. Syst.; 2022; 58, pp. 663-678. [DOI: https://dx.doi.org/10.1109/TAES.2021.3103140]

36. Yao, P.; Wang, H.; Su, Z. Real-time path planning of unmanned aerial vehicle for target tracking and obstacle avoidance in complex dynamic environment. Aerosp. Sci. Technol.; 2015; 47, pp. 269-279. [DOI: https://dx.doi.org/10.1016/j.ast.2015.09.037]

37. Gunji, H.; Yamazaki, T.; Yamamoto, R.; Miyoshi, T.; Ueda, K. Proactive Route Construction for UAV Delivery considering Distance and Safety using Wireless Multi-hop Network. IEICE Commun. Exp.; 2022; 11, pp. 411-416. [DOI: https://dx.doi.org/10.1587/comex.2022XBL0053]

38. Kokubun, Y.; Yamazaki, T.; Yamamoto, R.; Miyoshi, T.; Ueda, K. Reactive Route Construction for UAV Delivery considering Travel Time and Safety using Wireless Multi-hop Network. IEICE Commun. Exp.; 2022; 11, pp. 405-410. [DOI: https://dx.doi.org/10.1587/comex.2022XBL0054]

39. Zheng, Y.; Wang, Y.; Li, Z.; Dong, L.; Jiang, Y.; Zhang, H. A Mobility and Load Aware OLSR Routing Protocol for UAV Mobile Ad-Hoc Networks. Proceedings of the 2014 International Conference on Information and Communications Technologies (ICT 2014); Nanjing, China, 15–17 May 2014.

40. Dijkstra, E.W. A note on two problems in connexion with graphs. Numer. Math.; 1959; 1, pp. 269-271. [DOI: https://dx.doi.org/10.1007/BF01386390]

41. Larry, L.P.; Bruce, S.D. Computer Networks: A System Approach; 6th ed. Morgan Kaufmann: Burlington, MA, USA, 2021; pp. 295-298.

42. Jiang, M.; Li, J.; Tay, Y.C. Cluster Based Routing Protocol (CBRP) Functional Specification, IETF, INTERNET-DRAFT Retrieved 6, August 2018. Available online: https://datatracker.ietf.org/doc/html/draft-ietf-manet-cbrp-spec-01 (accessed on 1 January 2025).

43. Jiang, M. CBRP: A Cluster-Based Routing Protocol for Mobile Ad Hoc Networks. October 2018. Available online: https://www.slideshare.net/slideshow/cbrp/118567872 (accessed on 22 August 2024).

44. Narumi, H.; Shiraishi, Y.; Takahashi, O. A Reliable Cluster-Based Routing Algorithm for MANET. Doctoral Dissertation; Future University Hakodate: Hakodate, Japan, 2009; pp. 44-51.

45. Heinzelman, W.R.; Chandrakasan, A.; Balakrishnan, H. Energy-Efficient Communication Protocol for Wireless Microsensor Networks. Proceedings of the 33rd Annual Hawaii International Conference on System Sciences; Maui, HL, USA, 4–7 January 2000; pp. 1-10.

46. Tandel, R.I. Leach Protocol in Wireless Sensor Network: A Survey. Int. J. Comput. Sci. Inf. Technol.; 2016; 7, pp. 1894-1896.

47. Zhao, L.; Qu, S.; Yi, Y. A modified cluster-head selection algorithm in wireless sensor networks based on LEACH. J. Wireless Com. Netw.; 2018; 287. [DOI: https://dx.doi.org/10.1186/s13638-018-1299-7]

48. Mody, S.; Mirkar, S.; Ghag, R.; Kotecha, P. Cluster Head Selection Algorithm For Wireless Sensor Networks Using Machine Learning. Proceedings of the 2021 International Conference on Computational Performance Evaluation (ComPE); Virtual, 1–3 December 2021.

49. Baradaran, A.; Navi, K. HQCA-WSN: High-quality clustering algorithm and optimal cluster head selection using fuzzy logic in wireless sensor networks. Fuzzy Sets Syst.; 2020; 389, pp. 114-144. [DOI: https://dx.doi.org/10.1016/j.fss.2019.11.015]

50. Liu, X. Atypical hierarchical routing protocols for wireless sensor networks: A review. IEEE Sens. J.; 2015; 15, pp. 5372-5383. [DOI: https://dx.doi.org/10.1109/JSEN.2015.2445796]

51. Abbasi, A.A.; Younis, M. A survey on clustering algorithms for wireless sensor networks. Comput. Commun.; 2007; 30, pp. 2826-2841. [DOI: https://dx.doi.org/10.1016/j.comcom.2007.05.024]

52. Fujii, K.; Sasaki, T.; Nakano, H.; Utani, A.; Miyauchi, A.; Yamamoto, H. A relay sensor node selection scheme in wireless sensor networks using a chaotic neural network. Int. Sympo. Nonlinear Theory Its Appl.; 2010; 44, pp. 390-393.

53. Bruckner, D.; Picus, C.; Velik, R.; Herzner, W.; Zucker, G. Hierarchical semantic processing architecture for smart sensors in surveillance networks. IEEE Trans. Ind. Inform.; 2012; 8, pp. 291-301. [DOI: https://dx.doi.org/10.1109/TII.2012.2186142]

54. LoBello, L.; Toscano, E. An adaptive approach to topology management in large and dense real-time wireless sensor networks. IEEE Trans. Ind. Inform.; 2009; 5, pp. 314-324. [DOI: https://dx.doi.org/10.1109/TII.2009.2025656]

55. Kim, H.; Fujii, T.; Umebayashi, K. Relay Nodes Selection Using Reinforcement Learning. Proceedings of the 2021 International Conference on Artificial Intelligence in Information and Communication (ICAIIC); Jeju, Republic of Korea, 13–16 April 2021.

56. Menglei, J.; Qixun, Z.; Zhiyong, F.; Zhu, H.; Wei, L. Mobility Prediction Based Virtual Routing for Ad Hoc UAV Network. Proceedings of the 2019 IEEE Global Communications Conference (GLOBECOM); Waikoloa, HI, USA, 9–13 December 2019.

57. Yitao, L.; Ruiheng, W.; Lu, G.; Peng, H. Development of an Effective Relay Communication Technique for Multi-UAV Wireless Network. IEEE Access; 2024; 12, pp. 74087-74095.

58. Ding, R.; Chen, J.; Wu, W.; Liu, J.; Gao, F.; Shen, X. Packet Routing in Dynamic Multi-Hop UAV Relay Network: A Multi-Agent Learning Approach. IEEE Trans. Veh. Technol.; 2022; 71, pp. 10059-10072. [DOI: https://dx.doi.org/10.1109/TVT.2022.3182335]

59. ns-3 Network Simulator. Available online: https://www.nsnam.org/ (accessed on 10 June 2024).