Dynamic UAV Inspection Boosted by Vehicle Collaboration Under Harsh Conditions in the IoT Realm

Abstract

With the widespread adoption of the Internet of Things (IoT), UAV–vehicle collaborative inspection systems are crucial for large-scale, IoT-enabled monitoring. Empowered by the IoT, these systems optimize resource allocation and boost the efficiency of IoT-based applications. Nevertheless, variable vehicle and UAV speeds due to wind and precipitation complicate path planning and task scheduling in the IoT-integrated setup. To solve this, this study offers an adaptive solution for dynamic, complex-weather scenarios within the IoT framework. A dynamic task-processing model was developed first, using real-time IoT sensor data for better decisions. Then, the KGTSA optimization algorithm was designed. It combines K-means clustering, HGA, and TS, considering UAV and vehicle speed variations in complex weather and making full use of IoT-device data. K-means generates an initial solution, HGA refines it, and TS fine-tunes UAV routes and task assignments. The simulation results show that KGTSA significantly cuts data collection time while maintaining flexibility. It efficiently manages speed and path uncertainties in complex weather, optimizing task efficiency without weather forecasts. Compared to traditional algorithms, KGTSA shortens data collection time and adapts better to dynamic IoT environments for real-world efficiency.

1. Introduction

With the rapid advancement of science and technology, the Internet of Things (IoT) [1,2,3,4] has become a key driver in the modernization of various sectors. Through the integration of information and communication technologies, the IoT facilitates efficient management and optimal resource allocation across devices and systems [5,6,7,8,9]. However, traditional monitoring systems in the IoT suffer from limited coverage and a narrow perspective, making it challenging to comprehensively and in real-time grasp the complexity of the IoT ecosystem.

In recent years, UAV technology has emerged as a novel solution to address the monitoring and management challenges within the IoT. UAVs, with their flexibility and wide field of view, are capable of capturing real-time data across various dimensions. Researchers have also explored collaborative strategies for multi-UAV operations [10,11], significantly enhancing the operational capacity of UAV swarms, thereby enabling them to adapt to more complex task environments.

Meanwhile, the UAV logistics market is experiencing rapid growth, with significant expansion across global regions. According to recent data [12], the global UAV logistics market is expected to reach 2.151 billion by 2025, with an annual growth rate of 21.1%. Regionally, North America is projected to hold the largest market share at approximately 40.3%, while the Asia–Pacific region is experiencing the fastest growth, particularly in China, which is expected to capture a significant share by 2030. These trends indicate that, as technology advances and demand increases, UAV logistics will become a crucial component of the global transportation sector. Despite the significant potential of UAVs in the IoT, their limited endurance and communication range still constrain their application in large-scale inspections. Additionally, the computational and storage limitations of UAVs hinder their performance in large-scale data processing. To overcome these challenges, scholars have proposed new collaborative models that integrate UAVs with ground vehicles [13,14,15,16,17]. This model combines the aerial flexibility of UAVs with the ground stability of vehicles, significantly extending the operational range and enhancing data processing capabilities. The collaboration between UAVs and vehicles not only addresses limitations in endurance and communication but also improves data processing efficiency and depth, providing new solutions for the widespread application of UAV technology across various scenarios.

However, in practical applications, complex weather conditions can significantly disrupt the collaborative operation between UAVs and vehicles. Adverse weather factors, such as strong winds, precipitation, or low temperatures, reduce the flight speed and stability of UAVs, leading to longer task completion times. At the same time, harsh weather can destabilize ground traffic, causing issues like water accumulation, ice, or poor visibility, which slow down vehicle speed and further delay task execution. In time-sensitive scenarios, such as emergency rescue or logistics delivery, these delays not only hinder the timely delivery of critical goods but also risk missing essential response windows, potentially compromising public safety. Therefore, addressing the dynamic challenges posed by weather, optimizing path planning and scheduling strategies, and ensuring efficient collaboration between UAVs and ground vehicles to meet task deadlines are crucial issues that must be resolved.

To address these challenges, this paper introduces a novel problem, termed the “Dynamic Vehicle–UAV Collaborative Path Planning and Task Scheduling Problem”. Compared to traditional path planning problems, our approach is more complex because it not only focuses on optimizing the path but also ensures efficient collaboration between vehicles and UAVs, as well as dynamically adjusting task scheduling and allocation in an ever-changing environment. The model for this problem draws inspiration from the Dynamic Vehicle Routing Problem (DVRP) [18,19,20,21,22], which traditionally aims to minimize the travel distance or time for vehicles. However, the DVRP model does not account for the collaboration between vehicles and UAVs or the real-time scheduling of tasks in dynamic environments. In our model, UAV–vehicle collaboration involves not only path planning but also the efficient scheduling and allocation of tasks within a dynamic environment. First, appropriate collaborative nodes must be selected, which are key locations where vehicles interact with UAVs. These nodes serve as stops where vehicles launch or control UAV tasks. Second, the challenge lies in dynamically adjusting the paths of both vehicles and UAVs and reallocating tasks as task demands evolve, ensuring optimal resource utilization and timely responses. Lastly, due to environmental uncertainties and dynamic task changes, the scheduling system must respond in real time to new demands and emergencies, ensuring that tasks are completed within the required time frame.

This study proposes a dynamic adjustment method to address UAV speed fluctuations in complex weather environments. Such weather conditions lead to continuous fluctuations in flight speed, increasing the uncertainty in task execution. To mitigate this, this paper introduces a dynamic adjustment approach that periodically monitors UAV status, combining real-time flight data with task execution conditions, without relying on weather prediction models. At each time interval, the UAV’s current status is evaluated, completed task points are removed, and flight routes for remaining tasks are re-planned. The initial flight plan is adjusted based on multiple real-time monitoring results and gradually optimized through static optimization to accommodate speed fluctuations. This method effectively addresses the speed variations caused by complex weather, ensuring that UAVs can perform tasks efficiently and stably in dynamic environments, thus improving task reliability and efficiency. The main contributions of this paper are summarized as follows:

(1)

We propose a dynamic model for the multi-UAV–vehicle cooperative point patrol problem in dynamic scenarios. First, for the initial static task of the system, this paper establishes mathematical models for UAV flight routes and vehicle travel routes. Then, these two parts are combined as the optimization objective function in this paper, i.e., the research problem in this paper is modeled as a 0–1 integer programming problem. On the basis of the static model, this paper establishes a dynamic task processing problem model.

(2)

In the dynamic task processing scenario considering the speed variations of UAVs and vehicles under initial static tasks, we propose KGTSA (K-means clustering, hybrid genetic algorithm, and tabu search). The KGTSA is an iterative heuristic approach that first uses K-means clustering to group initial static task points and plan vehicle and UAV routes, assigning routes to multiple UAVs to create an initial feasible solution. Then, a hybrid genetic algorithm optimizes this solution to obtain a static optimized solution. For dynamic tasks, the algorithm performs real-time local dynamic optimization based on the current flight status of the UAVs, including position, power, and remaining endurance, to refine the UAV route planning and allocation within a single anchor point.

The rest of this paper is organized as follows: Section 2 discusses the research work related to the multi-UAV–vehicle cooperative problem; Section 3 establishes a model for the multi-UAV–vehicle cooperative inspection problem; Section 4 elaborates on the multi-UAV–vehicle cooperative data acquisition problem based on dynamic task processing and the KGTSA; Section 5 conducts simulation experiments for validation; and Section 6 draws conclusions.

2. Related Work

2.1. Heuristic Algorithms and Vehicle Routing Problems (VRPs)

In the field of operations research, the Vehicle Routing Problem (VRP) [23,24] has long been at the core of academic research and is crucial for solving complex logistics problems . Since its emergence, the VRP has drawn the attention of scholars worldwide and has developed into a complex research area. Initially, the traditional VRP focused on planning efficient routes for vehicles to serve customers, aiming to minimize various costs. With the rapid popularity of drones in modern logistics, the VRP has undergone changes, giving rise to the Vehicle Routing Problem with Drones (VRPD) [25,26,27]. This not only inherits the core challenges of the traditional VRP but also brings about new complexities due to the characteristics of drones, such as battery life limitations, payload constraints, and airspace regulation issues. Numerous heuristic algorithms have been proposed to solve VRPs and their variants. For example, Dorling et al. [28] proposed two multi-trip VRP models for drone delivery. They derived an energy consumption model for multi-rotor drones and established a mixed-integer linear programming model. A Simulated Annealing (SA) heuristic algorithm was then applied to find sub-optimal solutions for practical scenarios. Yang et al. [29] considered a scenario involving multiple trucks, multiple drone stations, and drones within each station serving customers in the VRPD. They proposed a bi-level approach that combines the Brain Storm Optimization algorithm and the Adaptive Large Neighborhood Search. Their research demonstrated the ability of this method to solve the problem and its research value. Han et al. [30] designed an improved artificial bee colony algorithm to solve a multi-objective vehicle routing problem with time window and drone transportation constraints, aiming to minimize the total energy consumption of trucks, drones, and the total number of trucks. Moreover, Russell et al. [31] focused on the development of effective heuristics for solving the vehicle routing and scheduling problem with time window constraints. Both tour construction and local search tour improvement heuristics were developed, and computational results were reported for test problems from the literature as well as real-world applications. Lee et al. [32,33] developed an SFT route optimization model using NSGA-II, considering travel time and cumulative strain, and applied it to the Mokpo-Jeju Island section, obtaining travel-time-saving optimal routes to facilitate decision-making. Additionally, they employed the Gaussian Mixture Model and the Vehicle Routing Problem with Time Windows model to develop a routing strategy for accessible taxis in Seoul, effectively reducing the total waiting time and travel distance of the vehicles. Sacramento et al. [34] formulated a mathematical model for a problem similar to the flying sidekick traveling salesman problem but for the capacitated multiple-truck case with time limit constraints and minimizing cost as the objective function.

2.2. UAV-Based Routing

In recent years, research on UAV-based routing has witnessed significant growth, driven by the expanding applications of UAVs in various fields, including surveillance, mapping, and delivery. Pereira Coutinho et al. [35] provided a formal definition of the UAV routing and trajectory optimization problem (UAV RTOP) and introduced a taxonomy. Some studies have concentrated on coverage and exploration path planning for UAVs. For instance, Li et al. [36] proposed an enhanced exact cellular decomposition method for UAV coverage path planning in polygon areas, reducing the convex polygon coverage problem to width calculation and demonstrating the feasibility of this method. Xu et al. [37] presented a complete coverage neural network (CCNN) algorithm for UAV path planning, which simplifies neural activity calculations to reduce calculation time and improve coverage efficiency. Regarding UAV-based delivery systems, Rai Vi et al. [38] surveyed emerging drone routing algorithms, highlighting three major aspects: trajectory planning, charging, and security. Deng et al. [39] introduced the Public Transport-Assisted Multi-UAV Parcel Delivery (PDD) algorithm, a new routing and scheduling method that iteratively combines segments of existing routes, integrates public transportation schedules, and jointly optimizes the distance and time costs of UAVs.

In addition, Hu et al. [40] introduced a vehicle-assisted multi-UAV inspection joint route and scheduling algorithm (VAMU) that enables a single vehicle and multiple UAVs to work in parallel to serve multiple targets, thereby optimizing the efficiency of large-scale inspection tasks and reducing time consumption. Poudel et al. [41] conducted a survey on bio-inspired optimization-based path planning algorithms in UAVs, analyzing their characteristics, principles, advantages, and limitations. In the area of multi-UAV formation, Yang et al. [42] reviewed UAV formation trajectory planning algorithms, proposed a framework, classified existing algorithms, and summarized the challenges and future directions.

However, most existing studies assume constant speeds for UAVs and vehicles, treating the task environment as static. These approaches often overlook dynamic factors, such as weather conditions, that affect the speeds of UAVs and vehicles. Consequently, task execution efficiency is significantly impacted by these dynamic factors, which have not been adequately addressed in previous work. In contrast, our research integrates dynamic environmental changes, such as fluctuating weather conditions, into the path planning process, resulting in a more realistic and adaptive optimization of task execution. This enhancement allows for improved real-time decision-making and overall task performance, addressing the limitations of static models commonly used in existing studies.

3. Problem Formulation

In this section, we closely examine the vehicle-assisted multi-UAV data acquisition system for data collection. This system uses a vehicle to transport multiple UAVs, enabling them to traverse data acquisition mission nodes across a large target area. The structure of this section is as follows: In Section 3.1, we introduce the initial static mission model for multi-UAV and vehicle collaboration in data collection. This model is based on the 2E-VRP (Two-Echelon Vehicle Routing Problem) and consists of two main components: vehicle route planning and UAV flight route planning. In Section 3.2, we present the dynamic task processing model, focusing on adjustments made in dynamic scenarios due to the speed variations of UAVs and vehicles. This section also covers modifications to the static model and the formulation of an optimization objective function. In Section 3.3, we introduce the energy consumption model for rotary-wing UAVs.

3.1. Initial Static Task Model

We abstract the entire process of multiple UAVs collaborating with vehicles for data acquisition into a UAV and vehicle route planning and synchronized scheduling problem based on the 2E-VRP (Two-Echelon Vehicle Routing Problem). Within this framework, the initial solution focuses on the vehicle route planning problem, specifically determining how to transport the UAVs to the vicinity of the task nodes. Once the UAVs are transported, they independently execute their respective data acquisition tasks in parallel after departing from the vehicle, forming their own local flight routes. The entire process is illustrated schematically in Figure 1.

To facilitate the depth of the research, we made the following assumptions regarding UAVs and vehicles:

(1)

The speed of the UAV was denoted as $v_{uav}$ and the speed of the vehicle was denoted as $v_c$.

(2)

The UAV landed on the vehicle for a negligible amount of time to replace the battery and it was considered to be $100\%$ charged after the battery replacement.

(3)

The time spent by the UAVs for data collection (photography) at each task point was negligible.

(4)

The communication radius of the UAV was denoted as $R_c$. To enable real-time communication between the UAV and the vehicle for transmitting collected data and receiving tasks, it was ensured that the distance between the UAV and the vehicle always remained less than $R_c$.

(5)

The maximum distance that a UAV could cover in a single flight was denoted as $d_{max}$.

(6)

Within the target area, the vehicle could travel more than 500 km on a full tank of gas. Therefore, in the problem scenario studied in this paper, the vehicle was assumed to have no range or communication limitations. It was also assumed that the vehicle maintained constant communication with the central console.

(7)

The communication latency between the UAV and the vehicle and the vehicle and the central console, as well as the data processing latency, were all considered negligible.

In the multi-UAV–vehicle collaborative data acquisition system, regardless of speed fluctuations, the initial static optimized solution is computed by the central console based on the received static task before the mission begins. This solution is generated using an initial greedy solution construction algorithm followed by optimization with the Hybrid Genetic Algorithm (HGA) [43] to provide optimal route planning and task assignments for the multi-UAVs and the vehicle. Next, we will specifically explore the initial static task model.

In the target region $\Omega$ ($\Omega \ne \varnothing$), scattered tasks need to be performed for data collection. Let the set of all initial task points be $P_0=\{p_1,p_2,\dots ,p_n\}$, where $p_i\in \Omega$ and $i=1,\dots ,n$. All initial task information is known. For each task point $p_i$ ($i=1,\dots ,n$), its position in two-dimensional Cartesian coordinates is denoted as $p_i=(x_{p_i},y_{p_i})$.

If there is a line segment connecting two tasks, the set of line segments is denoted as $E=\{(p_i,p_j)\mid p_i,p_j\in P,i\ne j\}$. The distance between tasks $p_i$ and $p_j$ is represented as $d_{p_i{p}_j}$.

If the task satisfies real constraints of the urban network, the data from the road network should be read to calculate the distance between points based on actual road conditions. Let the set of UAVs be $U=\{u_1,u_2,\dots ,u_k\}$. It is important to note that each point in the set P will be visited by a UAV exactly once and only once. Therefore, all data collection task points in the initial set must be assigned to these UAVs. This is similar to the Bin Packing Problem (BPP), but it also requires considering factors such as the locations of the task points and the battery capacity of the UAVs for the allocation. Multiple unmanned vehicles start from the initial point $A_{\mathrm{start}}$, perform all tasks, and then return to the initial point. To facilitate the recording of vehicle paths and determine vehicle stops near task points, this paper introduces the concept of “anchor points”.

In the target region $\Omega$ ($\Omega \ne \varnothing$), based on the clustering and zoning results, anchor points are set at regular intervals after processing scattered tasks. Let the set of candidate anchor points be $A=\{a_1,a_2,\dots ,a_l\}$, and the vehicle routes pass through these anchor points. Certain anchor points are selected as “stopping anchor points”, where vehicles stop to execute data collection tasks. The set of stopping anchor points is denoted as $A_C$ ($A_C\subseteq A$). Most of the complex notations used in this paper are detailed in

Table 1. Notation and terminology.

Notation	Definition
$P_0=\{p_1,p_2,\dots ,p_n\}$	Set of initial mission points
$E=\left\{(p_i,p_j)|p_i,p_j\in P,i\ne j\right\}$	Set of edges
$U=\{u_1,u_2,\dots ,u_k\}$	Set of UAVs
$A=\{a_1,a_2,\dots ,a_l\}$	Set of candidate anchor points
$A_c=\{a_{k_1},a_{k_2},\dots ,a_{k_n}\}(A_c\subseteq A)$	Set of vehicle route nodes
$P=\{p_1,p_2,\dots ,p_n\}$	Set of reset mission points
$r_0=\{A_{start},a_{k_1},a_{k_2},\dots ,a_{k_n},A_{start}\}$	Vehicle travel route
$Q=\{q_1,q_2,\dots ,q_s\}$	Set of data collection task points
$r_i=\{a_q,q_1,q_2,\dots ,q_n,a_q\}$	UAV one-way flight route
$R_{uav}=\{r_1,r_2,\dots ,r_{n_r}\}$	Set of UAV flight routes
$R=\{r_0,r_1,r_2,\dots ,r_{n_r}\}$	Set of global routes

.

3.1.1. Vehicle Route Planning Model

In the multi-UAV–vehicle cooperative data acquisition problem, the vehicle, upon receiving commands from the center console, sequentially transports m UAVs to the moorings near the target mission point according to a planned driving route. After the vehicle arrives at a particular docking anchor point, the UAVs disperse and take off to their respective mission points for data collection. In order to record the traveling route of the vehicle and determine the delivery and arrival points of the UAVs, we introduce the concept of anchor points. As shown in Figure 2, in the target region $\Omega$ ($\Omega \ne \varnothing$), based on the clustering and partitioning results, after the discretization process, one candidate anchor point is set at every certain distance. In order to improve the efficiency of the system, the route of the vehicle needs to be minimized as much as possible. Therefore, it is necessary to select certain suitable points from these candidate anchor points as stopping anchor points, where the vehicle will wait for the UAV to perform the data collection task, such that the set of vehicle route nodes is $A_c=\{a_{k_1},a_{k_2},\dots ,a_{k_n}\}(A_c\subseteq A)$, where $a_{k_i}\in A$ ($i=1,2,\dots ,n$). Once the stopping anchor points are determined, the vehicle’s route planning problem involves determining the route from the starting point, traversing each route node in the set $A_c$, and, finally, returning to the starting point.

We use the symbol $r_0$ to indicate that there is exactly one vehicle travel route. The vehicle travel route $r_0$ consists of the starting point $A_{\mathrm{start}}$ and the selected stop anchor points (all the points in the set $A_c$), denoted $r_0=\{A_{\mathrm{start}},a_{k_1},a_{k_2},\dots ,a_{k_n},A_{\mathrm{start}}\}$. That is, the vehicle starts from the starting point $A_{\mathrm{start}}$; passes through the stop anchors $a_{k_1}$, $a_{k_2}$, and so on in a sequential manner; and finally returns to the starting point $A_{\mathrm{start}}$. Let any two stop anchors $a_{k_i}$ and $a_{k_j}$ be separated by a distance $d_{a_{k_i},a_{k_j}}$; then, the time it takes for the vehicle to travel from anchor point $a_{k_i}$ to $a_{k_j}$ can be denoted as $t_{a_{k_i},a_{k_j}}^c$. The time $t_{a_{k_i},a_{k_j}}^c$ can be represented as follows:

$$t_{a_{k_i},a_{k_j}}^c={\displaystyle \frac{d_{a_{k_i},a_{k_j}}}{v_c}}$$

(1)

In addition, a variable $x(a_i,r_0)$ is introduced to indicate whether the candidate anchor point $a_i$ is selected as a stopping anchor point and included in the path $r_0$. If yes, then $x(a_i,r_0)=1$; otherwise, $x(a_i,r_0)=0$. Meanwhile, a binary auxiliary decision variable $p_{r_0}(a_i,a_j)$ is used to indicate whether the stopping anchor point $a_i$ in the path $r_0$ is adjacent to the anchor point $a_j$ and whether the anchor point $a_i$ appears before $a_j$. If so, then $p_{r_0}(a_i,a_j)=1$; otherwise, $p_{r_0}(a_i,a_j)=0$. Thus, the length of the vehicle path $r_0$ can be calculated using Equation (2). The total vehicle travel time $T_c$ is expressed in Equation (3).

$$l_{r_0}=\sum _{a_i\in A}\sum _{a_j\in A}{p}_{r_0}(a_i,a_j)d_{a_i,a_j}$$

(2)

$$T_c={\displaystyle \frac{l_{r_0}}{v_c}}={\displaystyle \frac{{\sum }_{a_i\in A}{\sum }_{a_j\in A}{p}_{r_0}(a_i,a_j)d_{a_i,a_j}}{v_c}}$$

(3)

3.1.2. UAV Flight Route Planning Model

In the multi-UAV–vehicle cooperative data acquisition problem studied in this paper, after the vehicle transports the multi-UAVs to a designated docking anchor point, the UAVs will disperse and take off to their respective mission points for data acquisition. The single-trip flight route planning problem for each UAV is essentially a closed-loop Traveling Salesman Problem (TSP). Specifically, the UAVs take off from the vehicle anchor point and return to the vehicle anchor point after visiting each task point, either to recharge for the next trip or dock and wait for the vehicle to travel to the next anchor point. The distance between any two mission points $p_i$ and $p_j$ is denoted as $d_{p_i,p_j}$. The time for UAV $u_k$ to fly from task node $p_i$ to $p_j$ is defined as $t_{p_i,p_j}^{u_k}$. $t_{p_i,p_j}^{u_k}$ is calculated as follows:

$$t_{p_i,p_j}^{u_k}={\displaystyle \frac{d_{p_i,p_j}}{v_{uav}}}$$

(4)

In a single-trip flight of a single UAV $u_k$, it is assumed that the set of data collection task points it needs to visit is $Q=\{q_1,q_2,\dots ,q_s\}$, where $Q\subseteq P$. The anchor point for takeoff is denoted as $a_q$, and, based on this set of task points, the flight route of UAV $u_k$ is generated. A particular single-trip flight route is denoted as $r_i=\{a_q,q_1,q_2,\dots ,q_n,a_q\}$, where $a_q\in A_c$ and $(q_1,\dots ,q_n\in Q)$. The route $r_i$ indicates that the UAV takes off from the anchor point $a_q$, sequentially visits the mission points $q_1$ to $q_n$, and, finally, returns to the anchor point $a_q$. Let us denote the number of UAVs as $M_{\mathrm{uav}}$. For all $M_{\mathrm{uav}}$ UAVs, we compile their flight routes into a set of UAV flight routes $R_{\mathrm{uav}}=\{r_1,r_2,\dots ,r_{n_r}\}$. Therefore, the set of global routes in the multi-UAV–vehicle coordination problem is $R=\{r_0,r_1,r_2,\dots ,r_{n_r}\}$. To determine if UAV $u_k$ flies from task node $q_i$ to $q_j$ in flight route $r_i$, we use the auxiliary decision variable $y_{r_i}(q_i,q_j)$ to represent it. If this is the case, then $y_{r_i}(q_i,q_j)=1$; otherwise, $y_{r_i}(q_i,q_j)=0$. Accordingly, the length $l_{r_i}$ of the flight route $r_i$ can be calculated by Equation (5). The time $t_{{a_q}_i}^{u_k}$ for UAV $u_k$ to make a single trip at the anchor point $a_q$ following the flight route $r_i$ is calculated by Equation (6).

$$l_{r_i}=\sum _{q_i\in Q}\sum _{q_j\in Q}{y}_{r_i}(q_i,q_j)d_{q_i,q_j}$$

(5)

$$t_{a_{q_i}}^{u_k}=\sum _{i=0}^{n-1}{t}_{q_i,q_{i+1}}^{u_k}+t_{q_n,q_0}^{u_k}={\displaystyle \frac{l_{r_i}}{v_{uav}}}$$

(6)

Due to the limited range and power of the UAV, only a few mission data points can be accessed for execution in a single flight. Therefore, UAV $u_k$ may have multiple trips at the anchor point $a_q$. Based on the UAV’s data collection task points, the center console will run the assigned algorithm to calculate the UAV route and the number of flight trips and then send the corresponding commands. Alternatively, a binary variable $\mathrm{z}(u_k,r_i)$ is used to indicate whether route $r_i$ is assigned to UAV $u_k$. Specifically, if the route is assigned, then $\mathrm{z}(u_k,r_i)=1$; otherwise, $\mathrm{z}(u_k,r_i)=0$. In the previous subsection, the variable $x(a_i,r_0)$ was used to indicate whether the candidate anchor point $a_i$ was selected as a stopping anchor point and included in the route $r_0$. In this subsection, the auxiliary decision variable $x(a_q,r_i)$ is used to indicate whether the docking anchor point $a_q$ is included in the single-trip route $r_i$ of a particular UAV. If it is included, then $x(a_q,r_i)=1$; otherwise, $x(a_q,r_i)=0$. The total route length $l_{a_q}^{u_k}$ of UAV $u_k$ at anchor point $a_q$ can be calculated by Equation (7). Assuming that UAV $u_k$ has a total of x flights at anchor point $a_q$, and since the charging time of the UAV is neglected according to the model assumptions, the total flight time $t_{a_q}^{u_k}$ of UAV $u_k$ at anchor point $a_q$ is calculated as shown in Equation (8).

$$l_{a_q}^{u_k}=\sum _{r_i\in R}\mathrm{z}(u_k,r_i)x\left(a_q,r_i\right)l_{r_i}$$

(7)

$$t_{a_q}^{u_k}=\sum _{i=1}^x{t}_{a_{q_i}}^{u_k}=\sum _{i=1}^x{\displaystyle \frac{l_{r_i}}{v_{uav}}}={\displaystyle \frac{l_{a_q}^{u_k}}{v_{uav}}}={\displaystyle \frac{{\sum }_{r_i\in R}z(u_k,r_i)x(a_q,r_i)l_{r_i}}{v_{uav}}}$$

(8)

When the vehicle is parked at the anchor point, a total of $M_{uav}$ UAVs take off simultaneously to perform the mission in parallel. Some UAVs may need to perform the mission repeatedly over multiple trips. The flight time of each UAV at anchor point $a_q$ can be calculated according to the relevant equations. The total mission execution time at a single stopping anchor point is determined by the longest delivery time of the UAV. Thus, after comparison, the total flight time of the longest UAV is taken as the mission delivery time for all UAVs at anchor point $a_q$, which is denoted as $t_{a_q}^{u_{max}}$. Let there be a total of K docking anchor points. The total flight time at each docking anchor point is summed to obtain the global flight duration $T_{uav}$, which is calculated by Equation (9).

$$T_{uav}=\sum _{i=1}^K{t}_{a_i}^{u_{max}}=\sum _{i=1}^K{\displaystyle \frac{l_{a_i}^{u_{max}}}{v_{uav}}}=\sum _{i=1}^K{\displaystyle \frac{{\sum }_{r_j\in R}z(u_k,r_j)x(a_i,r_j)l_{r_j}}{v_{uav}}}$$

(9)

3.1.3. Total Optimization Function and Constraints

For the global system, the total task execution time $T_{all}$ of the multi-UAV–vehicle cooperative data acquisition system is defined as shown in Equation (10). The total task execution time $T_{all}$ represents the completion time, or cost, of a global feasible solution S. Therefore, by minimizing the total task execution time $T_{all}$ as the objective function, the multi-UAV–vehicle cooperative data acquisition problem is modeled as a 0–1 integer programming problem. The expression of the total optimization function is shown in Equation (11).

$$T_{all}=T_c+T_{uav}={\displaystyle \frac{l_{r_0}}{v_c}}+\sum _{i=1}^K{\displaystyle \frac{l_{a_i}^{u_{max}}}{v_{uav}}}={\displaystyle \frac{{\sum }_{a_i\in A}{\sum }_{a_j\in A}{p}_{r_0}(a_i,a_j)d_{a_i,a_j}}{v_c}}+\sum _{i=1}^K{\displaystyle \frac{{\sum }_{r_j\in R}z(u_k,r_j)x(a_i,r_j)l_{r_j}}{v_{uav}}}$$

(10)

$$T=min\left({\displaystyle \frac{{\sum }_{a_i\in A}{\sum }_{a_j\in A}{p}_{r_0}(a_i,a_j)d_{a_i,a_j}}{v_c}}+\sum _{i=1}^K{\displaystyle \frac{{\sum }_{r_j\in R}z(u_k,r_j)x(a_i,r_j)l_{r_j}}{v_{uav}}}\right)$$

(11)

Equation (12) ensures that the number of UAVs is at least 2, which is required for load balancing among multiple UAVs. Equation (13) states that the single-trip flight distance for any UAV must not exceed its maximum flight distance $d_{max}$. In Equation (14), the distance from each data collection task point $p_j$ to anchor point $a_i$ must not exceed the communication radius $R_c$ of the UAV, ensuring access synchronization and communication safety between the UAV, the vehicle, and ground control. Equation (15) ensures that the distance from each data collection task point $p_j$ to anchor point $a_i$ does not exceed half of the UAV’s maximum flight distance $d_{max}$. Equation (16) ensures that all data collection task points are visited exactly once, where the symbol $N_p$ denotes the total number of task points. An auxiliary decision variable $x(p_i,r_i)$ is used to indicate whether data collection task point $p_i$ is included in a single-trip route $r_i$ of a UAV. If it is included, then $x(p_i,r_i)=1$; otherwise, $x(p_i,r_i)=0$. Equation (17) ensures that each data collection task point can only be assigned to one docking anchor point. A two-dimensional auxiliary decision variable $q(p_i,a_j)$ is used to indicate whether task point $p_i$ is assigned to anchor point $a_j$. If it is, then $q(p_i,a_j)=1$; otherwise, $q(p_i,a_j)=0$.

$$M_{uav}\ge 2$$

(12)

$$\sum _{q_i\in Q}\sum _{q_j\in Q}{y}_{r_i}(q_i,q_j)d_{q_i,q_j}\le d_{max},\forall r_i\in R_{uav}$$

(13)

$$d_{p_j,a_i}\le R_c,\forall p_j,a_i\in r_k$$

(14)

$$d_{p_j,a_i}\le {\displaystyle \frac{1}{2}}{d}_{max},\forall p_j,a_i\in r_k$$

(15)

$$\sum _{p_i\in R}\sum _{r_i\in R}x(p_i,r_i)=N_p$$

(16)

$$\sum _{a_j\in A_c}q(p_i,a_j)=1,\forall p_i\in R$$

(17)

3.2. Dynamic Task Processing Model

In the multi-UAV–vehicle cooperative data acquisition problem, the dynamic task processing primarily involves adjustments to the scheme due to changes in the speeds of UAVs and vehicles. In practice, factors such as terrain and weather may cause the speeds of UAVs and vehicles to fluctuate. Fluctuations in the vehicle’s speed have little effect on the delineation of anchor points, the vehicle’s routes, and the UAV’s routes, but they can alter the vehicle’s travel time, resulting in some fluctuations in the total time cost. However, when the UAV’s speed fluctuates, it may cause the originally planned single-trip UAV routes to either not be completed or be completed earlier, which significantly impacts the UAV route planning and task allocation scheme within the current anchor point. Therefore, this paper focuses on the optimization and adjustment of the dynamic scheme for UAV speed changes, specifically local optimization within the anchor point.

We monitor the current state of the multiple UAVs at fixed intervals $\tau$, remove the executed task points, and replan and reassign the UAVs’ flight routes for the remaining tasks within the anchor points. To evaluate the effectiveness of the new scheme after replanning and reallocation, we need to calculate its cost by considering the total execution time of the remaining tasks within a single anchor point $a_q$ as the optimization objective. Based on the total flight time of UAV $u_k$ at anchor point $a_q$ in Equation (8), we compare the total flight times of all UAVs to find the UAV with the longest time, denoted as $t_{a_q}^{u_{max}}$, also referred to as $T_{aq}$. The optimization objective is then expressed in Equation (18). This objective aims to find a route assignment scheme that minimizes the total time required for all UAVs to complete the mission within anchor point $a_q$, thereby improving the efficiency and responsiveness of the entire system. This approach ensures that the UAV–vehicle cooperative system maintains efficient and flexible mission execution, even in the face of uncertainties such as speed fluctuations.

$${\mathcal{T}}_{a_q}=min{t}_{a_q}^{u_{max}}=min{\displaystyle \frac{{\sum }_{r_j\in R}\mathrm{z}(u_k,r_j)x(a_i,r_j)l_{r_j}}{v_{uav}}}$$

(18)

3.3. Energy Consumption Model for Rotary-Wing UAV

UAV energy consumption [44] generally consists of two main components: communication-related energy and propulsion energy. However, since the energy required for communication is comparatively small, and propulsion energy is essential for keeping the UAV aloft and supporting its movement, we primarily focus on propulsion energy consumption. The propulsion power consumption can be expressed using the following formula:

$$\begin{array}{cc}\hfill \tilde{P}\left({\nu }_t\right)& =P_{\mathrm{BLA}}\left(1+{\displaystyle \frac{3{\nu }_{uav}^2}{U_{\mathrm{tip}}^2}}\right)+P_{\mathrm{IND}}{\left(\sqrt{1+{\displaystyle \frac{{\nu }_{uav}^4}{4{\nu }_0^4}}}-{\displaystyle \frac{{\nu }_{uav}^2}{2{\nu }_0^2}}\right)}^{{\displaystyle \frac{1}{2}}}+{\displaystyle \frac{1}{2}}{d}_0\rho s_0{A}_i{\nu }_{uav}^3\hfill \end{array}$$

(19)

where $P_{\mathrm{BLA}}$ and $P_{\mathrm{IND}}$ denote the power consumed by the blade and induced power, respectively, when the UAV hovers. The UAV’s speed at any given time t is represented as $v_{uav}$. $U_{\mathrm{tip}}$ denotes the tip speed of the rotor blade; $v_0$ is the mean rotor-induced velocity in hover; $d_0$ and $s_0$ are the fuselage drag ratio and rotor solidity, respectively; and $\rho$ and $A_i$ represent air density and rotor disc area, respectively.

4. Algorithm

To address the multi-UAV–vehicle cooperative point patrol problem under dynamic scenarios, we decompose this complex dynamic planning and scheduling problem into several sub-problems for separate solutions in a top-down manner. In this chapter, we provide a detailed top-down introduction of the solution approaches for each sub-algorithm module, mainly including the construction of the initial static solution, HGA static optimization, and the dynamic task processing algorithm. In Section 4.1, we introduce the static planning and scheduling algorithm. In Section 4.2, we propose the dynamic task processing algorithm based on the speed variations of UAVs and vehicles. In Section 4.3, we calculate the algorithm complexity.

4.1. Static Planning and Scheduling Algorithm

To solve the initial static solution, we selected a genetic algorithm due to its simplicity and small number of parameters. However, traditional genetic algorithms have drawbacks such as a tendency to fall into local optima and relatively low convergence accuracy, making them unsuitable for direct use in the cooperative optimization of multi-UAV and vehicle systems. Therefore, by exploring the characteristics of the multi-UAV and vehicle cooperative point patrol problem, we specifically improved the genetic algorithm to obtain route solutions during the initial static planning stage. First, an initial feasible solution construction algorithm based on K-means was proposed, followed by the design of a Hybrid Genetic Algorithm (HGA) [43] to optimize the initial solution and achieve a static optimized solution. The HGA combines local search techniques with the Genetic Algorithm (GA) to overcome GA’s tendency to converge prematurely. A set of feasible solutions is constructed using a greedy algorithm to generate the initial parent population. In each iteration, the HGA selects two parent solutions from the population, generates multiple offspring groups through merging and splitting, then evaluates and further optimizes the offspring solutions using local search. This determines whether to incorporate the optimized offspring into the current new population, replacing the parent solutions. Finally, an updated population is obtained.

4.1.1. Construct the Initial Greedy Solution

In the multi-UAV–vehicle cooperative data collection system, regardless of speed fluctuations, the central control unit plans and assigns routes for the UAVs and vehicles before they depart to execute tasks. This is completed based on the initially received static tasks and the computed initial static solution. The process of generating an initial greedy solution generally involves four steps: anchor point selection and the partitioning of anchor point task sets, the partitioning of routes within anchor points, UAV route assignment, and vehicle route planning. The Initial Greedy Solution Construction Algorithm (IGSCA) generates an initial solution that may not be optimal, but is certainly feasible. The initial parent population generated by this algorithm is optimized by the subsequent Hybrid Genetic Algorithm (HGA), continually producing more effective offspring solutions, eventually resulting in a near-optimal solution.

In Algorithm 1, first, the K-means algorithm is used to select K centroid anchor points based on K-means clustering and assign each data collection task point to the nearest anchor point, outputting the customer set corresponding to each anchor point. Second, for each anchor point, the task point set within that anchor point is processed by using Algorithm 2 to partition and obtain a set of UAV flight routes. Algorithm 3 is then used to assign each route in the UAV flight route set to various UAVs without repetition. Finally, Algorithm 4 is used to determine the vehicle driving route based on the UAV solution obtained from the previous steps, ultimately resulting in an initial greedy global solution S.

Algorithm 1 IGSCA Algorithm

Input:  Initial static task point set $P_0=\{p_1,p_2,\dots ,p_n\}$, the set of anchor points to be selected $A=\{A_{start},a_1,a_2,\dots ,a_l\}$, the anchor point location $a_q$ where the vehicle is currently located, the UAV state set U; Output:  Global solution S;   1: Set of task sets H ← Call K-means algorithm and select the docking anchors and the set of clients corresponding to each anchor point   2: for $a_i\in A$ do   3:    UAV flight route set $routes$ ← Call Algorithm 2   4:    Solution S within a single anchor ← Call Algorithm 3   5: end for   6: Global Solution S ← Call Algorithm 4   7: Return S;

4.1.2. Partitioning Routes Within Anchor Points

After K-means algorithm, each data collection point is assigned exactly one docking anchor point, meaning that each docking anchor point $a_i$ has a corresponding set of task points $E_i$. In this section, we describe the planning of routes for the task point sets of each anchor point and the output of a set of UAV flight routes. A diagram illustrating the division of routes within anchor points is shown in Figure 3.

In Figure 3, the gray areas represent clustered anchor-task sets, where each set is associated with one and only one docking anchor point, while the others are candidate anchor points. From the figure, it can be observed that within each gray area, routes are planned between various task nodes, forming multiple UAV flight routes.

This study employed a greedy approach to partition routes within anchor points. The algorithm for dividing routes within anchor points is outlined in Algorithm 2. First, an empty set of routes $routes$, the route $route$, and the current position are initialized. Then, a temporary task point set Q is set and the task points from the task point set $E_i$ are added to Q. Each time, a task point is randomly selected from the temporary task point set Q and added to the current single route $route$. It is checked whether traveling from the anchor point through the route $route$ and returning to the anchor point exceeds the UAV’s maximum flight distance $d_{max}$. If it is exceeded, the task point is removed from the route, added to the route set $routes$, and the route $route$ is reset. This step aims to maximize the collection of task points in a single UAV flight while satisfying the UAV’s flight distance constraint. The maximum iteration count is set to $max\_iter$, and the process continues until the temporary task point set Q is empty, at which point, the UAV flight route set at that anchor point is output. Here, $location$ is used to record the position of the last node in the current route.

The UAV flight route set generated through these steps represents a feasible greedy solution, but may not be optimal. Further iterations are required in subsequent steps to refine and produce the optimal UAV flight route solution.

4.1.3. UAV Allocation Routes

After dividing multiple UAV flight routes within a single docking anchor point, the next step involves assigning these routes to individual UAVs. To enhance the efficiency of the multi-UAV–vehicle collaborative patrolling system, the solution requires a more balanced distribution. Each UAV should execute tasks in parallel to minimize the execution time for tasks at a single anchor point.

Algorithm 2 Algorithm for Partitioning Routes within Anchor Points

Input:  Anchor point location $a_j$, customer set corresponding to the anchor point $E_i$; Output:  UAV flight route set routes;    1: Initialize the route set $routes\leftarrow \varnothing$    2: for $i=1$ to $max\_iter$ do    3:      temporary task point set $Q\leftarrow E_i$,$route\leftarrow \varnothing$    4:      while $Q\ne \varnothing$ do    5:          if $route=\varnothing$ then    6:               Randomly select a customer point $p_i$ from Q, current location $location=p_i$    7:               Add $p_i$ to $route$, and remove it from Q    8:          end if    9:          Find the task point $p_j$ in Q that is closest to $location$ and add it to $route$  10:          Calculate the distance d from the anchor point $a_i$ passing through all points in the route and returning to the anchor point $a_i$  11:          if $d\le d_{max}$ then  12:               Remove $p_j$ from Q, $location=p_j$  13:          else  14:               Remove customer point $p_j$ from $route$  15:               Add the route $route$ to the route set $routes$,$route\leftarrow \varnothing$  16:          end if  17:      end while  18:      if $route=\varnothing$ then  19:          Add the route $route$ to the set of routes $routes$  20:      end if  21: end for  22: Return $routes$;

The pseudocode for the UAV route assignment algorithm is shown in Algorithm 3. Initially, the status of all UAVs and the length of each route are iterated through. If there is a route $l_{r_i}$ with a length not exceeding the remaining flight range $x_{u_k}$ of a certain UAV $u_k$ (i.e., the distance from the current UAV position to the anchor point via all customers on the route), then this route $r_i$ is assigned to that UAV $u_k$ and removed from the set of UAV flight routes $routes$. Through this step, all UAVs will return to the anchor point, and the flag is set to True. At this point, the UAV’s position is updated to the anchor point, and the remaining flight range is reset to full battery status. The remaining UAV flight routes in the set are sorted in descending order by flight length (the distance from the anchor point to all task points in $routes$ and back to the anchor point). During each iteration through the flight route set, if there is a route that makes the total length of the routes currently assigned to a UAV the shortest, then this route is added to the solution set of that UAV. The above steps are repeated in a loop until all UAV routes are fully assigned.

Algorithm 3 UAV Route Assignment Algorithm

Input:  Anchor point position $a_i$, UAV flight route set $routes$, Set of UAVs U; Output:  The solution within a single anchor point $S_{part}$;    1: for $u_k\in U$ do    2:      for $route\in routes$ do    3:          if $l_{r_i}<x_{u_k}$ then    4:               Add this route to the solution set of the corresponding UAV and remove it from the route set    5:          else    6:               Set the UAV’s return-to-position flag to $True$, indicating that the UAV will fly directly back to the anchor point.    7:          end if    8:      end for    9: end for  10: Update the position of each UAV to the anchor point position $a_i$,$x_{u_k}=d_{max}$  11: Sort the remaining routes in the route set in descending order by flight length.  12: for $route\in routes$ do  13:      Select the UAV with the shortest total length of routes already scheduled.  14:      Add the route to the solution set of that UAV.  15: end for  16: Return $S_{part}$;

4.1.4. Vehicle Route Planning

After the route assignment for the UAVs, it is also necessary to plan the driving route for the vehicle, which involves sequential planning for all the anchor points in the set $A=\{A_{start},a_1,a_2,\dots ,a_l\}$.

First, we establish an empty vehicle order list, denoted as $truck\_order$. We add the current vehicle’s anchor point, $A_{start}$, as the starting point to the list and remove it from the set of anchor points. Then, during each iteration through the set, we select an anchor point that minimizes the route length within $truck\_order$ (the distance that passes through all the anchor points in $truck\_order$ and returns to the warehouse) and add it to $truck\_order$, also removing it from the set of anchor points. This process is repeated until the set of anchor points is empty, ultimately yielding the solution for the vehicle’s driving route.

4.1.5. HGA for Static Optimization

In the previous section, through the steps of anchor point selection and the division of anchor point task sets, the division of routes within anchor points, UAV route assignment, and vehicle route planning, a feasible greedy initial solution S was obtained. Next, it is necessary to optimize this solution. Generally, common optimization algorithms such as genetic algorithms and particle swarm optimization simulate the evolutionary processes or group behaviors in nature, which can quickly find high-quality solutions in complex search spaces.

This study adopted the HGA (Hybrid Genetic Algorithm) [43] to optimize the greedy initial solution. The HGA, as an optimization algorithm, combines the characteristics of the Genetic Algorithm (GA) with other optimization techniques. By introducing new operational strategies or improving certain aspects of the genetic algorithm, it enhances both the global search ability and local search ability of the algorithm, thereby better solving complex optimization problems.

Algorithm 4 The Vehicle Route Planning Algorithm

Input:  Global solution S; Output:  Global solution S;   1: Vehicle sequence list $trunk\_order$$\leftarrow \varnothing$   2: Extract all anchor points $anchors$ from S   3: Add the anchor point where the current vehicle is located to the $truck\_order$ as the starting point, and remove it from $anchors$   4: while $anchors\ne \varnothing$ do   5:    Select an anchor point from the remaining $anchors$ that, when added to the current $trunk\_order$, increases the route length the least   6:    Add the selected anchor point to the end of $trunk\_order$, and remove it from $anchors$   7: end while   8: Reorder the solution sets corresponding to each anchor point in S according to the $trunk\_order$ to obtain the final solution   9: Return S;

The HGA (Hybrid Genetic Algorithm) combines the traditional GA (Genetic Algorithm) with local search techniques to enhance algorithm performance. In each iteration, the HGA selects two parent solutions from the initial population, generates multiple offspring populations through genetic operations, evaluates these offspring solutions functionally, and further optimizes them using local search techniques. It then determines whether the optimized offspring solutions should replace the current parent solutions in the new population. This process results in an updated population.

Specifically, several different initial greedy solutions are first constructed and added to the global solution set, with the number of solutions recorded. A maximum population size and the number of iterations A are set. When the number of solutions is less than the population size value, a tournament method is used to select two global parent solutions from the global solution set. Algorithm 5 is then applied to these two parent solutions to generate an HGA-optimized solution, which is added to the global solution set. This process is repeated until the number of solutions reaches the set population size value. Subsequently, the solutions in the global solution set are sorted in ascending order by cost, and less effective solutions are removed. This completes one iteration of the solving process. After repeating these steps A times, all iterations are completed, and the best solution S in the global solution set is returned.

As shown in Algorithm 5, given two distinct global solutions $S_1$ and $S_2$, all routes are placed into $routes$ and all anchor points are placed into $anchors$. The final route set is recorded as $routes\_final$. The route with the minimum cost (cost defined as route length divided by the number of customer points in the route) is selected from $routes$ and added to $routes\_final$. All anchor points or task points included in the selected route are removed from all routes in $routes$, and empty routes in $routes$ are deleted. This process is repeated until $routes$ is empty. $anchor\_Solution$ records each anchor point and its corresponding route set. The starting anchor point is added to $anchor\_Solution$ and removed from $anchors$. The routes covered by this anchor point are removed from $routes\_final\_temp$. The anchor point covering the most routes in $routes\_final\_temp$ is selected from $anchors$, added to $anchor\_Solution$, and removed from $anchors$. The routes covered by this anchor point are removed from $routes\_final\_temp$. This step is repeated until $routes\_final\_temp$ is empty. Through these steps, the algorithm reorganizes the excellent gene fragments of the two parent solutions $S_1$ and $S_2$, i.e., it generates offspring solutions $routes\_final$ through genetic operations.

Then, each route in $routes\_final$ is optimized: an anchor point is selected from the anchor points included in $routes\_final\_temp$ such that the sum of distances from the anchor point to the route’s starting point and from the anchor point to the route’s endpoint is minimized. This route is added to the route set corresponding to this anchor point in $routes\_final\_temp$. After optimization, Algorithm 3 is called to obtain a global solution S. Algorithm 4 is then applied to optimize the vehicle routes of the global solution S, ultimately yielding the optimized global solution S.

Algorithm 5 HGA Optimization Algorithm

Input:  Global solution $S_1$, global solution $S_2$; Output:  Optimized global solution S;    1: Retrieve all routes from both solutions and place them into the route set $routes$    2: Retrieve all anchor points from both solutions and place them into the set $anchors$    3: $routes\_final\leftarrow \varnothing$    4: while $routes\ne \varnothing$ do    5:    Select the route with the minimum cost from $routes$    6:    Add that route to $routes\_final$    7:    Remove all customers contained in the selected route from $routes$    8:    Remove empty routes from $routes$    9: end while  10: $routes\_final\_temp=routes\_final$  11: $anchor\_Solution\leftarrow \varnothing$  12: Add the starting anchor point to $anchor\_Solution$, remove it from $anchors$, and delete the routes covered by this anchor point from $routes\_final\_temp$  13: while $routes\_final\_temp\ne \varnothing$ do  14:    Select from $anchors$ the anchor point that covers the most routes in $routes\_final\_temp$, add it to $anchor\_Solution$, and remove it from $anchors$  15:    Remove the covered routes from $routes\_final\_temp$  16: end while  17: for $route\in routes\_final$ do  18:    Select an anchor point from the anchors contained in $routes\_final\_temp$ such that the sum of the distances from this anchor point to the starting point and to the endpoint of the route is minimized  19:    Add the route to $routes\_final\_temp$ corresponding to the anchor point into which this route has been incorporated  20: end for  21: Apply Algorithm 3 to the optimized result to obtain a global solution S  22: vehicle route of the global solution S ← optimize using Algorithm  4  23: Return S;

4.2. Dynamic Task Processing Algorithm Based on the Speed Variation of UAVs and Vehicles

In real-world scenarios, complex weather changes can cause fluctuations in the speed of both UAVs and vehicles within a certain range. To address these variations in vehicle and UAV speeds due to complex weather conditions, corresponding dynamic task handling solutions are required. These solutions involve real-time dynamic route planning and scheduling to achieve adaptive dynamic adjustments.

In the multi-UAV and vehicle collaborative patrol point problem described in this paper, the vehicle is primarily responsible for transporting multiple UAVs to designated docking anchors and does not undertake the task of visiting data collection points. Fluctuations in vehicle speed have little impact on anchor point allocation, vehicle routes, and UAV routes, but will alter the vehicle travel time, thereby causing some variation in the total time cost. However, when UAV speed fluctuates, it may result in the current single UAV planned route either being unable to be completed or being completed ahead of schedule, causing significant changes to the UAV route planning and allocation scheme within the current single anchor point. Therefore, the focus below is on optimizing dynamic solutions for UAV speed variations.

4.2.1. Local Dynamic Optimization Based on Tabu Search

Tabu Search (TS) is an optimization search algorithm based on neighborhood selection, which uses a tabu list to record moves and avoid getting trapped in local optima after multiple iterations. In response to variations in UAV speed, this paper employs the Tabu Search algorithm to adjust the UAV routes within a single anchor point and outputs locally optimized solutions. This algorithm is named the TS-based Dynamic Processing Optimization Algorithm (TSDPOA).

The pseudocode for the anchor point optimization algorithm based on Tabu Search is shown in Algorithm 6. It defines two basic neighborhood search structures: (1) node swapping and (2) node insertion, as seen in lines 7–11. In each iteration, the algorithm generates $k_1$ swap neighborhood solutions and $k_2$ insertion neighborhood solutions, selects the optimal solution from the new neighborhood, and updates the tabu list $List$. This forms the basis for the Tabu Search operations. After $max\_iter$ iterations, an optimized solution $\tilde{S}$ is produced.

It is important to note that this local dynamic optimization algorithm performs optimization adjustments based on the original UAV flight route solution rather than reconstructing the UAV route solution from the remaining unserviced task points. This significantly reduces the algorithm’s running time. Consequently, the algorithm can quickly make decisions and generate adjusted optimal solutions in response to changes in vehicle and UAV speeds, allowing the UAVs to execute tasks according to the new flight route plan.

Algorithm 6 TSDPOA Algorithm

Require:  Solution S within a single anchor point; Ensure:  Optimized solution $\tilde{S}$;    1: Initialize the optimal solution $\tilde{S}\leftarrow S$ and update the current latest solution $\dot{S}\leftarrow S$    2: Taboo list $List=\varnothing$    3: while $max\_iter>0$ do    4:      Neighborhood $neigh=\varnothing$    5:      Count $count=0$    6:      while $count<k_1+k_2$ do    7:          if $count<k_1$ then    8:               Randomly pick two routes, and randomly select a customer point from each route to exchange    9:          else  10:               Randomly pick two routes, and randomly select a customer point from one route to add to the other route  11:          end if  12:          Reorder the newly formed two routes  13:          Delete any empty routes formed due to insertion operations  14:          Reassign routes for UAVs to generate solutions within a single anchor point ← Call Algorithm 3  15:          Insert the newly generated solution into the neighborhood $neigh$  16:      end while  17:      $\dot{S}\leftarrow \mathrm{the}\mathrm{best}\mathrm{solution}\mathrm{in}neigh$  18:      Update the taboo list $List$ based on $\dot{S}$  19:      Calculate the cost of the optimized solution $\tilde{S}$ and the solution $\dot{S}$, denoted as $\tilde{T}$ and $\dot{T}$ respectively  20:      if $\dot{T}<\tilde{T}$ then  21:          $\tilde{S}\leftarrow \dot{S}$  22:      end if  23: end while  24: Return $\tilde{S}$;

4.2.2. KGTSA Algorithm

In the dynamic scenario where the speeds of multiple UAVs and vehicles constantly fluctuate, the complete dynamic task handling algorithm primarily includes: constructing a global initial solution based on K-means clustering, HGA static optimization, and local dynamic optimization based on Tabu Search (TS). Therefore, the dynamic processing optimization algorithm based on UAV and vehicle speed variations is referred to as the KGTSA.

The KGTSA integrates K-means clustering, HGA, and Tabu Search to achieve efficient task scheduling and path planning. First, K-means clustering is used for the initial task clustering and partitioning, efficiently assigning tasks to different vehicles and UAVs by grouping data points based on similarity. Next, HGA is applied for the static optimization of vehicle routes and UAV flight paths, ensuring the optimal and efficient solution through a combination of evolutionary processes and selection strategies. Finally, Tabu Search is employed for local dynamic optimization, iteratively exploring the solution space to avoid local optima, further improving overall performance.

To address the joint optimization problem of vehicles and UAVs in a structured manner, it is divided into three steps: problem preprocessing, intra-cluster solution construction, and global solution construction. The construction of the global initial solution, HGA static optimization, and local dynamic optimization are all based on optimization adjustments from the first two steps.

In the dynamic scenario where the speeds of multiple UAVs and vehicles constantly fluctuate, the complete dynamic task handling algorithm primarily includes constructing a global initial solution based on K-means clustering, HGA static optimization, and local dynamic optimization based on Tabu Search (TS). Therefore, the dynamic processing optimization algorithm based on UAV and vehicle speed variations is referred to as the KGTSA. A schematic diagram of the KGTSA is shown in Figure 4.

The overall dynamic simulation process of the KGTSA is as follows: After the central console receives the initial static task, it uses Algorithms 1–5 to generate a static optimization solution, allowing multiple UAVs and vehicles to receive tasks and set off from the starting point. After departure, the speeds of the multiple UAVs and vehicles are in a constant state of random fluctuation, with certain range limits. After each short time interval $\tau$, if the vehicle is on its way to the next anchor point, the driving distance of the vehicle for the time $\tau$ is updated. Otherwise, this indicates that the vehicle is parked at the anchor point and that the UAVs are out performing tasks. In this case, the flight distance of each UAV for the time $\tau$ is updated, and Algorithm 6 is used to generate the local dynamic optimization solution within the current anchor point, allowing all UAVs to continue performing tasks according to the new flight route. This process is repeated until all task points are visited, at which point, the algorithm is ended.

4.3. Complexity Analysis

The task processing model proposed in this paper combines static path planning with dynamic adjustment optimization, and the algorithm’s time complexity can be divided into two phases. In the static path planning phase, the K-means clustering algorithm is used to perform the initial task allocation, with a time complexity of $O(k·n·t)$, where k represents the number of clusters, n is the number of task points, and t is the number of iterations. The vehicle path planning is based on a variant of the Traveling Salesman Problem (TSP), with a time complexity of approximately $O\left(n^2\right)$. The global optimization is achieved through the Hybrid Genetic Algorithm (HGA), with a complexity after multiple iterations of $O(m·n·logn)$, where m is the number of iterations. In the dynamic adjustment phase, Tabu Search (TS) is used to reallocate and optimize paths based on the real-time distribution of task points and the UAV status, with the complexity of UAV path optimization being $O(k·p)$, where k is the number of UAVs and p is the number of task points. Overall analysis shows that the static path planning phase has a higher complexity and, as the number of task points increases, it becomes the dominant factor affecting the model’s performance.

In real-world applications, especially under dynamic weather conditions, the complexity of the KGTSA can significantly impact real-time path optimization. The static path planning phase of the algorithm, particularly when the number of task points increases, has a high time complexity that may lead to delays in the path planning process, affecting the system’s responsiveness. In real-world environments, weather changes can cause rapid fluctuations in task point distribution and UAV status, requiring the system to adjust promptly. However, the complexity of static path planning makes it difficult for the system to quickly adapt to these changes. Specifically, when the number of task points increases significantly or when clusters change dramatically, the time required for recalculating the optimal path may affect real-time decision-making. To improve the algorithm’s real-time performance in practical applications, future work could explore parallel computing or adaptive simplifications of the path planning process to reduce its time complexity, ensuring that the algorithm maintains good responsiveness even in dynamic and complex environments.

5. Simulation

To thoroughly evaluate the performance results of the KGTSA, extensive simulation experiments were conducted in this chapter. In Section 5.1, we introduce the relevant evaluation metrics, comparison algorithms, and experimental simulation parameter settings. In Section 5.2, we present the simulation experiment results of the KGTSA based on UAV and vehicle speed variations and provide a detailed analysis of these results. In Section 5.3, we evaluate the battery level variations of the three UAVs. In Section 5.4, we present the trajectories of the three UAVs and the vehicle. In Section 5.5, we assess the time consumption of the algorithm.

It is important to emphasize that our study was primarily conducted through simulation. The following are the practical considerations for deploying the system in a real-world scenario. When using the system in a real-world scenario, several preparatory steps must be completed before the system is activated. First, the precise locations of all data collection points within the target area need to be determined. Subsequently, the vehicle and UAVs should be equipped with the necessary communication and data acquisition devices. The vehicle then transports the UAVs to the vicinity of the target area. After the system is activated, the central console uses a pre-designed algorithm to calculate the initial routes and task assignments for the vehicle and UAVs and sends these instructions accordingly.

During the operation, the UAVs continuously monitor and record the data collection status at each task point as well as their own flight status information, including position and remaining energy, and transmit this data back to the central console in real time. The central console optimizes the operation plans for the vehicle and UAVs based on the received information. If external factors such as weather cause changes in the speeds of the vehicle and UAVs, the central console will quickly generate new control instructions to ensure the efficient execution of data collection tasks. Additionally, in case of emergencies such as equipment failures, the central console can promptly adjust the task plan to ensure the normal operation of the system. Future work will focus on testing the scalability of the algorithm in real-world conditions, particularly for coordinating a single vehicle with multiple UAVs, and addressing potential limitations in terms of the number of UAVs being supervised and the challenges involved in the real-time monitoring of multiple UAVs.

5.1. Experimental Setup

5.1.1. Evaluation Metrics

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Time Cost

Time cost refers to the total time taken for the system to execute tasks, starting from the moment when multiple UAVs and vehicles receive the routes from the central console and depart from starting point $A_{start}$ and ending when the last task point is completed and the vehicles, carrying the UAVs, return to starting point $A_{start}$. For the entire dynamic process, each dynamic planning step aims to optimize time cost, enabling the UAVs to work collaboratively and complete the data collection from all task points as quickly as possible, which is of great significance for practical production and life. Therefore, time cost was the primary optimization objective and an important performance evaluation metric in this study.

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Vehicle Travel Distance

Section 3 provided a detailed description of the vehicle’s travel route $r_0$ and its length $l_{r_0}$, as referenced in Equation (2). The length calculated by this formula represents the vehicle’s travel route length in a static scenario, but in the case of dynamic task arrivals and handling, deviations from this theoretical value may occur. In dynamic scenarios, multiple dynamic route planning steps are performed, requiring route replanning after each fluctuation. Therefore, in simulation experiments, vehicle state values are set to track and update the vehicle’s position information at intervals of unit time $\tau$, with the final accumulated sum representing the actual travel distance of the vehicle. vehicle travel distance is a secondary metric for evaluating algorithm performance.

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UAV Flight Distance

This study utilized $M_{uav}$ UAVs to collaboratively collect data points, with their total flight distance representing the sum of all UAV routes $L_{uav}$. Due to multiple route replanning steps in the dynamic scenario presented in this paper, UAV state values were also set in simulation experiments to track and update UAV position information at intervals of unit time $\tau$. The final accumulated sum represented the actual flight distance of all UAVs. Accordingly, UAV flight distance served as a secondary performance metric for algorithm evaluation.

5.1.2. Comparison Algorithms

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Greedy Algorithm: The Greedy Algorithm is a simple constructive algorithm. In the dynamic scenario described in this paper, the steps to construct a feasible solution are as follows: anchor point selection, intra-anchor point route partitioning, UAV route allocation, and vehicle route planning. In the anchor point selection step, appropriate positions are selected as anchor points according to specific rules. These anchor points serve as the key hubs for the cooperation between vehicles and UAVs. Subsequently, the intra-anchor point route partitioning is carried out. The task points corresponding to each anchor point are reasonably planned to form the flight routes of UAVs. Next, according to the performance of UAVs and task requirements, the partitioned routes are allocated to different UAVs to complete the UAV route allocation. Finally, based on the UAV route allocation results, the vehicle’s driving route is planned to ensure that the vehicle can efficiently transport UAVs to various task areas.

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Hybrid Genetic Algorithm (HGA): In [43], the Hybrid Genetic Algorithm (HGA) was used to study the multi-UAV vehicle delivery problem in static scenarios. This method first generates an initial solution with the Greedy Algorithm. Although this initial solution may not be the optimal one, it is feasible. Subsequently, the Hybrid Genetic Algorithm is used to optimize it. The Hybrid Genetic Algorithm combines the global search ability of the Genetic Algorithm with local search techniques. By simulating the selection, crossover, and mutation operations in natural evolution, the initial solution is continuously improved, and then UAVs and vehicles are guided to execute tasks. However, since this research did not involve dynamic factors, in the dynamic task-processing context of this experiment, the HGA was reapplied to generate solutions for the unexecuted task points. That is, whenever the state of task points changed (such as UAV speed fluctuations, the emergence of new task points, etc.), the HGA was restarted to enable it to adapt to the dynamic environment and optimize the task execution plan.

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Static Optimization Algorithm (SOA): The Static Optimization Algorithm (SOA) is a deterministic method that does not consider dynamic changes in the environment. In the scenario set in this paper, the steps to construct a feasible solution are similar to those of other algorithms, including anchor point selection, intra-anchor point route partitioning, UAV route allocation, and vehicle route planning. However, it is completely different from the dynamic optimization method. The SOA cannot cope with the speed fluctuations of UAVs and vehicles. It provides a static solution and does not make dynamic adjustments according to environmental changes. This means that once the initial anchor points, routes, and task-allocation plans are determined, no matter how the speeds of UAVs and vehicles change subsequently, the SOA will not modify the plan. This may lead to a decrease in task execution efficiency and make it difficult to meet the task requirements in dynamic scenarios.

5.1.3. Experimental Parameter Settings

The target region $\Omega (\Omega \ne \varnothing )$ was defined as a square area with dimensions of 50 km by 50 km, where each side of the region measured 50 km. Within this region, 2000 data collection task points were randomly generated. Additionally, candidate anchor points were established at intervals of 2.5 km in both vertical and horizontal directions across the region. The starting point for the vehicle carrying multiple UAVs was positioned at the center of the region. The vehicle departed from this starting point, carrying 3 UAVs. The speed of the UAVs fluctuated randomly within the range of [7, 13] m/s, while the speed of the vehicle fluctuated randomly within the range of [10, 20] m/s. Furthermore, the communication distance and maximum single flight distance of the UAVs were both set to 15 km. The limitations and their impacts of these settings were as follows:

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Speed Fluctuation Range: The UAV speed fluctuated within [7, 13] m/s and the vehicle speed fluctuated within [10, 20] m/s. This range may not have fully captured extreme weather conditions, where UAV speeds could drop significantly lower or increase higher. In real-world applications, such extreme conditions could lead to longer task completion times and increased system inefficiency.

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Communication Delay: The model assumes negligible communication delay between UAVs and the vehicle. However, in complex urban environments with high-rise buildings or in remote areas with poor signal coverage, communication delays could be significant, affecting the real-time performance of the system.

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Battery and Communication Range: The model assumes that the vehicle has unlimited fuel and communication range. In practice, fuel limitations and communication range constraints could restrict the vehicle’s ability to reach certain anchor points, necessitating more frequent refueling stops or the use of relay stations.

This study primarily investigated the effects of varying the following parameters on algorithm performance: the number of task points, the range of the target area, and the number of UAVs. For these parameters, variations within specified ranges were set to observe their impact on algorithm performance. It is important to note that when one parameter varied, the principle of controlling variables was maintained by keeping the other parameters constant.

5.2. Performance Results and Analysis of Algorithms in Dynamic Task Handling Scenarios

We used the HGA, SOA, and Greedy Algorithm as benchmarks. The Static Optimization Algorithm (SOA) maintained the same algorithm when constructing the initial static solution and the static optimization solution. In other words, the SOA did not make dynamic optimization adjustments to the UAV and vehicle speed fluctuations; it was a static algorithm. By comparing the KGTSA proposed in this paper with the SOA, the improvements in system efficiency brought about by the proposed dynamic optimization adjustments could be observed, highlighting the necessity of designing dynamic optimization solutions. The following shows the experimental results and analysis of changes in the task point count, target area ranges, and number of UAVs.

5.2.1. Variation in Number of Task Points

To observe the impact of varying the number of task points on algorithm performance, the number of task points was varied within the range of $[1000,3000]$, while other parameters were kept at their default values.

As shown in Figure 5, as the number of task points increased, all four algorithms exhibited a linear growth trend, with the Greedy Algorithm’s curve being steeper. This indicated that the effectiveness of the Greedy Algorithm diminished with the increase in task points, making it unsuitable for handling large-scale data collection tasks. The dynamic KGTSA proposed in this paper showed a slight reduction in time cost compared to the static SOA. This was because the dynamic adjustments quickly reallocated UAVs to more suitable routes, enhancing operational efficiency, which demonstrated the effectiveness of dynamic optimization. Additionally, the time cost for the KGTSA was significantly lower compared to the dynamic HGA. This was due to the superior solutions for static problem-solving and dynamic optimization designed in this study.

As shown in Figure 6, as the number of task points increased, the vehicle travel distance did not show a direct correlation. The vehicle travel distance was primarily related to the number of docking anchor points, their positions, and the sequence of visits. In other words, an increase in the number of task points did not necessarily lead to an increase in docking anchor points, as the choice of docking anchor points was more influenced by their positions rather than the number of task points. This study used the K-means algorithm for clustering, where the number of centroids was determined by the area size and the maximum flight distance of the UAVs and was independent of the number of task points. To better optimize the total time cost, a higher number of centroids, i.e., docking anchor points, were set. Thus, the vehicle travel distances for the KGTSA and SOA were slightly higher than those for the other two algorithms.

As shown in Figure 7, the UAV flight distance increased with the number of task points, with the growth trends for the SOA and KGTSA being relatively gradual. Since time cost was the primary optimization objective of the dynamic KGTSA, when UAV speeds fluctuated, the KGTSA adjusted the route scheduling based on the current status, such as the remaining endurance of the UAVs, to minimize the total task execution time at the current anchor point. However, UAVs still needed to visit all points, so this adjustment did not significantly affect the total route distance.

5.2.2. Variation in Target Area Range

When studying the impact of the size of the target area on algorithm performance, the total number of task points was set to the default value of 2000 and the number of UAVs was set to 3. As shown in Figure 8, as the target area side length increased, the time cost showed a linear growth trend. Among the three dynamic algorithms, the Greedy Algorithm performed the worst, followed by the HGA, with the KGTSA performing the best. Additionally, the KGTSA slightly outperformed the static SOA, indicating that after speed fluctuations, the dynamic optimization adjustments for multi-UAV route allocation reduced the total time cost and improved system efficiency.

As shown in Figure 9, as the target area range increased, the vehicle travel distance also increased. The vehicle travel distances for the four algorithms were very similar, as the vehicle travel route was mainly related to the number and positions of docking anchor points in the static solution. The total vehicle travel distances obtained by different algorithms were nearly identical and close to optimal.

In Figure 10, the experimental results are very similar to those in Figure 11. This is because the vehicle travel distances in different algorithms were almost the same, and the total time cost differences were mainly due to the UAV task execution times. Among the three dynamic algorithms, the KGTSA performed the best. Additionally, the KGTSA slightly outperformed the static SOA, indicating that after speed fluctuations, the dynamic optimization adjustments for multi-UAV route allocation reduced the total UAV flight distance, thereby decreasing the overall time cost.

5.2.3. Variation in Number of UAVs

When studying the impact of varying the number of UAVs on algorithm performance, the total number of task points was set to the default value of 2000 and the target area side length was set to 50 km.

As shown in Figure 11, the time cost decreased rapidly at first as the number of UAVs increased, then slowed down, and gradually leveled off. The figure demonstrates that using multiple UAVs significantly improved efficiency compared to a single UAV, roughly doubling the work efficiency. However, the efficiency gains from adding more UAVs diminished as their number increased. Among the algorithms, the KGTSA performed the best, while the SOA performed slightly worse than the KGTSA.

As shown in Figure 12, since the number of UAVs did not affect the vehicle route planning, the vehicle travel distance remained almost independent of the number of UAVs. To better optimize the total time cost, a higher number of centroids, i.e., docking anchor points, were set. As a result, the vehicle travel distances for the KGTSA and SOA were slightly higher compared to the other two algorithms.

As shown in Figure 13, the total UAV flight distance showed almost no direct relationship with the number of UAVs. This was because the UAV route planning results were primarily determined by the clustering of task point locations, and the number of UAVs only affected the allocation of routes among them. As the number of UAVs increased, the UAV route planning did not change, so the total UAV flight distance remained constant. Additionally, the KGTSA outperformed both the HGA and the Greedy Algorithm due to the more optimal UAV route planning and allocation scheme proposed in this study. The KGTSA also slightly outperformed the static SOA as the dynamic optimization adjustments enhanced the efficiency of UAV cooperation.

5.3. UAV Energy Consumption

Figure 14 illustrates the variation in the remaining battery percentage of three UAVs over different time intervals. The x-axis represents time (in minutes), ranging from 0 to 300 min, while the y-axis represents the remaining battery percentage, ranging from 0% to 100%. Each curve, shown in a different color, represents the battery consumption of a single UAV during its flight. From the graph, it is evident that the battery levels of the three UAVs exhibited significant periodic fluctuations, with rapid declines in battery charge followed by gradual recoveries over time.

In practical applications, UAV battery consumption is influenced by various factors, including the complexity of the flight mission, flight speed, payload requirements, and external weather conditions. To ensure the continuity and reliability of UAV operations during long-duration missions and prevent interruptions due to battery depletion, the central control station plays a crucial role in monitoring the UAV’s battery levels and flight status. By continuously tracking the remaining battery charge, along with the UAV’s current location and task demands, the control station can effectively schedule subsequent data collection tasks. With precise predictions of battery consumption, the system ensures that the UAV returns to the base station for battery replacement before it is depleted, thus mitigating potential flight safety risks from over-discharge.

5.4. UAV Trajectories and Path Coordination in Task Execution Simulation

In this simulation, three UAVs performed tasks and navigated between distributed task points. The task points are represented by gray dots and the purple lines represent the vehicle trajectories responsible for transporting the UAVs. The trajectories of each UAV are distinguished by different colors: the first UAV’s trajectory is represented in green, the second in blue, and the third in pink. Figure 15, Figure 16 and Figure 17 display the trajectories of UAV $u_1$, UAV $u_2$, and UAV $u_3$, respectively. Figure 18 consolidates the results of the first three, illustrating the path coordination and interaction of the three UAVs executing tasks simultaneously. From the four figures, it is evident that all task points were successfully visited, further validating the effectiveness and rationality of the proposed algorithm in task allocation and path planning.

5.5. Algorithm Time Consumption

Comprehensive analysis reveals that the complexity of the static path planning stage was relatively high, and as the number of task points increased, it became the primary factor affecting the model’s performance. Figure 19 validates this conclusion from the time complexity analysis. As the number of task points increased, the time consumption exhibited a clear nonlinear growth trend. When the number of task points was small (1000 to 2000), the rapid increase in time cost reflected the high complexity of the static path planning stage, particularly the substantial computational resource demands of K-means clustering and TSP optimization. When the number of task points reached a larger scale (2000 to 3000), the growth trend of time consumption became even more pronounced, further demonstrating that the complexity of the static path planning stage was the primary source of time consumption as the number of task points increased.

6. Discussion and Conclusions

This paper proposed a collaborative path planning and task scheduling scheme for multi-UAV and vehicle systems designed to address large-scale data collection tasks in complex environments. By developing a dynamic task processing model and designing the KGTSA optimization algorithm (which integrates K-means clustering, the Hybrid Genetic Algorithm, and Tabu Search), the scheme demonstrated excellent performance in reducing data collection time and enhancing task execution efficiency. It is particularly suited for time-sensitive applications such as emergency response, environmental monitoring, and logistics delivery. Simulation experiments validated its advantages in terms of optimization performance and computational efficiency. However, the current research is limited to a simulation environment, and its applicability in real-world scenarios may be constrained. Future work will focus on validating the scheme in real-world conditions involving multiple vehicles and UAVs and exploring the following key research directions:

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Integrated Modeling of Heterogeneity and Task Prioritization: We will conduct in-depth research on the collaborative operation modes of multi-vehicle and multi-UAV systems, with a focus on developing a comprehensive model that accounts for the differences in payload capacity, speed, and endurance between vehicles and UAVs. Additionally, we will address task diversity and prioritization, which will further enhance the academic depth and practical value of the research.

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Large-scale Validation in Complex, Real-world Scenarios: We plan to expand the current simulation-based evaluation to field tests that include a variety of complex real-world scenarios and stochastic disturbances. We will prioritize challenging environments such as urban logistics delivery and large-scale event security. Field tests will provide a more comprehensive assessment of system performance, identify real-world challenges, and offer a foundation for further optimization.