Sequential Task Allocation of More Scalable Artificial Dragonfly Swarms Considering Dubins Trajectory

Abstract

With the rapid advancement of UAV technology and the increasing complexity of tasks, multi-UAV systems face growing challenges in task execution. Traditional task allocation algorithms often perform poorly when dealing with issues such as local optima, slow convergence speed, and low convergence accuracy, making it difficult to meet the demands for efficiency and practicality in real-world applications. To address these problems, this paper focuses on collaborative task allocation technology for multi-UAV. It proposes a collaborative task allocation strategy for multi-UAV in a multi-target environment, which comprehensively considers various complex constraints in practical application scenarios. The strategy utilizes Dubins curves for trajectory planning and constructs a multi-UAV collaborative task allocation model, with targets including the shortest total distance index, the minimum time index, and the trajectory coordination index. Each UAV is set as an artificial dragonfly by modifying the traditional dragonfly algorithm, incorporating differential evolution algorithms and their crossover, mutation, and selection operations to bring UAV swarms closer to the characteristics of biological dragonflies. The modifications can enhance the global scalability of artificial dragonfly swarms (ADSs), including wider search capacity, wider speed range, and more diverse search accuracy. Meanwhile, potential solutions with global convergence properties are stored to better support real-time adjustments to task allocation. The simulation results show that the proposed strategy can generate a conflict-free task execution scheme and plan the trajectory, which has advantages in changing the data scale of the UAV and the target and improves the reliability of the system to a certain extent.

1. Introduction

Unmanned aerial vehicles (UAVs), as a rapidly developing high-tech technology, have been widely used in various fields due to their advantages such as high efficiency, flexibility, autonomy, low cost, and low risk. In civilian applications, UAVs can be used for mapping, agriculture, aerial photography, logistics, emergency rescue, etc. [1,2,3,4]. In the military field, UAVs can serve as important tools for intelligence gathering, target strikes, battlefield surveillance, providing efficient and reliable intelligence support, and reducing risks to personnel [5]. Nowadays, UAVs have become an indispensable part of modern warfare. With the increasing complexity of future battlefield environments, the demands for UAV capabilities are also increasing. However, a single UAV, limited by its own structure, often cannot meet the requirements of multi-target collaborative operations in complex tasks. This requires coordinated efforts of multi-UAV technology to effectively complete such tasks. The technology for the task allocation of multi-UAV is a key issue for achieving UAV collaboration and improving task execution efficiency. With the rapid development of UAV technology, researching UAV task allocation problems is of great significance in enhancing the intelligence and autonomy of UAV applications [6,7,8].

The multi-UAV collaborative task allocation problem is a quintessential combinatorial optimization issue [9,10], necessitating the assignment of a certain number of tasks to UAVs based on task requirements and environmental conditions while also taking into account the capabilities and characteristics of the UAVs. The objective is to minimize the task execution costs and maximize the efficiency and effectiveness of task execution. This requires a comprehensive consideration of various factors, including the UAVs’ speed, operational range, and payload capacity, as well as the urgency, difficulty, and terrain conditions of the target tasks and environmental demands such as task coverage, damage requirements, and combat effectiveness, thereby achieving efficient, precise, and secure task execution. Task allocation serves as a critical technology for UAV formations to collaboratively execute complex tasks [11]. It is used to establish a mapping between UAVs and tasks. A well-designed multi-UAV collaborative task allocation method can significantly enhance the efficiency of task completion, but it also increases the complexity of the tasks. Task allocation, in addition to the complexity that may arise from collaborative cooperation, such as the size of the problem (for example, the number of UAVs, tasks, and constraints), is also influenced by the coupling of UAV flight trajectories with different dynamics. This significantly increases the complexity of the problem, necessitating multi-UAV path coordination. Conversely, without suitable solutions, sub-tasks among UAVs may lead to conflicts. In other words, achieving efficient collaboration among UAVs under complex constraints is a challenge for the task allocation problem, which requires considering task priorities, collaboration, and trajectory feasibility to establish the mapping relationship between UAVs and tasks. This issue comprises global planning involving the environment, task requirements, and UAV resources [12].

Classic task allocation models include the multiple traveling salesman problem [13,14], vehicle routing problem [15,16], mixed-integer linear programming [17,18], generalized assignment problem [19], network flow optimization [20], and collaborative task allocation models [21,22]. Considering that these models are often difficult to directly apply to task allocation problems, a study [23] proposes a cooperative multitask assignment problem (CMTAP) based on Mixed Integer Linear Programming (MILP) and network flow optimization (NFO). This model is suitable for more complex task allocation problems. The CMTAP involves assigning multiple UAVs to perform multiple tasks on targets in order to minimize the total consumption, essentially combining task allocation and path planning. The CMTAP simulates the typical scenario of multiple UAVs continuously executing multiple tasks, such as classifying, attacking, and verifying known stationary targets. Compared to the aforementioned models, the CMTAP offers better flexibility and focuses more on collaboration and kinematic constraints among UAVs. Importantly, it ensures collision-free assignments between tasks and UAVs. While different models have their own advantages, the CMTAP is generally applicable.

Given the characteristics of the constructed multi-UAV cooperative task allocation model, appropriate optimization algorithms need to be employed to solve the task planning model. Therefore, there are multiple optimization methods for solving the multi-UAV cooperative task allocation model. For the aforementioned task allocation model, the solution algorithms include exact algorithms, contract net algorithms, auction algorithms, heuristic algorithms, etc. The suitable solution method is adopted based on the mathematical characteristics of the objective function, constraints, and decision variables in the model. A study [24] solves the multi-UAV task allocation problem with various complex constraints using an integer linear programming method. Another study [25] improved the contract net algorithm through psychological factors, the blackboard model, and buffer pool mechanisms; the hybrid method of three improved contract net algorithms was applied to the dynamic cooperative task allocation of heterogeneous multi-UAV platforms. This not only improved the efficiency of task allocation but also made the results of cooperative task allocation more reasonable. A combination of contract net and ant colony search strategies is introduced in [26], which proposes an improved dynamic contract net and introduced the concept of task priority to accommodate the dynamic uncertainty in task allocation. Based on a hierarchical decision mechanism and an improved objective function, a hybrid “two-stage” auction algorithm is proposed in a study [27]. This algorithm achieves dynamic task allocation and obstacle avoidance path planning for multiple UAVs simultaneously considering the limited resources of each UAV. A distributed auction algorithm for task allocation of small UAVs is presented in a study [28]. Through the simulation of different target distributions and communication ranges while addressing the kinematic constraints and communication limitations of smalls, the performance of the task allocation scheme is validated.

With the rapid development of heuristic algorithms, complex multi-UAV task allocation problems can obtain local optimal or satisfactory solutions within an acceptable time range [29]. A study [30] presents a cooperative multitask assignment problem model with objective priority constraints. This model considers not only the kinematic constraints, resource constraints, and task priority constraints of UAVs, but also the objective priority constraints to achieve a more realistic scenario. In order to improve the efficiency of genetic algorithms in solving the multi-UAV task allocation problem, a study [31] introduces a secondary selection operation and applies an improved simulated annealing algorithm in the secondary selection operation. The promotion of population diversity in the secondary selection operation enhances the acceptance criteria for new solutions in SA by setting a threshold. A study [32] proposes a dynamic pigeon-inspired optimization algorithm based on hybrid architecture for multi-UAV search and attack task allocation problems. This pigeon-inspired algorithm employs dynamic concepts, discretization, and solution acceptance strategies, achieving good performance. In [33], a discrete adaptive search whale optimization algorithm is proposed. The algorithm uses a crossover-based update method, enabling it to solve discrete problems such as task allocation. Additionally, the study introduces a search intensity adaptive mechanism to reasonably optimize and balance the exploration and exploitation intensity within the solution space, allowing for the rapid achievement of high-quality task allocation results.

Currently, in the setup of multi-UAV collaborative task problems, there is a lack of consideration for the actual situation during the task execution process. Existing task allocation methods are relatively singular, only considering reconnaissance targets or dividing tasks into reconnaissance, decision-making, strike, and other independent tasks, with little involvement in the collaborative operations between different tasks. Defensive positions often exist in target areas, necessitating the use of attack strategies, such as attacks from the side or rear, and restricting the entry angle of UAVs at target points. Existing task allocation modeling problems only consider some of these factors. Therefore, in the study of multi-UAV collaborative task allocation, it is necessary to consider more practical factors and explore collaborative operations between different tasks.

This paper primarily investigates the issue of collaborative task allocation in multi-UAV systems, focusing on the synergy between different tasks while considering the angle restrictions present in target areas under realistic combat conditions. The task allocation modeling comprehensively takes into account various factors, providing important insights for future research on multifunctional collaboration. The main contributions of this paper regarding the collaborative task allocation problem for multi-UAVs are as follows:

• On the basis of fully considering the flight characteristics of UAVs and multiple constraints such as task execution timing, task coordination, and fuel, the trajectory planning is carried out in combination with the Dubins curve [34,35], and the task coordination and allocation system model is constructed with the optimization goal of minimizing the total flight distance, the task completion time, and range coordination.
• The task is divided into multiple sub-tasks through the encoding and decoding scheme, and these tasks are co-assigned to multiple UAVs so as to improve the efficiency and practicality of task allocation. In order to solve the problem that the traditional dragonfly algorithm can easily fall into local optimization and slow convergence speed [36], the traditional dragonfly algorithm was modified to set each UAV as an artificial dragonfly, combining the differential evolution algorithm and its crossover, mutation, and selection operations to make the UAV swarm closer to the characteristics of biological dragonflies. The improvements enhance the global scalability of the artificial dragonfly swarm (ADS), including wider search capabilities, wider speed ranges, and richer search accuracy.
• Through the comparative simulation experiments of different target numbers and UAVs, it is verified that the proposed HDEDA can effectively solve the problem of multi-UAV collaborative task allocation and obtain a conflict-free task assignment scheme that satisfies the constraints. The algorithm shows good practicability in the face of complex environments and unexpected situations, showing high practical application value in task execution efficiency, task allocation scheme generation, and task execution voyage planning.

The structure of the remaining parts of this paper is as follows: Section 2 constructs a collaborative task allocation model for multi-UAVs, covering the problem statement, constraint setting, trajectory planning based on Dubins curves, and fitness evaluation of the objective function; Section 3 presents a task planning model under dynamic adjustments; Section 4 provides a detailed introduction to the HDEDA algorithm, including the optimization of the traditional dragonfly algorithm, the integration of differential evolution strategies, and encoding and decoding mechanisms; Section 5 validates the effectiveness of the algorithm through simulation experiments, including the construction of the experimental environment, the presentation of task allocation schemes, the comparative analysis of algorithm performance, and dynamic task adjustment strategies; Section 6 summarizes the research and provides an outlook of future research directions.

2. Multi-UAV Cooperative Task Assignment Model

When establishing a collaborative task allocation model for multi-UAV systems, four aspects need to be considered: first, we must provide a clear and reasonable description of the multi-UAV task allocation problem and make appropriate assumptions based on the task scenario; second, we need to set constraint conditions according to the characteristics of the task; third, we need to select a suitable trajectory planning algorithm; and finally, we must define the objective function of the collaborative task allocation model.

2.1. Problem Description and Scenario Assumptions

In the scenario of wide-area search and attack, assuming that a multi-UAV operates in the task area, it is specified that there are $N_T$ suspected targets within the task area and the position of each target is known. The objective is to sequentially carry out reconnaissance, decision-making, and strike tasks on the identified suspected targets within the task area. On the one hand, it is important to conduct thorough reconnaissance of significant military targets, and on the other hand, real-time decision-making and strike operations must be executed in enemy territory. There are $N_V$ combat UAVs available. Under the premise of ensuring the effectiveness of the model, this section presents the following reasonable assumptions for the task coordination and allocation model:

• The UAVs take off simultaneously from their initial positions without taking into account the UAV takeoff and landing processes.
• There are no requirements for the time windows and priorities of the targets.
• During the task assignment process, the task network communication topology remains unchanged due to the high data transmission rate and low latency characteristics of the next-generation Internet of Things.
• The UAVs are equipped with advanced sensor systems and high-speed aerial configurations, providing a wide field of view for reconnaissance tasks, while possessing high maneuverability and the capability to carry weapons and ammunition, making them well suited for executing attack tasks.
• The task environment is known in advance.
• The UAVs used in this article are homogeneous drones, and a centralized control structure is adopted.

In response to the described task scenario, the OODA loop from modern military theory is referred to, simplifying its operational concept and designing three core functions for combat UAVs: reconnaissance, decision-making, and attack. Specifically, the reconnaissance function is responsible for carrying out intelligence gathering tasks in the target area, the decision-making function analyzes and processes the collected reconnaissance information and issues operational directives accordingly, and, finally, the attack function executes precise strikes on predetermined targets based on the commands issued by the decision-making function. On this basis, the coordinated task allocation problem for multi-UAVs becomes particularly critical, aiming to find a solution that not only meets the constraints of complex tasks but also enhances the reliability of UAV task execution. This problem falls within the scope of the CMTAP. This problem is equated as follows: Assuming that $UAV=\{{UAV}_1,{UAV}_2,{UAV}_3,\dots ,{UAV}_{N_V}\}$ is a collection of UAVs, each UAV is equipped with three functions: reconnaissance, decision-making, and attack. $T=\{T_1,T_2,T_3\dots ,T_{N_T}\}$ is a collection of $N_T$ targets. Use $S$, $D$, and $I$ to represent reconnaissance, decision-making, and attack tasks, respectively, Let $N_c=3\cdot N_T$ represent the total number of tasks that need to be executed by UAVs .The purpose of collaborative task allocation is to assign a task sequence to each ${UAV}_k$ as follows: ${UAV}_k{=\left\{\right(T}_i{,m}_j),\dots {,(T}_n{,m}_j\left)\right\} i,n \in (1,N_T)$, where $m_j\in (S,D,I)$. The execution of each task adheres to strict task coupling and task priority constraints. Specifically, task $D$ can only be executed after task $S$ is completed, and task $I$ can only be executed after the decision for task $D$ is made.

2.2. Constraint Conditions

The task allocation scheme based on $S$, $D$, and $I$ should consider the constraints between the UAVs and targets. To ensure that the task allocation scheme is applicable to complex environments and scientifically sound, various practical constraints must be considered when determining the task allocation scheme and resource consumption for multi-UAVs.

To establish a straightforward and easily solvable mathematical model, let $X_{(T_i,m_j)}^{UA{V}_k}\in \{0,1\}$ represent the decision variable for the ${UAV}_k$ performing task $m_j$ on target $T_i$. If $X_{(T_i,m_j)}^{UA{V}_k}=1$, it indicates that the task is being executed; otherwise, it is 0.

• Task timing constraints

Due to the temporal constraints of UAV formations, when a UAV formation is executing a task, tactical coordination is required, which is subject to time limitations and necessitates the consideration of the sequence of execution. Assuming the moments for conducting reconnaissance, decision-making, and attack on the suspected target $T_i$ are $t_S(T_i),t_D(T_i),t_I(T_i)$, respectively, the following conditions must be satisfied:

$$t_s(T_i)<t_D(T_i)<t_I(T_i)$$

(1)

• Task collaboration constraints

Under the constraint of task coordination in UAV formations, different tasks for the same target can only be executed once. In other words, the same target cannot undergo reconnaissance, decision-making, and strike tasks more than once. Each UAV can only perform one task at a time. Therefore, the following condition must be satisfied:

$${\displaystyle \sum _{k=1}^{N_v}{X}_{(T_i,m_j)}^{{\mathrm{UAV}}_k}\le 1}$$

(2)

All tasks should be executed, as captured by

$${\displaystyle \sum _{k=1}^{N_v}{\displaystyle \sum _{i=1}^{N_T}{X}_{(T_i,m_j)}^{{\mathrm{UAV}}_k}}=N_c}$$

(3)

• Energy constraints

During UAV formation flights, the fuel consumption of UAVs is limited; therefore, it is necessary to add the constraint of endurance, specifically the maximum flying range of the UAVs. Let us denote “$L_{max}$” as the maximum range of the UAV. During the execution of strike tasks, the ammunition resources carried by the UAVs are limited; hence, it is necessary to constrain the number of attack tasks that the UAVs can perform. Assuming that at the time of task assignment, each UAV has a maximum ammunition capacity of $I_{max}$, the following condition is given:

$$v_k{t}_{k,i}{X}_{(T_i,m_j)}^{{\mathrm{UAV}}_k}\le L_{\max }$$

(4)

$$I_k\le I_{MAX}$$

(5)

where $v_k$ represents the speed of each ${UAV}_k$, $t_{k,i}$ represents the time taken by each ${UAV}_k$ to perform the task on target $T_i$, and $I_k$ represents the number of attack tasks for each UAV.

2.3. Trajectory Planning Based on Dubins Curves

2.3.1. Dubins Curves

Considering the characteristics of UAVs in actual task scenarios, including the turning radius, heading angle, and presence of defensive positions in the target area, it is necessary to consider angle restrictions when entering the target. Due to the simplicity of existing path length calculations, they cannot meet the actual requirements. However, the Dubins curve is a type of curve that can connect two paths with determinate direction and finite curvature [37]. Therefore, the Dubins curve is adopted to generate flight paths, solving the problem of finding the shortest path from a given point in one direction to another given point in another direction, generating the shortest path between points $P_s\left(X_s,Y_s,{\phi }_s\right)$ and $P_f\left(X_f,Y_f,{\phi }_f\right)$. The path of a Dubins curve must be one of the six combinations of line segments and curvature arcs, including $\{RSR,RSL,RSR,LSL,LSR,LRL\}$. As shown in Figure 1, the shortest one among them will be selected as the final path.

Among them, R represents a clockwise turn, L represents a counterclockwise turn, and S represents a straight line.

Here, the example of the inscribed Dubins curve in Figure 2 is used to explain its generation process.

Let the starting position and ending position be denoted as $P_s(X_s,Y_s)$ and $P_f(X_f,Y_f)$, respectively. The direction angles of the initial velocity vector ${\nu }_s$ and final velocity vector $v_f$ are denoted as ${\phi }_s$ and ${\phi }_f$, respectively. The radii of the starting and ending circles are $R_s$ and $R_f$, respectively. Then, the solution of the Dubins curve can be represented as follows:

$$L_s(X_s,Y_s,{\phi }_s,R_s)\to L_f(X_f,Y_f,{\phi }_f,R_f)$$

(6)

According to the Euclidean geometry approach, the Dubins curve can be obtained through the following steps: First, calculate the coordinates of the centers of the initial and final circles, denoted as $O_s(x_{cs}.y_{cs})$ and $O_f(x_{cf}.y_{cf})$, respectively. Next, calculate the coordinates of the tangent points. Draw tangents between circle $C_S$ and circle $C_f$. The tangent point on the initial circle is the exit point of the desired Dubins curve, denoted as $P_1$. The tangent point on the final circle is the entry point, denoted as $P_2$. Finally, generate the Dubins curve. Draw an arc from $P_{\mathrm{s}}$ to $P_1$ with the center at $O_s$, and draw an arc from $P_2$ to $P_f$ with the center at $O_f$. The Dubins curve connecting $P_1$ and $P_2$ consists of two arcs and generates a straight line.

2.3.2. Multi-UAV Path Planning Model Based on Dubins Curves

In the process of task allocation, path planning is a critical factor in ensuring the success of multi-UAV collaborative tasks. To meet the trajectory requirements of UAVs in complex environments, the Dubins curve is applied to UAV path planning. Assuming that the UAV’s speed is constant at $v_k$ and the turning radius is $R$, its dynamic model can be expressed as follows:

$$\begin{array}{c}{\displaystyle \frac{dx}{dt}}=v\cdot \cos (\theta )\\ {\displaystyle \frac{dy}{dt}}=v\cdot \sin (\theta )\\ {\displaystyle \frac{d\theta }{dt}}={\displaystyle \frac{v}{R}}\cdot u\end{array}$$

(7)

In this context, $(x,y)$ represents the UAV’s position coordinates, $\theta$ denotes the heading angle, $R$ is the minimum turning radius, and $u\in \{-1,0,1)$ is the control input, representing a left turn, straight line, and right turn, respectively. The model optimizes flight paths after task allocation, fully accounting for constraints such as the UAVs’ turning radius and heading angle. Utilizing Dubins curves, the model calculates the shortest feasible path for each UAV from its starting point to the target, ensuring that each UAV can effectively execute its assigned tasks in the correct sequence. During the path generation process, the model selects the optimal combination of straight lines and curves, enabling the UAVs to efficiently complete their tasks with the shortest path, even in complex environments.

2.4. Fitness Calculation of the Objective Function

In the multi-UAV system, due to the existence of an optimal solution set for the multi-objective problem rather than a unique solution and the potential conflicts or constraints between different targets, this section uses the linear weighting method [38] to optimize the multi-objective function. The specific implementation is provided below. The setting of the weights directly affects the effectiveness of the optimal solution and the resulting task allocation scheme. Therefore, different weight values can be set based on the decision makers’ preferences or the complexity of the environment.

$$\min f={\displaystyle \sum _{i=1}^k{\omega }_i}{f}_i(x)$$

(8)

In the equation, $f_i(x)$ is one of the multi-objective functions, ${\omega }_i$ is the weight, and ${\displaystyle \sum _{i=1}^k{\omega }_i}$.

When UAVs plan routes for task allocation, the total flight distance for completing a task is positively correlated with the total resources consumed by the formation. The shorter the total flight distance, the fewer resources are consumed. However, the shortest total flight distance alone does not guarantee the shortest time for the formation to complete all tasks. The drawback of this consideration is that, based on the positional advantages of some UAVs, certain UAVs may be allocated more tasks than others, leading to an imbalance in the flight range coordination among UAVs, which disrupts flight synchronization. This also results in a longer overall time needed for the formation to complete all tasks. The main criteria for evaluating the efficiency of cooperative task allocation schemes include the following three aspects:

• The shortest indicator of the total flight range of multi-UAV

During the task execution process of the multi-UAV, in order to achieve optimal fuel consumption, the minimum total flight distance for the task can be quantified as follows

$$f_1=\min \sum _{k=1}^{N_V}\sum _{i=1}^{N_T}\sum _{j=1}^{N_T}{l}_{ij}\cdot X_{(q_i,q_j)}^{UA{V}_k}$$

(9)

where $l_{ij}$ represents the flight distance from target $q_i$ to target $q_j$ and $X_{(q_i,q_j)}^{UA{V}_k}$ is the decision variable indicating whether the $UA{V}_k$ executes the target from $q_i$ to $q_j$. If executed, the value is 1; otherwise, it is 0. For the shortest flight path $l_{ij}$, the introduced Dubins curve will be used for planning and solving as follows:

$$l_{ij}=\mathrm{Dubins}\mathrm{Curve}(d_{ij},R,v_k)$$

(10)

where $d_{ij}$ represents the straight-line distance from target $q_i$ to target $q_j$.

• The minimum time criterion for multiple UAVs to complete all tasks

To ensure efficient task completion and minimize the time required for multi-UAVs to complete all tasks, the minimum time metric for multi-UAV task execution is considered. The minimum time metric for completing all tasks is determined by the UAV with the longest flight distance in the task allocation set. This metric is expressed by

$$f_2=\underset{k\in N_V}{\max }\left\{{\displaystyle \frac{{\displaystyle \sum _{i=1}^{N_T}}{\displaystyle \sum _{j=1}^{N_T}}{l}_{ij}\cdot X_{(q_i,q_j)}^{UA{V}_k}}{v_k}}\right\}$$

(11)

• Multi-UAV flight coordination metric

The flight time of the UAVs affects the execution of complex tasks. Therefore, it is important to consider how to balance task assignments among multi-UAV systems to improve system efficiency. Using trajectory coordination as an evaluation metric, the objective is to minimize the differences in flight distances among the UAVs. The expression for this objective is as follows:

$$f_3=\min \underset{1\le k\le N_{\mathrm{v}}}{\mathrm{var}}\left\{D_k\right\}$$

(12)

where $D_k$ represents the flight distance between UAVs. The objective is to achieve as much consistency as possible in the flight distances of each UAV after target assignment and path planning. The expression for $D_k$ is as follows:

$$D_k=\sum _{i=1}^{N_T}\sum _{j=1}^{N_T}{l}_{ij}\cdot X_{(q_i,q_j)}^{UA{V}_k}$$

(13)

Assuming that the UAV speed is constant, the task completion time is proportional to the flight distance. Based on the three metrics of the shortest total distance index, minimum time index, and trajectory coordination index, a multi-objective function for the collaborative task allocation of multi-UAVs is designed as follows:

$$\min f={\omega }_1·\min \sum _{k=1}^{N_V}\sum _{i=1}^{N_T}\sum _{j=1}^{N_T}{l}_{ij}\cdot X_{(q_i,q_j)}^{UA{V}_k}+{\omega }_2·\underset{k\in N_V}{\max }\left\{{\displaystyle \frac{{\displaystyle \sum _{i=1}^{N_T}}{\displaystyle \sum _{j=1}^{N_T}}{l}_{ij}\cdot X_{(q_i,q_j)}^{UA{V}_k}}{v_k}}\right\}+{\omega }_3·\min \underset{1\le k\le N_{\mathrm{v}}}{\mathrm{var}}\{D_k\}$$

(14)

The main goal of solving the objective function is to find the optimal solution for each individual in a short period of time while retaining key information to achieve the minimal fitness value. The objective of multi-UAV cooperative task allocation is to enhance the execution efficiency and response speed of the UAVs while reducing resource waste and redundancy. In this section, the fitness value is derived from the objective function, representing the overall cost of task execution. The multi-UAV task allocation problem involves both equality and inequality constraints. Based on optimization theory and the previous analysis, this section establishes a multi-objective optimization model under multiple constraints as follows:

$$\begin{array}{l}\min f={\displaystyle \sum _{i=1}^k{\omega }_i}{f}_i(x)\\ st:\\ t_{\mathrm{s}}({\mathrm{T}}_i)<t_{\mathrm{D}}({\mathrm{T}}_i)<t_{\mathrm{I}}({\mathrm{T}}_i)\\ {\displaystyle \sum _{k=1}^{N_v}{X}_{(T_i,m_j)}^{{UAV}_k}\le 1}\\ {\displaystyle \sum _{k=1}^{N_v}{\displaystyle \sum _{i=1}^{N_T}{X}_{(T_i,m_j)}^{{UAV}_k}}=N_c}\\ v_k{t}_{k,i}{X}_{(T_i,m_j)}^{{UAV}_k}\le L_{\max }\\ I_k\le I_{MAX}\end{array}$$

(15)

3. Dynamic Task Adjustment Model

In the face of unforeseen situations in an unknown environment, the task environment will encounter numerous uncertainties. When a UAV is threatened and experiences a malfunction, it may be unable to execute the task. If $UA{V}_k$ fails, it is necessary to recalculate the formation and positions of the remaining operational UAVs. When computing a set of unexecuted tasks, the prioritized constraints of the tasks may impact the execution of tasks by other operational UAVs. For example, if the task assignment set for $UA{V}_k$ is $UA{V}_k=\{(T_3,S),(T_4,D),(T_7,I),(T_8,S),(T_{10},D)\}$, and if $UA{V}_k$ completes tasks $\left(T_3,S\right)$ and $\left(T_4,D\right)$ before experiencing a failure, the remaining task set for ${UAV}_k$ would be $(T_7,I),(T_8,S),(T_{10},D)$. Based on the priority constraints of tasks, it is evident that the non-completion of task $S$ by $T_8$ will affect the execution of tasks $D$ and $I$ by other UAVs. The same situation also applies to other targets. Therefore, it is necessary to represent the union of all remaining tasks that have not been executed on the targets at this time. After obtaining the set of UAVs and targets that become invalid, it is necessary to recalculate the number of tasks $m_{T_i}$ to be executed on each target and the total number of tasks $N_c$ that the UAVs need to execute. Then, the solving algorithm of the model is applied again to obtain a new task allocation plan to dynamically adjust the initial collaborative task allocation. Since a part of the tasks and targets has already been executed before becoming invalid, the recalculated task set and target size will be reduced; this also means that the time required for the algorithm to solve the problem will shorten, making it suitable for scenarios where real-time task allocation is required.

4. Multi-UAV Cooperative Task Allocation Solution Strategy

In the traditional dragonfly algorithm (DA), a specific number of individuals are randomly generated as the initial population based on the constraints of the problem and the search space. Each individual updates its position and velocity by acquiring optimal solution information from neighboring individuals. However, when the population becomes trapped in a local optimum, the entire population may be affected, leading to slower convergence speed, reduced convergence accuracy, and decreased stability. To address this issue and effectively formulate the task allocation scheme for multiple UAVs while obtaining the optimal solution set for cooperative task allocation, this paper proposes appropriate encoding and decoding rules considering task timing constraints, task cooperation constraints, and energy constraints. Subsequently, the model is solved using an improved hybrid differential evolution dragonfly algorithm (HDEDA). In this algorithm, each UAV is treated as an artificial dragonfly, and by integrating the crossover, mutation, and selection operations from the differential evolution algorithm (DE), the UAV swarm more closely mimics the behavioral characteristics of biological dragonflies. The global scalability of the artificial dragonfly swarm (ADS) has been enhanced, offering broader search capabilities, wider speed ranges, and higher search accuracy. Additionally, potential solutions with global convergence potential are stored in memory to better support real-time adjustments in task allocation.

4.1. Traditional Dragonfly Algorithm

The dragonfly algorithm requires initializing the population first, with the value range being determined by the number of UAVs in the swarm:

$$X_i=\alpha \times (u_b-l_b)+l_b$$

(16)

In the equation $\alpha \in \left(1,NP\right)$, $NP$ represents the population size of ADS, $u_b$ represents the upper bound, and $l_b$ represents the lower bound.

For each dragonfly, there are five basic behaviors: Separation $S_i$, Alignment $A_i$, Cohesion $C_i$, Prey $F_i$, and Predator $E_i$. The weights are randomly initialized, and the five behaviors are then calculated to update the dragonfly’s velocity and position. To avoid collisions, the expression for the separation behavior $S_i$ is as follows:

$$S_i=-{{\displaystyle \sum }}_{j=1}^N(X_i-X_j)$$

(17)

In the equation, $X_i$ represents the current position of the dragonfly individual, $X_j$ represents the position of the j-th neighboring dragonfly individual, and N represents the number of neighboring individuals around dragonfly $i$.

To achieve flocking behavior, the expression for the alignment behavior $A_i$ is as follows:

$$A_i={{\displaystyle \sum }}_{j=1}^N{V}_j/N$$

(18)

In the equation, $V_j$ represents the flying velocity of the j-th neighboring individual.

The aggregation behavior $C_i$ expression is as follows:

$$C_i={{\displaystyle \sum }}_{j=1}^N{X}_j/N-X_i$$

(19)

The foraging behavior $F_i$ expression is as follows:

$$F_i=X^{+}-X_i$$

(20)

where $X^{+}$ represents the food source.

The $E_i$ expression of the behavior of avoiding natural enemies is as follows:

$$E_i=X^{-}+X_i$$

(21)

where $X^{-}$ represents the location of the natural enemy.

The dragonfly algorithm considers the behavior of dragonflies as a combination of these five factors and to simulate the movement of dragonflies; the individual step length is updated by

$$\mathsf{\Delta }{X}_{t+1}=(s{S}_i+a{A}_i+c{C}_i+f{F}_i+e{E}_i)+w\mathsf{\Delta }{X}_t$$

(22)

In the equation, s represents the separation weight, a represents the alignment weight, c represents the cohesion weight, f represents the food factor, e represents the predator factor, w represents the inertia weight, and t represents the iteration count.

To enhance the global search capability and convergence accuracy of the dragonfly algorithm, two strategies have been proposed for updating the dragonfly positions. When a dragonfly has neighboring individuals around it, the position is updated using the following method:

$$X(t+1)=X_t+\mathsf{\Delta }{X}_{t+1}$$

(23)

To further enhance the algorithm’s performance, when there are no adjacent solutions near individuals of the same type, the dragonfly positions are updated by utilizing Levy flights to navigate the search space. This update is performed by

$$X(t+1)=X_t+\mathrm{Levy}(d)\times X_t$$

(24)

In the equation, $d$ represents the dimensionality of the position vector. The expression for Levy flight is shown as

$$\mathrm{Levy}(x)=0.01r_1\sigma \mid r_2{\mid }^{-1/\beta }$$

(25)

In the equation, r1 and r2 are random numbers in the range from 0 to 1 for each dimension. σ is the control parameter for Levy flight, and it is defined as follows:

$$\begin{array}{c}\sigma ={\left({\displaystyle \frac{\mathsf{\Gamma }(1+\beta )\times \sin (\pi \beta /2)}{\mathsf{\Gamma }(\frac{1+\beta }{2})\times \beta \times 2^{(\beta -1)/2}}}\right)}^{1/\beta }\\ \mathsf{\Gamma }(1+\beta )=(\beta )!\mathsf{\Gamma }({\displaystyle \frac{1+\beta }{2}})=({\displaystyle \frac{\beta -1}{2}})!\end{array}$$

(26)

4.2. HDEDA

To further enhance the diversity of multi-UAV cooperative task allocation and improve the performance of the DA, this paper proposes a hybrid method that combines the DE algorithm with the DA. The core of the HDEDA lies in introducing the mutation operation from the DE algorithm and incorporating it into the strategy of the DA. In HDEDA, mutation operations modify solutions with lower fitness values , thereby enhancing the diversity of the population and improving the overall search performance. The main purpose of the mutation operation is to accelerate the convergence of the algorithm, while in the evolutionary process, it tends to select individuals with higher fitness values.

A selected individual from the current best solution is mutated to introduce diversity into the population. This mutation operation increases diversity, and, when the algorithm is close to the optimal solution, the mutation algorithm enhances the ability of random exploration, thereby accelerating the convergence of the population to the optimal solution.

$${V_{ij}}^{(t+1)}={X_{ij}}^t+F_i^t\left({X_{r1}}^t-{X_{r2}}^t\right)$$

(27)

In the equation, r1 and r2 are random integers between 1 and NP (population size of ADS). ${V_{ij}}^{(t+1)}$ represents the mutated vector. $F_i^t$ is the adaptive amplification factor, which is independently adjusted based on the difference between the $F_i^t$ value of each individual and $f_{min}^t$:

$$F_i^t=(f_{\min }^{\mathrm{t}}-f(X_i^t))/(f_{\min }^t-f_{\mathrm{mean}}^{\mathrm{t}})$$

(28)

In the equation, $f(X_i^t)$ represents the fitness of the i-th objective vector. $f_{min}^t$ is the best fitness value in the current generation t. $f_{mean}^{\mathrm{t}}$ is the average fitness value.

To generate a trial vector, random components are selected from the mutation vector $V_i^t$ and the target vector $X_i^t$. The random selection process is as follows:

$$H_{i,j}^{\prime }=\left\{\begin{array}{l}{V}_{i,j}^t,ran{d}_j\le CR\mathrm{or}j=j_{rand}\\ X_{i,j}^t,otherwise\end{array}\right.$$

(29)

In the equation, $ran{d}_j$ represents a random variable uniformly distributed in the range (0, 1). $CR$ is the crossover probability in the range (0, 1), which controls the diversity of the population. $j_{rand}$ is randomly selected from the set {1, 2, ..., D}, ensuring that the trial vector $H_i^t$ has at least one component from the mutation vector $V_i^t$.

After introducing the mutation operation, a greedy strategy is applied for the selection operation. The fitness values of the individual vectors $X(t+1)$ produced by the DE algorithm and the new trial vector $H_i^t$ are compared. The superior one will be preserved in the next generation:

$$X_i^{t+1}=\left\{\begin{array}{l}{U}_i^t,f(H_i^t)\le f(X_i^t)\\ X_i^{t+1},others\end{array}\right.$$

(30)

$$F_i^t=(f_{\min }^{\mathrm{t}}-f(X_i^t))/(f_{\min }^t-f_{\mathrm{mean}}^{\mathrm{t}})$$

(31)

4.3. Encoding and Decoding Modes

To initialize the search space of the intelligent algorithm and determine the target positions for decoding the task allocation scheme, the initial positions of the constrained population coordinates must first be established. Then, using the HDEDA, each individual’s position is treated as a candidate solution, and the optimal solution is found through a population search and position updates. For the multi-UAV cooperative task allocation problem with task timing constraints, cooperation constraints, and task requirement constraints, a real-valued vector encoding method is adopted to establish the mapping relationship between the hybrid dragonfly positions and the task allocation scheme solutions. The dimension of the hybrid dragonfly’s position is related to the number of tasks $N_C$. The integer part [X] of each dimension of the hybrid dragonfly’s position represents the UAV assigned to execute that task. Tasks with the same integer value are assigned to the same UAV for execution. By limiting the upper and lower bounds of the integer part in each dimension, it is ensured that the UAV formations match their corresponding task types. The decimal part {X} of the dragonfly’s position represents the limited sequence of UAVs assigned to the corresponding tasks, with the numerical values indicating the relative order of the UAVs before and after executing that task.

Let us assume that the computed optimal task allocation scheme is shown in

Table 1. Task sequence allocation table.

Target	${\mathit{T}}_1$			${\mathit{T}}_2$			${\mathit{T}}_3$
task	$T_1,S$	$T_1,D$	$T_1,I$	$T_2,S$	$T_2,D$	$T_2,I$	$T_3,S$	$T_3,D$	$T_3,I$
X	2.5	3.1	3.3	1.91	3.6	2.3	1.1	2.4	1.8
[X]	2	3	3	1	3	2	1	2	1
{X}	0.5	0.1	0.3	0.1	0.2	0.3	0.1	0.4	0.8
UAV	${UAV}_2$	${UAV}_3$	${UAV}_3$	${UAV}_1$	${UAV}_3$	${UAV}_2$	${UAV}_1$	${UAV}_2$	${UAV}_1$

. The table consists of three targets and three UAVs collaborating to execute the tasks, totaling nine tasks. Taking ${UAV}_3$ as an example for analysis, the integer part [X] in the table with a value of three corresponds to three tasks: $T_1,D$ for 3.1; $T_1,I$ for 3.3; and $T_2,D$ for 3.6. By comparing the decimal part {X}, it can be concluded that ${UAV}_3$ should first execute $T_1,D$, followed by $T_1,I$ and, finally, $T_2,D$. According to the calculated time for each target, the first appearance is denoted as $S$, the second appearance as $D$, and the third appearance as $I$.

Based on the proposed HDEDA algorithm and encoding–decoding scheme, this paper further addresses the problem and designs a solution strategy for multi-UAV cooperative task allocation to effectively tackle complex task environments. Algorithm 1 shows the specific implementation process of the solution strategy for multi-UAV cooperative task allocation.

Algorithm 1 A solution strategy for multi-UAV cooperative task allocation

Input: the number of UAVs $N_V$, the number of targets $N_T$  Output: Multi-UAV collaborative task allocation plan

1: Initialize the population size of ADS, dimensions, the upper bound $u_b$, the lower bound $l_b$, weight coefficients, maximum iterations, mutation probability, crossover probability, population individual positions $X_i$, step vector 2: Encode the positions of the population individuals 3: For 1 maximum iteration, do 4: For each individual in the population, do 5: Calculate the fitness of all individuals according to Equation (14) 6: Determine and retain the optimal solution 7: Update $S_i$, $A_i$, $C_i$, $F_i$, $E_i$ according to Equations (17)–(21) 8: Update the weights 9: If exist neighboring individuals then 10: Update the ADS positions according to (23) 11: Else, update the ADS positions according to (24) 12: End if 13: Randomly select the dragonfly individual positions and perform mutation, crossover, and selection operations on them 14: Calculate the fitness of all individuals according to Equation (14) 15: If the new optimal solution is greater than the old optimal solution, then 16: Replace the old solution 17: Else, retain the old solution. 18: End if 19: Update the population 20: If the termination conditions are met, then 21: Output the optimal individual position, and the task allocation scheme and the optimal fitness value are obtained by decoding 22: Else, go back to step 5 23: End if 24: End for 25: End for

5. Simulation and Analysis

5.1. Simulation Environment Settings

MATLAB R2022a software was used to simulate a combat scenario involving multiple UAVs performing reconnaissance, decision-making, and engaging with multiple ground targets. The effectiveness of the proposed multi-UAV collaborative task planning algorithm was validated through experiments. The experimental environment and assumptions are as follows:

• Each UAV has a different initial positions and task conditions. The initial positions of the UAVs are pre-determined fixed points, and each UAV has a different initial heading angle, as shown in

  Table 2. UAV parameters.

  UAV	Initial Position (km)	Course Angle	Velocity (m/s)	Voyage Constraint (km)	Ammunition Restraint
  ${UAV}_1$	(3,3)	295°	100	250	3
  ${UAV}_2$	(3,13)	343°	100	250	2
  ${UAV}_3$	(3,23)	164°	100	250	3
  ${UAV}_4$	(3,43)	331°	100	250	3
  ${UAV}_5$	(13,3)	184°	100	250	3
  ${UAV}_6$	(23,3)	110°	100	250	2

  . The flight speed of all UAVs is uniformly set to 100 meters per second, with a maximum flight range of 250 kilometers for each UAV. In addition, each UAV is equipped with advanced reconnaissance equipment and weapon systems, enabling them to carry out reconnaissance, decision-making, and engagement tasks. Regarding ammunition usage, each UAV can perform a certain number of engagement tasks, with specific ammunition limitations detailed in the table.
• The position and angle information of each target is pre-determined, with the coordinates and corresponding angle parameters of ground targets detailed in

  Table 3. Target parameters.

  Target	Position (km)	Target Angle	Target	Position (km)	Target Angle
  $T_1$	(64,92)	107°	$T_7$	(78,87)	217°
  $T_2$	(34,66)	167°	$T_8$	(92,72)	281°
  $T_3$	(50,43)	301°	$T_9$	(25,34)	43°
  $T_4$	(25,56)	44°	$T_{10}$	(67,35)	141°
  $T_5$	(97,54)	45°	$T_{11}$	(70,72)	261°
  $T_6$	(59,58)	76°	$T_{12}$	(45,87)	106°

  . Each ground target is assigned three types of tasks: reconnaissance, decision-making, and engagement. The tasks must be completed in a strict sequence, with reconnaissance performed first, followed by decision-making and, finally, engagement.
• All UAVs take off simultaneously at the start of the task, with the specifics of takeoff and landing not being considered. The task environment remains constant throughout the entire simulation. The ground targets are stationary and have no defensive capabilities. During the task allocation process, the network communication topology remains unchanged due to the high data transmission rate and low latency characteristics of the next-generation Internet of Things.

As shown in Figure 3, the dots represent the initial positions of each UAV and the red stars represent the target positions. The simulation scene is the task execution area of $100 \mathrm{km} \times 100 \mathrm{km}$. Due to the influence of a complex environment, the coefficients of the objective function are, respectively, set as ${\omega }_1=0.7, {\omega }_2=0.15, {\omega }_3=0.15$.

5.2. Simulation Results

In the first simulation experiment, six UAVs are set to perform different tasks on twelve targets within the area. Figure 4 represents the average convergence curve obtained by the solution algorithm provided in this paper after 20 computations.

The optimal solution, which is close to the average task execution cost, is selected as the final collaborative task allocation scheme, and the task allocation results are shown in

Table 4. Collaboration task allocation results.

UAV	Task Allocation Results (t/min)	Total Flight Distance (/km)
${UAV}_1$	($T_6$,$D$,13.39)→($T_{11}$,$S$,17.25)→($T_8$,$S$,22.37) →($T_5$,$I$,26.82)→($T_7$,$D$,33.87)→($T_1$,$I$,37.37)	221.33
${UAV}_2$	($T_9$,$S$,5.2)→($T_3$,$S$,9.84)→($T_3$,$D$,10.63) →($T_3$,$I$,11.42)→($T_6$,$I$,14.49)→($T_{10}$,$S$,20.27)	122.68
${UAV}_3$	($T_4$,$S$,8.3)→($T_4$,$D$,9.09)→($T_4$,$I$,21.89) →($T_{10}$,$D$,30.22)→($T_{10}$,$I$,31.01)→($T_7$,$I$,41.67)	240.60
${UAV}_4$	($T_6$,$S$,10.3)→($T_1$,$S$,17.09)→($T_{12}$,$S$,20.84) →($T_{11}$,$D$,27.61)→($T_{11}$,$I$,28.4)→($T_1$,$D$,33.57)	199.18
${UAV}_5$	($T_4$,I,10.45)→($T_2$,S,13.84)→($T_2$,$D$,14.63) →($T_2$,I,15.42)→($T_{12}$,$D$21.25)→($T_9$,$D$,31.89)→($T_9$,I,32.68)	195.56
${UAV}_6$	($T_5$,S,15.7)→($T_5$,$D$,16.49)→($T_8$,S,20.7) →($T_7$,S,24.48)→($T_{12}$,I,30.69)	184.12

. The completion time of all tasks is 40 min, and the total voyage is 1169 km. Figure 5 records the task allocation time for each UAV, with the left end representing the UAV starting to execute the current task and the right end representing the UAV completing the current task. The time interval between blocks represents the duration of the UAV’s task execution. The experiment shows that the task allocation results obtained under this algorithm meet the task execution constraints, verifying the feasibility of the HDEDA in solving collaborative task allocation problems.

Based on the task assignment results for each UAV, the expected trajectory planning route is derived from the initial starting point, which is constrained by the heading angle between the UAV and the target. The cooperative task trajectory planning simulation graph, based on Dubins curves, is obtained as shown in Figure 6. The three different line types represent the different task types being executed.

5.3. Algorithm Performance Comparison and Analysis

5.3.1. Performance Comparison with Fixed Number of Targets and UAVs

In order to thoroughly evaluate the optimization performance of the HDEDA , this section compares it with the basic PSO algorithm, the DA, and the MODPSO algorithm [39]. As the multi-objective task planning problem in this paper is a typical combinatorial optimization problem, PSO and the DA are two classic algorithms widely applied to combinatorial optimization. MODPSO is an improved version of the traditional PSO algorithm, which handles multi-objective problems better than PSO and aligns more closely with the multi-objective functions in dynamic model. These algorithms have been extensively studied in the context of multi-UAV collaborative task allocation and have strong representativeness. Therefore, the above algorithms were chosen for comparison with the proposed algorithm. In order to verify that the algorithm of this article still has an advantage at different scales, Figure 7 provides a simulation comparison of four algorithms. Among them, $N_V=6$ and $N_T=12$. Twenty independent simulation experiments were conducted for each algorithm, and the convergence curves of the average fitness values were obtained; its value is expressed as the total cost of task execution.

As shown in Figure 7, the optimization objective of the PSO algorithm stabilizes after 40 iterations; however, due to its tendency to get trapped in local optima, it yields the worst optimization results. The DA has the slowest convergence speed, with the optimization objective stabilizing after 125 iterations. Although the MODPSO algorithm has a lower task execution cost than the PSO algorithm and the DA, its convergence speed is slow. In this study, the HDEDA enhances the population diversity after each iteration and the optimization objective stabilizes after 98 iterations. It demonstrates improved convergence speed compared to the DA and the MODPSO algorithms, along with better search efficiency. The experiments indicate that the HDEDA significantly improves the convergence and global search capability, making it the most comprehensive optimization algorithm among the four compared algorithms.

To verify that the HDEDA can maintain excellent performance under different objective scales, experiments will be conducted using simulations with varying numbers of targets and UAVs.

5.3.2. Performance Comparison Under Different Task Scales

First, we verify the effectiveness of the improved algorithm under different target task scales. In Figure 8, the number of UAVs is set to six, and the number of targets is increased from six to sixteen, meaning the number of tasks to be executed increases from eighteen to forty-eight. Simulations are conducted sequentially for each added objective point to verify the average task execution cost under different algorithms for each objective scale. The simulation results are shown in Figure 8.

As shown in Figure 8, the task execution cost under the HDEDA is the lowest as the number of targets increases. When the number of UAVs is fixed, the average task execution cost for each UAV gradually increases with the increasing number of targets. The experiments show that HDEDA can still maintain better performance advantages in small-scale, medium-scale, and large-scale task scenarios, maintain lower resource consumption, and reflect the adaptability and superiority of the algorithm.

5.3.3. Performance Comparison Under Different Numbers of UAVs

In order to verify the effectiveness of the algorithm at different UAV scales, setting the number of targets to twelve, corresponding to the thirty-six tasks to be executed, and increasing the number of UAVs from four to nine, simulations are conducted sequentially for each added UAV to verify the average task execution cost under different algorithms for different multi-UAVs scales. The simulation is repeated 20 times, and the average task execution cost is calculated. Figure 9 describes the average task execution cost function curve of the HDEDA under the UAV scale changes. It can be observed from the simulation that as the number of UAVs increases, the convergence speed of the HDEDA gradually decreases. This is because increasing the number of UAVs when the number of targets is fixed increases the search space, which slows down the algorithm’s solving speed. Additionally, when the number of UAVs is six, the task execution cost is the smallest, while it is at its largest when the number of UAVs is five. For cases where the number of UAVs is four, the task execution cost is intermediate. This is because when the number of targets is fixed, the total range obtained by UAVs does not change. However, the minimum time exponent range coordination exponent required to complete all tasks changes with the increase in the number UAVs. From the graph, it can be concluded that when six UAVs are selected, all three indicators of the objective function are optimal.

Figure 10 describes the task execution cost with varying numbers of UAVs across four algorithms. It can be seen that as the number of UAVs increases, the average task execution cost of the HDEDA decreases, and the difference between the maximum and minimum average task execution costs of the DA and the MODPSO algorithm is not significant. The overall task execution cost of the PSO algorithm and the other three algorithms is relatively high. In combining Figure 9, when considering the number of UAVs that can be deployed for tasks, from the perspective of UAV resources, this section selects a range planning option with a UAV number of six when selecting the optimal scale. This can ensure the reasonable utilization of UAV resources and the optimal consumption of task execution.

5.4. Dynamic Task Adjustments

In real-world environments, UAVs may experience communication failures or be shot down by the enemy, leading to their destruction and rendering them unable to complete the remaining tasks in their task sequence. To prevent a reduction in task execution efficiency, it is necessary to reassign the uncompleted tasks of the lost or destroyed UAVs to other capable UAVs. The aforementioned collaborative task allocation addresses the problem of task pre-allocation. After the failure of ${UAV}_4$, task redistribution is performed based on the dynamic task adjustment strategy. The remaining task set is adjusted accordingly, denoted as set

$\{(T_1,D),(T_1,I),(T_s,I),(T_7,D),(T_7,I),(T_9,I),(T_{10},D),(T_{10},I),(T_{11},D),(T_{11},I),(T_{12},I)\}$. The final dynamic adjustment scheme is shown in

Table 5. Dynamic task adjustment scheme after failure.

UAV	Task Allocation Results After Dynamic Task Adjustment (t/min)	Total Flight Distance (/km)
${UAV}_1$	($T_{10}$,$I$,32.67)→($T_1$,$I$,42.17)	116.5
${UAV}_2$	($T_5$,$I$,31.62)→($T_{11}$,$I$,37)	72.43
${UAV}_3$	($T_{10}$,$D$,31.77)→($T_1$,$D$,39.44)→($T_{12}$,$I$,42.72)	133.17
${UAV}_5$	($T_7$,$D$,31.24)→($T_7$,$I$,32.03)→($T_{11}$,$D$,38.07)	70.42
${UAV}_6$	($T_9$,$D$,33.42)→($T_9$,$I$,34.21)	62.17

 Figure 11 displays the time allocation graph indicating the failure of ${UAV}_4$ at $t=25\min$.

From Table 5, it can be observed that in the later stages of task execution, the majority of tasks are strike tasks, with a few reconnaissance tasks. However, strike tasks are often crucial in task execution, highlighting the necessity of dynamic task allocation. The difference between the total travel distance of the initial task allocation and the total travel distance after dynamic task adjustment is calculated to be 69 km, indicating that energy wastage was effectively avoided during redistribution and validating the effectiveness of the algorithm. Figure 11 shows the time allocation of six UAVs during the collaborative execution of tasks. At $t=25\min$, ${UAV}_4$ experiences a malfunction, and its unfinished tasks are dynamically reassigned to other UAVs to ensure the continued execution of the task. After a certain period of task execution, the remaining tasks are mainly reconnaissance or decision-making, satisfying the temporal constraints of the tasks. Figure 12 shows the trajectory map of ${UAV}_4$ after it completes task $(T_{12},S)$ at $t=25\min$ and subsequently experiences failure. The map illustrates the task redistribution through the dynamic task adjustment model.

6. Summary

This paper studies the problem of multi-UAV cooperative task assignment in a multi-objective environment. Through an in-depth analysis of the characteristics and challenges of the multi-UAV task system, a model of the task cooperative allocation system was established. Under the constraints of task timing, coordination, and requirements, Dubins curves were used for trajectory planning, with the total flight distance, task completion time, and range coordination being used as optimization targets. To comprehensively consider task priority, UAV capabilities, and resource constraints, a collaborative allocation algorithm was proposed. To address the issues of local optima, slow convergence speed, low convergence accuracy, and poor stability in traditional dragonfly algorithms, each UAV was modeled as an artificial dragonfly, incorporating differential evolution algorithms and their crossover, mutation, and selection operations, thus making the UAV swarm more similar to biological dragonflies. This approach enhances the algorithm’s global search capability and improves its convergence speed. The simulation results show that the proposed algorithm can effectively improve task execution efficiency, obtain an efficient task allocation scheme, and optimize the task execution range, demonstrating high practical application value. However, this study primarily focuses on multi-UAV task allocation in static task scenarios, with only partial consideration being given to dynamic task scenarios and without conducting a comprehensive analysis. In future research, the algorithm’s real-time computational capabilities will be further optimized to ensure quick responses and efficient task reallocation in the event of UAV failures or emergencies.