# Mathematical Problems in Engineering Improved CNP-Method-Based Local Real-Time Cooperative Task Allocation of Heterogeneous Multi-UAV in Communication-Constrained Environment

Authors: Tao Xie; Jiansheng Guo; Xiaofeng Zhang; Jiayang Yu; Zhe zhang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

UAVs are widely employed in military and civilian fields because of their inherent advantages. The cooperative task allocation of multi-UAV is more in conformity with the requirements of UAV application scenarios, which has become a hot research topic. However, resource consumption allocation and the application scenarios of communication constraints are often ignored. This paper proposes a distributed multi-UAV task allocation method based on improved CNP to solve the local cooperative task allocation problem of heterogeneous multi-UAV in the communication-constrained environment. The improved CNP-based method can be divided into four stages: task release, bid application, coalition formation, and signing contracts. In the task release stage, we proposed the adaptive maximum number setting method of information transfer times and the information consistency method to solve conflicts in the local communication network. In the process of coalition formation, the resource consumption allocation algorithm based on the Gini coefficient is proposed to keep the resource difference between UAVs in the coalition within a reasonable range. The simulation results demonstrate that improved CNP-method-based cooperative task allocation can handle the local real-time task allocation problem of heterogeneous multi-UAV under communication constraints; it obtains greater task rewards and spends less time on task completion than the resource-welfare-based method, PTCFA. Simultaneously, the resource consumption algorithm makes the UAV swarm maintain a more reasonable resource difference to maximize the number of missions completed.


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## Body

## 1. Introduction

Unmanned aerial vehicle (UAV) has major benefits in terms of survivability, cost-effectiveness radio, and specifications [1, 2]; it plays a wide role in the military and civilian fields, including fire detection, target reconnaissance, fire strikes, information countermeasures, and a variety of other mission situations [3, 4]. Due to the limitations of a single UAV’s autonomy and functional unit loads, such as sensors and weapons, a single UAV cannot meet the increasingly complex application environment and mission requirements [5]. Unlike a single UAV, multiple UAVs can share resources and cooperate to enhance the ability to perform tasks. The coordinated operation of multiple UAVs can better cope with the risks that may arise in the execution of tasks, shorten the task time, and improve the quality of task completion. Therefore, the UAV collaboration problem is an increasingly important area in UAV application research.The collaborative target allocation problem is establishing an association and mapping link between the multi-UAV and the tasks, which is a combinatorial optimization problem with numerous complex constraints [6]. Reasonable task allocation can help UAVs better complete tasks based on satisfying various constraints. The task allocation problem has gradually developed from a simple, small-scale ideal environment to a complex, large-scale real environment. The solution method has developed from a centralized method with low precision and strong global search ability to a distributed method with strong real-time performance. Faced with different environments, the requirements for solving algorithms are also different.This paper aims to solve the collaborative task allocation problem of heterogeneous multi-UAV in a communication-constrained environment. The main contributions of this paper can be summarized as follows:(1)
A method for information consistency and the information transfer strategy in a communication-constrained environment is proposed; it makes sure that the CNP algorithm runs smoothly by setting up a stable communication network between UAVs.(2)
A local real-time task allocation method based on CNP is proposed, which is applied in a distributed architecture. It considers various constraints in the communication-constrained task environment. Simultaneously, the Dubins curve is applied to the path planning of UAVs to meet the constraints of the minimum turning radius.(3)
The allocation method based on the Gini coefficient is designed for the resource consumption of UAVs during task allocation so that UAVs of the coalition can consume resources more rationally and hence execute subsequent tasks better.The remaining sections of this paper are organized as follows. Section2 introduces the current research on the collaborative task allocation problem. Section 3 describes the collaborative task allocation problem of heterogeneous multi-UAV and establishes mathematical models. In Section 4, a local real-time task allocation method based on CNP is proposed to solve the CMTAP problem with various constraints, and the allocation method based on the Gini coefficient is designed to reasonably control resource consumption. Section 5 illustrates the algorithm’s performance through simulation experiments. Section 6 gives corresponding conclusions and briefly takes over future work.


## 2. Related Work

Over the past decades, the task allocation of multi-UAV has become one of the focuses of research in UAVs, which is mainly because the existing tasks put forward higher requirements for UAVs, requiring larger-scale multi-UAV to work together. As scale increases, so does the heterogeneity of drones and missions. This section mainly reviews related research on mathematical models and solutions for multi-UAV task allocation.The task allocation problem is represented using one of many classical optimization problem models or variations after considering the task requirements, constraints, and characteristics of the UAV in a particular situation. The commonly used classic models are multiple traveling salesman problem (MTSP) [7], vehicle routing problem (VRP) [8], and other models. Zhu et al. [9] considered the limited resources of UAVs and modeled the task assignment problem as a capacity-constrained vehicle routing model (CVRP). Recently, the target allocation model study has focused mostly on the collaborative target allocation field.For modeling task allocation, many factors need to be considered, including UAV, task, and constraint, which contain resources, minimum/maximum speed, turn radius constraint, and so on. Moreover, the task model depends on the corresponding task scenario. Zhang et al. [10] proposed a UAV cooperative attack task allocation model and strategy for attacking enemy air defense systems in a specific area. The method meets the goal of real-time requirements in a dynamic environment. Wu et al. [11] modeled the task allocation problem of multiple heterogeneous fixed-wing UAVs on multiple targets performing confirmation, attack, and damage assessment as a CMTAP problem and used an improved genetic algorithm to solve the problem.Numerous centralized and distributed methods have been proposed [12, 13] to solve the multi-UAV task allocation problem. Centralized solutions, such as ant colony optimization [14], genetic algorithm [15, 16], and particle swarm optimization [17], rely on UAVs to communicate continually with the central station that creates a plan for the whole UAV swarm. Amorim et al. [18] proposed an improved Swarm-GAP method that can be applied to task assignment in dynamic military operations environments where UAVs are randomly destroyed. However, in the reallocation process of this method, more communication resources are required, and it is not suitable for a communication-constrained environment. Acevedo et al. [19] proposed an improved genetic algorithm, which considers more constraints for real task scenarios, including kinematic constraints, resource constraints (weapons and fuel), and time constraints. However, as a centralized algorithm, communication constraint is not considered. In the communication-constrained environment, centralized solutions respond slowly to dynamic changes [4, 19]. Then the distributed solution, such as contract net protocol (CNP) [20] and the consensus algorithm [21], is offered to resolve the issue. In the distributed solution, each UAV can directly process task information as a relatively independent decision-processing unit. It has strong fault tolerance, flexibility, and reliability. Additionally, each UAV should transmit bid information to the auctioneer, and this requires a stable connected topology in the CNP algorithm [22]. Xiang et al. [23] regarded the missile as an agent and proposed an improved CNP algorithm to ensure that the missile could be assigned to a better target by updating the contract. The consensus algorithm necessitates massive information transmission to achieve consistent convergence [21]. Duan et al. [24] proposed a new hybrid auction algorithm, which greatly improves the task allocation effect through hierarchical decision-making.However, numerous studies predicate that UAVs are homogeneous, targets’ information is known in advance, and communication is unrestricted. In the complicated military environment, these assumptions are often not established. For example, when UAVs perform missions, they only know the rough information of the mission before taking off and need to perform real-time task allocation reasonably, which needs to meet limits such as resources, simultaneous attacks, and so on. In a war scenario, the tasks faced by the UAV swarm are unpredictable, including time, position, and resource requirements. It requires resource consumption allocation to be reasonable enough. Kim et al. [25] proposed a coalition formation method that effectively uses resource welfare as a consumption strategy to use attack resources and enables the UAV swarm to execute follow-up missions more successfully.


## 3. Mission Description and Model

In this section, the mission scenario, UAV, and target are modeled, and the more scientific objective function is proposed.


### 3.1. Mission Scenario

According to the set path, heterogeneous UAVs conduct reconnaissance in the mission area. When they reach the mission area’s boundary, they take the shortest path back to the mission area. Furthermore, they enter the strike mission phase when they find the target. The relevant information about the target is unknown before the UAVs take off, but when the reconnaissance UAV finds it, specific target information is collected by the UAV that finds it. Based on the actual requirements of cooperative operations, the UAV that finds the target creates an attack coalition with the surrounding UAVs to carry out strike missions together in the communication-constrained environment. To simplify the end-strike model of the attack mission, the condition for the completion of the attack mission is that the UAV coalition carries the resources required to destroy the target and reach the target within a certain range.In this paper, various constraints are considered simultaneously in the study of cooperative heterogeneous multi-UAV task allocation, primarily the constraints of the UAV’s performance, the constraints of attack resources, the time constraints of simultaneous attacks, and the communication constraints between UAVs. The paper focuses on the local real-time heterogeneous multi-UAV task allocation method with limited communication.


### 3.2. UAV and Target Model

In this paper, the take-off and landing of the UAVs are not taken into account, and altitude layering is used to achieve collision avoidance between UAVs, with the height being constant during the flight.In the two-dimensional plane, the flight motion model of the UAV can be expressed as follows:(1)x˙=vcosψ,y˙=vsinψ,ψ˙=ωφ,where x,y is the current position coordinates of the UAV, v is the velocity of the UAV, ψ is the yaw angle of the UAV, and ωφ is the velocity of the yaw angle. This paper ignores the UAV’s aerodynamics and attitude, and striking missions do not necessitate a certain flight direction and angle.There are a total ofM static targets on the set mission area. When the UAV finds the target Tjj=1,2,…,M, it can directly obtain the resource requirements, including types and respective numbers of ammunition required to destroy the target. Resource requirements can be represented as a set of vectors:(2)RjT=Rj,1T,Rj,2T,…,Rj,mT,where m is the types of ammunition required for the target Tj to be destroyed and Rj,qTq=1,…,m is the number of ammunition required for the Tj to be destroyed. For example, RjT=2,3 represents that destroying the target requires two I−type resources and three II−type resources.There areN UAVs in the mission area before the reconnaissance mission begins, and the attack resources carried are not time-sensitive and do not alter as time passes. The heterogeneity of UAVs is set as the difference in attack resources. And attack resources of Uii=1,2,…,N can be represented as follows:(3)RiU=Ri,1U,Ri,2U,…,Ri,nU,where Ri,pUp=1,…,n is the number of type p resource of Ui and n is the number of types for the entire UAV swarm.In the communication-constrained environment, each UAV can only communicate with UAVs within its communication range. To avoid two UAVs being unable to communicate with each other after discovering the same target, two coalitions are established to attack the target, and the communication range and reconnaissance radius are configured asRcU>2RsU, where RcU is the communication range of UAV and RsU is the reconnaissance radius of UAV.


### 3.3. Objective Function and Constraints

#### 3.3.1. Cost Function of the Assault Coalition

(4)LCj=∑i=1ncτ⋅di+UiValue1−TThreat,where nc is the number of members for the attack coalition, τ is the fuel consumption coefficient, di is the flight distance of Ui, UiValue is the self-value of Ui, and TThreat∈0,1 is the threat level of the target. Cj is the attack coalition for Tj.


#### 3.3.2. Task Completion Revenue Function

(5)fjT=VTj·ζt,ζt=e−θt,,where VTj is the target value when it’s discovered, ζt is the time decay function, and t is the time interval between the discovery of the target and its destruction. And target time sensitivity is represented by θ. The higher the value, the quicker the goal value declines.


#### 3.3.3. Total Revenue Function

(6)J=w1⋅fjT−w2⋅LCi,where wi∈0,1 is weight coefficient; ∑i=12ωi=1. It is simple to change the orientation of the objective function by modifying the value. For example, raising w1 can hasten the completion of the mission, and raising w2 can form coalitions with fewer UAV losses and shorter total flight distance.The main constraints examined in the task allocation problem of heterogeneous UAVs performing real-time strike missions in a communication-constrained environment are as follows:(1)
Resource constraintsThe target destruction necessitates a certain amount of resources; thus, the combined resources of the attack coalition must satisfy the requirement:(7)∑i=1ncRi,pU≥Rj,pTp=1,…,n,and the quantity ofRi,pU is limited.(2)
UAV self-performance constraintsThe fuel resources must be sufficient to ensure that the UAV can complete the range required; otherwise, it will be unable to join the attack coalition. It is set that the fuel is proportional to the flight distance. The flying distance constraint can be converted from a fuel constraint. The UAV’s flying distance must match the following requirement:(8)pjT−piU≤di,remainderU,wherepjT and piU are the positions of the Tj and the Ui, respectively, and di,remainderU is the remaining flight distance of Ui. At the same time, the turning radius of a UAV is limited.(3)
Time constraintsTo ensure that the UAV coalition cooperative combat, all of the coalition’s UAVs must reach the target point simultaneously. When a UAV has a short flight distance and a short flight time, it might hover or slow down its speed to increase the time it takes to reach the target. It can be expressed as follows:(9)tiU=dijVi,t1U=tiU,i=1,2,…,n,wheretiU is the flight time of Ui. dij is the distance from Ui to Tj. Vi is the velocity of Ui, and Vi≥Vmin.(4)
Communication constraintsThe geometry of the air-to-air radio path is shown in Figure1; its communication range is limited by terrain height; however, when the radio path crosses the horizon between UAVs, the communication range between UAVs is unaffected by terrain height. In this paper, the UAV communication is unaffected by terrain height.Figure 1
UAV aerial radio communication link.In a communication-constrained environment, the two primary constraints are the communication range constraint and the time delay. The communication range constraint mainly means UAVs that are far away cannot communicate directly; out-of-range information transfer must be accomplished through a communication relay station. Communication time delay mainly refers to the time required to transmit information between UAVs.


## 3.1. Mission Scenario

According to the set path, heterogeneous UAVs conduct reconnaissance in the mission area. When they reach the mission area’s boundary, they take the shortest path back to the mission area. Furthermore, they enter the strike mission phase when they find the target. The relevant information about the target is unknown before the UAVs take off, but when the reconnaissance UAV finds it, specific target information is collected by the UAV that finds it. Based on the actual requirements of cooperative operations, the UAV that finds the target creates an attack coalition with the surrounding UAVs to carry out strike missions together in the communication-constrained environment. To simplify the end-strike model of the attack mission, the condition for the completion of the attack mission is that the UAV coalition carries the resources required to destroy the target and reach the target within a certain range.In this paper, various constraints are considered simultaneously in the study of cooperative heterogeneous multi-UAV task allocation, primarily the constraints of the UAV’s performance, the constraints of attack resources, the time constraints of simultaneous attacks, and the communication constraints between UAVs. The paper focuses on the local real-time heterogeneous multi-UAV task allocation method with limited communication.


## 3.2. UAV and Target Model

In this paper, the take-off and landing of the UAVs are not taken into account, and altitude layering is used to achieve collision avoidance between UAVs, with the height being constant during the flight.In the two-dimensional plane, the flight motion model of the UAV can be expressed as follows:(1)x˙=vcosψ,y˙=vsinψ,ψ˙=ωφ,where x,y is the current position coordinates of the UAV, v is the velocity of the UAV, ψ is the yaw angle of the UAV, and ωφ is the velocity of the yaw angle. This paper ignores the UAV’s aerodynamics and attitude, and striking missions do not necessitate a certain flight direction and angle.There are a total ofM static targets on the set mission area. When the UAV finds the target Tjj=1,2,…,M, it can directly obtain the resource requirements, including types and respective numbers of ammunition required to destroy the target. Resource requirements can be represented as a set of vectors:(2)RjT=Rj,1T,Rj,2T,…,Rj,mT,where m is the types of ammunition required for the target Tj to be destroyed and Rj,qTq=1,…,m is the number of ammunition required for the Tj to be destroyed. For example, RjT=2,3 represents that destroying the target requires two I−type resources and three II−type resources.There areN UAVs in the mission area before the reconnaissance mission begins, and the attack resources carried are not time-sensitive and do not alter as time passes. The heterogeneity of UAVs is set as the difference in attack resources. And attack resources of Uii=1,2,…,N can be represented as follows:(3)RiU=Ri,1U,Ri,2U,…,Ri,nU,where Ri,pUp=1,…,n is the number of type p resource of Ui and n is the number of types for the entire UAV swarm.In the communication-constrained environment, each UAV can only communicate with UAVs within its communication range. To avoid two UAVs being unable to communicate with each other after discovering the same target, two coalitions are established to attack the target, and the communication range and reconnaissance radius are configured asRcU>2RsU, where RcU is the communication range of UAV and RsU is the reconnaissance radius of UAV.


## 3.3. Objective Function and Constraints

### 3.3.1. Cost Function of the Assault Coalition

(4)LCj=∑i=1ncτ⋅di+UiValue1−TThreat,where nc is the number of members for the attack coalition, τ is the fuel consumption coefficient, di is the flight distance of Ui, UiValue is the self-value of Ui, and TThreat∈0,1 is the threat level of the target. Cj is the attack coalition for Tj.


### 3.3.2. Task Completion Revenue Function

(5)fjT=VTj·ζt,ζt=e−θt,,where VTj is the target value when it’s discovered, ζt is the time decay function, and t is the time interval between the discovery of the target and its destruction. And target time sensitivity is represented by θ. The higher the value, the quicker the goal value declines.


### 3.3.3. Total Revenue Function

(6)J=w1⋅fjT−w2⋅LCi,where wi∈0,1 is weight coefficient; ∑i=12ωi=1. It is simple to change the orientation of the objective function by modifying the value. For example, raising w1 can hasten the completion of the mission, and raising w2 can form coalitions with fewer UAV losses and shorter total flight distance.The main constraints examined in the task allocation problem of heterogeneous UAVs performing real-time strike missions in a communication-constrained environment are as follows:(1)
Resource constraintsThe target destruction necessitates a certain amount of resources; thus, the combined resources of the attack coalition must satisfy the requirement:(7)∑i=1ncRi,pU≥Rj,pTp=1,…,n,and the quantity ofRi,pU is limited.(2)
UAV self-performance constraintsThe fuel resources must be sufficient to ensure that the UAV can complete the range required; otherwise, it will be unable to join the attack coalition. It is set that the fuel is proportional to the flight distance. The flying distance constraint can be converted from a fuel constraint. The UAV’s flying distance must match the following requirement:(8)pjT−piU≤di,remainderU,wherepjT and piU are the positions of the Tj and the Ui, respectively, and di,remainderU is the remaining flight distance of Ui. At the same time, the turning radius of a UAV is limited.(3)
Time constraintsTo ensure that the UAV coalition cooperative combat, all of the coalition’s UAVs must reach the target point simultaneously. When a UAV has a short flight distance and a short flight time, it might hover or slow down its speed to increase the time it takes to reach the target. It can be expressed as follows:(9)tiU=dijVi,t1U=tiU,i=1,2,…,n,wheretiU is the flight time of Ui. dij is the distance from Ui to Tj. Vi is the velocity of Ui, and Vi≥Vmin.(4)
Communication constraintsThe geometry of the air-to-air radio path is shown in Figure1; its communication range is limited by terrain height; however, when the radio path crosses the horizon between UAVs, the communication range between UAVs is unaffected by terrain height. In this paper, the UAV communication is unaffected by terrain height.Figure 1
UAV aerial radio communication link.In a communication-constrained environment, the two primary constraints are the communication range constraint and the time delay. The communication range constraint mainly means UAVs that are far away cannot communicate directly; out-of-range information transfer must be accomplished through a communication relay station. Communication time delay mainly refers to the time required to transmit information between UAVs.


## 3.3.1. Cost Function of the Assault Coalition

(4)LCj=∑i=1ncτ⋅di+UiValue1−TThreat,where nc is the number of members for the attack coalition, τ is the fuel consumption coefficient, di is the flight distance of Ui, UiValue is the self-value of Ui, and TThreat∈0,1 is the threat level of the target. Cj is the attack coalition for Tj.


## 3.3.2. Task Completion Revenue Function

(5)fjT=VTj·ζt,ζt=e−θt,,where VTj is the target value when it’s discovered, ζt is the time decay function, and t is the time interval between the discovery of the target and its destruction. And target time sensitivity is represented by θ. The higher the value, the quicker the goal value declines.


## 3.3.3. Total Revenue Function

(6)J=w1⋅fjT−w2⋅LCi,where wi∈0,1 is weight coefficient; ∑i=12ωi=1. It is simple to change the orientation of the objective function by modifying the value. For example, raising w1 can hasten the completion of the mission, and raising w2 can form coalitions with fewer UAV losses and shorter total flight distance.The main constraints examined in the task allocation problem of heterogeneous UAVs performing real-time strike missions in a communication-constrained environment are as follows:(1)
Resource constraintsThe target destruction necessitates a certain amount of resources; thus, the combined resources of the attack coalition must satisfy the requirement:(7)∑i=1ncRi,pU≥Rj,pTp=1,…,n,and the quantity ofRi,pU is limited.(2)
UAV self-performance constraintsThe fuel resources must be sufficient to ensure that the UAV can complete the range required; otherwise, it will be unable to join the attack coalition. It is set that the fuel is proportional to the flight distance. The flying distance constraint can be converted from a fuel constraint. The UAV’s flying distance must match the following requirement:(8)pjT−piU≤di,remainderU,wherepjT and piU are the positions of the Tj and the Ui, respectively, and di,remainderU is the remaining flight distance of Ui. At the same time, the turning radius of a UAV is limited.(3)
Time constraintsTo ensure that the UAV coalition cooperative combat, all of the coalition’s UAVs must reach the target point simultaneously. When a UAV has a short flight distance and a short flight time, it might hover or slow down its speed to increase the time it takes to reach the target. It can be expressed as follows:(9)tiU=dijVi,t1U=tiU,i=1,2,…,n,wheretiU is the flight time of Ui. dij is the distance from Ui to Tj. Vi is the velocity of Ui, and Vi≥Vmin.(4)
Communication constraintsThe geometry of the air-to-air radio path is shown in Figure1; its communication range is limited by terrain height; however, when the radio path crosses the horizon between UAVs, the communication range between UAVs is unaffected by terrain height. In this paper, the UAV communication is unaffected by terrain height.Figure 1
UAV aerial radio communication link.In a communication-constrained environment, the two primary constraints are the communication range constraint and the time delay. The communication range constraint mainly means UAVs that are far away cannot communicate directly; out-of-range information transfer must be accomplished through a communication relay station. Communication time delay mainly refers to the time required to transmit information between UAVs.


## 4. The Improved CNP-Based Collaborative Task Allocation Method for Heterogeneous Multi-UAV

In this section, the improved contract net protocol (CNP) based collaborative task allocation method for heterogeneous multi-UAV is proposed for local real-time tasks of UAV swarms in a communication-constrained environment. The process of the target processing by the UAV is introduced in detail. This method can meet target resource requirements, time coordination, optimal range, UAV performance, communication constraints, and realize local real-time task allocation.


### 4.1. Local Real-Time Task Allocation Method with Limited Communication

Smith [26] firstly proposed the contract net protocol as a framework for solving distributed negotiation problems in 1980. In the market mechanism, the simulated bidding negotiation process is employed to find the optimal solution for the objective function. The CNP method has been shown that has superior scalability, robustness, and negotiation efficiency to other methods; it is suitable for local real-time task allocation.In the local real-time task allocation of heterogeneous multi-UAV, the steps of the local real-time task allocation method based on CNP are divided into task release, bid application, coalition formation, and sign contracts. The process of the contract network is shown in Figure2.Figure 2
The flow diagram of CNP.In the step of task release, a new communication method is designed according to the characteristics of communication constraints to ensure that the UAV information can reach an agreement within the scope of the local communication network. Moreover, a new resource consumption allocation method is designed in the bidding application information processing step, combining the Gini coefficient in economics, to ensure that the UAV swarms reserve reasonable attack resources to deal with unanticipated missions. The following are the specific details of the four steps.


#### 4.1.1. Task Release

AfterUi finds the target Tj, it judges whether RiU>RjT is established. If the condition establishes, Ui executes the task alone; if not, Ui becomes the leader of the coalition and sends task bidding information to all UAVs in its local communication network for seeking coalition formation.During the flight of the UAV swarm, the communication is formed into an ad hoc (point-to-point) network [27], and the location of UAVs is constantly changing. Depending on whether there is a communication node, the communication mode between UAVs can be divided into direct communication and indirect communication [28]. UAV swarms often use flooding to transmit information to other UAVs within the communication range, ensuring that all UAVs can receive information. However, there are often problems with implosion and broadcast storms [22]. Peng W et al. [29] proposed that limiting the number of broadcasts could help solve the issues mentioned above. The number of broadcasts can be limited in the task release and bid application stages. In the task release stage, the number of nodes between the single-link communication of the UAV can be limited, which is named as the maximum number of information transmission Hmax; in the bid application stage, the bidders’ conditions are strict to avoid environmental changes leading to contract breach, which causes waste of communication resources.To reduce the communication load between UAVs, a self-adaptive maximum number of information transmissions method based on the target level and resource requirement (AT-MIT) is proposed. AT-MIT can ensure that when attacking important targets, the coalition can be formed as successful as possible; when attacking secondary targets, it reasonably reserves communication resources and speeds up the formation of the coalition. It can be expressed as follows:(10)Hmax=⌈∂Dj+A⋅RjT⌉,where ∂ is the weight coefficient, Dj is the level of Tj, A is the weight vector used to transform the target’s resource requirement into the difficulty level of destruction, and ⌈⌉ is the roundup function.Before the coalition leaderUi performs the information transfer between UAVs, the remaining information transfer time Hji is first judged. Initial time, Hji=Hmax, and with each transmission, Hji is reduced by one. When Hji=0, information is no longer transmitted.For example, when theU0 finds the T1, it will get all information about T1, including the level and the resource requirement of T1. By calculating Hmax=2, then Hj0=Hmax=2. The local communication network of U0 is shown in Figure 3. The dotted circle around the coalition leader U0 indicates its reconnaissance range U0 and U1 can communicate directly, bidding information is transferred from U0 to U1, and Hji minus 1. Then U1 serves as a communication node and sends bidding information to U=U3,U4 within its communication range except U0. Although U5 is within the communication range of U3, Hj1=0; then the bidding information is not transmitted from U3 to U5.Figure 3
Local communication network of UAV swarm with limited communication.Before the coalition is formed successfully, the UAV swarm has been conducting reconnaissance according to the set reconnaissance route. Furthermore, its communication topology is in dynamic transformation, so it is critical to screen out coalition members to construct a stable communication topology. This paper selects the coalition members by judging the expected arrival position (EAP).AfterUi finds Tj, Ui transmits bid information to all UAVs in the local communication network. In order to screen out potential coalition members that constitute a stable communication topology, UAVs receiving bid information send the EAP at the moment of the successful coalition formation as part of the bid application to the coalition leader Ui. The moment of coalition formation successfully is expressed as follows:(11)tcj=tn+tf,where tcj, tn, and tf represent the moment of coalition formation, moment of Ui finding Tj, and time of coalition formation process, respectively. And coalition formation process includes coalition leader sending bid information, potential coalition members sending bid applications, bid application information processing, and signing contracts, which can be expressed as follows:(12)tf=3HmaxΔtd+tc+tb,where Δtd is a single information transfer time between UAVs, tc is the time to process bid information and plan the coalition’s offense, and tb is the time to calculate EAP.AfterUi finds Tj, Ui gets information about the target. The information can be expressed as Qj=pjT,RjT,lj,TThreat, where pjT, RjT, lj, andTThreat is the position, resource requirement, level, and threat of Tj, respectively. Coalition leader Ui sends bid information to UAVs within communication range. The information can be expressed as Oi=Iiu,Qj,tn,tf,fji,Hji, where Iiu is serial number and EAP of UAV. fji is the estimated revenue of the Tj. The bid information is transmitted to each UAV according to Algorithm 1 in the local communication network, and UAVs are consistent with the information.Algorithm 1: Task bidding.
(1)
Hji←Hmax(2)
ifHji>0then(3)
Hji←Hji−1(4)
Ui send Oi to its directly connected UAV(5)
end if(6)
fork=1: number of bid requests received do(7)
predict EAP ofUi in the moment of coalition formation(8)
if ETA is in the communication range of Uk(9)
and owe the resources needed ofTjthen(10)
iffji<fkithen(11)
Pi←Pk(12)
end if(13)
end if(14)
end forAs shown in Algorithm 1, UAVs in the local communication network transmit the task bidding information to the UAV, which can be directly connected (lines 1–5); then the UAV that receives the information judges whether it meets the communication conditions and resource requirements firstly and selects the optimal task bidding information according to the mission revenue (lines 6–14). The UAVs in the local communication network are consistent with the bid information through the information transmission.


#### 4.1.2. Bid Application

After step 1, each UAV in the local communication network ofUi retains the same bid information. The UAV swarm is in flight, and there is a communication time delay between UAVs. If each UAV calculates the estimated time of arrival (ETA) with the target according to the moment when it receives the bid, in the process of information exchange, the ETA will change and cause the performance of task allocation to be degraded. Therefore, each UAV needs to agree on a unified time. Because the bid information includes the moment of the target was discovered and the time of coalition forms, the UAV needs to calculate its EAP according to the moment of coalition formation. Then UAV uses EAP to calculate its ETA to the target and send the bid application to the coalition leader. The bid application of Uk can be expressed as follows:(13)Bk=Uk,Tj,RkU,PkU,tk,Hjk,where Uk is the UAV for bidding, RkU is the attack resource carried by Uk, PkU and tk are the EAP in the moment of coalition formation and ETA to the target, and Hjk=Hmax.


#### 4.1.3. Coalition Formation

After step 2, the coalition leaderUi receives all bid applications and needs to deal with the application information. Firstly, the leader should screen out coalition members that can stably exist in the local communication network. Then under the expectation of the minimum number of coalition members, the leader screens out optimal coalition combination CjT according to the objective function. After the coalition members are determined, members share the target’s attack resource requirements—the coalition leader Ui of CjT plans an attack scheme and resource consumption allocation scheme.


#### 4.1.4. Signing Contracts

The coalition leader transmits the information of the winning bid to the UAVs in the local communication network. Then the UAV that wins the bid adds the task of hitting the targetTj to its task sequence, and the members of CjT carry out the task according to the plan formulated by the leader. The members of the coalition who received the information earlier continue to perform the original task until tcj. In other words, members act simultaneously when the farthest UAV receives the winning bid information.


### 4.2. Resource Consumption Allocation Method Based on Gini Coefficient

After the coalition leader selects the combination of membersCjT, the UAVs in the coalition share the resources requirement. In the case of resource constraints, the greedy algorithm is often used to allocate the required attack resources. This algorithm leads to unscientific resource consumption in the UAV swarm; some UAVs are rendered incapacitated prematurely, resulting in lower success rates for subsequent coalition formations. It leads to a decline in the robustness of the UAV swarm in mission execution, the number of missions completed, and the dynamics of responding to unexpected missions. This paper proposes a resource consumption allocation method based on the Gini coefficient to solve the unreasonable allocation of resource consumption problem.


#### 4.2.1. Gini Coefficient

In 1912, the famous Italian statistician Corrado Gini proposed a coefficient to measure the degree of inequality in the distribution of wealth. The characteristic of the Gini coefficient lies in its integrity. It is often used to evaluate the degree of equality of wealth distribution in a country. When there are fewer residents in the country, the conclusion of its judgment is more reliable. The UAV swarm can be regarded as a temporary country, and the attack resources carried can be equivalent to wealth income. The Gini coefficient can measure the equilibrium degree of UAV attack resource allocation.The geometric meaning of the Gini coefficient is based on the Lorentz curve. When the Gini coefficient is used to measure the balance of the distribution of UAV attack resources, the definition of the Lorentz curve is to rank the UAV attack resources from low to high, and the cumulative percentage of the number of drones and the cumulative percentage of attack resources are calculated. The corresponding relationship is drawn on the graph; the Lorentz curve is obtained as shown in Figure4.Figure 4
Lorentz curve of UAVs resource.In Figure4, the calculation of the Gini coefficient can be considered as the ratio of the area formed by the connection of the absolute equilibrium curve and the Lorentz curve (A area in Figure 3) to the area formed by the absolute equilibrium curve and the horizontal axis (A+B area in Figure 3), which can be expressed as G=A/A+B, but the Lorentz curve is irregular; the area of A and B cannot be calculated directly. In this paper, the method of reference [30] is used to calculate G; the area of B is approximately divided into the area of several trapezoids [30], which can be shown as follows:(14)G=1−1n2∑i=1n−1Wi+1,where Wi is the percentage of the total resources from the UAV with the least resources to the i−th UAV.


### 4.3. Resource Consumption Allocation Method Based on Gini Coefficient

After the coalitionCjT to attack the target Tj is formed, the sum of various resources in the coalition satisfies task resource requirements, which can be expressed as Rj,qC≥Rj,qTq=1,…,m. For the q-type attack resources in the CjT, firstly, the coalition leader screen out the set of UAVs that contain q-type resources. Then the leader traverses all resource allocation combinations that meet the target resource requirements and calculates the Gini coefficient of the remaining resources for each combination separately. The combination of the optimal Gini coefficient is used as the allocation scheme of the q-type resource. The leader calculates the allocation scheme of other types of resources in turn and finally summarizes into the resource consumption allocation plan. The detail is described as Algorithm 2.Algorithm 2: Resource consumption allocation method based on Gini coefficient.
(1)
initialize(2)
for various types of resources for the Tjdo(3)
for all Uido(4)
add allRj,kU to array k(5)
from arrayk to traverse combination Vnk(6)
for all Vnkdo(7)
calculate remaining resources(8)
calculate the Gini coefficient(9)
if the Gini coefficient of Vnk is closest to the G value, then(10)
saveVnk to buffer array(11)
end if(12)
end for(13)
end for(14)
V=V1,V2,V3,…,Vk(15)
end for(16)
returnV


#### 4.3.1. Optimal Gini Coefficient Value

For a series of tasks on the battlefield, the resource consumption allocation method based on the Gini coefficient can effectively control the difference in resources among UAVs. Moreover, it improves the UAV swarm’s robustness, the number of tasks to be completed, and the dynamics of responding to sudden tasks improved. But the performance improvement is based on selecting the appropriate Gini coefficient (G) value. Therefore, the G value needs to set an appropriate evaluation function and corresponding experiments to select according to the characteristics of the mission scene.The selection of theG value is affected by many factors, such as the total number of tasks, the size of the UAV swarm, the location of a single UAV, and the number of resources initially carried by the UAV. In the communication-constrained environment, UAVs in the center of the UAV swarm are requested by more coalition and undertake more tasks. Because of its mission-critical status, it should carry more attack resources than UAVs at the edge of the UAV swarm. Therefore, the selection of the optimal G value should mainly be affected by the mission status of the UAV.


## 4.1. Local Real-Time Task Allocation Method with Limited Communication

Smith [26] firstly proposed the contract net protocol as a framework for solving distributed negotiation problems in 1980. In the market mechanism, the simulated bidding negotiation process is employed to find the optimal solution for the objective function. The CNP method has been shown that has superior scalability, robustness, and negotiation efficiency to other methods; it is suitable for local real-time task allocation.In the local real-time task allocation of heterogeneous multi-UAV, the steps of the local real-time task allocation method based on CNP are divided into task release, bid application, coalition formation, and sign contracts. The process of the contract network is shown in Figure2.Figure 2
The flow diagram of CNP.In the step of task release, a new communication method is designed according to the characteristics of communication constraints to ensure that the UAV information can reach an agreement within the scope of the local communication network. Moreover, a new resource consumption allocation method is designed in the bidding application information processing step, combining the Gini coefficient in economics, to ensure that the UAV swarms reserve reasonable attack resources to deal with unanticipated missions. The following are the specific details of the four steps.


### 4.1.1. Task Release

AfterUi finds the target Tj, it judges whether RiU>RjT is established. If the condition establishes, Ui executes the task alone; if not, Ui becomes the leader of the coalition and sends task bidding information to all UAVs in its local communication network for seeking coalition formation.During the flight of the UAV swarm, the communication is formed into an ad hoc (point-to-point) network [27], and the location of UAVs is constantly changing. Depending on whether there is a communication node, the communication mode between UAVs can be divided into direct communication and indirect communication [28]. UAV swarms often use flooding to transmit information to other UAVs within the communication range, ensuring that all UAVs can receive information. However, there are often problems with implosion and broadcast storms [22]. Peng W et al. [29] proposed that limiting the number of broadcasts could help solve the issues mentioned above. The number of broadcasts can be limited in the task release and bid application stages. In the task release stage, the number of nodes between the single-link communication of the UAV can be limited, which is named as the maximum number of information transmission Hmax; in the bid application stage, the bidders’ conditions are strict to avoid environmental changes leading to contract breach, which causes waste of communication resources.To reduce the communication load between UAVs, a self-adaptive maximum number of information transmissions method based on the target level and resource requirement (AT-MIT) is proposed. AT-MIT can ensure that when attacking important targets, the coalition can be formed as successful as possible; when attacking secondary targets, it reasonably reserves communication resources and speeds up the formation of the coalition. It can be expressed as follows:(10)Hmax=⌈∂Dj+A⋅RjT⌉,where ∂ is the weight coefficient, Dj is the level of Tj, A is the weight vector used to transform the target’s resource requirement into the difficulty level of destruction, and ⌈⌉ is the roundup function.Before the coalition leaderUi performs the information transfer between UAVs, the remaining information transfer time Hji is first judged. Initial time, Hji=Hmax, and with each transmission, Hji is reduced by one. When Hji=0, information is no longer transmitted.For example, when theU0 finds the T1, it will get all information about T1, including the level and the resource requirement of T1. By calculating Hmax=2, then Hj0=Hmax=2. The local communication network of U0 is shown in Figure 3. The dotted circle around the coalition leader U0 indicates its reconnaissance range U0 and U1 can communicate directly, bidding information is transferred from U0 to U1, and Hji minus 1. Then U1 serves as a communication node and sends bidding information to U=U3,U4 within its communication range except U0. Although U5 is within the communication range of U3, Hj1=0; then the bidding information is not transmitted from U3 to U5.Figure 3
Local communication network of UAV swarm with limited communication.Before the coalition is formed successfully, the UAV swarm has been conducting reconnaissance according to the set reconnaissance route. Furthermore, its communication topology is in dynamic transformation, so it is critical to screen out coalition members to construct a stable communication topology. This paper selects the coalition members by judging the expected arrival position (EAP).AfterUi finds Tj, Ui transmits bid information to all UAVs in the local communication network. In order to screen out potential coalition members that constitute a stable communication topology, UAVs receiving bid information send the EAP at the moment of the successful coalition formation as part of the bid application to the coalition leader Ui. The moment of coalition formation successfully is expressed as follows:(11)tcj=tn+tf,where tcj, tn, and tf represent the moment of coalition formation, moment of Ui finding Tj, and time of coalition formation process, respectively. And coalition formation process includes coalition leader sending bid information, potential coalition members sending bid applications, bid application information processing, and signing contracts, which can be expressed as follows:(12)tf=3HmaxΔtd+tc+tb,where Δtd is a single information transfer time between UAVs, tc is the time to process bid information and plan the coalition’s offense, and tb is the time to calculate EAP.AfterUi finds Tj, Ui gets information about the target. The information can be expressed as Qj=pjT,RjT,lj,TThreat, where pjT, RjT, lj, andTThreat is the position, resource requirement, level, and threat of Tj, respectively. Coalition leader Ui sends bid information to UAVs within communication range. The information can be expressed as Oi=Iiu,Qj,tn,tf,fji,Hji, where Iiu is serial number and EAP of UAV. fji is the estimated revenue of the Tj. The bid information is transmitted to each UAV according to Algorithm 1 in the local communication network, and UAVs are consistent with the information.Algorithm 1: Task bidding.
(1)
Hji←Hmax(2)
ifHji>0then(3)
Hji←Hji−1(4)
Ui send Oi to its directly connected UAV(5)
end if(6)
fork=1: number of bid requests received do(7)
predict EAP ofUi in the moment of coalition formation(8)
if ETA is in the communication range of Uk(9)
and owe the resources needed ofTjthen(10)
iffji<fkithen(11)
Pi←Pk(12)
end if(13)
end if(14)
end forAs shown in Algorithm 1, UAVs in the local communication network transmit the task bidding information to the UAV, which can be directly connected (lines 1–5); then the UAV that receives the information judges whether it meets the communication conditions and resource requirements firstly and selects the optimal task bidding information according to the mission revenue (lines 6–14). The UAVs in the local communication network are consistent with the bid information through the information transmission.


### 4.1.2. Bid Application

After step 1, each UAV in the local communication network ofUi retains the same bid information. The UAV swarm is in flight, and there is a communication time delay between UAVs. If each UAV calculates the estimated time of arrival (ETA) with the target according to the moment when it receives the bid, in the process of information exchange, the ETA will change and cause the performance of task allocation to be degraded. Therefore, each UAV needs to agree on a unified time. Because the bid information includes the moment of the target was discovered and the time of coalition forms, the UAV needs to calculate its EAP according to the moment of coalition formation. Then UAV uses EAP to calculate its ETA to the target and send the bid application to the coalition leader. The bid application of Uk can be expressed as follows:(13)Bk=Uk,Tj,RkU,PkU,tk,Hjk,where Uk is the UAV for bidding, RkU is the attack resource carried by Uk, PkU and tk are the EAP in the moment of coalition formation and ETA to the target, and Hjk=Hmax.


### 4.1.3. Coalition Formation

After step 2, the coalition leaderUi receives all bid applications and needs to deal with the application information. Firstly, the leader should screen out coalition members that can stably exist in the local communication network. Then under the expectation of the minimum number of coalition members, the leader screens out optimal coalition combination CjT according to the objective function. After the coalition members are determined, members share the target’s attack resource requirements—the coalition leader Ui of CjT plans an attack scheme and resource consumption allocation scheme.


### 4.1.4. Signing Contracts

The coalition leader transmits the information of the winning bid to the UAVs in the local communication network. Then the UAV that wins the bid adds the task of hitting the targetTj to its task sequence, and the members of CjT carry out the task according to the plan formulated by the leader. The members of the coalition who received the information earlier continue to perform the original task until tcj. In other words, members act simultaneously when the farthest UAV receives the winning bid information.


## 4.1.1. Task Release

AfterUi finds the target Tj, it judges whether RiU>RjT is established. If the condition establishes, Ui executes the task alone; if not, Ui becomes the leader of the coalition and sends task bidding information to all UAVs in its local communication network for seeking coalition formation.During the flight of the UAV swarm, the communication is formed into an ad hoc (point-to-point) network [27], and the location of UAVs is constantly changing. Depending on whether there is a communication node, the communication mode between UAVs can be divided into direct communication and indirect communication [28]. UAV swarms often use flooding to transmit information to other UAVs within the communication range, ensuring that all UAVs can receive information. However, there are often problems with implosion and broadcast storms [22]. Peng W et al. [29] proposed that limiting the number of broadcasts could help solve the issues mentioned above. The number of broadcasts can be limited in the task release and bid application stages. In the task release stage, the number of nodes between the single-link communication of the UAV can be limited, which is named as the maximum number of information transmission Hmax; in the bid application stage, the bidders’ conditions are strict to avoid environmental changes leading to contract breach, which causes waste of communication resources.To reduce the communication load between UAVs, a self-adaptive maximum number of information transmissions method based on the target level and resource requirement (AT-MIT) is proposed. AT-MIT can ensure that when attacking important targets, the coalition can be formed as successful as possible; when attacking secondary targets, it reasonably reserves communication resources and speeds up the formation of the coalition. It can be expressed as follows:(10)Hmax=⌈∂Dj+A⋅RjT⌉,where ∂ is the weight coefficient, Dj is the level of Tj, A is the weight vector used to transform the target’s resource requirement into the difficulty level of destruction, and ⌈⌉ is the roundup function.Before the coalition leaderUi performs the information transfer between UAVs, the remaining information transfer time Hji is first judged. Initial time, Hji=Hmax, and with each transmission, Hji is reduced by one. When Hji=0, information is no longer transmitted.For example, when theU0 finds the T1, it will get all information about T1, including the level and the resource requirement of T1. By calculating Hmax=2, then Hj0=Hmax=2. The local communication network of U0 is shown in Figure 3. The dotted circle around the coalition leader U0 indicates its reconnaissance range U0 and U1 can communicate directly, bidding information is transferred from U0 to U1, and Hji minus 1. Then U1 serves as a communication node and sends bidding information to U=U3,U4 within its communication range except U0. Although U5 is within the communication range of U3, Hj1=0; then the bidding information is not transmitted from U3 to U5.Figure 3
Local communication network of UAV swarm with limited communication.Before the coalition is formed successfully, the UAV swarm has been conducting reconnaissance according to the set reconnaissance route. Furthermore, its communication topology is in dynamic transformation, so it is critical to screen out coalition members to construct a stable communication topology. This paper selects the coalition members by judging the expected arrival position (EAP).AfterUi finds Tj, Ui transmits bid information to all UAVs in the local communication network. In order to screen out potential coalition members that constitute a stable communication topology, UAVs receiving bid information send the EAP at the moment of the successful coalition formation as part of the bid application to the coalition leader Ui. The moment of coalition formation successfully is expressed as follows:(11)tcj=tn+tf,where tcj, tn, and tf represent the moment of coalition formation, moment of Ui finding Tj, and time of coalition formation process, respectively. And coalition formation process includes coalition leader sending bid information, potential coalition members sending bid applications, bid application information processing, and signing contracts, which can be expressed as follows:(12)tf=3HmaxΔtd+tc+tb,where Δtd is a single information transfer time between UAVs, tc is the time to process bid information and plan the coalition’s offense, and tb is the time to calculate EAP.AfterUi finds Tj, Ui gets information about the target. The information can be expressed as Qj=pjT,RjT,lj,TThreat, where pjT, RjT, lj, andTThreat is the position, resource requirement, level, and threat of Tj, respectively. Coalition leader Ui sends bid information to UAVs within communication range. The information can be expressed as Oi=Iiu,Qj,tn,tf,fji,Hji, where Iiu is serial number and EAP of UAV. fji is the estimated revenue of the Tj. The bid information is transmitted to each UAV according to Algorithm 1 in the local communication network, and UAVs are consistent with the information.Algorithm 1: Task bidding.
(1)
Hji←Hmax(2)
ifHji>0then(3)
Hji←Hji−1(4)
Ui send Oi to its directly connected UAV(5)
end if(6)
fork=1: number of bid requests received do(7)
predict EAP ofUi in the moment of coalition formation(8)
if ETA is in the communication range of Uk(9)
and owe the resources needed ofTjthen(10)
iffji<fkithen(11)
Pi←Pk(12)
end if(13)
end if(14)
end forAs shown in Algorithm 1, UAVs in the local communication network transmit the task bidding information to the UAV, which can be directly connected (lines 1–5); then the UAV that receives the information judges whether it meets the communication conditions and resource requirements firstly and selects the optimal task bidding information according to the mission revenue (lines 6–14). The UAVs in the local communication network are consistent with the bid information through the information transmission.


## 4.1.2. Bid Application

After step 1, each UAV in the local communication network ofUi retains the same bid information. The UAV swarm is in flight, and there is a communication time delay between UAVs. If each UAV calculates the estimated time of arrival (ETA) with the target according to the moment when it receives the bid, in the process of information exchange, the ETA will change and cause the performance of task allocation to be degraded. Therefore, each UAV needs to agree on a unified time. Because the bid information includes the moment of the target was discovered and the time of coalition forms, the UAV needs to calculate its EAP according to the moment of coalition formation. Then UAV uses EAP to calculate its ETA to the target and send the bid application to the coalition leader. The bid application of Uk can be expressed as follows:(13)Bk=Uk,Tj,RkU,PkU,tk,Hjk,where Uk is the UAV for bidding, RkU is the attack resource carried by Uk, PkU and tk are the EAP in the moment of coalition formation and ETA to the target, and Hjk=Hmax.


## 4.1.3. Coalition Formation

After step 2, the coalition leaderUi receives all bid applications and needs to deal with the application information. Firstly, the leader should screen out coalition members that can stably exist in the local communication network. Then under the expectation of the minimum number of coalition members, the leader screens out optimal coalition combination CjT according to the objective function. After the coalition members are determined, members share the target’s attack resource requirements—the coalition leader Ui of CjT plans an attack scheme and resource consumption allocation scheme.


## 4.1.4. Signing Contracts

The coalition leader transmits the information of the winning bid to the UAVs in the local communication network. Then the UAV that wins the bid adds the task of hitting the targetTj to its task sequence, and the members of CjT carry out the task according to the plan formulated by the leader. The members of the coalition who received the information earlier continue to perform the original task until tcj. In other words, members act simultaneously when the farthest UAV receives the winning bid information.


## 4.2. Resource Consumption Allocation Method Based on Gini Coefficient

After the coalition leader selects the combination of membersCjT, the UAVs in the coalition share the resources requirement. In the case of resource constraints, the greedy algorithm is often used to allocate the required attack resources. This algorithm leads to unscientific resource consumption in the UAV swarm; some UAVs are rendered incapacitated prematurely, resulting in lower success rates for subsequent coalition formations. It leads to a decline in the robustness of the UAV swarm in mission execution, the number of missions completed, and the dynamics of responding to unexpected missions. This paper proposes a resource consumption allocation method based on the Gini coefficient to solve the unreasonable allocation of resource consumption problem.


### 4.2.1. Gini Coefficient

In 1912, the famous Italian statistician Corrado Gini proposed a coefficient to measure the degree of inequality in the distribution of wealth. The characteristic of the Gini coefficient lies in its integrity. It is often used to evaluate the degree of equality of wealth distribution in a country. When there are fewer residents in the country, the conclusion of its judgment is more reliable. The UAV swarm can be regarded as a temporary country, and the attack resources carried can be equivalent to wealth income. The Gini coefficient can measure the equilibrium degree of UAV attack resource allocation.The geometric meaning of the Gini coefficient is based on the Lorentz curve. When the Gini coefficient is used to measure the balance of the distribution of UAV attack resources, the definition of the Lorentz curve is to rank the UAV attack resources from low to high, and the cumulative percentage of the number of drones and the cumulative percentage of attack resources are calculated. The corresponding relationship is drawn on the graph; the Lorentz curve is obtained as shown in Figure4.Figure 4
Lorentz curve of UAVs resource.In Figure4, the calculation of the Gini coefficient can be considered as the ratio of the area formed by the connection of the absolute equilibrium curve and the Lorentz curve (A area in Figure 3) to the area formed by the absolute equilibrium curve and the horizontal axis (A+B area in Figure 3), which can be expressed as G=A/A+B, but the Lorentz curve is irregular; the area of A and B cannot be calculated directly. In this paper, the method of reference [30] is used to calculate G; the area of B is approximately divided into the area of several trapezoids [30], which can be shown as follows:(14)G=1−1n2∑i=1n−1Wi+1,where Wi is the percentage of the total resources from the UAV with the least resources to the i−th UAV.


## 4.2.1. Gini Coefficient

In 1912, the famous Italian statistician Corrado Gini proposed a coefficient to measure the degree of inequality in the distribution of wealth. The characteristic of the Gini coefficient lies in its integrity. It is often used to evaluate the degree of equality of wealth distribution in a country. When there are fewer residents in the country, the conclusion of its judgment is more reliable. The UAV swarm can be regarded as a temporary country, and the attack resources carried can be equivalent to wealth income. The Gini coefficient can measure the equilibrium degree of UAV attack resource allocation.The geometric meaning of the Gini coefficient is based on the Lorentz curve. When the Gini coefficient is used to measure the balance of the distribution of UAV attack resources, the definition of the Lorentz curve is to rank the UAV attack resources from low to high, and the cumulative percentage of the number of drones and the cumulative percentage of attack resources are calculated. The corresponding relationship is drawn on the graph; the Lorentz curve is obtained as shown in Figure4.Figure 4
Lorentz curve of UAVs resource.In Figure4, the calculation of the Gini coefficient can be considered as the ratio of the area formed by the connection of the absolute equilibrium curve and the Lorentz curve (A area in Figure 3) to the area formed by the absolute equilibrium curve and the horizontal axis (A+B area in Figure 3), which can be expressed as G=A/A+B, but the Lorentz curve is irregular; the area of A and B cannot be calculated directly. In this paper, the method of reference [30] is used to calculate G; the area of B is approximately divided into the area of several trapezoids [30], which can be shown as follows:(14)G=1−1n2∑i=1n−1Wi+1,where Wi is the percentage of the total resources from the UAV with the least resources to the i−th UAV.


## 4.3. Resource Consumption Allocation Method Based on Gini Coefficient

After the coalitionCjT to attack the target Tj is formed, the sum of various resources in the coalition satisfies task resource requirements, which can be expressed as Rj,qC≥Rj,qTq=1,…,m. For the q-type attack resources in the CjT, firstly, the coalition leader screen out the set of UAVs that contain q-type resources. Then the leader traverses all resource allocation combinations that meet the target resource requirements and calculates the Gini coefficient of the remaining resources for each combination separately. The combination of the optimal Gini coefficient is used as the allocation scheme of the q-type resource. The leader calculates the allocation scheme of other types of resources in turn and finally summarizes into the resource consumption allocation plan. The detail is described as Algorithm 2.Algorithm 2: Resource consumption allocation method based on Gini coefficient.
(1)
initialize(2)
for various types of resources for the Tjdo(3)
for all Uido(4)
add allRj,kU to array k(5)
from arrayk to traverse combination Vnk(6)
for all Vnkdo(7)
calculate remaining resources(8)
calculate the Gini coefficient(9)
if the Gini coefficient of Vnk is closest to the G value, then(10)
saveVnk to buffer array(11)
end if(12)
end for(13)
end for(14)
V=V1,V2,V3,…,Vk(15)
end for(16)
returnV


### 4.3.1. Optimal Gini Coefficient Value

For a series of tasks on the battlefield, the resource consumption allocation method based on the Gini coefficient can effectively control the difference in resources among UAVs. Moreover, it improves the UAV swarm’s robustness, the number of tasks to be completed, and the dynamics of responding to sudden tasks improved. But the performance improvement is based on selecting the appropriate Gini coefficient (G) value. Therefore, the G value needs to set an appropriate evaluation function and corresponding experiments to select according to the characteristics of the mission scene.The selection of theG value is affected by many factors, such as the total number of tasks, the size of the UAV swarm, the location of a single UAV, and the number of resources initially carried by the UAV. In the communication-constrained environment, UAVs in the center of the UAV swarm are requested by more coalition and undertake more tasks. Because of its mission-critical status, it should carry more attack resources than UAVs at the edge of the UAV swarm. Therefore, the selection of the optimal G value should mainly be affected by the mission status of the UAV.


## 4.3.1. Optimal Gini Coefficient Value

For a series of tasks on the battlefield, the resource consumption allocation method based on the Gini coefficient can effectively control the difference in resources among UAVs. Moreover, it improves the UAV swarm’s robustness, the number of tasks to be completed, and the dynamics of responding to sudden tasks improved. But the performance improvement is based on selecting the appropriate Gini coefficient (G) value. Therefore, the G value needs to set an appropriate evaluation function and corresponding experiments to select according to the characteristics of the mission scene.The selection of theG value is affected by many factors, such as the total number of tasks, the size of the UAV swarm, the location of a single UAV, and the number of resources initially carried by the UAV. In the communication-constrained environment, UAVs in the center of the UAV swarm are requested by more coalition and undertake more tasks. Because of its mission-critical status, it should carry more attack resources than UAVs at the edge of the UAV swarm. Therefore, the selection of the optimal G value should mainly be affected by the mission status of the UAV.


## 5. Simulation and Analysis

In this section, four simulation experiments have been performed to verify the performance of the improved CNP-method-based communication-constrained task allocation. In the first group, the method proposed is used in the example scenario to illustrate the whole process of heterogeneous multi-UAV performing cooperative tasks. The second group contrasts the polynomial time coalition formation algorithm (PTCFA), resource welfare-based algorithm, and the improved CNP-based algorithm to analyze the algorithm performance. In the third group, experiments compare the performance between the AD-MIT and the fixed maximum number of information transfers in the example scene by the Monte Carlo method. And, in the fourth group, the greedy algorithm, balance consumption algorithm, and resource consumption based on the Gini coefficient algorithm are compared.All simulation experiments in this paper are implemented on the MATLAB 2019b version of the 16 GB Intel(R) Core(TM) i7-10875H. The relevant parameter settings are described in detail in the experimental settings of each section.


### 5.1. Heterogeneous Multi-UAV Collaborative Task Scenario

The mission area is set to 3200 m. The UAV swarm comprises six observation strike integrated UAVs; each UAV’s type and the number of attack resources are different. There are two task objectives in the mission area, and the information is shown in Table1. Before the UAV swarm takes off, there is no prior information about the target until a UAV finds it and starts the local real-time task allocation. The information on UAVs at the initial moment are shown in Table 2. The relevant parameter settings are as follows: UAV reconnaissance range, communication range, and flight velocity are 250 m, 1,000 m, and 50 m/s, respectively.Table 1
Information of the targets.
NumberPositionResourceValueθLevel1(2,000, 1,700)(4, 3, 1)5000.612(2,500, 700)(1, 2, 0)2000.51Table 2
Initial moment information of the UAVs.
NumberPositionHeading angleResourceTurning radiusValue1(0, 0)5(2, 1, 2)501002(200, 500)4(1, 0, 0)501003(1,000, 1,000)5(3, 2, 1)1003004(200, 1,500)0(2, 2, 0)1003005(300, 2,000)335(1, 1, 0)502006(400, 2,500)40(2, 1, 0)50200At the initial moment, the UAV swarm performs the reconnaissance mission according to the set path. TheU4 finds the T1 in 33.0 seconds. U4 becomes the coalition leader after assessing that its resource is insufficient to meet the requirements of T1. Then it sends bid information within its communication network. Hmax=2 can be calculated according to equation (10), and the local communication network of U4 is shown in Figure 5; the solid line is the track of the UAV when it performs the reconnaissance mission; and the end of the solid line is the position of each UAV when T1 was discovered by U4. Then the UAVs connected by the dotted line express that communication is possible at present. According to the bid application submitted by the UAVs in the communication network, C1T=U3,U4 is formed to attack T1. The Dubins track of U3, U4 attacking T1 and the actual distance to the T1 are shown in Figures 6 and 7, respectively. According to Figure 6, it can be seen that the planned track meets the minimum turning radius constraint, and it can be seen from Figure 6 that UAVs in the coalition can reach the target at the same time.Figure 5
The status of each UAV at 33.0 s.Figure 6
The planning track ofC1T attacks T1.Figure 7
Actual distance betweenT1 and UAV of C1T.TheU2 finds the T2 in 41.3 seconds. After U2 judges that its resources cannot meet the requirements, it sends the task bid information to other UAVs in the local communication network. And Hmax=1 is calculated based on target information. The local communication network of U2 and the path of U3,U4 execution of the task is shown in Figure 8. But U3,U4 are in the execution stage and do not participate in the bid of the T2. In the same way, C2T=U1,U5 is screened out to attack T2. The Dubins track of the UAV in the coalition and the actual distance to T2 are shown in Figures 9 and 10, respectively. It can also be seen that the UAVs in the coalition can reach T1 at the same time and track satisfies minimum turning radius constraint.Figure 8
The status of each UAV at 41.3 s.Figure 9
The planning track ofC2T attacks T2.Figure 10
The actual distance betweenT2 and UAV of C2T.When all targets have been hit, the track of all UAVs is shown in Figure11. After the UAV reaches the boundary of the mission area, it returns to the area by the shortest path. After completing the mission, the UAV continues to perform the reconnaissance mission to find the next target such as the U1 and U5.Figure 11
Full track of each UAV when completing all missions. Performance comparison of different coalition formation algorithms.The formation of the coalition in the process of task allocation is an important link in determining the quality of task allocation. The experiment in this section compares the performance of the three algorithms resource welfare-based algorithms [25], PTCFA [31], and improved CNP-based algorithms.The mission area is set to 5,000 m. There are 30 randomly distributed fixed targets in the mission area. Each target requires three types of attack resources to destroy, and the demand for each type of resource is a random integer between 1 and 10. The task level is a random integer between 1 and 3. The experiment set up five groups of UAVs with the numbers 5, 10, 15, 20, and 25. Each UAV’s number of various attack resources is a random integer between 1 and 5. Each group of experiments is carried out 100 times simulation. The reconnaissance range of the UAV is set to be 300 m; the communication range is 600 m; and the communication time delay between UAVs is 0.1 s. In the simulation experiment, the UAVs start from random positions on the west side of the mission edge with different heading angles.When the number of UAVs changes, different coalition formation algorithms are used to perform tasks. The average time and average task revenue recorded are shown in Figures12(a) and 12(b), respectively.Figure 12
Performance comparison of different coalition formation algorithms with the increasing number of UAVs: (a) average time per task and (b) average profit per task.
(a)(b)Figure12(a) shows that as the number of UAVs increases, the average time to perform the task for the three construction methods gradually decreases. At the same time, PTCFA has the shortest average time to finish the mission among the three algorithms, regardless of the number of UAVs. It is due to the process of PTCFA, which aims to screen out members that take the shortest time to complete missions. The method proposed in this paper is better than resource welfare algorithms but slightly worse than PTCFA in task completion time.Figure12(b) shows that the average avenue obtained by the three coalition formation algorithms for performing missions increases as the number of UAVs increases. When the number of UAVs grows from 15 to 20, the resource welfare algorithm shows a lower growth trend than the other two algorithms. The main reason is that there is no minimum requirement for the number of UAVs during the establishment of the coalition. As shown in Figure 12(b), the algorithms proposed in this paper can obtain higher task revenue than the other two algorithms.


### 5.2. Performance Comparison of Different Information Transfer Times

The maximum number of information transfers affects the efficiency of the UAV in accomplishing the mission in the communication-constrained environment. In this group of experiments, the fixed maximum information transfer times and AT-MIT are compared.The mission area, target, and UAV setting are consistent with the previous section. All targets can only be found by any UAV in the experiments once, and UAV resources do not decrease after executing the mission. When the number of UAVs rises, the experiment compares the average number of successful coalition formations and the average time using different information transfer times.As Figure13(a) illustrates, the number of completed missions rises as the number of UAVs in the mission area increases. However, when Hmax=3 and numbers of UAVs are 5 and 25, there is no significant advantage compared to other information transformation times. Because when the number of UAVs is too small, the distance between UAVs is too far. There is no directly connected UAV, and the number of information transmissions is ineffective; when the number is too large, the number of directly connected UAVs is frequently sufficient to form the coalition successfully. At the same time, AT-MIT is better than Hmax=2 but inferior to Hmax=3 in the number of completions.Figure 13
Performance comparison of different information transformation times with an increasing number of UAVs. Performance of different resource consumption allocation methods: (a) average number of tasks and (b) average profit per task.
(a)(b)Figure13(b) demonstrates that when AT-MIT is used for task allocation, the average benefit is greater than for Hmax=2 and Hmax=3 but less than for Hmax=1. The reason is that increasing the number of information transformations directly results in a longer time required to form the coalition, reducing the benefits of task completion. At the same time, due to the small number of information transmissions and UAVs in the local communication network, it is impossible to choose the optimal one during the coalition formation process.The method of resource consumption among UAVs affects the robustness of the UAV swarm performing tasks. By varying theG value, experiments analyze the influence of the G value on the performance of the method. And the performance of three resource consumption methods is studied by experiments: the Gini-coefficient-based algorithm, the greedy algorithm, and the balance algorithm.The 6 UAVs executed the 30 missions in the mission area, and when the UAVs could not complete the task, the experiment was terminated. The mission target needs 3 different types of resources to destroy. The demand for each resource type is a random integer between 1 and 50, and the mission level is a random integer between 1 and 3. Experiments run 100 times, and the tasks are reset for each experiment. When theG value varies from 0 to 1, the average number of tasks completed by the UAV fleet is shown in Figure 13.As illustrated in Figure14, when G equals 0.31, the average number of tasks completed reaches the maximum value of 27.8. It is primarily because UAVs in the middle of the mission area receive more coalition formation requests and are required to perform more tasks in the communication-constrained environment. Therefore, in the resource consumption allocation scheme, the UAV in the middle of the mission should maintain a resource advantage over the UAV in the edge position. However, if the resource difference is too big, the UAV’s resources in the edge position will be consumed prematurely, and the corresponding mission will not be completed.Figure 14
Average number of tasks completed with increasingG value.As illustrated in Figure15, the resource consumption algorithm based on the Gini coefficient completes more tasks on average than the other two resource consumption algorithms. The reason is that the other two algorithms neglect to account that the quantity of tasks performed by UAVs in different positions varies significantly in a communication-constrained environment.Figure 15
Average number of tasks completed under three algorithms.Figure16(a) shows that the resource consumption algorithm based on balance maintains consistency in the coalition’s UAV resource allocation. UAV1and UAV2 of Figure 16(a) are incompatible with other UAV resources because they have fewer coalitions with other UAVs on missions. As Figure 16(b) show, the algorithm based on the greedy algorithm is similar to the algorithm based on the Gini coefficient (G value is too large), leading to the large difference in resources between UAVs. Simultaneously, we can notice that the algorithm based on the Gini coefficient can maintain a reasonable resource differential between UAVs, which is more beneficial to the execution of the following tasks.Figure 16
Residual resources of UAVs over task under three algorithms: (a) balanced algorithm, (b) greedy algorithm, and (c) Gini-coefficient-based algorithm.
(a)(b)(c)


## 5.1. Heterogeneous Multi-UAV Collaborative Task Scenario

The mission area is set to 3200 m. The UAV swarm comprises six observation strike integrated UAVs; each UAV’s type and the number of attack resources are different. There are two task objectives in the mission area, and the information is shown in Table1. Before the UAV swarm takes off, there is no prior information about the target until a UAV finds it and starts the local real-time task allocation. The information on UAVs at the initial moment are shown in Table 2. The relevant parameter settings are as follows: UAV reconnaissance range, communication range, and flight velocity are 250 m, 1,000 m, and 50 m/s, respectively.Table 1
Information of the targets.
NumberPositionResourceValueθLevel1(2,000, 1,700)(4, 3, 1)5000.612(2,500, 700)(1, 2, 0)2000.51Table 2
Initial moment information of the UAVs.
NumberPositionHeading angleResourceTurning radiusValue1(0, 0)5(2, 1, 2)501002(200, 500)4(1, 0, 0)501003(1,000, 1,000)5(3, 2, 1)1003004(200, 1,500)0(2, 2, 0)1003005(300, 2,000)335(1, 1, 0)502006(400, 2,500)40(2, 1, 0)50200At the initial moment, the UAV swarm performs the reconnaissance mission according to the set path. TheU4 finds the T1 in 33.0 seconds. U4 becomes the coalition leader after assessing that its resource is insufficient to meet the requirements of T1. Then it sends bid information within its communication network. Hmax=2 can be calculated according to equation (10), and the local communication network of U4 is shown in Figure 5; the solid line is the track of the UAV when it performs the reconnaissance mission; and the end of the solid line is the position of each UAV when T1 was discovered by U4. Then the UAVs connected by the dotted line express that communication is possible at present. According to the bid application submitted by the UAVs in the communication network, C1T=U3,U4 is formed to attack T1. The Dubins track of U3, U4 attacking T1 and the actual distance to the T1 are shown in Figures 6 and 7, respectively. According to Figure 6, it can be seen that the planned track meets the minimum turning radius constraint, and it can be seen from Figure 6 that UAVs in the coalition can reach the target at the same time.Figure 5
The status of each UAV at 33.0 s.Figure 6
The planning track ofC1T attacks T1.Figure 7
Actual distance betweenT1 and UAV of C1T.TheU2 finds the T2 in 41.3 seconds. After U2 judges that its resources cannot meet the requirements, it sends the task bid information to other UAVs in the local communication network. And Hmax=1 is calculated based on target information. The local communication network of U2 and the path of U3,U4 execution of the task is shown in Figure 8. But U3,U4 are in the execution stage and do not participate in the bid of the T2. In the same way, C2T=U1,U5 is screened out to attack T2. The Dubins track of the UAV in the coalition and the actual distance to T2 are shown in Figures 9 and 10, respectively. It can also be seen that the UAVs in the coalition can reach T1 at the same time and track satisfies minimum turning radius constraint.Figure 8
The status of each UAV at 41.3 s.Figure 9
The planning track ofC2T attacks T2.Figure 10
The actual distance betweenT2 and UAV of C2T.When all targets have been hit, the track of all UAVs is shown in Figure11. After the UAV reaches the boundary of the mission area, it returns to the area by the shortest path. After completing the mission, the UAV continues to perform the reconnaissance mission to find the next target such as the U1 and U5.Figure 11
Full track of each UAV when completing all missions. Performance comparison of different coalition formation algorithms.The formation of the coalition in the process of task allocation is an important link in determining the quality of task allocation. The experiment in this section compares the performance of the three algorithms resource welfare-based algorithms [25], PTCFA [31], and improved CNP-based algorithms.The mission area is set to 5,000 m. There are 30 randomly distributed fixed targets in the mission area. Each target requires three types of attack resources to destroy, and the demand for each type of resource is a random integer between 1 and 10. The task level is a random integer between 1 and 3. The experiment set up five groups of UAVs with the numbers 5, 10, 15, 20, and 25. Each UAV’s number of various attack resources is a random integer between 1 and 5. Each group of experiments is carried out 100 times simulation. The reconnaissance range of the UAV is set to be 300 m; the communication range is 600 m; and the communication time delay between UAVs is 0.1 s. In the simulation experiment, the UAVs start from random positions on the west side of the mission edge with different heading angles.When the number of UAVs changes, different coalition formation algorithms are used to perform tasks. The average time and average task revenue recorded are shown in Figures12(a) and 12(b), respectively.Figure 12
Performance comparison of different coalition formation algorithms with the increasing number of UAVs: (a) average time per task and (b) average profit per task.
(a)(b)Figure12(a) shows that as the number of UAVs increases, the average time to perform the task for the three construction methods gradually decreases. At the same time, PTCFA has the shortest average time to finish the mission among the three algorithms, regardless of the number of UAVs. It is due to the process of PTCFA, which aims to screen out members that take the shortest time to complete missions. The method proposed in this paper is better than resource welfare algorithms but slightly worse than PTCFA in task completion time.Figure12(b) shows that the average avenue obtained by the three coalition formation algorithms for performing missions increases as the number of UAVs increases. When the number of UAVs grows from 15 to 20, the resource welfare algorithm shows a lower growth trend than the other two algorithms. The main reason is that there is no minimum requirement for the number of UAVs during the establishment of the coalition. As shown in Figure 12(b), the algorithms proposed in this paper can obtain higher task revenue than the other two algorithms.


## 5.2. Performance Comparison of Different Information Transfer Times

The maximum number of information transfers affects the efficiency of the UAV in accomplishing the mission in the communication-constrained environment. In this group of experiments, the fixed maximum information transfer times and AT-MIT are compared.The mission area, target, and UAV setting are consistent with the previous section. All targets can only be found by any UAV in the experiments once, and UAV resources do not decrease after executing the mission. When the number of UAVs rises, the experiment compares the average number of successful coalition formations and the average time using different information transfer times.As Figure13(a) illustrates, the number of completed missions rises as the number of UAVs in the mission area increases. However, when Hmax=3 and numbers of UAVs are 5 and 25, there is no significant advantage compared to other information transformation times. Because when the number of UAVs is too small, the distance between UAVs is too far. There is no directly connected UAV, and the number of information transmissions is ineffective; when the number is too large, the number of directly connected UAVs is frequently sufficient to form the coalition successfully. At the same time, AT-MIT is better than Hmax=2 but inferior to Hmax=3 in the number of completions.Figure 13
Performance comparison of different information transformation times with an increasing number of UAVs. Performance of different resource consumption allocation methods: (a) average number of tasks and (b) average profit per task.
(a)(b)Figure13(b) demonstrates that when AT-MIT is used for task allocation, the average benefit is greater than for Hmax=2 and Hmax=3 but less than for Hmax=1. The reason is that increasing the number of information transformations directly results in a longer time required to form the coalition, reducing the benefits of task completion. At the same time, due to the small number of information transmissions and UAVs in the local communication network, it is impossible to choose the optimal one during the coalition formation process.The method of resource consumption among UAVs affects the robustness of the UAV swarm performing tasks. By varying theG value, experiments analyze the influence of the G value on the performance of the method. And the performance of three resource consumption methods is studied by experiments: the Gini-coefficient-based algorithm, the greedy algorithm, and the balance algorithm.The 6 UAVs executed the 30 missions in the mission area, and when the UAVs could not complete the task, the experiment was terminated. The mission target needs 3 different types of resources to destroy. The demand for each resource type is a random integer between 1 and 50, and the mission level is a random integer between 1 and 3. Experiments run 100 times, and the tasks are reset for each experiment. When theG value varies from 0 to 1, the average number of tasks completed by the UAV fleet is shown in Figure 13.As illustrated in Figure14, when G equals 0.31, the average number of tasks completed reaches the maximum value of 27.8. It is primarily because UAVs in the middle of the mission area receive more coalition formation requests and are required to perform more tasks in the communication-constrained environment. Therefore, in the resource consumption allocation scheme, the UAV in the middle of the mission should maintain a resource advantage over the UAV in the edge position. However, if the resource difference is too big, the UAV’s resources in the edge position will be consumed prematurely, and the corresponding mission will not be completed.Figure 14
Average number of tasks completed with increasingG value.As illustrated in Figure15, the resource consumption algorithm based on the Gini coefficient completes more tasks on average than the other two resource consumption algorithms. The reason is that the other two algorithms neglect to account that the quantity of tasks performed by UAVs in different positions varies significantly in a communication-constrained environment.Figure 15
Average number of tasks completed under three algorithms.Figure16(a) shows that the resource consumption algorithm based on balance maintains consistency in the coalition’s UAV resource allocation. UAV1and UAV2 of Figure 16(a) are incompatible with other UAV resources because they have fewer coalitions with other UAVs on missions. As Figure 16(b) show, the algorithm based on the greedy algorithm is similar to the algorithm based on the Gini coefficient (G value is too large), leading to the large difference in resources between UAVs. Simultaneously, we can notice that the algorithm based on the Gini coefficient can maintain a reasonable resource differential between UAVs, which is more beneficial to the execution of the following tasks.Figure 16
Residual resources of UAVs over task under three algorithms: (a) balanced algorithm, (b) greedy algorithm, and (c) Gini-coefficient-based algorithm.
(a)(b)(c)


## 6. Conclusion

This paper proposes an improved CNP-based method, which solves the heterogeneous multi-UAV task allocation with resource constraints, UAV self-performance constraints, time constraints, and communication constraints. This paper proposes AD-MIT, and the information consistency method to solve conflicts in the communication-constrained environment. Meanwhile, this paper proposes a resource consumption allocation method based on the Gini coefficient to keep the resource difference between UAVs and then improve the ability to deal with unplanned tasks. The experimental results demonstrate that the improved CNP-based method can obtain a higher performance in time and reward the accomplished task accomplished compared to the other two methods. Simultaneously, compared with the setting of a fixed number of information transformations, AD-MIT can rationally utilize communication resources and accelerate coalition formation to ensure the number of tasks completed in the communication-constrained environment. Under resource constraints, the Gini-coefficient-based resource consumption allocation method is better than the greedy method and the balanced method in the number of tasks accomplished. The method can reasonably regulate the degree of resource differentiation between UAVs to increase the swarm’s robustness in a variety of mission scenarios and deal with unplanned tasks.In future studies, the relationship between the optimalG value and numerous task scenario factors will be further investigated, which is the premise of applying it to practical scenarios, and it is worth continuing to study.



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*Source: 6568334-2022-06-29.xml*