Intelligent Planning Modeling and Optimization of UAV Cluster Based on Multi-Objective Optimization Algorithm

: As a ﬂight tool integrating carrier and reconnaissance, unmanned aerial vehicles (UAVs) are applied in various ﬁelds. In recent years, mission planning and path optimization have become the most important research focuses in the ﬁeld of UAVs. With the continuous maturity of artiﬁcial intelligence technology, various search algorithms have been applied in the ﬁeld of unmanned aerial vehicles. However, these algorithms have certain defects, which lead to problems, such as large search volume and low efﬁciency in task planning, and cannot meet the requirements of path planning. The objective optimization algorithm has a good performance in solving optimization problems. In this paper, the intelligent planning model of UAV cluster was established based on multi-objective optimization algorithm, and its path is optimized. In the aspect of modeling, this paper studied and analyzed online task planning, search rules and cluster formation control using an agent-based intelligent modeling method. For mission planning and optimization, it combined multi-objective optimization algorithm to build the model from three aspects of mission allocation, route planning and planning evaluation. The ﬁnal simulation results showed that the UAV cluster intelligent planning modeling method and path optimization method based on multi-objective optimization algorithm met the requirements of route design and improved the path search efﬁciency with 2.26% task completion satisfaction.


Introduction
At present, the traditional task planning algorithm exposes many defects, resulting in low efficiency of path planning. This paper poses an attempt to apply multi-objective optimization algorithm to UAV mission planning and path optimization. In this paper, online task planning, search rules and clustering formation control are studied and analyzed using an agent-based intelligent modeling method, and then combined with multi-objective optimization algorithm. UAV task planning and optimization are innovated from three aspects of task allocation, route planning and planning evaluation. The research shows that the optimization method proposed in this paper improves the path search efficiency and task completion of UAV.
With the development of science and technology, the application of UAV has become more and more extensive, and the research on modeling is also ever increasing. Baldi Simone proposed a new design method of adaptive autopilot, and studied the uncertain Eulerian Lagrangian dynamics based on UAV, in which the control can explicitly consider the driving problem in dynamics and reduce the structural knowledge of cross coupling and trim points [1]. Wang Ximan proposed a new vector field rule, which can deal with the uncertain course time constant and state related uncertainty in course dynamics caused by coupling. Then the stability is studied under the framework of Lyapunov, and the reliability of the proposed method is tested on the loop UAV simulator. Simulation results show that the proposed method is superior to the standard vector field method in the presence of such uncertainty [2]. Spandan Roy has studied an autopilot framework in

UAV Cluster Intelligent Planning Modeling Method
The intelligent modeling of UAV cluster is mainly embodied in three aspects: online task planning, search rules and cluster formation control.
(1) Online task planning UAV cluster online mission planning is a task to be completed during the flight process of UAV, mainly including task allocation and path planning. This paper presented a distributed online task planning method for UAV cluster based on the agent. Under this method, the content of online task planning for each UAV agent includes individual task execution, state evaluation, cluster state prediction, and local task planning. In these planning contents, status assessment is not easy to understand. It refers to the assessment of task status according to task requirements, such as the risk level of the task, the time spent on the task, etc.
(2) Search rules and search algorithms A. Search Rules Search rules are the premise of UAV cluster search, in which target search rules and path selection rules are the most important at the decision-making point of UAV flight mission, that is, the direction of each UAV search path. The most common search rule is random search with infinite angles, which easily leads to repeated search and low efficiency. In order to improve the search efficiency, we must try to avoid repeated search. In addition, search rules can usually be arranged with search algorithm or target optimization algorithm. The path selection rule is used to select an optimal path from the starting point to the destination, which requires the support of the corresponding objective optimization algorithm, such as the multi-objective optimization algorithm applied in this paper. In unfamiliar flight environments, for relatively small targets, UAVs can only use a simple agent to complete the search task, but the agent must have a certain computing power. Through the interaction between these agents and the environment, a group system is finally formed to optimize the search path until the target location is found.
B. Multi UAV cooperative search algorithm based on coevolutionary genetic algorithm This paper adopts the rolling optimization idea, that is, at time t , limit each UAV to plan a path forward. UAVs only execute the first step of the planned path. At time 1 + t , they re-plan the path based on the new system state and environmental information. Use

UAV Cluster Intelligent Planning Modeling Method
The intelligent modeling of UAV cluster is mainly embodied in three aspects: online task planning, search rules and cluster formation control.
(1) Online task planning UAV cluster online mission planning is a task to be completed during the flight process of UAV, mainly including task allocation and path planning. This paper presented a distributed online task planning method for UAV cluster based on the agent. Under this method, the content of online task planning for each UAV agent includes individual task execution, state evaluation, cluster state prediction, and local task planning. In these planning contents, status assessment is not easy to understand. It refers to the assessment of task status according to task requirements, such as the risk level of the task, the time spent on the task, etc.
(2) Search rules and search algorithms A. Search Rules Search rules are the premise of UAV cluster search, in which target search rules and path selection rules are the most important at the decision-making point of UAV flight mission, that is, the direction of each UAV search path. The most common search rule is random search with infinite angles, which easily leads to repeated search and low efficiency. In order to improve the search efficiency, we must try to avoid repeated search. In addition, search rules can usually be arranged with search algorithm or target optimization algorithm. The path selection rule is used to select an optimal path from the starting point to the destination, which requires the support of the corresponding objective optimization algorithm, such as the multi-objective optimization algorithm applied in this paper. In unfamiliar flight environments, for relatively small targets, UAVs can only use a simple agent to complete the search task, but the agent must have a certain computing power. Through the interaction between these agents and the environment, a group system is finally formed to optimize the search path until the target location is found.
B. Multi UAV cooperative search algorithm based on coevolutionary genetic algorithm This paper adopts the rolling optimization idea, that is, at time t, limit each UAV to plan a path forward. UAVs only execute the first step of the planned path. At time t + 1, they re-plan the path based on the new system state and environmental information. Use m subpopulations to evolve the search path of m UAVs respectively. If the UAV is located in cell (x, y) at time t, the result of path planning at time t is a path with a length of starting from (x, y). (3) Cluster formation control The control of UAV cluster is used not only to maintain the cluster shape, but also to transform and rotate the formation and avoid obstacles. UAV cluster formation control can be divided into centralized control and distributed control. This paper prefers distributed control. The reason is that distributed control requires less information and is simple to calculate with the advantages of high reliability, which is more suitable for controlling the formation of small UAV clusters.

Task Planning of UAV Based on Multi-Objective Optimization Algorithm
Combined with the multi-objective algorithm, this paper analyzed the modeling from three aspects: task allocation, route planning and planning evaluation. Figure 2 showed the specific process of UAV mission planning combined with multi-objective optimization algorithm. First, after receiving the task, the data are collated and analyzed, and the task target is analyzed according to the collated content; next, the load, track and link are planned as a whole through environment modeling; Finally, the planning result is output and sent to the terminal device. (3) Cluster formation control The control of UAV cluster is used not only to maintain the cluster shape, but also to transform and rotate the formation and avoid obstacles. UAV cluster formation control can be divided into centralized control and distributed control. This paper prefers distributed control. The reason is that distributed control requires less information and is simple to calculate with the advantages of high reliability, which is more suitable for controlling the formation of small UAV clusters.

Task Planning of UAV Based on Multi-Objective Optimization Algorithm
Combined with the multi-objective algorithm, this paper analyzed the modeling from three aspects: task allocation, route planning and planning evaluation. Figure 2 showed the specific process of UAV mission planning combined with multi-objective optimization algorithm. First, after receiving the task, the data are collated and analyzed, and the task target is analyzed according to the collated content; next, the load, track and link are planned as a whole through environment modeling; Finally, the planning result is output and sent to the terminal device.  (1) Task assignment The task allocation problem of the clustered UAV system belongs to the basic combinatorial optimization problem. At the beginning of the model establishment, the model elements UAV and task are set up first. It is supposed that there are n tasks, and the task set of m UAVs is   n Task  Task  Task  Task ..., , ,..., ,  (1) Task assignment The task allocation problem of the clustered UAV system belongs to the basic combinatorial optimization problem. At the beginning of the model establishment, the model elements UAV and task are set up first. It is supposed that there are n tasks, and the task set of m UAVs is Task = {Task 1 , Task 2 . . . , Task n }; the UAV set is UAV = {UAV 1 , UAV 2 , . . . , UAV m }. As the task planning forms of rotary wing UAV and fixed wing UAV are basically similar, this paper takes the rotary wing UAV as an example to show pictures. The allocation model shown in Figure 3 can be established based on whether the number of UAVs performing tasks m 1 and the number of tasks n are the same in the system of m UAVs.  Task1   Task2   Task3   Task4   Task1   Task2   Task1  Task2  Task7  Task4 Task3 Task5 Task6 Figure 3. UAV task assignment model.

A.
1 m n = is a single task performed by a single UAV, and its model is: A. n = m 1 is a single task performed by a single UAV, and its model is: n < m 1 is a single task performed by multiple UAVs, and its model is: n > m 1 is a multi-task performed by a single UAV, and its model is: Based on the above three formulas, a unified mathematical distribution model can be further established: Different allocation models have different cost matrices [13]. The following is the cost matrix corresponding to the above models.
When it is n = m 1 , the cost matrix of single task performed by a single UAV is: In the formula, C 1 is a square matrix, and C nm represents the cost of task n completed by UAV m.
When it is n < m 1 , the cost matrix of single task performed by multiple UAVs is: In the formula, C 3 is a square matrix, and C nm represents the cost of task n completed by UAV m.
When it is n > m 1 , the cost matrix of multiple tasks performed by a single UAV is: Among them, G represents the cost matrix between the UAV performing the task and the corresponding task, and g nm represents the cost of task n completed by UAV m. H represents the cost matrix between tasks. h i 1 i 2 represents the cost of UAV from task i 1 to task i 2 . In order to make the model clearer, the distance cost and the maximum flight time of the three models are obtained by Equations (8) and (9).
Among them, d ij represents the flight distance of UAV j to complete Task i . v j is the speed of UAV j . d iu represents the distance between Task i and Task u .
The goal of task allocation is to minimize the global objective function, which can be expressed as follows: Among them, J can be obtained by Equation (11).
(2) Track planning Track planning is used to find the optimal track composed of an ordered sequence from the starting point to the target point when the specific boundary conditions and performance indicators in the planning space are fully considered. Its objective function can be expressed as: Among them, x = (x 1 , x 2 , . . . , x n ) T ∈ R represents the decision variable and Ω ⊂ R n represents the constraint set; f (x) represents the objective function.
Smoothness refers to whether the UAV can fly smoothly along the planned track. The track generated by conventional algorithm is basically formed by connecting the track points into a straight line, which can lead to discontinuity [14]. If this problem needs to be solved, the track has to be smoothed. The common processing methods include cubic spline interpolation, B-spline curve and Bezier curve.
Bezier curve is a polynomial curve fitted by a few control nodes [15]. If there are n + 1 control points with coordinate value of p i (i = 0, 1, . . . , n), the parameter equation of each point on the n-order Bezier curve can be expressed as: Among them, B i,n (u) = C i n u i (1 − u) n − 1 , and i = 0, 1, . . . , n. n refers to the n-times Bezier curves. The k-order B-spline of n + 1 control nodes (x 0 , y 0 , z 0 ), (x 1 , y 1 , z 1 ),..., (x n , y n , z n ) in three-dimensional space is as follows: Among them, 0 ≤ t ≤ 1 and B i,k (t) are k-times B-spline basis functions. When it is i < k, then note i = 0; when k ≤ i < n, then note i = i − k + 1; when n < i, then note i = n − k + 2, which can be expressed as: ,ĝ(x) and g(x) are continuous in the interval [a, b] and meet the following conditions.
The n + 1 interpolation conditions are: g(x i ) is continuous at the interpolation point: At the interpolation point, the first and second derivatives of b are continuous: Since there are 4n − 2 equations from Equation (17) to Equation (20) and 4n unknowns to be solved, the first or second derivative value 0 of the two endpoints is usually added, which is: (3) Evaluation of route planning After the optimal track is obtained through model construction and algorithm operation, the track quality must be evaluated before it can be put to use. Generally, the constraint index function is constructed according to the track quality index, and then the track quality is evaluated again according to the value of the comprehensive constraint index function [16]. Figure 4 is the corresponding UAV track planning evaluation index chart, including flight time, track length, threat avoidance capability and track reliability. Track quality can be quantified using comprehensive constraint index function, which can be expressed as:  Flight time refers to the time from the starting point to the destination. The flight time of UAV on the planned route shall be less than the set value because the smaller the value, the less fuel the UAV consumes and the higher the track quality.
The track length refers to the length from the starting point to the destination of the UAV. The planned route length shall be less than the maximum allowed flight. The shorter the search route length is, the less fuel the UAV consumes in flight, which can reduce the probability of encountering threats and improve the track quality.
Threat avoidance capability refers to the ability of UAVs to avoid threats such as mountains, hills and houses. The stronger the ability of UAV to avoid threats, the stronger the search track, which can reduce the possibility of re-planning and improve the track quality [17].
Track reliability refers to the possibility of safe flight plan route of UAV under space and time constraints. The higher the reliability of the route, the less likely the UAV is to be destroyed when confronted with threats and the higher the track quality.

Experimental Results of Task Planning Method Combined with Multi-Objective Optimization Algorithm
In order to verify the effectiveness of the new UAV mission planning method, the flight mission was tested in the MATLAB 2016b simulation platform with an area of 500 m × 500 m. First, the distance, time and task completion degree of a single UAV were tested in a fixed task. Mission planning methods are divided into traditional methods and new methods. Threat factors are set in the flight area and the type of UAV is a consumer Among them, J is the comprehensive constraint index function, and ω 1 + ω 2 + ω 3 + ω 4 = 1 is the flight time, which is also the time required for the UAV to complete the task after the flight route planning.
Flight time refers to the time from the starting point to the destination. The flight time of UAV on the planned route shall be less than the set value because the smaller the value, the less fuel the UAV consumes and the higher the track quality.
The track length refers to the length from the starting point to the destination of the UAV. The planned route length shall be less than the maximum allowed flight. The shorter the search route length is, the less fuel the UAV consumes in flight, which can reduce the probability of encountering threats and improve the track quality.
Threat avoidance capability refers to the ability of UAVs to avoid threats such as mountains, hills and houses. The stronger the ability of UAV to avoid threats, the stronger the search track, which can reduce the possibility of re-planning and improve the track quality [17].
Track reliability refers to the possibility of safe flight plan route of UAV under space and time constraints. The higher the reliability of the route, the less likely the UAV is to be destroyed when confronted with threats and the higher the track quality.

Experimental Results of Task Planning Method Combined with Multi-Objective Optimization Algorithm
In order to verify the effectiveness of the new UAV mission planning method, the flight mission was tested in the MATLAB 2016b simulation platform with an area of 500 m × 500 m. First, the distance, time and task completion degree of a single UAV were tested in a fixed task. Mission planning methods are divided into traditional methods and new methods. Threat factors are set in the flight area and the type of UAV is a consumer class 4-axis UAV. The normal flight speed of the UAV is 60 km/h. The test results are shown in Table 1. From the data in Table 1, it can be concluded that under the two task planning methods, there is a significant gap in the distance, time and task completion of the UAV. Under the same task, the distance of the traditional method is nearly 40 m higher than that of the new method, and it takes more than 2 s compared to the new method. However, the task completion under the traditional method is not as high as that under the new method. These three types of data clearly show that the task completion efficiency under the new method is better.
Track planning is mentioned in the analysis of UAV mission planning methods, which is the core of mission execution. The selection of an optimal track plays a decisive role in the completion of the UAV mission. The shorter the length of the optimal track, the higher the flight efficiency of the UAV. The traditional method is defined as Method A, and the method in this paper is defined as Method B. The optimal path planning length of five flight missions under the two methods is tested, and the test results are shown in Figure 5.
Electronics 2022, 11, 4238 10 From the data in Table 1, it can be concluded that under the two task planning m ods, there is a significant gap in the distance, time and task completion of the UAV. Un the same task, the distance of the traditional method is nearly 40 m higher than that of new method, and it takes more than 2 s compared to the new method. However, the completion under the traditional method is not as high as that under the new meth These three types of data clearly show that the task completion efficiency under the method is better.
Track planning is mentioned in the analysis of UAV mission planning meth which is the core of mission execution. The selection of an optimal track plays a deci role in the completion of the UAV mission. The shorter the length of the optimal track higher the flight efficiency of the UAV. The traditional method is defined as Method and the method in this paper is defined as Method B. The optimal path planning len of five flight missions under the two methods is tested, and the test results are show Figure 5. It is easy to see from the histogram in Figure 5 that the optimal path planning len under method B is shorter than that under method A in the five flight missions. Am them, the planning length gap of task 5 is the smallest, and that of task 4 is the larg When the track length of Task 4 is planned, the length planned by Method A exceeds m, and the length planned by Method B is still below 200 m. These results show that optimal track planned in this paper is shorter than that planned by traditional meth and it can provide the shortest and optimal path for UAV mission execution.
Generally, before performing UAV tasks, the UAV operators need to check and e uate the route planning. Figure 6 shows the ratings given by operators for the route p ning under the two methods, the flight missions of which are still the five missions m tioned above. The traditional method refers to the route planning method without spe optimization algorithm. It is easy to see from the histogram in Figure 5 that the optimal path planning length under method B is shorter than that under method A in the five flight missions. Among them, the planning length gap of task 5 is the smallest, and that of task 4 is the largest. When the track length of Task 4 is planned, the length planned by Method A exceeds 200 m, and the length planned by Method B is still below 200 m. These results show that the optimal track planned in this paper is shorter than that planned by traditional methods, and it can provide the shortest and optimal path for UAV mission execution.
Generally, before performing UAV tasks, the UAV operators need to check and evaluate the route planning. Figure 6 shows the ratings given by operators for the route planning under the two methods, the flight missions of which are still the five missions mentioned above. The traditional method refers to the route planning method without specific optimization algorithm. It can be seen from Figure 6 that the UAV operators are very strict in their assessm and scoring of the route planning, and the scores are basically below 9 points. The sc of route planning under the new method is higher than that under the traditional met in the five missions. In the route planning of Task 3, both methods get the highest sc the traditional method is more than 8 points, while the new method is more than points. These scoring results can reflect that the quality of route planning under the n method is better than that of the traditional method.
In this paper, multi-objective optimization algorithm is applied to UAV mission p ning to improve the efficiency of mission planning. For the specific effect, the time of U task planning is tested under the two algorithms. The specific flight tasks are the five ta mentioned above, and the test results are shown in Figure 7. It can be seen that in the five tasks, the time spent for UAV task planning under two algorithms is very different. As far as the planning of task 3 is concerned, it tak lot of time under both algorithms. The conventional algorithm takes more than 70 s, w the multi-objective optimization algorithm takes more than 60 s. In general, in each t  It can be seen from Figure 6 that the UAV operators are very strict in their assessment and scoring of the route planning, and the scores are basically below 9 points. The score of route planning under the new method is higher than that under the traditional method in the five missions. In the route planning of Task 3, both methods get the highest score: the traditional method is more than 8 points, while the new method is more than 8.5 points. These scoring results can reflect that the quality of route planning under the new method is better than that of the traditional method.
In this paper, multi-objective optimization algorithm is applied to UAV mission planning to improve the efficiency of mission planning. For the specific effect, the time of UAV task planning is tested under the two algorithms. The specific flight tasks are the five tasks mentioned above, and the test results are shown in Figure 7. It can be seen from Figure 6 that the UAV operators are very strict in their assessm and scoring of the route planning, and the scores are basically below 9 points. The s of route planning under the new method is higher than that under the traditional me in the five missions. In the route planning of Task 3, both methods get the highest sc the traditional method is more than 8 points, while the new method is more than points. These scoring results can reflect that the quality of route planning under the method is better than that of the traditional method.
In this paper, multi-objective optimization algorithm is applied to UAV mission p ning to improve the efficiency of mission planning. For the specific effect, the time of U task planning is tested under the two algorithms. The specific flight tasks are the five t mentioned above, and the test results are shown in Figure 7. It can be seen that in the five tasks, the time spent for UAV task planning unde two algorithms is very different. As far as the planning of task 3 is concerned, it tak lot of time under both algorithms. The conventional algorithm takes more than 70 s, w the multi-objective optimization algorithm takes more than 60 s. In general, in each  It can be seen that in the five tasks, the time spent for UAV task planning under the two algorithms is very different. As far as the planning of task 3 is concerned, it takes a lot of time under both algorithms. The conventional algorithm takes more than 70 s, while the multi-objective optimization algorithm takes more than 60 s. In general, in each task, the task planning under the multi-objective optimization algorithm takes less time than the conventional algorithm, which also shows that the task planning method combined with the multi-objective optimization algorithm is more efficient.
After the flight mission, there is a satisfaction survey of completion. In this paper, 20 conventional tasks are selected to be executed by UAVs in turn, and their satisfaction with the completion of tasks is investigated. Task planning routes include those under conventional algorithms and those under multi-objective optimization algorithms. The results of the survey are shown in Figure 8.
Electronics 2022, 11,4238 the task planning under the multi-objective optimization algorithm takes less tim the conventional algorithm, which also shows that the task planning method com with the multi-objective optimization algorithm is more efficient.
After the flight mission, there is a satisfaction survey of completion. In this pa conventional tasks are selected to be executed by UAVs in turn, and their satisfactio the completion of tasks is investigated. Task planning routes include those under c tional algorithms and those under multi-objective optimization algorithms. The re the survey are shown in Figure 8. It can be seen that the satisfaction of each task is different based on whether t planning route is conducted under the conventional algorithm or the multi-object timization algorithm. Generally, it shows a fluctuating trend, because each task ha ferent number of tasks. In contrast, the satisfaction of multi-objective optimizatio rithm in each task is higher than that of conventional algorithm, and the overall s tion is 2.26% higher.

Discussion
In recent years, the path planning algorithm of UAV has become increasingly gent and complex. The manual planning on paper maps has gradually changed t puter-based planning using digital maps. For different threat environments, find corresponding route planning algorithm is the focus of future UAV route plannin traditional UAV trajectory planning method is only a method to avoid dangerous in theory, which is mainly based on the completion of tasks. However, consider limitations of UAV, the existing planning methods are no longer applicable. In this future research must also take into account the physical constraints of the UAV i route planning, and plan accurate, short-time flights that meet all constraints. Fina existing UAV route planning algorithms are mainly concentrated on a single UAV joint military and multi task areas, more research and resources need to be inve extend the route planning method to the joint planning field involving multiple U

Conclusions
With the progress of technology, the application field of UAV has become i ingly extensive and mature. When a UAV executes flight mission, task allocati  It can be seen that the satisfaction of each task is different based on whether the task planning route is conducted under the conventional algorithm or the multi-objective optimization algorithm. Generally, it shows a fluctuating trend, because each task has a different number of tasks. In contrast, the satisfaction of multi-objective optimization algorithm in each task is higher than that of conventional algorithm, and the overall satisfaction is 2.26% higher.

Discussion
In recent years, the path planning algorithm of UAV has become increasingly intelligent and complex. The manual planning on paper maps has gradually changed to computer-based planning using digital maps. For different threat environments, finding the corresponding route planning algorithm is the focus of future UAV route planning. The traditional UAV trajectory planning method is only a method to avoid dangerous spaces in theory, which is mainly based on the completion of tasks. However, considering the limitations of UAV, the existing planning methods are no longer applicable. In this regard, future research must also take into account the physical constraints of the UAV itself in route planning, and plan accurate, short-time flights that meet all constraints. Finally, the existing UAV route planning algorithms are mainly concentrated on a single UAV. In the joint military and multi task areas, more research and resources need to be invested to extend the route planning method to the joint planning field involving multiple UAVs.

Conclusions
With the progress of technology, the application field of UAV has become increasingly extensive and mature. When a UAV executes flight mission, task allocation and route planning are the fundamental preconditions to complete the mission successfully. At present, the traditional task planning methods and path search algorithms are too outdated to keep up with the technological developments, resulting in low efficiency of task planning, which hinders the successful completion of tasks. Multi-objective optimization algorithm is the product of intelligent technology and information technology. Its application in UAV intelligent planning modeling and path optimization is conducive to promoting the development of and research into UAVs.

Conflicts of Interest:
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.