Table of Contents Author Guidelines Submit a Manuscript
International Journal of Aerospace Engineering
Volume 2019, Article ID 3504248, 12 pages
https://doi.org/10.1155/2019/3504248
Research Article

A Two-Layer Task Assignment Algorithm for UAV Swarm Based on Feature Weight Clustering

1School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710129, China
2Shaanxi Key Laboratory of Integrated and Intelligent Navigation, Xi’an 710068, China
3The 20th Research Institute of CETC, Xi’an 710068, China

Correspondence should be addressed to Xiaowei Fu; nc.ude.upwn@wxf

Received 13 March 2019; Accepted 3 September 2019; Published 26 November 2019

Academic Editor: Jeremy Straub

Copyright © 2019 Xiaowei Fu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For the large-scale operations of unmanned aerial vehicle (UAV) swarm and the large number of UAVs, this paper proposes a two-layer task and resource assignment algorithm based on feature weight clustering. According to the numbers and types of task resources of each UAV and the distances between different UAVs, the UAV swarm is divided into multiple UAV clusters, and the large-scale allocation problem is transformed into several related small-scale problems. A two-layer task assignment algorithm based on the consensus-based bundle algorithm (CBBA) is proposed, and this algorithm uses different consensus rules between clusters and within clusters, which ensures that the UAV swarm gets a conflict-free task assignment solution in real time. The simulation results show that the algorithm can assign tasks effectively and efficiently when the number of UAVs and targets is large.

1. Introduction

UAV swarm consists of a large number of small UAVs [1], and the cooperative task and resource assignment of UAV swarm is to real-time coordinate the UAV swarm in order to achieve an overall mission objective. A mission can be divided into different tasks, and a number of specialized UAVs are then assigned to solve each task cooperatively [24].

The CBBA algorithm is a kind of the distributed auction-based algorithms to resolve multiple agent task assignment problem [5], and it is a multiassignment decentralized auction approach with a consensus protocol that guarantees a conflict-free solution despite possible inconsistencies in situational awareness. An extension to CBBA [6] has enabled incorporation of heterogeneity in the UAV capabilities and task time windows, which significantly extends the mission characteristics that can be handled. Coupled CBBA is designed to create feasible assignments for a network of autonomous UAVs in the presence of the temporal coupling constraints [7], and temporal constraints include several specified relationships between the chosen visit times for a subset of tasks. The consensus phase of the CBBA algorithm relies on coordinated communication between all UAVs, which is achieved by propagating UAVs’ bid information through the communication links. As the number of UAVs in the network increases, this consensus approach may overflow the network bandwidth. But in these works, the communication links between all UAVs have high bandwidth, low latency, low cost, and high reliability. However, the real communication links between UAVs do not possess all of these characteristics. Asynchronous CBBA extends CBBA to account for more realistic asynchronous communication protocols by minimizing communication load while preserving the convergence properties [8], and it produces consistent task assignments using relatively little bandwidth and without requiring artificial time delays. The comparisons between global and local convergence in asynchronous consensus algorithms are discussed in [9]. Bid warped consensus-based bundle algorithm deals with the task assignment problems that global information consistency assumptions are difficult to enforce [10], and it relies only on a local best estimate of the global information state, which is referred to as local information consistency. CBBA with partial replanning (CBBA-PR) extends the CBBA algorithm to allocate new appeared tasks quickly without a full reallocation of existing tasks [11], and it enables multi-UAV team to trade-off between convergence time and increased coordination by resetting a portion of their previous allocation at every round of bidding on tasks.

For the task assignment problem of the UAV swarm, the existing CBBA algorithm will need more communication times as the number of UAVs increases; moreover, each UAV of the swarm may have different capacity and number of resources, which are not considered in the existing CBBA algorithms.

Although the aforementioned works have made some improvements of the CBBA algorithm, they still cannot adapt to the characteristics of large number of UAVs in the UAV swarm. The computational complexity of task assignment is still a crucial problem in the use of the UAV swarm. The hierarchical method is a feasible approach to reduce the computation cost of complex optimization problems, which divides the problem into several levels of subproblems. Each level of subproblem has its own objectives and constraints. The output of one level becomes the input of the next level. By solving the subproblems on different levels in order, the original problem can be solved. Although this approach may miss the best solution, it can produce satisfactory solutions in much less time than other methods.

This paper proposes a two-layer task assignment algorithm based on feature weight clustering, which could decompose the large-scale task assignment problem of the UAV swarm effectively, and the efficiency of task assignment is greatly improved.

2. Task Assignment Model of the UAV Swarm

In a prior work [12], the task resource, task reward, and task assignment models are presented as follows.

2.1. Task Resource Model

Given a swarm of heterogeneous UAVs and a set of targets , the UAV swarm is divided into two subsets according to the task resource type of each UAV; is the set of electronic interfering UAVs and is the set of attack UAVs. Each UAV belongs to only one of the two subsets, and it carries kinds of task resources. The task resource vector of the attack UAV is represented by , where , , indicates the quantity of th type of weapons carried by UAV ; and the task resource vector of the electronic interfering UAV is represented by , where , , indicates the quantity of th type of electronic interfering resources carried by UAV .

To attack target , the required type and quantity of weapons are , where , , indicates the required quantity of th type of weapons to attack target . To interfere target , the required type and quantity of electronic interfering resources are , where , , indicates the required quantity of th type of resources to interfere target .

To interfere and attack target , the total amount of task resources carried by UAVs must meet the task requirements. where and , respectively, indicate whether the th weapon resource or interference payload of is used to the tasks on the target; and indicate the number of the th weapon resources or interference payload of , respectively.

2.2. Task Reward Model

Definition 1 (the initial reward of attack task). Suppose the damage probability of to one target is , the initial reward of attack task is defined as where and are the value and threat level of target .
The attack task reduces the threat level of the target; therefore, the threat level of target that has been attacked is

Definition 2 (the initial reward of electronic interference task). As shown in Figure 1, the electronic interference task is related to the attack task, and it should be performed before attack task a certain period of time. The UAV swarm assigns an attack task to a target at first and then estimates the start time of electronic interference task according to the time of the attack task.

Figure 1: Schematic diagram of electronic interference process [12].

The maximum interference distance is a function of and the angle , which is

The reward of the electronic interference task is defined as where indicates the maximum interference distance of UAV and represents the distance between the UAV and the target .

2.3. Task Assignment Model

The task and resource assignment model of the UAV swarm is described as where denotes whether UAV is assigned to target . represents the maximum number of tasks of each UAV. Vector represents an ordered sequence of task path of . indicates the length of the path that the UAV performs the current task sequence. The fractional function represents the total task reward that is calculated as described in equations (2) and (5). denotes whether UAV with th resource is assigned to target . indicates the number of the th resources of that is assigned to target , and indicates the number of the th resources of . indicates the required number of the th resources for the tasks on target .

3. UAV Clustering Based on Distance and Task Resources

3.1. Mathematical Model of Cluster Analysis

Cluster analysis is the process of partitioning a set of data objects into subsets. Each subset is a cluster, such that objects in a cluster are similar to one another yet dissimilar to objects in other clusters [13].

Given a set of data points in space, the position with the smallest distance from point to the positions is called the nearest position of the point . The distance measure to the nearest position is recorded as , where is called as the distance measure from point to position . The sum of the minimum distance metrics for points is .

According to the above description, the clustering problem can be converted into an optimization problem, which is described as

Input. data points in ;

Output. positions in so that the sum of the minimum distance measures of points is minimized.

3.2. -Medoids Clustering Algorithm

Generally, compared to -means clustering algorithm, -medoids clustering algorithm showed its superiority in execution time, sensitivity towards outlier data, and reduction of noise since it employs the method of minimization of the sum of dissimilarities of datasets [14]. Although there are many enhanced -means algorithms [15, 16], we still choose the -medoids algorithm for clustering from the aspects of computational complexity and algorithm efficiency.

The optimization objective function of the -medoids clustering algorithm can be generally defined as follows: where represents the sum of the deviations between each data point in the data point set and its cluster center point; represents the points in ; represents the center point of cluster (both and are -dimensional); represents the -order metric between and , typically the square of the Euclidean distance in the distance space () is used.

The -medoids clustering algorithm is described as [17]

Input. The number of clusters , a set of data points containing points

Output. clusters and the subset of data points they contain.

Step 1. From the data point set, data points are randomly selected to form a current cluster center point set. Each of the data point represents the initial center point of a cluster.

Step 2. Calculate the objective function value according to equation (10) and assign all data points to the cluster represented by the nearest center point.

Step 3. For each point of the data point set, the following procedure is performed. Try to replace each existing center point with the current point , and calculate the objective function value according to equation (10). Compare the objective function values of all candidate alternatives, and the center point of the cluster with the minimum value is replaced by .

Step 4. Finally, the clusters and their center points are obtained; the optimized clustering results of the data points contained therein are collected.

3.3. Clustering Model Based on Feature Weight

In the cluster analysis, in order to reflect the different effects of each attribute pair on forming a good structural clustering subset and to describe the difference between point and point , a weighted “distance” metric can be defined (Norm), i.e., [18] where the specific definition of th attribute is determined according to its characteristics. If the th attribute is an unordered category attribute, it is defined as

If the th attribute is an ordered attribute, it is defined as

For the feature weight assignment problem, the optimal assignment of feature weight parameters should be determined by using the distribution of data point sets and class attribution. Feature weights must meet the following constraints:

The optimization objective function of the algorithm is where represents a hard-divided membership matrix; represents a cluster center point set; represents feature weight parameters. When the data point belongs to a cluster with a cluster center , ; otherwise, .

3.4. UAV Clustering Based on Distance and Task Resources

To measure the similarity between UAVs, two attributes are used to build the objective function model. In addition to the distance attribute, the balance of task resource of each UAV cluster is also taken as the optimization objective. The UAV swarm has types of different task resources, and the UAV resource vector is expressed as

All task resources in UAV cluster is described as

Then, the balance of task resource of UAV cluster is evaluated by the variance of various task resources: where

In addition, the distance measurement of UAVs is where is the position of and is the position of center point of UAV cluster .

In summary, the final objective function is where is the feature weight of the distance metric, and is the feature weight of the balance of task resource. Choosing a reasonable feature weight matrix can ensure that the task resources in the UAV cluster are relatively balanced on the basis of the smallest distance.

4. Two-Layer Task Assignment Algorithm Based on Feature Weight Clustering

4.1. Algorithm Description

According to the objective function (equation (18)), the UAV swarm is partitioned into UAV clusters represented by . For UAV cluster , .

Each UAV cluster initially assigns tasks of the target set based on the CBBA algorithm, and , , and represent the task bundle, the list of winning UAVs, and the list of winning scores of UAV cluster , respectively. The consensus rule between UAV clusters is shown as Table 1.

Table 1: The consensus rules between UAV clusters.

In Table 1, and represent the winning cluster that should be assigned to target from the view of the sender cluster and the receiver cluster , respectively.

According to the results of the consensus between UAV clusters, UAVs in the same cluster will negotiate to get a conflict-free task assignment solution. In this process, the successful bidders of some tasks may come from other clusters, so the consensus rules need to be modified, as shown in Table 2, and represent the winning UAV that should be assigned to target from the view of the sender UAV and the receiver UAV , respectively.

Table 2: The consensus rules between UAVs within a UAV cluster.
4.2. Fault Tolerance Analysis

One of the advantages of the UAV swarm is its high fault tolerance. This algorithm can successfully assign tasks for a certain UAV that cannot communicate with others at a certain time.

It is assumed that a UAV cannot communicate with others at a certain time. If the task assignment procedure has not been triggered, the tasks will be assigned between UAVs that can communicate with each other after the procedure triggered. The proposed algorithm does not need to know the number of UAVs prior to the procedure. If has been assigned some tasks, maybe it will affect the effectiveness of the UAV swarm. The UAV swarm will redistribute the remaining tasks as needed after tasks are finished.

4.3. Performance Analysis

Compared with the baseline CBBA algorithm, the proposed two-layer algorithm can significantly reduce the number of communication times and the corresponding iteration round required to achieve task consensus, thus improving the computational efficiency. This performance improvement is mainly due to the communication mode in consensus process of the two-layer structure.

In the consensus of the baseline CBBA algorithm, each UAV must send local task assignment information to all other UAVs while receiving task assignment information from them. Figure 2 shows the communication mode of in the consensus process in the baseline CBBA algorithm. sends its local task assignment information to other drones in the UAV swarm and updates the local information according to the consensus rules after receiving the information from other UAVs.

Figure 2: The communication mode in the consensus process in the baseline CBBA algorithm.

The proposed two-layer algorithm divides the UAV swarm into a two-layer structure, which separates the consensus process into the consensus process between clusters and within each cluster, and reduces the complexity of consensus. As shown in Figure 3, that belongs to cluster only needs to transmit the local task assignment information to the other 3 UAVs in cluster to achieve local consensus within the cluster. Cluster then communicates with other UAV clusters, which in turn achieves global task assignment consensus.

Figure 3: The communication mode in the consensus process in the two-layer algorithm.

Extending the above comparison to all UAVs among the UAV swarm, it can be seen from this comparison that the number of communication times to achieve task consensus is significantly reduced. Through the two-layer structure, the complexity of the consensus process is significantly reduced, thereby improving the computational efficiency.

5. Simulation

In order to prove the validity and efficiency of the two-layer task assignment algorithm for the UAV swarm with feature weight clustering, several sets of simulation experiments were designed and compared with the CBBA algorithm in [5].

In this study, the energy consumption is not considered, after the mission objective is achieved, and the operator in the ground control station will send return to base command to the swarm. We assumed that each UAV flies autonomous and can communicate information with others of the UAV swarm as necessary.

5.1. Algorithm Validation

Six attack UAVs are marked , 6 electronic interference UAVs are marked , and 6 targets are in a rectangular area. The speed of each UAV is 50 m/s, and the maximum detection distance is 300 m. Assume that the UAV swarm is set to form four equal-sized UAV clusters.

The initial positions and task resource vectors of all UAVs and targets are generated in a random manner. Each UAV has three kinds of task resources, that is, attack UAVs have three kinds of weapons, and electronic interference UAVs have three kinds of interference payloads. Correspondingly, each target’s attack task and electronic interference task also require three kinds of task resources. The initial states of the attack UAVs and the electronic interference UAVs are shown in Tables 3 and 4, respectively. The initial state of the target is shown in Table 5.

Table 3: The initial state of attack UAVs.
Table 4: The initial state of electronic interference UAVs.
Table 5: The initial state of targets.
5.1.1. Feature Weight Clustering Validity Verification

If the UAV swarm is clustered according to the distance measure, the clustering results obtained are shown in Figure 4. The clustering results based on the distance and task resource feature weights proposed in this paper are shown in Figure 5. In these figures, denotes UAV ID, and indicates the cluster ID to which the UAV belongs. The attack UAVs are denoted by a triangle, and the electronic interference UAVs are denoted by a circle. Each UAV cluster is denoted by a different color. Table 6 shows the comparison of cluster members and task resources between the two clustering results.

Figure 4: The clustering result obtained by normal cluster.
Figure 5: The clustering result obtained by the feature weight cluster.
Table 6: The cluster member and task resource obtained by two kinds of clustering.

It can be seen from Figure 4 and Table 6 that the task resources of the clusters that are partitioned according to distance are completely unbalanced. For example, the weapon resource of cluster is seriously unbalanced; cluster contains only one attack UAV and there is no third type of weapon resource; contains only one interference UAV and there is no second type of interference payload. This unbalance will seriously affect the task resource assignment process and greatly increase the difficulty of achieving consensus distribution results.

It can be seen from Figure 5 and Table 6 that the clusters that are partitioned according to the feature weight clustering not only maintain the relatively close spatial distance between the UAVs among clusters but also achieve the balance of task resources. All three clusters have all types of task resources, and the number of various task resources is relatively balanced.

5.1.2. Algorithm Effectiveness Verification

To verify the effectiveness of the proposed algorithm, the task and resource assignment results obtained by the basic CBBA algorithm of [5] and the two-layer task assignment algorithm proposed in this paper are compared in the same scenario and initial state (as described in Tables 35). Figures 6 and 7 show the task sequence of the UAV swarm obtained by the CBBA algorithm of [5] and the two-layer assignment algorithm proposed in this paper, respectively. In these figures, the horizontal axis represents the timeline, and 12 rows on the vertical axis represent the task sequence of 12 UAVs. On the time axis, different color cylinders are used to represent the time intervals of UAV’s tasks.

Figure 6: The task assignment obtained by the CBBA algorithm of [5].
Figure 7: The task sequence obtained by the two-layer algorithm.

From the comparison of the two figures, the following can be seen. (1) The basic CBBA algorithm cannot fully utilize the resources of all the UAVs in the swarm, and the task assignment is unbalanced. For example, and are assigned 4 tasks, while only has one task, and is not assigned any task. The two-layer assignment algorithm makes full use of the resources of each UAV, and the task assignment solution is balanced.

(2) Due to the unbalanced results of CBBA task allocation, the task completion time of the UAV swarm will increase correspondingly. Because the two-layer assignment algorithm can make full use of the performance and resources of each UAV, the UAV swarm can complete the task earlier. Under the scenario, the task completion time of the CBBA algorithm is 106 s, while the two-layer assignment algorithm is only 84 s.

Task assignment results for the UAV swarm was shown in Table 7.

Table 7: The task assignment result obtained by the two-layer algorithm.
5.2. Performance Analysis of the Two-Layer Task Assignment Algorithm

In order to comprehensively explore and compare the performance of the two-layer task assignment algorithm and the CBBA algorithm, this section takes the number of targets and UAVs as independent variables and compares the algorithm time, total task score, task completion rate, task completion time, and the number of communication times. The initial positions and task resource vectors for all UAVs and targets are generated in a random manner.

5.2.1. Number of UAVs

In order to explore the adaptability of the algorithm to the number of UAVs, the number of targets is set to 12, and the number of UAVs in the swarm is set to 5, 10, 15, 20, and 25, respectively. Among the swarm, the number of attack UAVs and electronic interference UAVs is equal (or approximately equal). The UAV swarm is partitioned into different number of clusters, shown in Table 8.

Table 8: The clustering form of the two-layer algorithm.

The statistical results of task completion rate, algorithm calculation time, and communication times are shown in Figures 810. From the statistical results presented, the following can be seen: (1)When the number of UAVs is small (for example, 5 UAVs perform tasks on 12 targets), the task completion rates of the two algorithms are lower. The reason is that the resources of the UAV swarm are too insufficient to meet the need of tasks for all targets. Even in this situation, the task completion rate of the two-layer assignment algorithm is still higher than that of the CBBA algorithm. This is due to fact that the two-layer assignment algorithm can make full use of the resources of each UAV to ensure the balance of task assignment(2)With the increase of the number of UAVs, the calculation time of the two algorithms increases correspondingly. However, the CBBA algorithm increases exponentially, while the two-layer assignment algorithm grows slowly. The reason is that the two-layer assignment algorithm divides large-scale cooperative problems into several small-scale problems(3)With the increase of the number of UAVs, the communication times increase correspondingly. The two-layer assignment algorithm increases slowly due to the fact that each UAV only needs to communicate with other UAVs in the same cluster in most situations, while in the CBBA algorithm, each UAV theoretically needs to communicate with all the UAVs in the whole swarm

Figure 8: The comparison of task completion rate obtained by two types of algorithm.
Figure 9: The comparison of calculation time obtained by two types of algorithm.
Figure 10: The comparison of communication processing times obtained by two types of algorithm.
5.2.2. Number of Targets

In order to explore the adaptability of the algorithm to the number of targets, the number of targets is set to 5, 10, 15, 20, and 25, respectively. The UAV swarm consists of 12 UAVs, including 6 attack UAVs and 6 electronic interference UAVs. Four sets of simulation examples are set up, as shown in Table 9. For each set of examples, the algorithm calculation time, total task score, and task completion rate are compared and analyzed.

Table 9: Simulation examples.

The statistical results of task completion rate, algorithm calculation time, and total task score for are shown in Figures 1113, respectively. From the statistical results presented, the following can be seen: (1)As the number of targets increases, the task completion rates of both algorithms decrease accordingly. Overall, the two-layer assignment algorithm has a higher task completion rate than the CBBA algorithm. As mentioned above, the two-layer assignment algorithm can make full use of the resources of each UAV to ensure the balance of task assignment. From the three examples of the two-layer task assignment algorithm, it can be seen that when the number of targets is not particularly large (within 20), the third case (4 UAV clusters) has the best effect; but when the number of targets increases to 25, the difference in task completion rates of the three samples is small. This is due to the fact that the number of tasks exceeds the upper limit of what the UAV swarm can accomplish(2)With the increase of the number of targets, the calculation time of the CBBA algorithm increases exponentially, while that of the two-layer assignment algorithm increases relatively slowly. From the three examples of the two-layer task assignment algorithm, it can be seen that when the swarm is grouped into four UAV clusters, the calculation time of the algorithm is relatively short, but the advantage is not obvious(3)As the number of targets increases, the total task scores of the two algorithms increase accordingly. This is due to the fact that the more the number of targets, the more tasks are assigned and the higher the total task score obtained. Overall, the total task score obtained by the two-layer assignment algorithm is smaller than the CBBA algorithm. This is due to the fact that the CBBA algorithm assigns tasks from a global perspective at the expense of longer computation time and more complex consensus processes and achieves an approximate optimal solution for the entire UAV swarm. The two-layer algorithm sacrifices some task rewards and achieves the real-time and high efficiency of task assignment when the number of targets is large. It can be seen from the three examples of the two-layer task assignment algorithm that the smaller the number of UAV clusters, the greater is the task reward

Figure 11: The comparison of total completion rate obtained by two types of algorithm.
Figure 12: The comparison of calculation time obtained by two types of algorithm.
Figure 13: The comparison of total task score obtained by two types of algorithm.

In summary, the proposed two-layer task assignment algorithm can make full use of task resources and has better real-time performance with the sacrifice of the global task reward. The two-layer task assignment algorithm has better adaptability to the number of UAVs and targets and is more suitable for the high real-time requirements of the UAV swarm task assignment problem. Different numbers of UAV clusters have a certain impact on the performance of the two-layer task assignment algorithm. The smaller number of UAV clusters does not reflect the advantages of the two-layer structure. The larger number of clusters leads to too many iterations of intercluster consensus. It can be seen from the simulation verification that when the number of UAV clusters is approximately equal to the number of UAVs among each cluster, the best comprehensive performance can be obtained.

6. Conclusion

In this paper, the feature weight clustering algorithm is applied to UAV swarm clustering, and a two-layer task assignment algorithm based on the basic CBBA algorithm is proposed. The feature weight clustering algorithm can make the two-layer task assignment algorithm more effectively. The algorithm uses different consistency rules between clusters and within clusters and can achieve task assignment consensus quickly and efficiently. The simulation results show that compared with the basic CBBA algorithm, the proposed algorithm can assign tasks effectively in real time when the number of UAVs and targets is large.

Data Availability

The numerical data used to support the findings of this study is included within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Acknowledgments

This research was funded by the foundation of Shaanxi Key Laboratory of Integrated and Intelligent Navigation (grant number SKLIIN-20180104) and the Natural Science Foundation of Shaanxi Province (grant number 2019JQ-936).

References

  1. S. Cambone, Unmanned Aircraft Systems Roadmap 2005-2030, United States dept. of Defense office of the Secretary of Defense, 2005.
  2. A. K. Whitten, H. L. Choi, L. B. Johnson, and J. P. How, “Decentralized task assignment with coupled constraints in complex tasks,” in Proceedings of the American Control Conference, pp. 1642–1649, San Francisco, CA, USA, 2011. View at Publisher · View at Google Scholar
  3. L. F. Bertuccelli and M. L. Cummings, “Scenario-based robust scheduling for cooperative human-UAV visual search tasks,” in IEEE Conference on Decision and Control and European Control Conference, pp. 5702–5707, Orlando, FL, USA, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. J. George, P. B. Sujit, and J. B. Sousa, “Search strategies for multiple UAV search and destroy tasks,” Journal of Intelligent & Robotic Systems, vol. 61, no. 1-4, pp. 355–367, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. H. L. Choi, L. Brunet, and J. P. How, “Consensus-based decentralized auctions for robust task assignment,” IEEE Transactions on Robotics, vol. 25, no. 4, pp. 912–926, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Ponda, J. Redding, H.-L. Choi, J. P. How, M. A. Vavrina, and J. Vian, “Decentralized planning for complex missions with dynamic communication constraints,” in Proceedings of the 2010 American Control Conference, Baltimore, MD, USA, 2010. View at Publisher · View at Google Scholar
  7. A. K. Whitten, H. L. Choi, L. B. Johnson, and J. P. How, “Decentralized task assignment with coupled constraints in complex missions,” in Proceedings of the 2011 American Control Conference, pp. 1642–1649, San Francisco, CA, USA, 2011. View at Publisher · View at Google Scholar
  8. L. B. Johnson, S. Ponda, H.-L. Choi, and J. P. How, “Improving the efficiency of a decentralized tasking algorithm for UAV teams with asynchronous communications,” in AIAA Guidance, Navigation, and Control Conference (GNC), Toronto, Ontario, Canada, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. L. B. Johnson, S. S. Ponday, H.-L. Choi, and J. P. How, “Asynchronous decentralized task allocation for dynamic environments,” in Infotech@Aerospace 2011, American Institute of Aeronautics and Astronautics, St. Louis, Missouri, 2011. View at Google Scholar
  10. L. B. Johnson, H. L. Choi, S. S. Ponda, and J. P. How, “Decentralized task allocation using local information consistency assumptions,” Journal of Aerospace Information Systems, vol. 14, no. 2, pp. 103–122, 2017. View at Publisher · View at Google Scholar · View at Scopus
  11. N. Buckman, H. L. Choi, and J. P. How, “Partial replanning for decentralized dynamic task allocation,” in AIAA Scitech 2019 Forum, San Diego, California, 2019. View at Publisher · View at Google Scholar
  12. X. Fu, P. Feng, and X. Gao, “Swarm UAVs task and resource dynamic assignment algorithm based on task sequence mechanism,” IEEE Access, vol. 7, no. 1, pp. 41090–41100, 2019. View at Publisher · View at Google Scholar
  13. J. Han, Data Mining: Concepts and Techniques, Elsevier, 2005.
  14. K. G. Soni and A. Patel, “Comparative analysis of K-means and K-medoids algorithm on IRIS data,” International Journal of Computational Intelligence Research, vol. 13, no. 5, pp. 899–906, 2017. View at Google Scholar
  15. S. Visalakshi and V. Radha, “An enhanced K-means clustering based outlier detection techniques to improve water contamination detection and classification,” Computational Intelligence in Data Mining - Volume 1, vol. 31, pp. 303–313, 2015. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Chen, “Nonlinear time series modelling and prediction using Gaussian RBF networks with enhanced clustering and RLS learning,” Electronics Letters, vol. 31, no. 2, pp. 117-118, 1995. View at Publisher · View at Google Scholar · View at Scopus
  17. A. K. Jain and R. C. Dubes, “Algorithms for clustering data,” Technometrics, vol. 32, no. 2, pp. 227–229, 1988. View at Google Scholar
  18. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, En Broeck the Statistical Mechanics of Learning Rsity, 2nd edition, 2000.