Research on Reconfiguration Control Strategy of UAV Cluster

1. Introduction

With the development of artificial intelligence and UAV technology, UAV cluster has attracted more and more attention [1]. Compared with individuals, clusters have greater advantages in the difficulty and complexity of executing tasks, but different from a single or fewer drone formations, clusters have dozens or even more drones, and their formation control has become a prerequisite for use. Many scholars have conducted a lot of theoretical and experimental research on UAV formation control [2,3,4,5,6,7,8]. The methods of algorithm design, communication interaction and obstacle avoidance control are commonly used to analyze the formation change of UAV cluster formation. Liao [9] has studied the UAV formation reconstruction control based on the variable step size MPC-APCMPIO algorithm, and established the UAV movement model and the virtual leader group formation control structure. Fu [10] realized the reconstruction method of distributed obstacle avoidance control of UAV formation by designing the position and speed consistency control law among UAV, each UAV and virtual leader. Song [11] divided the route planning of UAV formation change into two stages: rough planning and fine planning, and completed UAV formation change under two scenarios. Peng [12] regards UAV formation transformation as a minimum matrix transformation problem and proposes a UAV formation flight algorithm based on greedy path strategy to solve the sub-optional solution of this problem. The above studies have discussed formation control methods, but there are few studies on the measurement of cluster capability and reconstruction cost in UAV cluster formation reconstruction.

Therefore, this paper first analyzes the cluster capability measurement according to the cluster configuration change, formation reconstruction principle, and configuration execution ability. Then the group behavior is modeled by group behavior rules, reconfiguration topology analysis, and reconfiguration cost measurement. Finally, based on the cluster parameters and configuration characteristics, simulation experiments were carried out to obtain the change curve of the reconstruction cost with time and the trajectory movement diagram of the UAV in different configurations. The main contributions of this paper are as follows:

• Carry out the mechanism analysis of cluster reconstruction and give the measurement method of cluster capability.
• Modeling the cluster behavior rules and formation reconfiguration cost for reconfiguration strategy.
• Analyzing the simulation analysis by reconstructing cluster variety of 10 drone formation as an example, obtained the related characteristic of the cluster refactoring changes.

2. Related Work

2.1. Basic Conception

A cluster is composed of multiple groups, and a Group is composed of multiple units. Of course, a group can also be subdivided into a group I and a Group II, etc. A group I consists of multiple groups II, and a group II consists of groups of a lower group, up to the smallest group of 2 or 3 individuals. The purpose of using cluster strategy is to achieve “1+1>2 “effect.

2.2. Flight Formation Mechanism

A cluster drones usually maintain a certain formation during formation flight, the common formation has echelons, wedges, columns, horizontal lines, serpentine teams, etc., the configuration is triangular, humanoid, diamond, arrow, dart, wedge, room shape, etc. In the same way, drone clusters fly in organized formations when carrying out missions, and not every drone flies completely free. Although the scale of the cluster is much larger than the traditional formations with several sorties, there are still similarities in the flight formation. As shown in Figure 1, the formation of the three-aircraft formation is basically the same as that of the multi-aircraft cluster.

2.3. Control Logic Method

Cluster motion control is the modeling of relationships between units and groups, groups and clusters, usually following the basic rules of “separation”, “cohesion” and “alignment”. There are many similarities between drone cluster and biological cluster [13]. There is no central control node in biological cluster, and there is no traditional command and control station in UAV cluster. Each UAV makes decisions and actions independently according to its own perceived information [14].

The control structure of UAV cluster can be divided into three categories: centralized control, distributed control and distributed control [15]. Centralized control uses one center or multiple sub-centers to effectively control the cluster. Some studies also refer to the sub-center mode as hierarchical control [16]. Contact with assigned drones through the center. Distributed control mimics biological groups, where individuals are connected to each other and work together to accomplish tasks through information exchange. Distributed control [17], also known as hybrid control [18], realizes the full control of UAV clusters through the combination of centralized mutual cooperation and distributed autonomy [19].

3. Clustering Capability Measure

3.1. Ability Formation Mechanism

Suppose that cluster C is composed of m groups G, each group contains k (unequal) unit U, a total of n, the cluster capacity is represented by E, the group capacity is represented by E_i, and the unit capacity is represented by e_j. The UAV cluster shown in Figure 2, whether it is unit-to-group central point G_i0 or group-to-cluster central point C₀, will generate capability contribution.

The contribution coefficient a expressed as function f(s) related to the distance s, measured as equation 1; Distance s represents the distance between an unit and the central point of the group, or the distance between the group and the central point of the group. s_max represents the maximum distance an unit or group can contribute. The measures of group capacity E_i and group capacity E are shown in equation 2 and 3 respectively.

$$\alpha =f\left(s\right)=\frac{s_{max}-s}{s_{max}}$$

(1)

$$E_i={\sum }_1^{k}f\left(s\right)\ast e_j$$

(2)

$$\mathit{E}={\sum }_1^m\left(f\left(s\right)\ast \left(E_i+{\sum }_1^k{e}_j\right)+E_i\right)$$

(3)

3.2. Principle of Formation Reconstruction

The cluster control of UAVs follows the principle of maximum cluster capability E_max, so the cluster formation is always restructured around maintaining maximum capability. Considering the wide scope of the UAV cluster mission area airspace, each group is a scattered point relative to the cluster, and each UAV can be approximately regarded as one overlapping point in the center of its group relative to the cluster. Therefore, at the three levels of clusters, groups and units, not only is the distance S_j from each UAV j in each group Q_i to the group center Q_i0 equal, but the S_j of different groups is also approximately equal, expressed as the group radius S₁, so the ability contribution coefficient of individuals to the group α denoted as α₁. Similarly, relative to the whole task area, the distance between different groups from the cluster center can also be considered as approximately equal, expressed as the cluster radius S₂, then the ability contribution coefficient of the group to the cluster α denoted as α₂. Thus, the approximate measure E_s of cluster capability E can be obtained.

$$\begin{gathered} {\mathit{E}}_{\mathit{s}}={\sum }_1^m\left({\alpha }_2\ast \left(E_i+{\sum }_1^k{e}_j\right)+E_i\right) \\ ={\sum }_1^m\left({\alpha }_2\ast \left({\sum }_1^{k}f\left(s\right)\ast e_j+{\sum }_1^k{e}_j\right)+{\sum }_1^{k}f\left(s\right)\ast e_j\right) \\ ={\sum }_1^m\left({\alpha }_2\ast \left({\sum }_1^k{\alpha }_1\ast e_j+{\sum }_1^k{e}_j\right)+{\sum }_1^k{\alpha }_1\ast e_j\right) \\ ={\sum }_1^m\left({\alpha }_2\ast \left(1+{\alpha }_1\right){\sum }_1^k{e}_j+{\sum }_1^k{\alpha }_1\ast e_j\right) \\ ={\sum }_1^m\left(\left({{\alpha }_1+{\alpha }_2+\alpha }_1\ast {\alpha }_2\right){\sum }_1^k{e}_j\right) \\ =\left({{\alpha }_1+{\alpha }_2+\alpha }_1\ast {\alpha }_2\right){\sum }_1^m{\sum }_1^k{e}_j \\ =\left(3-\frac{2\left(S_1+S_2\right)}{s_{max}}+\frac{\left(S_1\ast S_2\right)}{s_{max}^2}\right){\sum }_1^m{\sum }_1^k{e}_j \\ =\left(3-\frac{2\left(S_1+S_2\right)}{s_{max}}+\frac{\left(S_1\ast S_2\right)}{s_{max}^2}\right){\sum }_1^n{e}_j \end{gathered}$$

(4)

The mission airspace range is denoted as S, the number of UAVs performing cluster tasks is n, and the density of UAVs is denoted as ρ. The metric calculation is shown in equation 5.

$$\rho =\frac{n}{\mathit{S}}$$

(5)

The density threshold is expressed as θ, when ρ<θ_min, let α₂=0; When ρ>θ_max, let S₁=0. In this case, the approximate measure of clustering capability E is E_ρ, as shown in equation 6.

$${\mathit{E}}_{\mathit{\rho }}=\left\{\begin{array}{c}\begin{array}{cc}\left(1-\frac{S_1}{s_{max}}\right){\sum }_1^n{e}_j & , \rho <{\theta }_{min}\end{array}\\ \begin{array}{cc}{\mathit{E}}_{\mathit{s}}& ,{\theta }_{min}<\rho <{\theta }_{max}\end{array}\\ \begin{array}{cc}\left(3-\frac{2S_2}{s_{max}}\right){\sum }_1^n{e}_j& ,\rho >{\theta }_{max}\end{array}\end{array}\right.$$

(6)

3.3. Comparison of Configuration Execution Ability

In this study, a cluster consisting of 10 UAVs was taken as an example. Among the common configurations of the formation, triangle, diamond, arrow and snake configurations as shown in Figure 3 were selected for comparison.

The radius of the executable task is denoted by S₂, the area of the task coverage area is denoted by S_f, and the area coverage coefficient is denoted by γ, then its measurement is shown in equation 7.

$$\gamma =\frac{{\mathit{S}}_{\mathit{f}}}{\mathit{S}}=\frac{\pi {\ast S}_2^2}{\mathit{S}}$$

(7)

Configuration execution capability is represented as Z, which is mainly affected by cluster capability E and area coverage coefficient γ. The measurement method is shown in equation 8.

$$\mathit{Z}=\gamma \ast \mathit{E}$$

(8)

Cluster flight is constrained by configuration. Assuming that different configurations can all fly according to the pattern shown in Figure 4, for cluster flight, the UAV in the dotted circle represents the center of the group and the cluster radius S₂.

Without considering the scaling of cluster configuration, the regional coverage coefficients γ are equal at the same cluster radius S₂. However, the group ability E of triangle, diamond, arrow and snake configurations is not equal, which is mainly affected by group ability E_i. Assuming that the radius S₁ of each population in different configurations is also equal, not only the clustering ability E is equal, but also the configuration execution ability Z is equal.

4. Cluster Behavior Modeling

4.1. Group Behavior Rule

Cluster behavior is multiple groups behavior movement around a task, and its center is the cluster center under the task goal and the group center under the task subgoal. What determines the change of cluster configuration is the dynamic change of group behavior, so cluster behavior can be regarded as the behavioral interaction between groups and the adjustment of functions within groups. According to the division of responsibilities, group G in cluster C can be divided into three categories: task group T, guarantee group P and reserve group B.

Task group T has a clear mission and is distributed in the task area when executing the task. The security group P and the reserve group B can be in a group G_i, and the reserve group B can either undertake the security work of the security group P or take over the security work at any time. Therefore, the group relationship of the cluster is shown in equation 9, where the symbol⊕represents the group fusion relationship.

$$\mathit{C}=\mathit{T}+(\mathit{P}\oplus \mathit{B})$$

(9)

Therefore, the group behavior mainly includes: (1) The reserve group B supports the existing task group T and guarantees the replacement of group P. (2) A new sub-target task group T_i is formed, which is fully supported by the reserve group B or assigned part of the existing task group T; (3) Assign new sub-targets to existing task group T_j by default, and those that are not supported by reserve group B and other groups T_m remain group T_j.

4.2. Reconstruction Topology Analysis

Taking triangular to diamond reconstruction as an example, as shown in Figure 5, when a new group G₄ is generated, G₂ and G₃ contribute UAV U₆ and formation F₁ composed of U₇ and U₁₀ respectively. At this time, the initial state of G₄ is obtained, and the group presents a disorder state. Then G₄ group internal adjustment into the final attitude, at this time the diamond cluster into a stable state. The diamond cluster includes the new groups G_2′, G_3′, and G₄, as well as G_1′(equal to the original group G₁).

Group G₄ can be generated by G₁, G₂, and G₃ contributing U₁, U₆, and U₁₀, respectively. In this case, the formation reconstruction can directly enter the final posture G₄ without internal group adjustment. But different groups support drones for new groups depending on their circumstances. When each group can contribute drones to the new group, it is necessary to maintain the topological stability of the original configuration of the cluster. The triangular configuration of cluster C is denoted C₁, the diamond configuration is denoted C₂, and G₄ is denoted by C₃, then C₂=C₁+C₃. Let (C, d) be a compact metric space, and if f: C₁→C₁, then C₁ and C₁ are homeomorphic when d(f)≤δ, and f is topologically stable. It can be seen that triangle, diamond and arrow are mutually stable configurations, but snake with the above three reconstructions is unstable. Configuration reconstruction is generally based on its stability, but individual selection is based on the principle of minimum loss.

4.3. Cost Measurement Mechanism

Taking the reconstruction in Figure 5 as an example, the reconstruction cost W includes three parts: the cost of the formation process W₁, the cost of internal group attitude adjustment W₂ and the cost of group catch-up W₃. The cost is a function related to distance L and time t.

$$\mathit{W}=W_1+W_2+W_3$$

(10)

Set energy consumption V(t) within individual unit distance and energy consumption coefficient η within group unit distance. The initial state distance of G₄ of U₆ from the triangular configuration to the diamond configuration is L₁, and the formation F₁ composed of U₇ and U₁₀ (quantity is denoted by k) to G₄ is the initial state distance L₂, so the process cost W₁ metric is:

$$W_1=V\left(t_1\right)\ast {\mathrm{L}}_1+\eta \ast V\left(t_2\right)\ast {\mathrm{L}}_2\ast k$$

(11)

The transition from the disordered state of group G₄ to the stable state is the adjustment of the position of k unmanned aerial vehicles within the new group G₄ to ensure a flight attitude of group G₄, the flight distance L₃, so the cost of attitude adjustment within the group W₂ is measured as:

$$W_2={\sum }_1^{k}V\left(t_{3k}\right)\ast {\mathrm{L}}_{3k}$$

(12)

In the stable state, the velocity of group G₄ is not consistent with the velocity in the direction of movement of part of the group in C₁ configuration. At this time, the group pursuit cost W₃ that G₄ needs to consume in order to reach the cluster velocity and reach the configuration position L₃ is measured as follows:

$$W_3=\eta \ast V\left(t_3\right)\ast {\mathrm{L}}_3\ast k$$

(13)

5. Simulation Experiment

5.1. Models and Constraints

Considering that the above configuration is a two-dimensional planar graph, the cluster is a three-dimensional spatial space in actual flight, so a three-dimensional coordinate cluster model is established. Figure 6 is the schematic diagram of the reconstructed three-dimensional coordinate model of the cluster. Formation F₁ and UAV U₆ first fly horizontally towards the center G₄₀ of the new group G₄, and the center of F₁ and U₆ coincide with the vertical projection of G₄₀ in the Z direction. Then fly from the initial state to their respective stable positions according to the group G₄ attitude.

Constraints: (1) All groups in the cluster and all drones in the cluster can fly at different plane heights; (2) Ignoring the UAV steering problem during cluster reconstruction, the velocity v has three directions (x, y, z); (3) Do not consider the additional energy consumption of upward flight; (4) Keep the original flight shape unchanged when the formation is reconstructed towards the group center; (5) In the stable state, there are no multiple UAVs in the vertical Z direction.

5.2. Simulation Analysis

There are 10 points are randomly generated in the three-dimensional space, and then clustered into 3 clusters. Each point of each cluster is arranged according to the formation configuration, and the Central Line of the cluster is a triangle, forming a triangle configuration cluster. Then, points are adjusted adaptively from the three clusters to form diamond, arrow and snake shapes respectively, and the fourth cluster is generated, so as to obtain the change curve of the relationship between cost and time, and the trajectory movement of points when forming different configurations. The simulation process of cluster formation reconstruction is shown in the algorithm in Table 1.

The motion position change of the reconstructed particle is obtained by simulation. When reconstructed into diamond shape, arrow shape and snake shape, its motion trajectory is shown in Figure 7, Figure 8 and Figure 9, respectively.

At the same time, the cost curves of three different configurations are obtained, as shown in Figure 10. The cost of diamond reconstruction is the least, the time of arrow reconstruction is the longest, and the cost of snake reconstruction is the most.

6. Conclusion

Through theoretical formula derivation and simulation experiment, the UAV cluster reconfiguration research is carried out, and the cluster movement trajectory diagram and the change curve of the reconfiguration cost and time are obtained. The results show that the diamond reconstruction cost is the least, the arrow reconstruction time is the longest and the snake reconstruction cost is the most when the triangle is adjusted to the other three shapes.