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Abstract
Aiming at the problem that the strong electromagnetic interference environment restricts the communication of the Unmanned Aerial Vehicle(UAV) formation, which affects the rapid assembly of the UAV formation, a wireless ultraviolet cooperative UAV formation rapid assembly algorithm is proposed to realize the fixed-point assembly of the UAV formation in the airspace. First, the Ultraviolet(UV) light beacon model is used to realize the information interaction of the UAV formation. secondly, the UV four-node positioning algorithm is used to realize the three-dimensional positioning of the UAV formation. Combined with the method, the UAV formation can reach a consensus speed when assembling. The simulation results show that when there are more than 6 reference nodes, the three-dimensional space positioning accuracy can reach 96%. The assembly algorithm can realize the fixed-point assembly of the UAV formation, and can maintain the circular motion trajectory after the assembly is completed.
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1. Introduction
With the continuous development of unmanned aerial vehicle(UAV) technology, UAVs are gradually applied in military and civilian fields. However, a single UAV cannot meet the requirements of performing tasks, so UAVs often appear in the form of formation coordination [1,2]. The UAV formation control technology mainly includes: formation assembly, formation maintenance, formation transformation and reconstruction, collision avoidance and collision avoidance [3]. When the UAV formation receives the mission command, the first thing to face is the problem of formation assembly. Formation assembly refers to the process in which multiple UAVs take off from the initial position to the target position according to a fixed formation, and the formation needs to be maintained after the assembly is completed [4].
In terms of formation assembly, Reynolds [5] proposed a distributed assembly control scheme by studying the movement process of aggregated animals in nature. The scheme is mainly based on the dynamic perception of the surrounding environment to control the gathering movement of each member in the cluster to prevent separation between members. Reference [6] studied the formation tracking problem of quadrotors, proposed a layered-based UAV formation control algorithm. Under this algorithm, UAVs only communicate with UAVs in the neighborhood. By introducing a saturation control strategy to synthesize the reference trajectory of the UAV, the experimental results show that the control algorithm can effectively track the quadrotor formation. Reference [7] proposes a segmented assembly strategy for the tight assembly problem of UAV formations, divides the formation assembly problem into three processes: reference assembly point selection, reference assembly point allocation and formation of a tight formation. The final track control of the formation is achieved through the consistency of speed and attitude, which improves the stability of formation. Reference [8] analyzed the aggregation effect of the pilot-following method, used the sub-gradient method to continuously update the control strategy of the pilot and the follower. The follower always sends its own strategy information to the pilot for the pilot to make decisions. Finally, the simulation verified the program effectiveness. literature [9] proposes a build-up strategy based on a time-varying vector field, adjusts the UAVs path and speed information in real time through the vector field, so that the UAV can be successfully assembled within a fixed time. Huang [10] studied the formation control problem of UAVs under unknown interference, designed an adaptive controller to realize the UAV attitude tracking, which avoided the adverse effects of unknown interference on the formation. The controller can make the drone reach the designated area safely. The above literatures are based on the distributed control scheme combined with other algorithms to realize the formation of the UAV formation, but there is little research on the formation of a fixed formation. When the number of UAV formations increases, the stability analysis and verification of the formation assembly algorithm has not been analyzed. These problems restrict the development of the UAV formation assembly direction.
In terms of UAV formation communication, because UAV formations are often affected by complex atmospheric environments or strong electromagnetic interference areas when performing combat missions [11], network communication failures in UAV formations will affect the execution of tasks. Therefore, a communication network with strong anti-interference ability is needed as an auxiliary support [12]. The wireless ultraviolet (UV) light communication transmits the signal through the scattering of atmospheric molecules and aerosol particles [13,14]. It has the advantages of all-weather work, non-direct line of sight communication, strong anti-interference ability, etc. It can provide the communication network for the formation of UAVs in complex environments reliable guarantee. Reference [15] designed an omnidirectional antenna for the fuselage of the UAV based on the eigenmode analysis of the UAV, which expanded the coverage of the UAV formation network, and verified it on the UAV flight formation. For communication failure networks, an event-triggered mechanism can be designed to reduce the information exchange within the formation, the synchronization error stability can be used to ensure the gain of the flight controller, thereby reducing the communication energy consumption of the system [16]. In order to solve the problem that the communication network of the UAV formation is limited in the strong electromagnetic interference environment, which affects the formation assembly. This paper proposes a wireless ultraviolet cooperative UAV formation rapid assembly algorithm, solves the UAV formation assembly through the ultraviolet light node positioning algorithm. The formation problem is fixed, the pilot following method is combined with the consistency theory, so that other UAVs can follow the pilot's trajectory to complete the rapid assembly.
2. UAV model and UV positioning
2.1 UAV motion model
This paper mainly analyzes the formation and maintenance of UAVs in the process of formation assembly. The UAVs communicate with each other through the topology structure. The UAV motion equation used is:
In formula (1), $({x_i},{y_i},{z_i})$ represents the position information of the UAV i in space, ${V_i}$ is the flight speed of the UAV, ${\theta _i}, {\varphi _i}$ is the pitch angle and heading angle of the UAV. $u = [{T_i},{L_i},{\psi _i}]$ is the control input of the UAV system, ${T_i}$ represents the thrust of the engine, ${L_i}, {\psi _i}$ represents the aerodynamic lift and the roll angle of the UAV, ${D_i}, {m_i}, g$ are air resistance, drone mass, and gravitational acceleration.
Assuming that the formation consists of n UAVs, a single UAV is regarded as a single node, the communication relationship between the UAVs is regarded as the edge of the node. Then the communication topology of the UAV formation can be represented by $G = (W,E,A)$, $W = \{ {w_i}|i = 1,2, \cdots n\} $ represents a collection of drone nodes, $E = \{ {e_{ij}}|i,j \in W\} $ represents a set of edges, the overall topological relationship of the formation can be represented by $A = {({a_{ij}})_{n \times n}}$, which can be specifically described as:
In formula (2), ${N_i} = \{ {w_j}|{e_{ij}} \in E,j \equiv i\} $ represents the set of communication with the UAV j, the diamond formation used in this paper is shown in Fig. 1, which ${w_1}$ is defined as the leader UAV, and the rest are follower UAVs.
It can be seen from Fig. 1 that the UAV formation communication structure is bidirectional, each UAV has the ability to receive and send its own status information at the same time. The set of formation nodes is $W = \{ {w_1},{w_2},{w_3},{w_4}\} $. The set of edges is $E = \{ {e_{12}},{e_{23}},{e_{34}},{e_{14}}\} $. The communication between UAV formations is determined by the corresponding adjacency matrix.
2.2 UV four-node localization algorithm
The premise of UAV formation to achieve aerial assembly is to determine the position information of UAVs in three-dimensional space and provide a reference for the formation of formations. Therefore, this paper builds a UV beacon model to realize the node positioning of UAV formations. Wireless ultraviolet light communication often uses the hemispherical ultraviolet light-emitting diode (LED) as shown in Fig. 2 as the beacon model. The LEDs installed on the model are arranged in the way of longitude and latitude, and each LED has its corresponding. The UV signal sent contains the status information of the drone and its own ID number. For example, the LED number at the intersection of the 5th warp and the 4th weft is (5,4). The beacon model is mounted on the drone to realize omnidirectional communication between the drone formations.
When the UAV in the neighborhood receives the UV signal, the distance between it and the UAV that sends the signal can be obtained according to its UV light power and receiving angle information, and its UV light receiving light power [17] is:
In formula (3), ${P_{r,NLOS}}$ is the received optical power of the ultraviolet signal, ${P_t}$ is the transmitted optical power, ${A_r}$ is the receiving aperture area, ${K_e}$ is the atmospheric channel attenuation coefficient, ${K_s}$ is the scattering coefficient, ${P_s}$ is the scattering phase function, ${\theta _1}, {\theta _2}$ are the transmit elevation angle and the receive elevation angle, respectively, ${\phi _1}, {\phi _2}$ are the divergence angle of the transmitter and the field of view of the receiver. According to Eq. (3) and the lambertw function, the maximum communication distance between the UAVs can be obtained as [17]:
After obtaining the distance between the UAVs, the position coordinates of the unknown UAV nodes in the three-dimensional space can be solved according to the four-node localization algorithm. The four-node localization model [17] is shown in Fig. 3.
It can be seen from Fig. 3 that when the coordinates of the four reference nodes are known as $A({x_1},{y_1},{z_1})$, $B({x_2},{y_2},{z_2})$, $C({x_3},{y_3},{z_3})$, $D({x_4},{y_4},{z_4})$ and the distance from the position node $M({x_m},{y_m},{z_m})$ to ABCD. The position coordinates of the unknown node can be obtained as:
3 Algorithms for rapid assembly of formations
When the UAV formation receives an assembly instruction, the formation must determine the assembly point location and assembly range in advance. After the assembly point location is set, the UAV can fly to the assembly point to form a preset formation. However, since the initial position, speed, heading and other information of each UAV within the formation are different, the method of first-point assembly and then semi-aircraft assembly is used to complete the formation assembly task. First, the formation is realized according to the formation geometry, then the state information of each UAV is gradually adjusted by using the information consistency. When the speed and position of all UAVs in the formation are stable, the assembly task is completed.
Each UAV in the formation uses a line to cut into the predetermined track. The cut-in direction of each UAV and the track are perpendicular to each other, the vertical point between the UAV and the track ${q_{di}} = {({x_{di}},{y_{di}},{z_{di}})^T}$ is set as the cut-in point. Assuming that there are four UAVs in the formation, the schematic diagram of the UAV formation entry point is shown in Fig. 4.
After determining the entry point of each UAV in the formation, take the average of the coordinates of the entry point of all UAVs in the formation to obtain the reference assembly point ${q_{\bar{t}}} = {[{x_{\bar{t}}},{y_{\bar{t}}},{z_{\bar{t}}}]^T}$, then there are
After the formation reference rendezvous point is determined, each UAV forms a corresponding target rendezvous point according to the expected distance from the reference rendezvous point, each UAV has a corresponding target rendezvous point. Taking the diamond formation as an example, the schematic diagram of the corresponding target rendezvous point is shown in Fig. 5.
When the target rendezvous point is determined, it is necessary to reasonably allocate the UAV according to the task requirements and allocation principles when assigning the target rendezvous point to the UAV, so as to maximize the allocation of resources. Figure 6 shows the allocation process of target rendezvous points, the rendezvous point ${t_2}$ is the optimal choice for $UA{V_1}$ and $UA{V_2}$ at the same time, and the rendezvous point ${t_3}$ is also the optimal choice for $UA{V_3}$ and $UA{V_4}$. If the ${t_2}$ rendezvous point is assigned to $UA{V_1}$, the rendezvous point ${t_1}$ or ${t_3}$ can only be assigned to $UA{V_2}$, although this can also complete the task of UAV formation, this allocation method will only increase the time required for the UAV to be assembled. When using the maximum distance priority allocation, because the distance between $UA{V_2}$ and rendezvous point ${t_2}$ is greater than $UA{V_1}$, the rendezvous point ${t_2}$ is preferentially allocated to $UA{V_2}$, and the rendezvous point ${t_1}$ is allocated to $UA{V_1}$. Similarly, for the assignment of the target rendezvous point ${t_3}$, the rendezvous point ${t_3}$ is assigned to $UA{V_3}$, and the rendezvous point ${t_4}$ is assigned to $UA{V_4}$.
Combined with the above analysis process, the specific allocation steps of rendezvous points can be expressed as follows:
Step 1: Each drone in the drone formation selects the location of its nearest rendezvous point, record the distance between the drone $UA{V_i}$ and the nearest rendezvous point as ${d_i}$;
Step 2: For any assembly point, compare the UAVs in the formation and the assembly point ${d_i}$, then assign the assembly point to the farthest UAV. The distance from the assembly point is ${d_{\max }}$;
Step 3: Re-match the remaining drones with the rendezvous points that have not been assigned yet, and record the corresponding distances ${d^{\prime}_i}$;
Step 4: Select any assembly point from the remaining assembly points, assign the assembly point to the UAV with the largest distance from the assembly point;
Step 5: Continue with nearby selection until all staging points are assigned to drones.
After all UAVs in the formation are assigned the target assembly point. When all drones receive the assembly command, they will fly to the target assembly point to generate a formation geometric formation. The UAV formation assembly process is shown in Fig. 7.
As can be seen from Fig. 7, the formation of UAVs first establishes a communication link between ultraviolet light machines, the location information of adjacent UAVs can be further determined according to the ultraviolet light node positioning algorithm. Then the UAV formation generates the required reference rendezvous point and target rendezvous point information according to the task instruction, and assigns the generated target rendezvous point to all UAVs in the formation according to the principle of maximum distance priority allocation. Determine whether all drones in the formation have been assigned staging points, and if not, reassign the remaining drones to staging points. All UAVs start to fly to the target rendezvous point after allocating the rendezvous point, the UAVs that have arrived start the formation control algorithm to maintain the movement trajectory until all UAVs reach the target rendezvous point.
4. Algorithm simulation and experimental results
4.1 UV positioning simulation and analysis
In order to verify the performance of the UV four-node localization algorithm, localization experiments were carried out in two-dimensional and three-dimensional spaces respectively. Neighboring reference nodes are located using neighboring located nodes. The UAV positioning accuracy is defined as:
In formula (7) ${L_{ac}}$ is the positioning accuracy, ${N_{loc}}$ is the number of nodes that have been located, ${N_{un}}$ is the number of all unknown nodes.
In the two-dimensional space, 20 UAV nodes are selected and deployed randomly in the area $200m \times 200m$. The communication distance of each UAV node is a circular area $d = 100m$. At least three reference nodes are required to locate the unknown UAV node in the two-dimensional space. 2D UAV formation network node positioning simulation is shown in Fig. 8.
In Fig. 8, “${\ast} $” is the reference node, “$o$” is the blind node, that is the node that has not been successfully located, “¶” is the node that has been located. It can be seen that three blind nodes among the 17 unknown nodes have not been successfully located, the positioning accuracy of the algorithm is 82.3%, the average positioning error is less than 10 m.
In the same three-dimensional space, 20 UAV nodes are randomly deployed in the area $200m \times 200m \times 200m$. The communication distance of the UAV nodes is set to 200 m, four nodes are selected as reference nodes. The positioning simulation of the three-dimensional UAV formation network nodes is shown in Fig. 9 shown.
As can be seen from Fig. 9, there are a total of 20 nodes in the three-dimensional space, of which 16 unknown nodes need to be located. However, when four nodes are selected as reference nodes in the three-dimensional space, only two blind nodes among the 16 unknown nodes are not successfully positioned. The positioning accuracy of the algorithm is 87.5%, the average positioning error is less than 10 m. From the two-dimensional and three-dimensional positioning results, it can be seen that the positioning accuracy of the algorithm varies with the number of selected reference nodes. Therefore, the positioning accuracy in two-dimensional and three-dimensional space is analyzed by changing the number of selected reference nodes, the result is shown in Fig. 10.
It can be seen from Fig. 10 that the accuracy of 2D and 3D positioning increases with the increase of reference nodes. But the accuracy of 2D positioning rises to the maximum when there are 6 reference nodes. The 3D positioning accuracy rate is better than the 2D positioning when the number of reference nodes is greater than 5, and the final positioning accuracy is 96%. Therefore, when the actual UAV formation is positioned, the selection of 6 reference nodes should be given priority.
4.2 Simulation and analysis of UAV formation assembly
In order to verify the assembly effect of the proposed wireless ultraviolet cooperative UAV formation rapid assembly algorithm, this paper builds a UAV formation simulation environment on MATLAB, 2019b, for verification. The main verification contents of this experiment are 1) The fixed-point assembly process of multiple UAVs from the initial position to the air target area, a fixed formation will be formed in the assembly area; 2) After a fixed formation is formed in the air, the state information of all UAVs in the UAV formation tends to be consistent, the formation is maintained while flying in the air following a fixed trajectory.
The drone numbered 1 in the formation is used as the leader, the remaining drones are used as followers. The followers only receive the instructions from the leader and fly to the target point together to complete the flight mission. When verifying that the formation is assembled into a fixed formation, the given potential field function parameters between UAVs are: formation expected distance is $d = 1.5m$, attraction function step size is $\lambda = 0.1$, repulsion function coefficient is ${C_r} = 1,\mu = 0.1$.The schematic diagram of the formation assembly simulation is shown in the Fig. 11.
In order to further analyze the performance of the algorithm when the UAV formations are assembled into a fixed formation in Fig. 11. A comparative analysis of the assembly time and the number of iterations corresponding to the four UAV formations is carried out, the comparison data of UAV fixed formation assembly time is obtained as shown in Table 1.
Table 1. Comparison of UAV fixed formation assembly time
It can be seen from Table 1 that the time and algorithm iterations required when the UAV formation is assembled into a triangular formation are the least. But as the number of UAVs increases, the time spent in the formation assembly will increase exponentially. This is because the change of the formation makes the UAV formation topology more complex, which leads to the increase of difficulty when the UAV formation is assembled into a fixed formation. It can be seen that the cost of the UAV formation assembly time is positively correlated with the number of drones.
On the basis of ensuring the number of UAVs, the formation assembly time and the number of algorithm iterations are considered. Using the above diamond formation, adjust the drone assembly height to $z = 10m$, all UAVs make circular motions in the airspace and still maintain a stable diamond formation. The initial speed of UAVs in the formation is set to zero, the coordinates of their formation positions are shown in Table 2.
Table 2. UAV initial position information
Figure 12 shows the UAV formation escort assembly in the 3D scene, Fig. 12(a) shows the process of escort assembly in a diamond formation, Fig. 12(b) is the top view scene from the z-plane of the rhombus formation escort assembly in Fig. 12(a). The triangle in Fig. 12(a) is the target assembly point of the leader UAV, the square is the target assembly point of the follower UAV, the asterisks are the initial position coordinates of all UAVs.
As can be seen from Fig. 12(a), the four UAVs first wait for the assembly command at the initial position. After receiving the assembly command, each UAV starts to move upward from the initial position, its movement shape is circular, finally assembled in the airspace. It can be seen from Fig. 12(b) that the circular trajectory of the four UAVs is relatively loose at the beginning of the assembly process, but the final formation forms a circular trajectory and can be assembled into a diamond-shaped formation with no followers. The drone can follow the leader drone in a circular motion in the airspace, and can keep the formation stable.
In order to further analyze the formation changes, the position of the leader UAV and the positions of the three follower UAVs during the formation assembly process are respectively made difference, the relative position change curve of the follower UAVs is obtained as shown in Fig. 13 shown.
As can be seen from Fig. 13, the positional changes of the three follower UAVs and the leader UAV gradually tend to a fixed value as the number of algorithm iterations increases, which also shows that the UAVs can finally show formation . When the number of iterations is 3000, the distance between the No. 2 UAV and the No. 3 UAV and the No. 1 UAV is small, indicating that there is a problem that the UAVs in the formation are relatively close in the process of assembling. However, as the number of iterations increases, the distances between the No. 2 and No. 4 drones and the No. 1 drone gradually become stable. On the whole, the relative position change curve of the follower can reflect the position change of the UAV in the process of assembly in the air.
When the UAV formation is assembled to a fixed target, in order to discuss the consistency change of the UAV assembly process, analyze the consistency relationship change of the UAV formation during the assembly process, and analyze the UAV formation in the assembly process. Figure 14 shows the speed change curves of the four UAVs during the assembly process.
From Fig. 14(a) and Fig. 14(b), it can be seen that when the UAV formation is assembled upward, the speed of the four UAVs at the initial moment varies greatly. This is because the initial positions of the drone formations are different, and the drones in the formation need to adjust their speed to keep up with the formation. With the increase of the number of algorithm iterations, the speed change curves in the x-direction and the y-direction show periodicity, the speed curves of the UAV formation are basically the same when the corresponding algorithm iteration times are 5000 times. As can be seen from Fig. 14(c), the trend of the speed change curve of the UAV formation in the z direction is to increase first and then decrease. This is because the UAV formation needs to increase its speed to fly to the designated airspace after receiving the assembly command, then reduce its speed to achieve speed consistency between the formations.
In order to verify the robustness of the assembly algorithm, the number of the above-mentioned UAV formations was doubled, and a diamond-shaped formation was also used, 8 UAVs were set up in the airspace for group assembly. All UAVs are assembled into a diamond formation in the airspace and adjust the drone assembly height to $z = 10m$, and the location information of all UAVs when they are assembled in groups is shown in Table 3.
Table 3. Initial position information of UAV group assembly
Figure 15 shows the formation and grouping of UAVs in a 3D scene. Figure 15(a) is a schematic diagram of the formation and grouping. Figure 15(b) is a top view of the z-plane of the formation and grouping scene. The triangle in Fig. 15(a) is the leader drone, the rest are follower drones, and the asterisk is the initial position of each drone. The four UAVs in the UAV formation are divided into one group, the distance between the two formations is 5 m, and the UAVs in each formation follow the leader to complete the assembly task.
It can be seen from Fig. 15(a) that when the group is assembled, the UAVs in the formation are waiting for the assembly command at the initial position. When the assembly command is received, the UAVs in each group start to move upward, and the trajectory shape presents a circular shape. Finally each group of formations can complete the assembly task in the area of $z = 10m$. It can be seen from Fig. 15(b) that the initial trajectories of the UAVs in the two groups are relatively loose, but as the number of iterations of the algorithm increases, the UAVs in the group can finally be assembled into a diamond formation at the same time. Continue to do a circular motion, and the formation of the assembled formation remains stable. In order to further analyze the consistency of the UAV formation during group assembly, the speed of the UAV formation during the ascent process was analyzed, the speed change curve of the UAV formation during group assembly was obtained as shown in Fig. 16.
It can be seen from Fig. 16(a) and Fig. 16(b) that when the algorithm iteration is less than 2000, the velocity changes of all UAVs in the formation in the x and y directions increase first and then decrease. Since the UAVs in the group need to quickly keep up with the speed adjustment made by the leader UAV, when the algorithm iteration times are 5000 times, the speed changes of each UAV tend to be consistent, indicating that the formation has reached a stable state at this time, so the speed change curves of the four UAVs basically overlap. It can be seen from Fig. 16(c) that the speed change of the formation in the z direction also increases first and then decrease, but the speed fluctuates greatly. This is because the initial heights of all UAVs are different. The UAVs need to increase the speed to achieve the same height of the assembly task, and start to slow down after the UAV formation reaches the same height to complete the consistency of the speed.
5. Conclusion
The strong electromagnetic interference environment will affect the information interaction between the UAV formations, so that the UAV formations cannot be quickly assembled into formations. In view of the above problems, this paper uses wireless ultraviolet light to realize the communication positioning between UAV formations, combines the consistency theory with the pilot-following method, so that the follower can obtain the status information of the pilot UAV, the rapid assembly potential field function is given to achieve this. UAV formations are assembled at fixed points in the air. The simulation results show that when the reference node is greater than 6, the positioning accuracy of 3D UV four nodes can reach 96%.
Funding
Yulin City Science and Technology Plan Project (2019-145); Xi'an Forest District Science and Technology Plan Project (GX1921); Shaanxi Provincial Department of Education Research Project (17-JF024); Shaanxi Provincial Key R&D Program General Project (2021GY-044); National Natural Science Foundation of China (61971345).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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