Unmanned aerial vehicle cluster encirclement tracking control method simulating pigeon flock limited neighbor interaction

Abstract

The invention discloses an unmanned aerial vehicle cluster encirclement tracking control method simulating pigeon flock limited neighbor interaction, and the method comprises the steps: 1, carrying out the kinematics modeling of an unmanned aerial vehicle and a target, and determining the initial states of the unmanned aerial vehicle and the target, and an expected encirclement configuration; 2, dividing the unmanned aerial vehicles in the cluster into information individuals and non-information individuals according to the acquisition authority of the target state, and artificially selecting directed connection from the information individuals to the non-information individuals by imitating a nearest neighbor interaction rule of the pigeon flock; 3, introducing communication distance limitation to delimit a non-information individual neighbor set; and the like. The method is easy to implement, the proposed pigeon inspired limited interaction neighbor selection rule can greatly reduce communication load in formation encircling control, control convergence speed is increased, and a robust solution is provided for topology construction in a communication limited environment and control protocol design for switching topology.

Description

Technical Field

[0001] The invention relates to an unmanned aerial vehicle cluster encirclement tracking control method imitating the limited neighbor interaction of a pigeon group, and belongs to the technical field of unmanned aerial vehicle cluster cooperative control. Background Art

[0002] UAV formation, obstacle avoidance, and encirclement control have always been the focus of attention and research in the field of swarm intelligence. By distributing control and decision algorithms in a swarm system composed of multiple UAVs, it is expected that the control response speed and control accuracy can be comparable to those under ideal conditions under conditions such as limited communication or link failure. Encirclement control and target tracking of UAV swarms are common demonstration and verification assumptions for unmanned swarm combat in modern military battlefield environments. UAVs track a leader node or local target in a specific formation according to the expected given configuration, and multiple UAV nodes can maintain the formation consistently. During the tracking process, the communication topology can be dynamically adjusted according to constraints such as communication distance without destroying the stability of the formation configuration. By distributing the control system on each UAV airborne end, the computing load pressure of the ground control station can be effectively reduced.

[0003] At present, common UAV swarm collaborative control algorithms are mainly divided into several categories, including behavior-based, energy-based and consistency-based control methods. Behavior-based control includes utilizing the action characteristics of group motion such as coordinated motion, obstacle avoidance and topology reconstruction, designing certain behavior rules and trigger conditions, and acting on the cluster in the form of control inputs such as virtual forces according to weights or priorities. Energy-based control is to act on the system through gradient information such as energy function or rate of change of potential field intensity to drive it to evolve towards a steady-state equilibrium point. When dealing with the formation control problem of large-scale swarms, the above control methods have significant defects such as weak generalization, limited control accuracy and large communication load. When UAVs have certain communication range constraints, it is difficult to maintain an undirected connected interactive topology under ideal conditions, so some consistency control protocols that have assumptions about the communication topology are invalid at this time.

[0004] In the formation encirclement task with limited communication interaction, the reference state of the target cannot be guaranteed to be continuously acquired in real time by all nodes in the cluster. The present invention aims to achieve a consistent estimation of the target state through hierarchical interaction in the communication topology by designing a distributed observer, so as to supplement the missing leader reference information in the formation encirclement controller. In addition, the present invention proposes a set of time-varying switching communication topology construction rules that imitate the limited interaction of pigeon groups, which can generate a tree network topology with a small communication load and support for information cascade transmission under the premise of dividing the drones in the cluster into different information acquisition authority levels such as information individuals and non-information individuals, and its root node is located in the information individual, which can ensure that the situation information of the target can be fully covered in the communication topology formed by such limited neighbor interaction and hierarchical interaction rules. The communication topology formation mechanism, distributed observer, and controller established by the present invention can effectively improve the control response capability of the drone cluster in a communication-restricted environment, enhance the adaptive regulation performance of the drone cluster for the limited interaction topology rules, and improve the robustness of the drone to severe interference such as link damage and partial node communication interruption. Summary of the invention

[0005] The purpose of the present invention is to provide a method for encirclement and tracking control of a drone cluster by imitating the limited neighbor interaction of a pigeon flock, and to address the problem of encirclement control of a multi-drone formation under low interactive load conditions in a communication restricted environment. A limited neighbor interaction rule imitating a pigeon flock is established, and a fixed-time consistency distributed observer is designed. In the case where non-information individual drones in some clusters lack target state information, in a topological structure that switches in real time related to the cluster node position, a drone cluster containing information individuals and non-information individuals is implemented to stably and collaboratively track the target, effectively improving the control performance of the drone cluster in a restricted communication environment and its ability to resist interference to communication links.

[0006] Aiming at the topological construction and formation cooperative control problems of UAV clusters in communication-restricted environments, the present invention invents a UAV cluster encirclement tracking control method that imitates the limited neighbor interaction of pigeon flocks. The algorithm implementation flow chart is as follows: Figure 1 As shown in the figure, it includes cluster state initialization, neighbor selection topology construction mechanism imitating limited interaction of pigeon swarm, distributed target state observer of fixed-time drone swarm, and consistent distributed encirclement tracking controller imitating limited interaction of pigeon swarm. The specific implementation steps are as follows:

[0007] Step 1: UAV and target kinematic modeling, scene and state information initialization.

[0008] Specifically: kinematic modeling is performed on the UAV and the target, and the UAV is considered to be in the same height plane after vertical take-off. The UAV is set to a four-rotor configuration for vertical take-off and landing, and the target is set to an omnidirectional Mecanum wheeled unmanned vehicle configuration for translation in the plane. In the present invention, the focus is on the collaborative encirclement control task of multiple UAVs on a single target, so the algorithm simulation verification scenario is simplified, the UAVs are set at the same height, and only two-dimensional plane coordinates are considered.

[0009] The target motion model is established as:

[0010]

[0011] In the formula, represents the target three-dimensional position vector, represents the target three-dimensional velocity vector, Represents the target three-dimensional acceleration vector.

[0012] The kinematic model of the UAV is established as:

[0013]

[0014] Where P i =[P i x ,P i y ,P i z ] T Represents the three-dimensional position vector of drone node i, V i =[V i x ,V i y ,V i z ] T represents the three-dimensional velocity vector, g is the gravitational acceleration, T i Represents the thrust of the drone, m i represents the mass of the drone, R i represents the attitude rotation matrix, is a unit vector.

[0015] In cluster distributed control, since the attitude rotation angle is small, the UAV can be controlled to move in a two-dimensional plane to verify the formation encirclement algorithm. The control quantity can be regarded as Therefore, it can be simplified to the differential equation of the second-order agent in the two-dimensional plane:

[0016]

[0017] Where P i xy =[P ix ,P i y ] T Represents the position vector of drone node i in the two-dimensional plane, V i xy =[V i x ,V i y ] T represents the velocity vector in a two-dimensional plane, represents a two-dimensional control input with U i The first two components of .

[0018] Assume that there are two different types of drones in the drone cluster, namely information individual drones (hereinafter referred to as information individuals) and non-information individual drones (hereinafter referred to as non-information individuals). It is assumed that information individuals can directly obtain target information and can unidirectionally transmit their own status to some non-information individuals, while non-information individuals do not have the ability to directly obtain the status of the target to be surrounded, and need to communicate with information individuals or neighboring non-information individuals in a hierarchical structure similar to that of pigeon flocks to complete the encirclement task. Represents a collection of information individuals, using Represents a set of non-information individuals, and Represents the total set of drone nodes that perform encirclement tasks, where Set up information individual collection The number of drones in is N L , a set of non-information individuals The number of drones is N F , consider that there are N drones in the cluster, with the relationship N = N F +N L , the two types of drone node sets are respectively recorded as and

[0019] Initialize the position of the target in the plane area at the origin of the relative coordinate system Target speed and the acceleration of the target Random in a preset area Initialize the initial position of the non-information individual drone in the area Initialize the position of the individual information in the information, and set other initial state information of the drone node, including the position P of drone i i xy =[P i x ,P i y ] T ,speed when When , it indicates a non-information individual state, when When it indicates the individual status of information.

[0020] Step 2: Determine the non-information individual neighbor nodes for the information individual nodes according to the nearest neighbor interaction principle of the pigeon flock.

[0021] Specifically: according to the randomly initialized position distribution of each drone in a certain area in step 1, inspired by the interaction preference behavior between the pigeon group and the nearest neighbor individuals, the nearest neighbor rule of relative position is used to calculate the position distribution of each information individual in the drone cluster. Determine specific non-information individual neighbors, for non-information individuals Given a neighbor selection set, the neighbor selection mechanism established for information individuals can be expressed as:

[0022]

[0023] For a specific non-information individual i, if its neighbor set determined by formula (4) A non-empty set, that is Then it shows that there is a directed edge from information individual l to non-information individual i. For each information individual, Each determines a non-information individual that can obtain its state and satisfies Directed connection with it.

[0024] The directed topology from the information individual to the non-information individual obtained by constructing the nearest neighbor selection mechanism of the pigeon flock given by formula (4) is: Its edge set satisfies Determine the topology The corresponding weighted adjacency matrix is When non-information individuals Individuals who can receive information When the state information is transmitted, the corresponding element in the weight matrix On the contrary, the weight in the topology Represents the exchange of no information from a non-informative individual to an informative individual.

[0025] Step 3: Introduce communication distance range restrictions, combined with the manually set maximum interaction radius, and preliminarily determine the undirected communication topology between non-information individuals in the drone cluster.

[0026] Specifically: For non-information individuals as well as The positions of the current time step are P i (t) and P j (t), the threshold of the interactive communication radius between non-information individuals in a given cluster In order to limit the communication range between the drone and its neighbors, the pigeon flock is simulated to interact only with neighboring individuals within a limited communication range, and non-information individuals within the communication radius are selected as neighbors. The first step of the neighbor selection rule for non-information individuals can be expressed as:

[0027]

[0028] The undirected interaction topology constructed based on formula (5) is denoted as Its edge set satisfies The weighted adjacency matrix of this topology is is a symmetric matrix.

[0029] Step 4: Combined with the limited field of view interaction mechanism of the pigeon flock, the neighbor nodes determined by the neighbor selection rule in formula (5) in step 3 are divided into circular areas within the surrounding communication radius with equal angles. The drone closest to the current individual in each area is selected according to the nearest neighbor principle and added to its neighbor node set to construct a streamlined interaction topology.

[0030] Specifically: For non-information node i, use Represents a set of position points within its communication range, and defines the azimuth relative to UAV i with the positive direction of the x-axis as zero degrees as: P a ∈Φ i Drawing on the limited field of view interaction habits of pigeons, each individual prefers to interact with a fixed number of individuals in each visual range around it. In order to effectively and evenly reduce the number of neighbor nodes of non-information individuals within the communication radius, the drone nodes are placed The area within its perception range is divided equally according to the angles around it. Sub-areas According to the azimuth relative to UAV i given above The definition of determines the neighbor set in the sub-region around drone node i:

[0031]

[0032] According to the definition of formula (6), represents the neighbor set selected by the neighbor selection rule given by formula (5) in step 3 The subset distributed in the kth subregion around the node in .

[0033] The present invention follows the pattern that a flock of pigeons selects a fixed number of neighbors to interact with within a specific visual range, and selects the neighbor sets of each sub-area constructed by formula (6) without loss of generality. The nodes closest to the current UAV in the equation constitute a new neighbor set. This ensures that the current non-information individual can obtain information about individuals in each sight angle range. The second-step neighbor selection rule of the non-information individual given on the basis of formula (5) can be written as:

[0034]

[0035] According to the neighbor selection mechanism in formula (7), the interaction topology is written as Its topological weight adjacency matrix is ​​recorded as

[0036] Step 5: Expand the interaction topology determined in step 4 according to the pigeon flock's limited field of view interaction mechanism into an undirected topology, ensuring that the two nodes connected by edges of any direction in the interaction topology obtained in step 4 are expanded into bidirectional connections, which is equivalent to the undirected graph augmented topology of the interaction topology.

[0037] Specifically: Using the neighbor selection mechanism established by formula (7) to obtain the directed topology The weight matrix may have the following relationship: It can also be written as Make Therefore, the interactive topology constructed in step 4 is expanded to an undirected topology with a bidirectionally connected edge set. The third-step neighbor selection rule of the non-information individual can be expressed as:

[0038]

[0039] The neighbor selection rule in formula (8) can be updated to obtain the undirected communication topology Contains bidirectionally connected edge sets The corresponding weighted adjacency matrix is ​​denoted as The elements in the weight matrix are updated according to the following formula:

[0040]

[0041] Based on formula (9), the weight matrix can be updated to obtain the set of bidirectionally connected edges:

[0042] Step 6: Prune the undirected graph augmented interaction topology obtained after step 5, and refer to the hierarchical interaction rules of the pigeon flock to obtain a non-information individual interaction topology containing a directed spanning tree with the information individual as the root node, ensuring that all nodes can recursively obtain the information of the target to be encircled.

[0043] Specifically: By referring to the hierarchical interaction rules of the pigeon flock hierarchy, it can be seen that the cluster interaction topology established according to steps 2 to 5 is not the simplest topological connection form that can support the encirclement control protocol. First, the interaction topology generated by the neighbor selection mechanism given by formula (8) in step 5 is given: The corresponding Laplace matrix can be expressed as:

[0044]

[0045] Define the auxiliary Laplacian matrix based on it in is the topological weight matrix of the directed transmission from the information individual to the non-information individual defined in step 2 Find the row and get. Calculate The minimum eigenvalue of The corresponding eigenvector is denoted by The components of this eigenvector are expressed as

[0046] In the leader-follower architecture, the cluster interaction topology contains at least one directed spanning tree with the leader as the root node, which is a necessary condition to ensure that the basic consistency control tends to be stable. Then the present invention can refer to this theorem and regard the cluster composed of information individuals and non-information individuals as a multi-leader leader-follower architecture, and regard the information individual set as It is expected that by pruning the topology obtained in step 5, a set of N L The interactive topology of a directed spanning tree is a tree with each information individual as the root node, and the union of the spanning trees can cover all non-information individuals. Step 5 The Laplacian matrix of the topological structure obtained is based on the components of the eigenvector corresponding to the minimum eigenvalue The size relationship is used to select neighbors again, and the fourth step neighbor selection rule of non-information individuals is obtained as follows:

[0047]

[0048] Based on the neighbor selection rule given by formula (11), a directed interactive topology is formed The corresponding topological weight adjacency matrix is This topology can ensure that each directed spanning tree formed starting from each information individual can completely cover all non-information individuals.

[0049] Step 7: Based on the neighbor selection mechanism given in steps 2 to 6, combined with the fixed-time target state distributed observer designed in this step, a distributed encirclement tracking consistency control protocol is designed for the information individual and non-information individual levels, which enables the information individuals and non-information individuals in the cluster to form a formation to encircle and track the target in a preset formation. Among them, the fixed-time target state distributed observer includes a fixed-time target acceleration distributed observer, a fixed-time target velocity distributed observer, and a fixed-time target position distributed observer.

[0050] Specifically: Based on the one-way interaction topology between the information individual level and the non-information individual level established in step 2 And the interaction topology between the non-information individuals given in step 6 Under the premise of this hierarchical interactive topology, the fixed-time target acceleration distributed observer is designed as:

[0051]

[0052] In the formula, Indicates the current drone's control input to the target The observed value of Represents neighboring non-information individual drones The target acceleration observer output calculated by the expression below formula (12) is: Represents neighbor information individual According to the target acceleration observer output calculated by the expression above formula (12), the observed value of the target control input by the information individual is the true value of the target acceleration. The parameter design of the fixed-time target acceleration distributed observer given in formula (12) satisfies the condition: α u >h max ρ max / λ min (G), β u >0,γ>1, The definition has been given in the implementation process of step 6. To solve the matrix H, we need to set By dividing the corresponding components, we get Thus, the symmetric matrix G is obtained.

[0053] Each UAV can estimate the target acceleration control input stably within a fixed time according to the fixed-time target acceleration distributed observer given by equation (12), and further estimate the target speed through the following fixed-time target speed distributed observer [such as equation (13)]:

[0054]

[0055] In the formula, and They represent the speed observation values ​​of the target to be surrounded calculated by the current UAV, the neighbor non-information individual and the neighbor information individual based on formula (13). The parameter design of the fixed-time target speed distributed observer designed in formula (13) satisfies: v >h max / λ min (G), β v >0.

[0056] After each UAV estimates the target speed based on the fixed-time target speed distributed observer calculated by formula (13), it uses its observation results to establish a fixed-time target position distributed observer, as shown in formula (14):

[0057]

[0058] In the formula, and They represent the position observation values ​​of the current UAV, neighboring non-information individuals, and neighboring information individuals for the target to be surrounded. The fixed-time target position distributed observer parameter design given in formula (14) satisfies: p >h max / λ min (G), β p > 0. Each information individual can directly obtain the target motion state, and each non-information individual drone can estimate the target motion state within a fixed time using equations (12)-(14). Therefore, even if the target state is only published to information individuals and is published to some non-information individual drones through directed communication of information individuals, non-information individual drones that do not directly obtain the target state can also perform distributed estimation through the states of the neighbors selected in steps 2 to 6, thereby indirectly observing the target information.

[0059] Step 8: Based on the directed interaction topology established in steps 2 to 6, combined with the fixed-time target state distributed observer given by formula (12) to formula (14) in step 7, a distributed encirclement and tracking consistency control protocol is designed for information and non-information individuals, which enables the information and non-information UAVs in the cluster to form a fixed formation to encircle and track the target.

[0060] Specifically: For drone nodes use Denotes the set of non-information individual drone neighbors of drone i, and Represents the set of information individual drone neighbors of drone i. With properties Able to directly obtain the target's true status and Design the distributed control protocol as follows:

[0061]

[0062] For non-information individual drones Based on the topology generated from step 2 to step 6 and For non-information individuals, Design the distributed control protocol as follows:

[0063]

[0064] The distributed control protocol in formulas (15) and (16) uses the observation output of the target state from formulas (12) to (14) to achieve the offset when the information individual and non-information individual drones maneuver around the target using the interactive topology generated by steps 2 to 6. The specific configuration of the target is used to complete the dynamic encirclement tracking. Substitute the control inputs of the information individual and the non-information individual calculated by equations (15) and (16) in step 8 into the UAV kinematic equation (3), and obtain the speed of the UAV by two integrations. and position P i xy .

[0065] 3. Advantages and effects:

[0066] The present invention proposes a UAV cluster encirclement tracking control method that imitates the limited neighbor interaction of a pigeon flock, establishes a hierarchical interaction structure between the target and information individuals and non-information individuals, and proposes a limited neighbor interaction mechanism that imitates the pigeon flock to form a cluster interaction topology with fewer connected links and lower communication load, and designs a target state distributed observer and a consistency control protocol to solve the target encirclement tracking problem under communication restricted conditions. The encirclement control framework proposed in the present invention has the following advantages: first, in the actual encirclement task, due to the limitation of communication resources, the target information cannot reach all the drone nodes in the cluster. The hierarchical interaction mode and neighbor selection mechanism of the pigeon-like flock established by the present method can construct a hierarchical topological structure with a directed spanning tree from the target to the information node and then to the non-information node, thereby ensuring the hierarchical and progressive state estimation in the absence of target information; secondly, the present invention proposes a fixed-time distributed target state observer that can effectively estimate the target position / speed / acceleration and other states, and the cascade design form of the observer can realize fully distributed airborne deployment; in addition, by designing a consistency control protocol, the drone can complete distributed encirclement control of the dynamic target based on the pruned directed topology interaction network, and the control protocol involved does not depend on a specific topological structure in terms of stability, and can be applied to the switching interaction topology generated by the neighbor selection mechanism established by the present invention. Under the initial condition that the UAVs are randomly distributed within the interaction range, the present invention can ultimately achieve stable encirclement and tracking of the target, and effectively reduces the information transmission load on the communication link by imitating the neighbor selection method of limited interaction of a pigeon flock, providing a feasible solution to the formation problem under communication restricted conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 Flowchart of drone cluster encirclement control based on limited neighbor interaction of pigeon flocks

[0068] Figure 2a Initial UAV cluster communication topology divided by communication distance limit at simulation t=6s

[0069] Figure 2b The UAV swarm communication topology generated by the limited interaction mechanism of pigeon flocks when t=6s is simulated

[0070] Figure 3a Initial UAV cluster communication topology divided by communication distance limit at simulation t=12s Figure 3b The UAV swarm communication topology generated by the limited interaction mechanism of pigeon flocks when t=12s is simulated Figure 4a Initial UAV cluster communication topology divided by communication distance limit at simulation t=18s Figure 4b The UAV swarm communication topology generated by the limited interaction mechanism of pigeon flocks at simulation t=18s Figure 5aInitial UAV cluster communication topology divided by communication distance limit at simulation t=24s Figure 5b The UAV swarm communication topology generated by the limited interaction mechanism of pigeon flocks when t=24s is simulated Figure 6 Trajectory diagram of drone cluster encircling and tracking dynamic targets with limited interaction imitating pigeon flocks

[0071] Figure 7a Results of the distributed observer with fixed-time target acceleration

[0072] Figure 7b Results of the distributed observer with fixed-time target speed

[0073] Figure 7c Results of the distributed observer for fixed-time target positions

[0074] Figure 8a Simulating the limited interaction of pigeon flocks UAV cluster consistency encirclement tracking control speed error Figure 8b The numbers and symbols in the position error diagram of the pigeon-like limited interaction drone cluster are as follows:

[0075] ——UAV interaction topology ——Information individual interaction topology ——Non-information individual interaction topology ——Neighbor selection mechanism Generated interaction topology ——Directed interaction weight between information individuals and non-information individuals ——Neighbor selection mechanism among non-information individuals The generated interaction weights ——All drone nodes collection ——Information individual node collection ——A collection of non-information individual nodes ——All drones gather together ——Information individual edge set

[0076] ——Non-information individual edge set

[0077] ——The set of neighboring drone nodes within the sight angle around drone i

[0078] P i x ——X coordinate of drone i location information

[0079] P i y ——Y coordinate of drone i position information

[0080] ——UAV i speed information X coordinate

[0081] ——UAV i speed information Y coordinate

[0082] ——X direction control input information of drone i

[0083] ——Y direction control input information of drone i

[0084] X——Plane position X coordinate

[0085] Y——plane position Y coordinate

[0086] ——The observed value of the acceleration of the target in the X direction by drone i

[0087] ——The observed value of the Y-direction acceleration of the target by drone i

[0088] ——The observed value of the target's X-direction speed by drone i

[0089] ——The observed value of the Y-direction speed of the target by drone i

[0090] ——UAV i’s observation value of the target’s X-direction position

[0091] ——UAV i’s observation value of the target’s Y direction position

[0092] ——UAV i’s tracking error of target’s speed in X direction

[0093] ——UAV i’s tracking error of target’s Y-direction velocity

[0094] ——UAV i’s tracking error of the target’s X-direction position

[0095] ——UAV i’s tracking error of the target in Y direction DETAILED DESCRIPTION

[0096] The simulation process framework is shown in Figure 1 The following is a scenario in which a heterogeneous drone cluster containing information individuals and non-information individuals surrounds a moving target in a communication-restricted environment to verify the effectiveness of the drone cluster encirclement tracking control method proposed in the present invention that simulates the limited neighbor interaction of a pigeon group. The specific steps of the simulation verification process are as follows:

[0097] Step 1: Initialize the scene and drone / target status information. Considering that the drone and the target are moving at the same height, only their plane position coordinates are considered in the simulation, and the simulation is performed on the rectangular coordinate plane. Set the target to be at the origin of the coordinate system, that is, the target position is The target initial speed is set to Set the maximum communication radius to The initialization range of the position of non-information individuals is in,

[0098] Initialization information Individual drone position range is set to The range of this area is the same as the setting area of ​​non-information individuals. Randomly initialize the positions of information individuals and non-information individuals in the set plane position area. The total number of drone clusters is set to N = 23, where the number of information individuals is set to N L =3, the state information of the target can be directly obtained in real time; the number of non-information individuals is set to N F = 20, unable to communicate with the target. Set the target's movement speed to: The time function expression of the X-direction movement speed is: The expression of the moving speed in the Y direction is: Target movement acceleration and the acceleration derivative The maximum value of the target acceleration derivative can be obtained by taking the first and second derivatives of the target position. The coefficients of the fixed-time target state distributed observer given by formulas (12) to (14) in step 7 are used. as well as By integration, we can get the target moving trajectory as follows: Set the simulation time T tol =30s.

[0099] Step 2: Enter the current time step t k The simulation process is as follows: according to the position of the drone initialized in step 1, the information individual neighbor selection rule of the pigeon flock nearest neighbor interaction given by formula (4) is used to traverse each information individual drone. Select the nearest non-information individual drone to enter the neighbor set, and get the directed topology from the information individual to the non-information individual: and confirm The corresponding weighted adjacency matrix is Since the information of each information individual can only be obtained by the non-information individual closest to it, it is obvious that each row of W0 has one and only one 1, and the rest are 0.

[0100] Step 3: Set the maximum communication radius to For non-information individuals, the first step neighbor selection mechanism given by formula (5) is applied according to the communication radius limit, and the interaction topology can be preliminarily obtained: The weighted adjacency matrix of this topology is At the four time nodes t = 6s, 12s, 18s, and 24s, the basic communication topology given by formulas (4) to (5) in steps 2 to 3, which only introduces the communication radius restriction and the nearest neighbor selection mechanism of the information individual, is drawn as follows: Figure 2a , Figure 3a , Figure 4a as well as Figure 5a As shown, the figure shows the location coordinates of each drone node and the communication topology connection status, and the node number is marked next to the location of each drone node.

[0101] Step 4: Set the angle area around the non-information individual Therefore, for non-information individuals Consider its surroundings The six neighbor sets within the line of sight in the range are selected, and the non-information individual second-step neighbor selection mechanism of the pigeon flock limited field of view interaction given by formula (7) is applied to select a nearest neighbor non-information individual node from each set to join the new neighbor set. If the selected neighbor node set within the fixed line of sight is is an empty set, and the value of k can be in the range Then we give up selecting neighbors within the line of sight and select a new neighbor set using the second step neighbor selection rule given by formula (7): The number of internal elements is ≤ 6, so the new non-information individual interaction topology can be recorded as The topological weight adjacency matrix is ​​recorded as

[0102] Step 5: Weighted adjacency matrix of interaction topology of non-information individuals Then, the weight matrix is ​​modified according to the calculation method of formula (9), and the third step neighbor selection rule of non-information individuals given by formula (8) is applied to expand it into a new undirected topology Its undirected topological connection matrix is

[0103] Step 6: Calculate the undirected topology formed in step 7 according to formula (10) The corresponding Laplace matrix And further calculate Find its minimum eigenvalue The eigenvector corresponding to this eigenvalue Combining the eigenvector components The size of is selected according to formula (11) to obtain the final non-information individual drone interaction topology. And record its topological weight adjacency matrix as At the four time nodes t = 6s, 12s, 18s, and 24s, the directed topologies generated by the neighbor selection mechanism given in steps 2 to 6, which contain directed spanning trees with each information individual as the root node, are drawn as follows: Figure 2b , Figure 3b , Figure 4b as well as Figure 5b As shown in the figure, the position coordinates of each drone node and the communication topology connection are displayed. The edge connections between nodes are directed line segments with arrows, and the node numbers are marked next to the drone nodes.

[0104] Step 7: The position trajectory, velocity, acceleration and other simulation settings of the target movement can be obtained set up By dividing the corresponding components, we get And then through Obtain the matrix G and select the fixed time target acceleration distributed observer coefficient as α u =1.2h max ρ max / λ min (G), β u =α u / 40, γ=2; select the fixed time target speed distributed observer coefficient as α v =1.2h max / λ min (G), β v =α v / 20; Select the fixed time target position distributed observer coefficient as α p =h max / λ min (G), β p =α p / 10. The output of the fixed-time target acceleration distributed observer is as follows: Figure 7a As shown in Figure 2, the result of the target speed observer is as follows: Figure 7b As shown, the result of the target position observer is as follows Figure 7c As shown; the upper and lower sub-figures in these three figures respectively represent the estimation results of the target state in the X direction and the Y direction.

[0105] Step 8: Set the relative expected position of the encirclement formation to: The expected offset of the information individual relative to the target is The expected offset of the non-informative individual relative to the target is Design the consistency control protocol used for encirclement control, write the controller stack as follows, and the non-information individual control protocol can be written as a stacked vector expression: The message entity control protocol can be written as a stacked vector expression: Using the stability condition of the Lyapunov function, the LMI solution can be used to calculate the control parameters in formula (15) and formula (16) in step 8:

[0106] The control gain coefficient of the consistency controller is set accordingly. The position change of the dynamic moving target encircled and tracked by the drone cluster on the two-dimensional plane is as follows: Figure 6 As shown in Figure 2, the cluster contains 3 information individual drones and 20 non-information individual drones. The drone cluster formation configurations at several typical time nodes in the 30-second simulation cycle are Figure 2b , Figure 3b , Figure 4b and Figure 5b The figure shows the location distribution of the drones at that time node and the directed connection of the communication topology. Figure 6 Corresponding. Setting information Individual UAV position tracking error relative to the target in The position tracking error of the non-information individual UAV relative to the target is: in Informational / non-information UAV speed tracking error Then the position and speed errors of the drone cluster's encirclement control of the dynamic moving target are as follows: Figure 8a and 8b shown.

Claims

1. A UAV cluster encirclement tracking control method that imitates the limited neighbor interaction of pigeon flocks, Features: The steps of this method are as follows: Step 1: UAV and target kinematic modeling, scene and state information initialization; where, the UAV cluster contains two different types of UAVs, namely, information individual UAVs, hereinafter referred to as information individuals; and non-information individual UAVs, hereinafter referred to as non-information individuals; Step 2: Determine the non-information individual neighbor nodes for the information individual nodes according to the nearest neighbor interaction principle of the pigeon flock; Step 3: Introduce the communication distance range limit, combine it with the manually set maximum interaction radius, and preliminarily determine the undirected communication topology between non-information individuals in the drone cluster; Step 4: Combined with the limited field of view interaction mechanism of the pigeon flock, the circular area within the communication radius of the undirected communication topology determined in step 3 is divided, and the drone closest to the current individual in each area is selected according to the nearest neighbor principle to add it to its neighbor node set to construct a streamlined interaction topology; Step 5: Expand the interaction topology determined in step 4 according to the pigeon flock limited field of view interaction mechanism into an undirected topology, ensuring that the two nodes connected by edges of any direction in the interaction topology obtained in step 4 are expanded into bidirectional connections, which is equivalent to the undirected graph augmented topology of the interaction topology; Step 6: Prune the undirected graph augmented interaction topology obtained after step 5, and refer to the hierarchical interaction rules of the pigeon flock to obtain a non-information individual interaction topology containing a directed spanning tree with the information individual as the root node, ensuring that all nodes can recursively obtain the information of the target to be encircled; Step 7: Based on the neighbor selection mechanism given in steps 2 to 6, design a fixed-time target acceleration, velocity, and position distributed observer to estimate the target state for both informative and non-informative individuals; Step 8. Based on the directed interactive topology established in steps 2 to 6 and combined with the fixed-time target state distributed observer given in step 7, a distributed encirclement and tracking consistency control protocol is designed for information and non-information individuals, which enables the information and non-information UAVs in the cluster to encircle and track the target in a fixed formation.

2. The method according to claim 1, Features: The step 1 is as follows: kinematic modeling of the UAV and the target, The target motion model is established as: In the formula, represents the target three-dimensional position vector, represents the target three-dimensional velocity vector, Represents the target three-dimensional acceleration vector; The kinematic model of the UAV is established as: In the formula, represents the three-dimensional position vector of drone node i, represents the three-dimensional velocity vector, g is the gravitational acceleration, T i Represents the thrust of the drone, m i represents the mass of the drone, R i represents the attitude rotation matrix, is a unit vector; In cluster distributed control, since the attitude rotation angle is small, the UAV can be controlled to move in a two-dimensional plane to verify the formation encirclement algorithm. The control quantity can be regarded as Therefore, it can be simplified to the differential equation of the second-order agent in the two-dimensional plane: In the formula, represents the position vector of drone node i in the two-dimensional plane, represents the velocity vector in a two-dimensional plane, represents a two-dimensional control input with U i The first two components of .

3. The method according to claim 1, Features: The specific steps of step 2 are as follows: according to the relative position nearest neighbor rule, each information individual in the drone cluster is Determine specific non-information individual neighbors, for non-information individuals Given a neighbor selection set, the neighbor selection mechanism established for information individuals can be expressed as: The directed topology from the information individual to the non-information individual obtained by constructing the nearest neighbor selection mechanism of the pigeon flock given by formula (4) is: Its edge set satisfies Determine the topology The corresponding weighted adjacency matrix is When non-information individuals Individuals who can receive information When the state information is transmitted, the corresponding element in the weight matrix On the contrary, the weight in the topology Represents the exchange of no information from a non-informative individual to an informative individual.

4. The method according to claim 1, Features: The specific details of step 3 are as follows: as well as The positions of the current time step are P i (t) and P j (t), the threshold of the interactive communication radius between non-information individuals in a given cluster In order to limit the communication range between the drone and its neighbors, the pigeon flock is simulated to interact only with neighboring individuals within a limited communication range, and non-information individuals within the communication radius are selected as neighbors. The first step of the neighbor selection rule for non-information individuals can be expressed as: The undirected interaction topology constructed based on formula (5) is denoted as Its edge set satisfies The weighted adjacency matrix of this topology is is a symmetric matrix.

5. The method according to claim 1, Features: The specific steps of step 4 are as follows: For non-information node i, use Represents a set of position points within its communication range, and defines the azimuth relative to UAV i with the positive direction of the x-axis as zero degrees as: Drawing on the limited field of view interaction habits of pigeons, each individual prefers to interact with a fixed number of individuals in each visual range around it. In order to effectively and evenly reduce the number of neighbor nodes of non-information individuals within the communication radius, the drone nodes are placed According to the area within its perception range, it is divided equally into l according to the angles around it. sub Sub-areas According to the azimuth relative to UAV i given above The definition of determines the neighbor set in the sub-region around drone node i: According to the definition of formula (6), represents the set of neighbors selected according to the neighbor selection rule given in step 3 The subset distributed in the kth sub-region around the node in; The present invention follows the pattern that a flock of pigeons selects a fixed number of neighbors to interact with within a specific visual range, and selects the neighbor sets of each sub-area constructed by formula (6) without loss of generality. The nodes closest to the current UAV in the equation constitute a new neighbor set. This ensures that the current non-information individual can obtain information about individuals in each sight angle range. The second-step neighbor selection rule of the non-information individual given on the basis of formula (5) can be written as: According to the neighbor selection mechanism in equation (7), the interaction topology is written as Its topological weight adjacency matrix is ​​recorded as 6. The method according to claim 1, Features: The specific steps of step 5 are as follows: According to the neighbor selection mechanism established in step 4, a directed topology is obtained. The weight matrix may have the following relationship: It can also be written as Make Therefore, the interactive topology constructed in step 4 is expanded to an undirected topology with a bidirectionally connected edge set. The third-step neighbor selection rule of the non-information individual can be expressed as: The neighbor selection rule in formula (8) can be updated to obtain the undirected communication topology Contains bidirectionally connected edge sets The corresponding weighted adjacency matrix is ​​denoted as The elements in the weight matrix are updated according to the following formula: Based on formula (9), the weight matrix can be updated to obtain the bidirectionally connected edge set 7. The method according to claim 1, Features: The specific details of step 6 are as follows: First, the interaction topology generated by the neighbor selection mechanism given in step 5 is given The corresponding Laplace matrix can be expressed as: Define the auxiliary Laplacian matrix based on it in is the topological weight matrix of the directed transmission from the information individual to the non-information individual defined in step 2 Find the row and get; calculate The minimum eigenvalue of The corresponding eigenvector is denoted by The components of this eigenvector are expressed as The cluster composed of information individuals and non-information individuals is regarded as a leader-follower structure with multiple leaders, and the information individuals are grouped together. It is expected that by pruning the topology obtained in step 5, a set of N L The interactive topology of a directed spanning tree is a tree with each information individual as the root node, and the union of the spanning trees can cover all non-information individuals; the Laplacian matrix of the topological structure obtained in step 5 is based on the components of the eigenvector corresponding to the minimum eigenvalue The size relationship is used to select neighbors again, and the fourth step neighbor selection rule of non-information individuals is obtained as follows: Based on the neighbor selection rule given by formula (11), a directed interactive topology is formed The corresponding topological weight adjacency matrix is This topology can ensure that each directed spanning tree formed starting from each information individual can completely cover all non-information individuals.

8. The method according to claim 1, Features: The specific details of step 7 are as follows: Based on the one-way interaction topology between the information individual level and the non-information individual level established in step 2 And the interaction topology between the non-information individuals given in step 6 Under the premise of this hierarchical interactive topology, the fixed-time target acceleration distributed observer is designed as: In the formula, Indicates the current drone's control input to the target The observed value of Represents neighboring non-information individual drones The target acceleration observer output calculated by the expression below formula (12) is: Represents neighbor information individual The output of the target acceleration observer calculated by the expression above formula (12) is the observed value of the target control input by the information individual, which is the true value of the target acceleration; the parameter design of the fixed-time target acceleration distributed observer given in formula (12) satisfies the condition: α u >h max ρ max / λ min (G), β u >0,γ>1, The definition has been given in the implementation process of step 6. To solve the matrix H, we need to set By dividing the corresponding components, we get Thus, the symmetric matrix G is obtained; Each UAV can estimate the target acceleration control input stably within a fixed time according to the fixed-time target acceleration distributed observer given by equation (12), and further estimate the target speed through the following fixed-time target speed distributed observer: In the formula, and They represent the speed observation values ​​of the target to be surrounded calculated by the current UAV, the neighbor non-information individual and the neighbor information individual based on formula (13); the fixed-time target speed distributed observer parameter design in formula (13) satisfies: v >h max / λ min (G), β v >0; After each UAV estimates the target speed based on the fixed-time target speed distributed observer calculated by formula (13), it uses its observation results to establish a fixed-time target position distributed observer, as shown in formula (14): In the formula, and Respectively represent the position observation values ​​of the current UAV, neighboring non-information individuals, and neighboring information individuals for the target to be encircled; The fixed-time target position distributed observer parameter design given in equation (14) satisfies: p >h max / λ min (G), β p >0; each information individual can directly obtain the target motion state, and each non-information individual drone can estimate the target motion state within a fixed time using equations (12)-(14). Therefore, even if the target state is only published to information individuals and is published to some non-information individual drones through directed communication of information individuals, non-information individual drones that do not directly obtain the target state can also perform distributed estimation through the states of the neighbors selected in steps 2 to 6, thereby indirectly observing the target information.

9. The method according to claim 1, Features: The specific steps of step eight are as follows: use Denotes the set of non-information individual drone neighbors of drone i, and Represents the neighbor set of information individual drones of drone i; for information individual drones With properties Able to directly obtain the target's true status and Design the distributed control protocol as follows: For non-information individual drones Based on the topology generated from step 2 to step 6 and For non-information individuals, Design the distributed control protocol as follows: The distributed control protocol in formulas (15) and (16) uses the observation output of the target state from formulas (12) to (14) to achieve the offset when the information individual and non-information individual drones maneuver around the target using the interactive topology generated by steps 2 to 6. The specific configuration completes dynamic encirclement and tracking of the target.

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