A UAV swarm tracking control method based on limited neighbor interaction of pigeon flocks

Abstract

The present invention discloses a method for encirclement and tracking control of drone swarms, emulating the limited neighbor interaction of pigeon flocks. The method comprises nine steps: step 1: kinematic modeling of drones and targets, determining their initial states and the intended encirclement configuration; step 2: dividing drones in the swarm into information individuals and non-information individuals based on their access rights to the target state, and artificially selecting directed connections from information individuals to non-information individuals according to the nearest neighbor interaction rules of pigeon flocks; and step 3: introducing communication distance restrictions to define the neighbor sets of non-information individuals. The method is simple to implement, and the proposed pigeon-like limited interaction neighbor selection rules can significantly reduce the communication load in formation encirclement control, increase the control convergence speed, and provide robust solutions to difficult problems such as topology construction in communication-restricted environments and control protocol design for switching topologies.

Description

Technical Field

[0001] The present invention relates to a method for encircling and tracking a cluster of unmanned aerial vehicles (UAVs) that simulates the limited neighbor interaction of a pigeon flock, and belongs to the technical field of cooperative control of UAV clusters. Background Art

[0002] UAV formation, obstacle avoidance, and encirclement control have long been key areas of focus and research in the field of swarm intelligence. By distributing control and decision-making algorithms across a multi-UAV swarm system, the goal is to achieve control response speeds and accuracy comparable to ideal conditions under conditions such as limited communication or link failures. Encirclement control and target tracking within a swarm of UAVs are common demonstration and verification scenarios for unmanned swarm combat in modern military battlefields. UAVs, in a predetermined configuration, perform a specific formation around a leader or local target, ensuring that multiple UAV nodes maintain their formation consistently. During the tracking process, the communication topology can be dynamically adjusted according to constraints such as communication distance without disrupting the stability of the formation. By distributing control systems onboard each UAV, the computational load on the ground control station can be effectively reduced.

[0003] Currently, common cooperative control algorithms for drone swarms fall into several categories, including behavior-based, energy-based, and consensus-based control methods. Behavior-based control utilizes the swarm's motion characteristics, such as coordinated movement, obstacle avoidance, and topology reconstruction, to design specific behavioral rules and trigger conditions. These control inputs, such as virtual forces, are applied to the swarm according to weights or priorities. Energy-based control applies gradient information, such as the energy function or the rate of change of potential field intensity, to the system to drive its evolution toward a steady-state equilibrium point. These control methods, when applied to large-scale swarm formation control, suffer from significant drawbacks, including poor generalization, limited control accuracy, and heavy communication overhead. When drones are constrained by communication range, it is difficult to maintain an ideal undirected, connected interactive topology. Therefore, some consensus control protocols that assume a specific communication topology are ineffective.

[0004] In a formation encirclement task with limited communication interaction, the reference state of the target cannot be guaranteed to be continuously and in real time acquired 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 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. Under the premise of dividing the drones in the cluster into different information acquisition authority levels such as information individuals and non-information individuals, a tree network topology with low communication load and support for information cascade transmission is generated. Its root node is located at the information individual, which can ensure that the situation information of the target can be fully covered and transmitted in the communication topology formed by this 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 drone clusters in communication-restricted environments, enhance the adaptive control performance of drone clusters for limited interaction topology rules, and improve the robustness of drones to harsh 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 UAV cluster encirclement and tracking control method that imitates the limited neighbor interaction of a pigeon flock. In order to solve the multi-UAV formation encirclement control problem under low interactive load conditions in a communication restricted environment, a pigeon flock-like limited neighbor interaction rule is established, and a fixed-time consistency distributed observer is designed. In the case that the non-information individual UAVs in some clusters lack the target state information, in a topological structure that switches in real time related to the cluster node position, the UAV cluster containing information individuals and non-information individuals is realized to stably coordinate and track the target, effectively improving the control performance of the UAV cluster in a restricted communication environment and the antagonism ability to communication link interference.

[0006] Aiming at the topological construction and formation cooperative control problems of UAV clusters in communication-restricted environments, this paper invented 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 several parts, such as 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 of the UAV and the target is performed, considering that the UAV is at the same height plane after vertical takeoff, the UAV is set to a four-rotor configuration for vertical takeoff and landing, and the target is set to an omnidirectional Mecanum wheeled unmanned vehicle configuration for translation in the plane. In this 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] Where, 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 acceleration due to gravity, T i Indicates the thrust of the drone, m i represents the quality 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 two-dimensional plane velocity vector, 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). Assume 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. They need to communicate and interact with information individuals or neighboring non-information individuals in a hierarchical structure similar to that of a pigeon flock to complete the encirclement task. Represents a collection of information individuals, using Represents a set of non-information individuals, using Represents the total set of drone nodes that perform encirclement tasks, where Set 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 target's acceleration 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 represents the non-information individual state, when When indicates the individual status of information.

[0020] Step 2: Determine the non-information individual neighbor nodes for the information individual nodes based on 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 relative position nearest neighbor rule 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 the pigeon-like nearest neighbor selection mechanism 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 transmitting state information, the corresponding elements 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 and combine them with the manually set maximum interaction radius to 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 interaction radius between non-information individuals in a given cluster In order to limit the communication range between the drone and its neighbors, and to imitate the characteristic of pigeons that they only interact with neighboring individuals within a limited communication range, 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 communication radius of equal angles around them. According to the nearest neighbor principle, the drone closest to the current individual in each area is selected and added to its neighbor node set to construct a streamlined interaction topology.

[0030] Specifically: For non-information node i, use Represents the set of position points within its communication range, and defines the azimuth angle relative to drone 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 neighboring nodes of non-information individuals within the communication radius, the drone nodes are placed The area within its perception range is divided into equal parts according to the angles around it. sub-regions According to the azimuth angle relative to UAV i given above The definition of determines the neighbor set in the sub-area around the 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 of a flock of pigeons selecting a fixed number of neighbors to interact with within a specific visual range, and selects the neighbor sets of each sub-region constructed by formula (6) without loss of generality. The nodes closest to the current UAV in the network form 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 augmentation topology of the interaction topology.

[0037] Specifically: The neighbor selection mechanism established using formula (7) obtains the directed topology The weight matrix may have the following relationship: It can also be written as Make Therefore, the interaction 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 uninformed 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 augmentation 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: Based on the hierarchical interaction rules of the pigeon flock hierarchy, it can be seen that the cluster interaction topology established in 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 Laplace matrix based on it in The topological weight matrix of the directed transmission from the information individual to the non-information individual defined in step 2 is Find the row sum. Calculate The minimum eigenvalue of The corresponding eigenvector is denoted as 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 the 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 Laplace matrix of the topological structure obtained in step 5 is based on the components of the eigenvector corresponding to the minimum eigenvalue. The neighbor selection rule of the fourth step of non-information individuals is:

[0047]

[0048] Based on the neighbor selection rule given by formula (11), a directed interaction 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 presented in Steps 2-6 and the fixed-time target state distributed observer designed in this step, a distributed encirclement tracking consistency control protocol is designed for both the informational and non-informational levels. This enables the informational and non-informational individuals within the cluster to form a formation and encircle and track the target. 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 follows:

[0051]

[0052] Where, 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 individuals 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 of step 6. To solve the matrix H, we need to set Obtained by dividing the corresponding components 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 formula (12), and further estimate the target speed through the following fixed-time target velocity distributed observer [as shown in formula (13)]:

[0054]

[0055] Where, and They represent the speed observation values ​​of the target to be surrounded calculated by the current UAV, the neighboring non-information individual, and the neighboring 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] Where, and Respectively 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 formulas (12) to (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 information individual drone neighbor set of drone i. With properties Able to directly obtain the target's true status and Design distributed control protocol as follows:

[0061]

[0062] For non-information individual drones Based on the topology generated from steps 2 to 6 and For non-information individuals, Design 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 realize the offset of the information individual and non-information individual UAVs when they are maneuvering at the target using the interactive topology structure 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 UAV's speed by two integrations. and position P i xy .

[0065] 3. Advantages and effects:

[0066] The present invention proposes a UAV cluster encirclement and tracking control method that imitates the limited neighbor interaction of pigeon flocks, establishes a hierarchical interaction structure between targets and information individuals and non-information individuals, and proposes a limited neighbor interaction mechanism that imitates pigeon flocks to form a cluster interaction topology with fewer connected links and lower communication load. In addition, a target state distributed observer and a consistency control protocol are designed to solve the target encirclement and tracking problem under communication-restricted conditions. The encirclement control framework proposed in the present invention has the following main advantages: first, in actual encirclement tasks, 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 group established by this method can construct a hierarchical topology structure containing a directed spanning tree from the target to the information node and then to the non-information node, ensuring the hierarchical progressive state estimation in the absence of target information; second, 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 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 topology 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 drones 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 Drone swarm encirclement control flow chart imitating 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 Simulation t=6s UAV cluster communication topology generated by the limited interaction mechanism of pigeon flock

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

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

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

[0073] Figure 7c Results of a distributed observer with fixed-time target positions

[0074] Figure 8a Speed ​​error of limited interaction UAV cluster with pigeon-like consistency encirclement tracking control Figure 8b The numbers and symbols in the position error diagram of the pigeon-like limited interaction UAV 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 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’s location information

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

[0080] ——X coordinate of drone i speed information

[0081] ——Y coordinate of drone i speed information

[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] ——Observation value of the X-direction acceleration of the target by drone i

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

[0088] ——UAV i's observation value of the target's X-direction velocity

[0089] ——Observation value of the target's Y-direction velocity 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 X-direction velocity

[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 the Y direction DETAILED DESCRIPTION

[0096] The simulation process framework is shown in Figure 1 The following simulation verifies the effectiveness of the proposed method for tracking and encircling a moving target by using a heterogeneous drone swarm consisting of both informative and non-informative individuals in a communication-restricted environment. 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 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 target's status information 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 acceleration derivatives The maximum value of the target acceleration derivative can be obtained by taking the first and second derivatives of the target position respectively. 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 movement 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 traversed to 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 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) and (5) in steps 2 and 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 in the figure, the location coordinates of each drone node and the communication topology connection status are shown, 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 to divide the total Therefore, for non-information individuals Consider its surroundings The six neighbor sets within the sight range are selected, and the second-step neighbor selection mechanism of the non-information individual of the pigeon flock limited field of view interaction given by formula (7) is applied. A nearest neighbor non-information individual node is selected from each set to join the new neighbor set. If the selected neighbor node set within the fixed sight range is Is an empty set, the k value can be in the range Then we give up selecting neighbors within the sight range and select a new neighbor set according to 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 the non-information individual 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 Combine 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 edges between nodes are directed line segments with arrows, and the node numbers are marked next to the drone nodes.

[0104] Step 7: The target moving position trajectory, speed, acceleration and other simulation settings can be obtained set up Obtained by dividing the corresponding components 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, 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 in the figure; 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 expected relative position of the encirclement formation to: The expected offset of the information individual relative to the target is The expected offset of the non-information individual relative to the target is Design the consistency control protocol used for encirclement control. The controller stack is expressed as follows. The non-information individual control protocol can be expressed as a stacked vector: 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 the figure, 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 30s simulation cycle are Figure 2b 、 Figure 3b 、 Figure 4b and Figure 5b The figure shows the location distribution of the UAVs and the directed connection of the communication topology at that time node. Figure 6 Corresponding. Set the 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 Information / non-information UAV speed tracking error Then the position and speed errors of the UAV cluster's encirclement control of the dynamic moving target are as follows: Figure 8a and 8b shown.

Claims

1. A method for encircling and tracking drone clusters by imitating the limited neighbor interaction of pigeon flocks, characterized by: The steps of this method are as follows: Step 1: Kinematic modeling of drones and targets, and initialization of scene and state information. Assume that the drone cluster contains two different types of drones: information-based drones (hereinafter referred to as information-based drones) and non-information-based drones (hereinafter referred to as non-information-based drones). Assume that information-based drones can directly obtain target information and unidirectionally transmit their own states to some non-information-based drones. Non-information-based drones, on the other hand, do not have the ability to directly obtain the state of the target to be surrounded and need to communicate with information-based drones or neighboring non-information-based drones in a hierarchical structure similar to that of a pigeon flock to complete the encirclement task. Step 2: Determine the non-information individual neighbor nodes for the information individual node based on the nearest neighbor interaction principle of the pigeon flock; Step 3: Introduce the communication distance range limit and combine it with the manually set maximum interaction radius to 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. According to the nearest neighbor principle, the drone closest to the current individual in each area is selected and added 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 to be bidirectionally connected, that is, equivalent to the undirected graph augmentation topology of the interaction topology; Step 6: Prune the undirected graph augmentation interaction topology obtained in step 5. By referring to the hierarchical interaction rules of the pigeon flock, a non-information individual interaction topology containing a directed spanning tree with the information individual as the root node is obtained, 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 interaction 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 form a fixed formation to encircle and track the target.

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

3. The method according to claim 2, wherein: 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 the neighbors of non-information individuals, for non-information individuals Given a neighbor selection set, the neighbor selection mechanism established for information individuals is expressed as: The directed topology from the information individual to the non-information individual obtained by the pigeon-like nearest neighbor selection mechanism 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 transmitting state information, the corresponding elements 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 3, wherein: The specific steps 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 interaction radius between non-information individuals in a given cluster In order to limit the communication range between the drone and its neighbors, and to imitate the characteristic of pigeons that they only interact with neighboring individuals within a limited communication range, non-information individuals within the communication radius are selected as neighbors. The first step of the neighbor selection rule for non-information individuals is 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 4, characterized in that: The specific steps of step 4 are as follows: For non-information node i, use Represents the set of position points within its communication range, and defines the azimuth angle relative to drone 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 interval around it. In order to effectively and evenly reduce the number of neighboring nodes of non-information individuals within the communication radius, the drone nodes are placed The area within its perception range is divided into l by the angles around it. sub sub-regions According to the azimuth angle relative to UAV i given above The definition of determines the neighbor set in the sub-area around the drone node i: According to the definition of formula (6), Represents the neighbor set selected according to the neighbor selection rule given in step 3 The subset distributed in the kth subregion around the node in; Following the pattern of a flock of pigeons selecting a fixed number of neighbors to interact with within the sight interval, the neighbor sets of each sub-region constructed by formula (6) are The nodes closest to the current UAV form 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) is recorded as: According to the neighbor selection mechanism in formula (7), the interaction topology is written as Its topological weight adjacency matrix is ​​recorded as 6. The method according to claim 5, characterized in that: 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 has the relationship: Or it can be written as Make Therefore, the interaction 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 uninformed individual is expressed as: The neighbor selection rule in formula (8) is 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: Update the weight matrix based on formula (9) to obtain the set of bidirectionally connected edges 7. The method according to claim 6, characterized in that: The sixth step is as follows: First, the interaction topology generated by the neighbor selection mechanism given in step five is given. The corresponding Laplace matrix is ​​expressed as: Define the auxiliary Laplace matrix based on it in The topological weight matrix of the directed transmission from the information individual to the non-information individual defined in step 2 is Find the row and get; calculate The minimum eigenvalue of The corresponding eigenvector is denoted as 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 Laplace matrix of the topological structure obtained in step 5 is based on the components of the eigenvector corresponding to the minimum eigenvalue The neighbor selection rule of the fourth step of non-information individuals is: Based on the neighbor selection rule given by formula (11), a directed interaction 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 7, wherein: The specific steps 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 follows: Where, 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 individuals 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 of step 6. To solve the matrix H, we need to set Obtained by dividing the corresponding components 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 formula (12), and further estimate the target speed through the following fixed-time target velocity distributed observer: Where, and They represent the speed observation values ​​of the target to be surrounded calculated by the current UAV, the neighboring non-information individual, and the neighboring information individual based on formula (13); the parameters of the fixed-time target speed distributed observer designed in formula (13) are designed to meet the following requirements: 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): Where, 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 UAV can estimate the target motion state within a fixed time using formulas (12)-(14). Therefore, even if the target state is only released to information individuals and is released to some non-information individual UAVs through directed communication of information individuals, the non-information individual UAVs that do not directly obtain the target state or make distributed estimates through the states of the neighbors selected in steps 2 to 6 can indirectly observe the target information.

9. The method according to claim 8, characterized in that: 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 information individual drone neighbor set of drone i; for information individual drone With properties Able to directly obtain the target's true status and Design distributed control protocol as follows: For non-information individual drones Based on the topology generated from steps 2 to 6 and For non-information individuals, Design 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 realize the offset of the information individual and non-information individual UAVs when they are maneuvering at the target using the interactive topology structure generated by steps 2 to 6. The configuration completes dynamic encirclement and tracking of the target.

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