A Multi-Agent Ungrouped Cooperative Encirclement and Control Method

Abstract

This invention discloses a multi-agent, non-formational cooperative encirclement control method, relating to the field of multi-agent automation control. Addressing the problem of cooperative encirclement control of moving targets in a dual-integral multi-agent system, this invention proposes a non-formational cooperative encirclement controller. The controller utilizes a distributed fixed-time estimator to obtain the unknown position of the moving target. The controller ensures that the moving target is encircled within the convex hull formed by the multi-agent system, without pre-specifying the final encirclement formation or the relative distance between agents and the moving target. This invention solves the problem of multi-agent cooperative encirclement of moving targets with unknown time-varying speeds. The encirclement controller design does not require pre-specifying the shape of the final encirclement formation, nor the relative positions between agents or between agents and the target point, thus exhibiting better adaptability and scalability. Furthermore, it ensures that collisions do not occur between agents during the encirclement process, guaranteeing the system's safety and reliability.

Description

Technical Field

[0001] This invention relates to the field of multi-agent automated control, specifically to a multi-agent non-formational cooperative encirclement control method. Background Technology

[0002] Compared to individual agents, multi-agent systems, through information exchange and collaborative work among their agents, can accomplish complex tasks that a single agent cannot, greatly improving their ability to handle large-scale, complex operations. Currently, multi-agent cooperative control is widely used in intelligent unmanned systems, including multiple UAVs, multiple unmanned surface vessels, and multiple unmanned underwater vehicles. Cooperative encirclement control is a specific manifestation of multi-agent cooperative control. This control aims to design a cooperative encirclement controller to drive a multi-agent system to encircle stationary targets or moving targets into the interior of a convex hull formed by the multiple agents. Multi-agent target encirclement control enables real-time monitoring of the target's surrounding environment, providing a safe operating area for the target, and has very broad application prospects in both military and civilian fields.

[0003] Currently, in the design of multi-agent cooperative encirclement controllers, the encirclement formation of the multiple agents needs to be specified in advance, such as conventional rings, ellipses, regular polygons, etc. Some encirclement controller designs, while not specifically specifying the encirclement formation, still require specifying the final relative distances between the multiple agents and the target point. This poses challenges to the practicality, timeliness, and security of encirclement control. Practicality: In real-world applications, due to the uncertainty of the system model and the presence of external interference, it is impossible to specify a suitable encirclement formation or the stalemate distance between the agents and the target in advance. Timeliness: In military encirclement and strike operations against enemy targets or the encirclement and protection of friendly targets, where timeliness is crucial, encircling the target within the convex hull formed by the agents is the primary task, without needing to specifically specify the shape of the convex hull. Security: Any restrictions on the formation of multi-agent cooperative encirclement formations may introduce security risks. Fixed multi-agent encirclement formations or pre-defined relative positions between agents and between agents and the target often hinder obstacle avoidance, with this safety risk being particularly pronounced in complex environments. Therefore, existing multi-agent cooperative encirclement control methods need to be improved to address these issues. Summary of the Invention

[0004] In order to solve the problem that the existing multi-agent cooperative encirclement control requires preset positions and is not conducive to the system's obstacle avoidance, the present invention provides a multi-agent non-formation cooperative encirclement control method.

[0005] This invention is achieved through the following technical solution: a multi-agent non-formational cooperative encirclement and control method, comprising the following steps:

[0006] Step 1: The multi-agent system consists of N identical agents, which are modeled using the following second-order dynamic model: Where, x i v i u i These represent the position, velocity, and control input of agent i, respectively;

[0007] Step 2: Define the location distribution of multiple agents and the convex hull co(x) corresponding to the position distribution = {Σ i∈N λ i x i :λ i ≥0andΣ i∈N λ i =1};

[0008] Step 3: Define the convex hull center According to the definition of convex hull, the center x of the convex hull is an interior point of the convex hull;

[0009] Step 4: Define the target dynamic as Where the target state matrix The target is a moving target, and the moving target moves in a circle at an angular frequency ω; and the target state matrix is ​​global information that can be acquired by multiple agents.

[0010] Step 5: Define the distance between the moving target x0 and the convex hull co(x) as P. x0 (x)=inf η∈co(x) ||η-x0||, if and only if x0∈co(x), we have This indicates that multiple agents have achieved coordinated encirclement and control of moving targets;

[0011] Step 6: The capture controller needs the interaction information between the agent and its neighboring nodes to achieve cooperative control. The nearest neighbor rule is used to define the neighboring nodes of agent i as N. i ={j∈N,j≠i:||x i -x j ||≤μ}, where μ is the perception distance of the agent and satisfies μ>d>0, and d is the collision distance between agents;

[0012] Step 7: Due to distance limitations or obstacles, some agents are unable to obtain the position of the moving target. The agents utilize a distributed fixed-time estimator η i Estimate the position of the moving target;

[0013] The design expression for the distributed fixed-time estimator is:

[0014]

[0015] Where η i Let η0 be the estimate of the moving target x0 by agent i, and η0 = x0. If agent i can detect the location of the moving target, then a i0 =1, otherwise a i0 =0, meaning that at least one agent in the multi-agent system can detect the location of the moving target; a ij >0 indicates that agent i and agent j are neighboring nodes, and the network topology of the multi-agent system is an undirected graph; element a ii =0, meaning the network topology does not consider self-loops; the Laplace matrix corresponding to the multi-agent network topology is L = [l ij ]∈R n×n The elements of the Laplace matrix satisfy And l ij =-a ij .

[0016] Furthermore, step 7 also includes setting the parameters of the distributed fixed-time estimator and calculating the fixed time for convergence, where c1 > 0, c2 > 0, μ1 > 1; defining matrix B = diag{a i0 a i1 , ..., a iN} and matrix H = L + B; the fixed time for convergence of the distributed fixed-time estimator in λ1 represents the smallest eigenvalue of matrix H, and λ1 > 0.

[0017] Step 8: The agent determines its position based on its own location information x. i The relative position information x with neighboring nodes i -x j Its own speed information v i The global state matrix S of the moving target, and the distributed fixed-time estimator η i This is used to design the following multi-agent control inputs:

[0018]

[0019] in, And k2>0; α(·) is the obstacle function. When the distance between agents approaches the collision distance, the repulsive force between agents gradually increases to ensure that no collision occurs between agents.

[0020] Compared with the prior art, the present invention has the following beneficial effects: The multi-agent non-formation cooperative encirclement control method provided by the present invention solves the problem of multi-agent cooperative encirclement of targets moving at unknown time-varying speeds. The encirclement controller design does not require pre-specifying the shape of the final encirclement formation, nor does it require specifying the relative positions between agents or between agents and the target point. Therefore, it has better adaptability and scalability. At the same time, it can ensure that no collisions occur between agents during the encirclement process, thus ensuring the safety and reliability of the system. Attached Figure Description

[0021] Figure 1 Position estimation error under the action of a distributed fixed-time estimator (1) The convergence process.

[0022] Figure 2 The trajectory of a multi-agent system collaboratively capturing a moving target under the control strategy, i.e., under the action of formula (2).

[0023] Figure 3 For the control strategy, i.e., under the action of formula (2), the average position error The convergence process.

[0024] Figure 4 For the control strategy, i.e., under the action of formula (2), the distance ||x| between multiple agents ij The convergence process of ||. Detailed Implementation

[0025] The present invention will be further described below with reference to specific embodiments.

[0026] A multi-agent, non-formational cooperative encirclement control method includes the following steps:

[0027] Step 1: The multi-agent system consists of N identical agents, which are modeled using the following second-order dynamic model: Where, x i v i u i These represent the position, velocity, and control input of agent i, respectively;

[0028] Step 2: Define the location distribution of multiple agents and the convex hull co(x) corresponding to the position distribution = {Σ i∈N λ i x i :λ i ≥0andΣ i∈N λ i =1};

[0029] Step 3: Define the convex hull center According to the definition of convex hull, the center x of the convex hull is an interior point of the convex hull;

[0030] Step 4: Define the target dynamic as Where the target state matrix The target is a moving target, and the moving target moves in a circle at an angular frequency ω; and the target state matrix is ​​global information that can be acquired by multiple agents.

[0031] Step 5: Define the distance between the moving target x0 and the convex hull co(x) as P. x0 (x)=inf η∈co(x) ||η-x0‖, if and only if x0∈co(x), we have This indicates that multiple agents have achieved coordinated encirclement and control of moving targets;

[0032] Step 6: The capture controller needs the interaction information between the agent and its neighboring nodes to achieve cooperative control. The nearest neighbor rule is used to define the neighboring nodes of agent i as N. i ={j∈N,j≠i:||x i -x j ||≤μ}, where μ is the perception distance of the agent and satisfies μ>d>0, and d is the collision distance between agents;

[0033] Step 7: Due to distance limitations or obstacles, some agents are unable to obtain the position of the moving target. The agents utilize a distributed fixed-time estimator η i Estimate the position of the moving target;

[0034] The design expression for the distributed fixed-time estimator is:

[0035]

[0036] Where η i Let i be the agent i's estimate of the moving target x0 and If agent i can detect the location of the moving target, then a i0 =1, otherwise a i0 =0, meaning that at least one agent in the multi-agent system can detect the location of the moving target; a ij >0 indicates that agent i and agent j are neighboring nodes, and the network topology of the multi-agent system is an undirected graph; element a ii =0, meaning the network topology does not consider self-loops; the Laplace matrix corresponding to the multi-agent network topology is L = [l ij ]∈R n×n The elements of the Laplace matrix satisfy And l ij =-a ij .

[0037] Continue with the steps of setting the parameters of the distributed fixed-time estimator and calculating the fixed time for convergence, where c1 > 0, c2 > 0, μ1 > 1; define matrix B = diag{a i0 a i1 , ..., a iN} and matrix H = L + B; the fixed time for convergence of the distributed fixed-time estimator in λ1 represents the smallest eigenvalue of matrix H, and λ1 > 0, defining the position estimator error. Then at a fixed time T * Afterwards, the error It converges to zero.

[0038] Step 8: The agent determines its position based on its own location information x. i The relative position information x with neighboring nodes i -x j Its own speed information v i The global state matrix S of the moving target, and the distributed fixed-time estimator η i This is used to design the following multi-agent control inputs:

[0039]

[0040] in, And k2>0; α(·) is the obstacle function. When the distance between agents approaches the collision distance, the repulsive force between agents gradually increases to ensure that no collision occurs between agents.

[0041] The barrier function α(·) is α(||x ij ||), When ||x ij When ||>μ, α(||x) ij If ||) is zero, it indicates that agent i and agent j are not neighboring nodes and have no repulsive force on each other.

[0042] The controller (2) described above can achieve a cooperative encirclement task without collisions between the agents. The proof is as follows:

[0043] Define the position error vector Mean position error vector

[0044] Taking its second derivative with respect to time, we get:

[0045]

[0046] Based on the symmetry of the network topology, it is easy to know Σ i∈N φi =0, therefore we have:

[0047]

[0048] parameter k2>0, therefore system (3) satisfies the input state stability condition, and because of the estimator error If it converges to zero within a fixed time, we can obtain... It is easy to see from the definition of the convex hull center Therefore, it can be known that when At that time, the moving target x0 and the center of the convex hull overlap, indicate That is, multiple agents achieved coordinated encirclement and control of moving targets;

[0049] This invention uses proof by contradiction to prove that no collisions occur between intelligent agents. First, Lyapunov alternative functions are defined:

[0050]

[0051] Differentiating with respect to V, we get:

[0052]

[0053] In the formula, make because If it converges to zero within a fixed time, then It exists, therefore W has a lower bound. Taking the first derivative of W with respect to time yields... This indicates that W is a non-increasing function, i.e., W is a bounded function; assuming a collision occurs between the agents, then... There is ||x i (T0)-x j (T0)||=d, i≠j∈N, therefore we have:

[0054]

[0055] The above equation contradicts the boundedness of W, therefore no collisions occur between any intelligent agents. Q.E.D.

[0056] This embodiment uses a multi-agent system with five dual-integral agents for simulation verification. The initial position of the agents is: x i (0)=15×[cos(i-1)2π / 5,sin(i-1)2π / 5] T [m], i∈N, the global state matrix of the moving target. The initial position of the moving target is x0 = [50, -50]. T [m], The parameters of the distributed fixed-time estimator (1) are set to c1=1, c2=1. The parameters of the collaborative encirclement controller (2) are set to k1=3, k2=3, and the obstacle function parameters are set to μ=14, d=10;

[0057] Under the action of the distributed fixed-time estimator (1), the position estimation error The convergence process is as follows Figure 1 As shown. The results show that the position estimation error can converge to zero within a fixed time, that is, the multi-agent system can obtain the unknown position of the moving target through the distributed fixed-time estimator (1) within a fixed time; under the control strategy (2), the trajectory of the multi-agent system cooperating to capture the moving target is shown in the figure. Figure 2 As shown, the average position error The convergence process is as follows Figure 3 As shown, the distance ||x between multiple agents ij The convergence process of || is as follows Figure 4 As shown. The results indicate that the multi-agent system can achieve the encirclement and control of moving targets, and the distance between agents ||x| during the encirclement process is [data missing]. ij || is always greater than d, meaning that the agent will not collide at any time.

[0058] It should be noted that the specific implementation schemes are merely for the purpose of helping to understand the method and core ideas of the present invention, and should not be used to limit the scope of protection. The scope of protection claimed by the present invention is not limited to the above specific embodiments, and for those skilled in the art, the present invention can have various modifications and alterations. Any modifications, improvements, and equivalent substitutions made within the concept and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-agent, non-formational cooperative encirclement and control method, characterized in that: Includes the following steps: Step 1: The multi-agent system consists of N identical agents, which are modeled using the following second-order dynamic model: Where, x i v i u i These represent the position, velocity, and control input of agent i, respectively; Step 2: Define the location distribution of the multi-agents and the convex hull co(x) corresponding to the position distribution = {Σ i∈N λ i x i :λ i ≥0andΣ i∈N λ i =1}; Step 3: Define the convex hull center From the definition of convex hull, we can know the center of the convex hull. It is an interior point of the convex hull; Step 4: Define the target dynamic as Where the target state matrix The target is a moving target, and the moving target moves in a circle at an angular frequency ω; and the target state matrix is ​​global information that can be acquired by multiple agents. Step 5: Define the distance between the moving target x0 and the convex hull co(x) as... If and only if x0∈co(x), then This indicates that multiple agents have achieved coordinated encirclement and control of moving targets; Step 6: The capture controller needs the interaction information between the agent and its neighboring nodes to achieve cooperative control. The nearest neighbor rule is used to define the neighboring nodes of agent i as N. i ={j∈N,j≠i:||x i -x j ||≤μ}, where μ is the perception distance of the agent and satisfies μ>d>0, and d is the collision distance between agents; Step 7: Due to distance limitations or obstacles, some agents are unable to obtain the position of the moving target. The agents utilize a distributed fixed-time estimator η i Estimate the position of the moving target; Step 8: The agent determines its position based on its own location information x. i The relative position information x with neighboring nodes i -x j Its own speed information v i The global state matrix S of the moving target, and the distributed fixed-time estimator η i It is used to design multi-agent control inputs.

2. The multi-agent non-formational cooperative encirclement control method according to claim 1, characterized in that: In step 7, the design expression for the distributed fixed-time estimator is: Where η i Let η0 be the estimate of the moving target x0 by agent i, and η0 = x0. If agent i can detect the location of the moving target, then a i0 =1, otherwise a i0 =0, meaning that at least one agent in the multi-agent system can detect the location of the moving target; a ij >0 indicates that agent i and agent j are neighboring nodes, and the network topology of the multi-agent system is an undirected graph; element a ii =0, meaning the network topology does not consider self-loops; the Laplace matrix corresponding to the multi-agent network topology is L = [l ij ]∈R n×n The elements of the Laplace matrix satisfy And l ij =-a ij .

3. The multi-agent non-formational cooperative encirclement control method according to claim 2, characterized in that: In step 7, the parameters of the distributed fixed-time estimator are set, and the fixed time for convergence is calculated, where c1 > 0, c2 > 0, μ1 > 1; the matrix B is defined as diag{a i0 a i1 , ..., a iN } and matrix H = L + B; the fixed time for convergence of the distributed fixed-time estimator in λ1 represents the smallest eigenvalue of matrix H, and λ1 >

0.

4. The multi-agent non-formational cooperative encirclement control method according to claim 3, characterized in that: The design of the collaborative capture controller is as follows: In step 8, the intelligent agent determines its position information x. i The relative position information x with neighboring nodes i -x j Its own speed information v i The global state matrix S of the moving target, and the distributed fixed-time estimator η i This is used to design the following multi-agent control inputs: in, And k2>0; α(·) is the obstacle function. When the distance between agents approaches the collision distance, the repulsive force between agents gradually increases to ensure that no collision occurs between agents.

5. The multi-agent non-formational cooperative encirclement control method according to claim 4, characterized in that: The barrier function α(·) is α(||x ij ||), When ||x ij When ||>μ, α(||x) ij If ||) is zero, it indicates that agent i and agent j are not neighboring nodes and have no repulsive force on each other.

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