Three-dimensional multi-agent formation consistent control method based on self-organizing topology

Abstract

According to the three-dimensional multi-agent formation consistent control method based on the self-organizing topology, generation can be carried out only by utilizing the relative position information fed back to the host by each agent, and the generated three-dimensional communication topology is of a minimum rigid structure, so that the three-dimensional communication topology has the advantages of the three-dimensional communication topology and also has the advantages of the three-dimensional communication topology. The three-dimensional communication topology structure has the advantages that the three-dimensional communication topology structure has the stability of a rigid structure so as to maintain the stability of multi-agent communication and has the property of a minimum rigid structure so as to reduce the communication redundancy of the multi-agent, and the three-dimensional communication topology structure allows the agents to receive communication in three dimensions, so that space resources can be more effectively utilized, and the communication redundancy of the multi-agent can be reduced. The overall efficiency of the communication network is improved; the three-dimensional communication topological structure is beneficial to reducing the congestion area and improving the overall network performance, the communication path between the nodes is more uniform, and the occurrence of communication bottlenecks is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent control and artificial intelligence technology, and in particular relates to a three-dimensional multi-agent formation consistent control method based on self-organizing topology. Background Art

[0002] With the continuous development of robotics, computer science, electronic information and other technologies, multi-agent formations have attracted more and more attention from researchers. Multi-agent formations refer to the design of appropriate control strategies to enable multiple agents to work together in an orderly manner to form a formation with superior overall performance. In a multi-agent formation, each agent is an independent entity with the ability to perceive, make decisions and execute autonomously. Agents communicate and collaborate with each other, and adjust their movements according to certain rules and algorithms to form an overall formation. The formation can be divided into two-dimensional plane formations and three-dimensional space formations according to the movement of the agents. The three-dimensional formation includes: UAV formations and underwater robot formations.

[0003] Currently, many scholars have conducted research on the consistency control of three-dimensional formations. For example, Gou Jinlu studied the trajectory planning of UAV formations based on consistency theory. Zhou Zhibo used consistency theory and designed a sliding membrane controller to control the UAV formation and achieved consistency in speed and yaw angle. Yang Hui, Wang Chuanfeng and others used consistency theory and speed communication topology to control the maintenance of multiple underwater navigation formations and achieve consistency in speed and heading.

[0004] It is known that whether multiple agents can achieve consistent control often depends on whether they have a good communication topology structure, and the communication topology structure of most formations is currently preset manually. This method has great limitations and cannot cope with emergencies. For example, if an agent is damaged during movement, the entire communication topology structure will be destroyed. Of course, some scholars have also conducted research on self-organizing two-dimensional communication topology. Although this method can solve the limitations of artificial preset topology and can self-generate topology structure according to the two-dimensional position of the agent, this method is only applicable to two-dimensional formations in planar motion and is difficult to apply to three-dimensional space formations such as drone formations and underwater robot formations. This is because the generation of three-dimensional communication topology is complex and requires many steps, and there is relatively little research on the self-generation of three-dimensional communication topology. Therefore, the present invention proposes a method for self-organizing and generating three-dimensional communication topology structure. Summary of the invention

[0005] In view of the problems existing in the prior art, the purpose of the present invention is to provide a three-dimensional multi-agent formation consensus control method based on self-organizing topology.

[0006] To solve the above problems, the present invention adopts the following technical solutions:

[0007] A three-dimensional multi-agent formation consensus control method based on self-organizing topology, comprising a plurality of agents, characterized in that the following steps are included:

[0008] Step 1: Analyze the communication topology of the formation based on graph theory, and define G = (V, E, A) as an undirected graph with N nodes, where V = 1, 2, ..., N is the set of N nodes, E = {(i, j), i ≠ j, i, j ∈ V} is the set of undirected edges, and A = (a ij )∈R N×N is the adjacency weight matrix, R N×N represents the real number field, if (i,j)∈E then a ij =c, otherwise a ij = 0, where c is the weight of the edge, and the three-dimensional state of the agent is defined as p i =[x i ,y i ,z i ] T , the three-dimensional state sequence is Define the three-dimensional stiffness matrix F∈R Num(E)×3N , the row corresponding to (i,j) in F is represented as Defining a directed graph Represents the topological structure of a team containing N agents. Where V = 1, 2, ..., N represents the set of N agents; is a set of directed edges, Indicates that agent i in the formation can receive information sent by neighbor agent j; Represents the adjacency matrix in the formation, if but on the contrary The out-degree matrix D = diag(d1, d2, ..., d N ),in Connection matrix B = diag(b1,b2,…,b N ), if agent i is a neighbor of the leader, then b i =1, otherwise b i =0;

[0009] Step 2: Based on graph theory analysis and the conditions required for communication topology, a self-organizing three-dimensional topology generation method is designed;

[0010] Step 3: Using the three-dimensional communication topology obtained in step 2 and combining it with consistency theory, a consistency error model is constructed. The goal of consistent control is to keep multiple agents consistent during the movement process, that is, to keep their relative positions and speeds consistent in space, thereby forming a certain collective behavior, which can be expressed as Expression 1: The consistency error model can be written as Expression 2:

[0011] Define the expected relative state sequence of the multi-agent formation as in Denotes the expected relative position d ix and the expected relative velocity d iv ;

[0012] According to the consistency theory and purpose, it is expected that the state of the intelligent agent can eventually be consistent and maintain the desired formation movement. Combined with the virtual leader method, the time-varying consistent formation led by the virtual leader can rewrite expression 1 into the following expression 3:

[0013] In a multi-agent formation, an agent can only receive communication information from adjacent agents. The communication topology of the entire formation is obtained by step 2. Based on the three-dimensional communication topology and local state information, the agent's consistency error model expression 2 can be rewritten as expression 4:

[0014]

[0015] make Expression 4 can be rewritten as Expression 5:

[0016]

[0017] In practice, it is more realistic to abstract the agent model into a second-order system model, so we develop it for the second-order agent system and define the control input sequence as Taking the derivative of expression 5, we get expression 6:

[0018]

[0019] Step 4: Design a controller to control u so that the consistency error model ζ converges to zero within a limited time, thereby realizing the generation of a multi-agent formation.

[0020] Preferably, it is characterized in that the three-dimensional communication topology structure of the multi-agent formation needs to meet the following conditions:

[0021] Condition 1: Rigid graph condition: Each node has at least three neighbor nodes, and the node cannot be in the same plane with all its neighbor nodes;

[0022] Condition 2: Minimum rigid edge number constraint: Num(E) = 3Num(V) - 6, Num(g) represents the number;

[0023] Condition 3: Agent communication constraints: d out (i)≤3 d out(i) represents the out-degree of agent i, that is, an agent only receives communication information from no more than three neighbors;

[0024] Condition 4: Navigator communication restrictions: d out (Leader) = 0 means that the out-degree of the leader is zero. The leader can only receive information from the host and cannot receive information from other agents, so its out-degree is zero;

[0025] Condition 5: Multi-agent formation communication restriction: At least three agents have an out-degree less than three.

[0026] Preferably, the condition 1 and condition 2 can be further rewritten as Rank(F)=3Num(V)-6, where Rank(g) represents the rank of the matrix.

[0027] Preferably, the self-organizing three-dimensional topology generation method in step 2 can be subdivided into the following steps:

[0028] Step 2 (a), obtain the position information of N agents at time t, and define the position of the agent at time t as: p i (t) = [x i (t),y i (t),z i (t)] T (i∈V), where x i (t),y i (t),z i (t) represents the position coordinates of agent i at time t;

[0029] Step 2 (ii), treating the agents in the formation as points, numbering each agent, and drawing a three-dimensional scatter plot;

[0030] Step 2 (3), using the 3D-Delaunay Triangulation function to perform three-dimensional triangulation on the scatter plot to obtain a three-dimensional triangulation graph G at time t. The 3D-Delaunay Triangulation function connects the three-dimensional scattered points by stacking multiple tetrahedrons, so G is a rigid graph;

[0031] Step 2 (IV): According to Calculate the length of each edge in step 2 (3), and use the edge length as the weight of each edge;

[0032] Step 2 (v), construct a rigid matrix F, and arrange the row vectors of F in descending order according to the weights;

[0033] Step 2 (vi), delete the redundant edges in G in step 2 (iii), starting from the first row of F. If Rank (F) > 3Num (V) - 6 after deletion, continue to delete. If Rank (F) < 3Num (V) - 6 after deletion, delete from the next row and keep that row.

[0034] Step 2 (VII), repeat step 2 (VI) to delete rows until Rank (F) = 3Num (V) - 6 is satisfied, and the minimum rigid graph G is obtained. R ;

[0035] Step 2 (eight): Select an agent R from the agent formation L As a leader, the R L Can only receive commands from the host, but not from other agents. If its number is Leader, then d out (Leader)=0,all R L The neighbor nodes of R need to be connected in out-degree form L , the directions of the remaining edges are determined by the distance R L Far nodes point to nearby nodes, thus obtaining a directed graph

[0036] Step 2 (nine), create five number sequences d0, d1, d2, d3, d 3+ Store the node numbers with degrees of zero, one, two, three, and greater than three respectively;

[0037] Step 2 (10): 3+ One directed edge of each node is inverted and d0,d1,d2,d3,d 3+ ;

[0038] Step 2 (11), repeat step 2 (10) until d 3+ The sequence becomes empty, that is, it satisfies d out (i)≤3,

[0039] Step 2 (XII): Check whether there is only a Leader node in d0, that is, only one node has an out-degree of zero, and at least three nodes have an out-degree less than three;

[0040] Step 2 (13), the directed graph That is the three-dimensional communication topology structure generated by self-organization.

[0041] Preferably, the directed edges in step 2 (10) have negation rules, which are:

[0042] Rule 1: Each node can only perform one directed edge inversion at a time, d 3+ After all nodes in the table are inverted, d needs to be updated.3+ ;

[0043] Rule 2: d 3+ It can only invert its own neighbor nodes, and cannot invert the nodes with R L The connected directed edges are reversed;

[0044] Rule 3: If d 3+ If a node has multiple neighboring nodes that can be negated, the negation priority of the directed edge is d0>d1>d2>d3.

[0045] Preferably, if there are other nodes in step 2 (twelve), it is necessary to perform a negation process on each of them for a directed edge, and the negation process rule is the negation rule in step 2 (ten), and the negation priority is d3>d2.

[0046] Preferably, ξ in expression 1 in step 3 is i (t) is the state quantity of the agent, expression 2 is a real number, ξ0 in expression three is the state quantity of the virtual leader, f in expression six is ​​determined by the specific model of the intelligent agent and the external environment, u0 in expression six is ​​the control input of the virtual leader, m in expression five is the dimension of the state quantity of the required control intelligent agent, A, B and D in expression five are the adjacency matrix, connection matrix and out-degree matrix of the three-dimensional communication topology respectively.

[0047] Preferably, the controller in step 4 needs to be designed in combination with factors such as the specific model of the intelligent body, the state quantity of control and the external environment.

[0048] Compared with the prior art, the advantages of the present invention are:

[0049] 1. The present invention can be generated only by using the relative position information fed back by each intelligent agent to the host, and the generated three-dimensional communication topology is a minimum rigid structure, which has both the advantages of the three-dimensional communication topology itself and the stability of the rigid structure to maintain the stability of multi-agent communication, and also has the properties of the minimum rigid structure to reduce the communication redundancy of multiple intelligent agents. The advantages are as follows: the three-dimensional communication topology allows the intelligent agent to receive communications in three dimensions, which can more effectively utilize spatial resources and improve the overall efficiency of the communication network; the three-dimensional communication topology helps to reduce congested areas, improve overall network performance, and make the communication paths between nodes more uniform, reducing the occurrence of communication bottlenecks.

[0050] 2. The present invention can also use three-dimensional communication topology to construct a time-varying consistency error model, so that the intelligent agent can reach the desired formation position. The three-dimensional communication topology structure can then be updated to maintain the stability of multi-agent communication and avoid communication disorder among multiple agents after movement changes due to the use of the connection relationship represented by the previous topology.

[0051] 3. The present invention is applicable to three-dimensional formations, such as drone formations, underwater robot formations, land and air robot formations, etc. It can self-organize these formations to generate three-dimensional communication topology structures and design consistency error models. Finally, it is only necessary to design a suitable controller to control multiple agents to collaboratively perform tasks. In addition, the present invention can be combined with event triggering technology to improve the autonomy of the entire system. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a simulation schematic diagram of the present invention.

[0053] Figure 2 This is an example diagram of consistent control of the present invention.

[0054] Figure 3 This is an example diagram of the present invention applied to a consistent formation. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] The present invention is a three-dimensional multi-agent formation consensus control method based on self-organizing topology, which includes multiple agents, and the generation of the control method can be roughly divided into four steps, namely:

[0057] Step 1: Analyze the communication topology structure of the formation based on graph theory;

[0058] Step 2: Based on graph theory analysis and the conditions required for communication topology, a self-organizing three-dimensional topology generation method is designed;

[0059] Step 3: Using the three-dimensional communication topology structure obtained in step 2 and combining it with consistency theory, a consistency error model is constructed;

[0060] Step 4: Design a controller to control u so that the consistency error model ζ converges to zero within a limited time, thereby achieving consistent control of three-dimensional multi-agents.

[0061] Each of these steps can be explained in more detail.

[0062] Extended explanation for step 1:

[0063] Based on graph theory, the communication topology of the formation is analyzed, and G = (V, E, A) is defined as an undirected graph with N nodes, where V = 1, 2, ..., N is the set of N nodes, E = {(i, j), i ≠ j, i, j ∈ V} is the set of undirected edges, and A = (a ij )∈R N×N is the adjacency weight matrix, R N×N represents the real number field, if (i,j)∈E then a ij =c, otherwise a ij = 0, where c is the weight of the edge, and the three-dimensional state of the agent is defined as p i =[x i ,y i ,z i ] T , the three-dimensional state sequence is Define the three-dimensional stiffness matrix F∈R Num(E)×3N , the row corresponding to (i,j) in F is represented as Defining a directed graph Represents the topological structure of a team containing N agents. Where V = 1, 2, ..., N represents the set of N agents; is a set of directed edges, Indicates that agent i in the formation can receive information sent by neighbor agent j; Represents the adjacency matrix in the formation, if but on the contrary The out-degree matrix D = diag(d1, d2, ..., d N ),in Connection matrix B = diag(b1,b2,…,b N ), if agent i is a neighbor of the leader, then b i =1, otherwise b i =0.

[0064] Extended explanation for step 2:

[0065] The self-organizing three-dimensional topology generation method in the design step 2 can be subdivided into the following steps:

[0066] Step 2 (a), obtain the position information of N agents at time t, and define the position of the agent at time t as: p i (t) = [x i (t),y i (t),z i (t)] T (i∈V), where xi (t),y i (t),z i (t) represents the position coordinates of agent i at time t;

[0067] Step 2 (ii), treating the agents in the formation as points, numbering each agent, and drawing a three-dimensional scatter plot;

[0068] Step 2 (3), using the 3D-Delaunay Triangulation function to perform three-dimensional triangulation on the scatter plot to obtain a three-dimensional triangulation graph G at time t. The 3D-Delaunay Triangulation function connects the three-dimensional scattered points by stacking multiple tetrahedrons, so G is a rigid graph;

[0069] Step 2 (IV): According to Calculate the length of each edge in step 2 (3), and use the edge length as the weight of each edge;

[0070] Step 2 (v), construct a rigid matrix F, and arrange the row vectors of F in descending order according to the weights;

[0071] Step 2 (vi), delete the redundant edges in G in step 2 (iii), starting from the first row of F. If Rank (F) > 3Num (V) - 6 after deletion, continue to delete. If Rank (F) < 3Num (V) - 6 after deletion, delete from the next row and keep that row.

[0072] Step 2 (VII), repeat step 2 (VI) to delete rows until Rank (F) = 3Num (V) - 6 is satisfied, and the minimum rigid graph G is obtained. R ;

[0073] Step 2 (eight): Select an agent R from the agent formation L As a leader, the R L Can only receive commands from the host, but not from other agents. If its number is Leader, then d out (Leader)=0,all R L The neighbor nodes of R need to be connected in out-degree form L , the directions of the remaining edges are determined by the distance R L Far nodes point to nearby nodes, thus obtaining a directed graph

[0074] Step 2 (nine), create five number sequences d0, d1, d2, d3, d 3+ Store the node numbers with degrees of zero, one, two, three, and greater than three respectively;

[0075] Step 2 (10):3+ One directed edge of each node is inverted and d0,d1,d2,d3,d 3+ ;

[0076] Step 2 (11), repeat step 2 (10) until d 3+ The sequence becomes empty, that is, it satisfies d out (i)≤3,

[0077] Step 2 (XII): Check whether there is only a Leader node in d0, that is, only one node has an out-degree of zero, and at least three nodes have an out-degree less than three;

[0078] Step 2 (13), the directed graph That is the three-dimensional communication topology structure generated by self-organization.

[0079] Extended explanation for step 3:

[0080] Using the three-dimensional communication topology obtained in step 2 and combining it with the consistency theory, a consistency error model is constructed. The goal of consistent control is to make multiple agents consistent during the movement process, that is, to keep their relative positions and speeds consistent in space, thereby forming a certain collective behavior, which can be expressed as Expression 1: The consistency error model can be written as Expression 2:

[0081] Define the expected relative state sequence of the multi-agent formation as in Denotes the expected relative position d ix and the expected relative velocity d iv ;

[0082] According to the consistency theory and purpose, it is ultimately expected that the states of the intelligent agents can converge to consistency and maintain the desired formation movement. Combined with the virtual leader method, the time-varying consistency formation led by the virtual leader can rewrite Expression 1 into the following Expression 3:

[0083] In a multi-agent formation, an agent can only receive communication information from adjacent agents. The communication topology of the entire formation is obtained by step 2. Based on the three-dimensional communication topology and local state information, the agent's consistency error model expression 2 can be rewritten as expression 4:

[0084]

[0085] make Expression 4 can be rewritten as Expression 5:

[0086]

[0087] In practice, it is more realistic to abstract the agent model into a second-order system model, so we develop it for the second-order agent system and define the control input sequence as Taking the derivative of expression 5, we get expression 6:

[0088]

[0089] Extended instructions for step 4:

[0090] The controller is designed to control u so that the consistency error model ζ converges to zero within a limited time, so that the generation of multi-agent formations can be achieved. The controller needs to be designed based on factors such as the specific model of the agent, the controlled state quantity and the external environment.

[0091] It should be noted that the three-dimensional communication topology structure of the multi-agent formation must meet the following conditions:

[0092] Condition 1: Rigid graph condition: Each node has at least three neighbor nodes, and the node cannot be in the same plane with all its neighbor nodes;

[0093] Condition 2: Minimum rigid edge number constraint: Num(E) = 3Num(V) - 6, Num(g) represents the number;

[0094] Condition 3: Agent communication constraints: d out (i)≤3 d out (i) represents the out-degree of agent i, that is, an agent only receives communication information from no more than three neighbors;

[0095] Condition 4: Navigator communication restrictions: d out (Leader) = 0 means that the out-degree of the leader is zero. The leader can only receive information from the host and cannot receive information from other agents, so its out-degree is zero;

[0096] Condition 5: Multi-agent team communication restriction: at least three agents have an out-degree less than 3. Conditions 1 and 2 can be further rewritten as Rank(F)=3Num(V)-6, where Rank(g) represents the rank of the matrix.

[0097] It should be noted that the directed edges in step 2 (10) have inversion rules, which are:

[0098] Rule 1: Each node can only perform one directed edge inversion at a time, d 3+ After all nodes in the table are inverted, d needs to be updated. 3+ ;

[0099] Rule 2: d 3+ It can only invert its own neighbor nodes, and cannot invert the nodes with R L The connected directed edges are reversed;

[0100] Rule 3: If d 3+ If a node has multiple neighboring nodes that can be inverted, the priority of inverting the directed edge is d0>d1>d2>d3. If there are other nodes in the subsequent step 2 (twelve), it is necessary to invert one directed edge for each of them. The inverting rules also refer to the above inverting rules, and the inverting priority is d3>d2.

[0101] It can be further described that the ξ in expression 1 in step 3 is i (t) is the state quantity of the agent, expression 2 is a real number, ξ0 in expression three is the state quantity of the virtual leader, f in expression six is ​​determined by the specific model of the intelligent agent and the external environment, u0 in expression six is ​​the control input of the virtual leader, m in expression five is the dimension of the state quantity of the required control intelligent agent, A, B and D in expression five are the adjacency matrix, connection matrix and out-degree matrix of the three-dimensional communication topology respectively.

[0102] Based on the above technical solution, Figures 1 to 3 Provide explanation.

[0103] Figure 1 This is a simulation diagram of the self-organizing three-dimensional topology generation method, where Figure 1 Figures (a) to (c) in the figure represent the process of generating the minimum rigid graph, that is, step 2 (a) to step 2 (seven) in step 2, and Figure 1 Figure (d) in the figure is the initial directed process, that is, step 2 (eight) in step 2. Figure 1 Figure (e) is the final generated directed graph, i.e., the three-dimensional communication topology structure, where Figure 1 The circled positions in Figure (d) and Figure (e) are the directed edges that need to be reversed, namely, steps 2(10) to 2(12) in step 2.

[0104] Figure 2 This is an example diagram of consistent control based on the present invention. The simulation objects are set to 9 intelligent agents. These intelligent agents all adopt the simplest second-order derivative particle model, that is, Where [u ix ,u iy ,u iz ] T is the control input of the intelligent agent; the state quantity that needs to be controlled to be consistent with the intelligent agent is the position state quantity [x i ,y i,z i ] T and velocity state quantity [v ix ,v iy ,v iz ] T ; Sliding mode control is used to control the control input of the intelligent agent; the movement duration is T = 10s, the sampling time is t = 0.05s, and the reference trajectory is [x0 = 0.25-0.05t, y0 = 0.5 + 0.02t, z0 = 0.5] T .in Figure 2 Figure (a) is an image of the trajectory and the self-organizing three-dimensional topological structure. It is easy to see that the consistency error model constructed using the communication topology generated by the present invention can make multiple agents quickly converge to a consensus. Figure 2 Figure (b) shows the consistency position error and Figure 2 As shown in Figure (c), the consistency speed error can converge to zero quickly, which proves the feasibility of the present invention.

[0105] Figure 3 The present invention is applied to the consistent formation, and the data used are all Figure 2 The data of the consistent control example diagram is the same, the expected formation, that is, the expected relative position sequence, is a triangular prism with three layers and three triangles, and their respective expressions are:

[0106]

[0107]

[0108]

[0109] The expected relative speed sequence is zero, which means that the speeds of multiple agents tend to be consistent.

[0110] Figure 3 Figure (a) is a motion trajectory image, and the black triangular prism in it is the desired formation. It can be seen that the agent formation of multiple agents can maintain the desired formation movement; Figure 3 In the figure (b), at 3s, the black dotted line of the agent formation and the three-dimensional communication topology image is the formation, and the blue directed line segment is the three-dimensional communication topology structure self-organized and generated at this moment; multiple agents move from the initial scattered positions to the desired relative positions. If the connection relationship represented by the communication topology at the initial moment is continued to be used, the communication topology structure will lose its rigidity, making it difficult to maintain the stability of communication. Therefore, at this time, the communication topology generated by the self-organization of the present invention can maintain the stability of subsequent movement communication and better maintain the formation. Figure 3 Figures (c) and (d) are consistency errors used to verify the feasibility of the present invention, and the final results are feasible.

[0111] The present invention proposes a formation generation method based on self-organizing three-dimensional topology and consistency error model. The method can self-generate a three-dimensional communication topology structure by using the position information of multiple agents. The three-dimensional communication topology structure allows the agents to receive communications in three dimensions, so that spatial resources can be more effectively utilized and the overall efficiency of the communication network can be improved. Such a three-dimensional communication topology structure helps to reduce congested areas, improve the overall network performance, make the communication paths between nodes more uniform, and reduce the occurrence of communication bottlenecks. The three-dimensional communication topology structure generated by the present invention meets the minimum rigidity, and only needs to use the minimum communication links to maintain the stability of the three-dimensional formation, thereby reducing the communication redundancy in the formation movement. It is worth mentioning that the three-dimensional communication topology designed by the present invention can be updated to better construct a time-varying consistency error model, and will not cause the overall communication network of the formation to be damaged due to emergencies and the agents cannot move to the desired formation position. In addition, when the agents can reach the desired formation position, the three-dimensional communication topology structure can be updated to maintain the stability of multi-agent communication, avoiding the communication disorder between multiple agents after the movement change due to the connection relationship represented by the previous topology.

[0112] In the description of the present invention, it is necessary to understand that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "axial", "radial", "circumferential" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0113] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0114] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, an electrical connection, or a communication; it can be a direct connection, or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0115] In the present invention, unless otherwise clearly specified and limited, the first feature "on" or "under" the second feature may be that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. In the description of this specification, the description with reference to the terms "one scheme", "some schemes", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the scheme or example are included in at least one scheme or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same scheme or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more schemes or examples in a suitable manner.

Claims

1. A three-dimensional multi-agent formation consensus control method based on self-organizing topology, comprising multiple agents, It is characterized in that The steps are as follows: Step 1: Analyze the communication topology of the formation based on graph theory, and define G = (V, E, A) as an undirected graph with N nodes, where V = 1, 2, ..., N is the set of N nodes, E = {(i, j), i ≠ j, i, j ∈ V} is the set of undirected edges, and A = (a ij )∈R N×N is the adjacency weight matrix, R N×N represents the real number field, if (i,j)∈E then a ij =c, otherwise a ij = 0, where c is the weight of the edge, and the three-dimensional state of the agent is defined as p i =[x i ,y i ,z i ] T , the three-dimensional state sequence is Define the three-dimensional stiffness matrix F∈R Num(E)×3N , the row corresponding to (i,j) in F is represented as Defining a directed graph Represents the topological structure of a team containing N agents. Where V = 1, 2, ..., N represents the set of N agents; is a set of directed edges, Indicates that agent i in the formation can receive information sent by neighbor agent j; Represents the adjacency matrix in the formation, if but on the contrary The out-degree matrix D = diag(d 1 ,d 2 ,…,d N ),in Connection matrix B = diag(b 1 ,b 2 ,…,b N ), if agent i is a neighbor of the leader, then b i =1, otherwise b i =0; Step 2: Based on graph theory analysis and the conditions required for communication topology, a self-organizing three-dimensional topology generation method is designed; Step 3: Using the three-dimensional communication topology obtained in step 2 and combining it with consistency theory, a consistency error model is constructed. The goal of consistent control is to keep multiple agents consistent during the movement process, that is, to keep their relative positions and speeds consistent in space, thereby forming a certain collective behavior, which can be expressed as Expression 1: The consistency error model can be written as Expression 2: Define the expected relative state sequence of the multi-agent formation as in Denotes the expected relative position d ix and the expected relative velocity d iv ; According to the consistency theory and purpose, it is expected that the state of the intelligent agent can eventually be consistent and maintain the desired formation movement. Combined with the virtual leader method, the time-varying consistent formation led by the virtual leader can rewrite expression 1 into the following expression 3: In a multi-agent formation, an agent can only receive communication information from adjacent agents. The communication topology of the entire formation is obtained by step 2. Based on the three-dimensional communication topology and local state information, the agent's consistency error model expression 2 can be rewritten as expression 4: make Expression 4 can be rewritten as Expression 5: In practice, it is more realistic to abstract the agent model into a second-order system model, so we develop it for the second-order agent system and define the control input sequence as Taking the derivative of expression 5, we get expression 6: Step 4: Design a controller to control u so that the consistency error model ζ converges to zero within a limited time, thereby achieving consistent control of three-dimensional multi-agents.

2. A three-dimensional multi-agent formation consensus control method based on self-organizing topology according to claim 1, It is characterized in that The three-dimensional communication topology structure of the multi-agent formation must meet the following conditions: Condition 1: Rigid graph condition: Each node has at least three neighbor nodes, and the node cannot be in the same plane with all its neighbor nodes; Condition 2: Minimum rigid edge number constraint: Num(E) = 3Num(V) - 6, Num(g) represents the number; Condition 3: Agent communication restrictions: d out (i) represents the out-degree of agent i, that is, an agent only receives communication information from no more than three neighbors; Condition 4: Navigator communication restrictions: d out (Leader) = 0 means that the out-degree of the leader is zero. The leader can only receive information from the host and cannot receive information from other agents, so its out-degree is zero; Condition 5: Multi-agent formation communication restriction: At least three agents have an out-degree less than three.

3. A three-dimensional multi-agent formation consensus control method based on self-organizing topology according to claim 2, It is characterized in that The first and second conditions can be further rewritten as Rank(F)=3Num(V)-6, where Rank(g) represents the rank of the matrix.

4. A three-dimensional multi-agent formation consensus control method based on self-organizing topology according to claim 1, It is characterized in that The self-organizing three-dimensional topology generation method in the design step 2 can be subdivided into the following steps: Step 2 (a), obtain the position information of N agents at time t, and define the position of the agent at time t as: p i (t) = [x i (t),y i (t),z i (t)] T (i∈V), where x i (t),y i (t),z i (t) represents the position coordinates of agent i at time t; Step 2 (ii), treating the agents in the formation as points, numbering each agent, and drawing a three-dimensional scatter plot; Step 2 (3), using the 3D-Delaunay Triangulation function to perform three-dimensional triangulation on the scatter plot to obtain a three-dimensional triangulation graph G at time t. The 3D-Delaunay Triangulation function connects the three-dimensional scattered points by stacking multiple tetrahedrons, so G is a rigid graph; Step 2 (IV): According to Calculate the length of each edge in step 2 (3), and use the edge length as the weight of each edge; Step 2 (v), construct a rigid matrix F, and arrange the row vectors of F in descending order according to the weights; Step 2 (vi), delete the redundant edges in G in step 2 (iii), starting from the first row of F. If Rank (F) > 3Num (V) - 6 after deletion, continue to delete. If Rank (F) < 3Num (V) - 6 after deletion, delete from the next row and keep that row. Step 2 (VII), repeat step 2 (VI) to delete rows until Rank (F) = 3Num (V) - 6 is satisfied, and the minimum rigid graph G is obtained. R ; Step 2 (eight): Select an agent R from the agent formation L As a leader, the R L Can only receive commands from the host, but not from other agents. If its number is Leader, then d out (Leader)=0, all R L The neighbor nodes of R need to be connected in out-degree form L , the directions of the remaining edges are determined by the distance R L Far nodes point to nearby nodes, thus obtaining a directed graph Step 2 (9), create five number series d 0 ,d 1 ,d 2 ,d 3 ,d 3+ Store the node numbers with degrees of zero, one, two, three, and greater than three respectively; Step 2 (10): 3+ One directed edge of each node is inverted and d is updated 0 ,d 1 ,d 2 ,d 3 ,d 3+ ; Step 2 (11), repeat step 2 (10) until d 3+ The sequence becomes empty, that is, it satisfies Step 2 (XII), check d 0 Is there only a Leader node in the network, that is, only one node has an out-degree of zero, and at least three nodes have an out-degree less than three; Step 2 (13), the directed graph That is the three-dimensional communication topology structure generated by self-organization.

5. A three-dimensional multi-agent formation consensus control method based on self-organizing topology according to claim 4, It is characterized in that In step 2 (10), the directed edges have the inversion rules, which are: Rule 1: Each node can only perform one directed edge inversion at a time, d 3+ After all nodes in the table are inverted, d needs to be updated. 3+ ; Rule 2: d 3+ It can only invert its own neighbor nodes, and cannot invert the nodes with R L The connected directed edges are reversed; Rule 3: If d 3+ If a node has multiple neighboring nodes that can be negated at the same time, the negation priority of the directed edge is d 0 >d 1 >d 2 >d 3 .

6. A three-dimensional multi-agent formation consensus control method based on self-organizing topology according to claim 4, It is characterized in that If there are other nodes in step 2 (XII), it is necessary to perform a directed edge inversion processing on each of them. The inversion processing rule is the inversion rule in step 2 (X), and the inversion priority is d 3 >d 2 .

7. A three-dimensional multi-agent formation consensus control method based on self-organizing topology according to claim 1, It is characterized in that The ξ of expression 1 in step 3 i (t) is the state quantity of the agent, expression 2 is a real number, expression three 0 is the state quantity of the virtual leader, f in expression 6 is determined by the specific model of the intelligent agent and the external environment, and u in expression 6 0 is the control input of the virtual leader, m in expression 5 is the dimension of the state quantity required to control the intelligent agent, A, B and D in expression 5 are the adjacency matrix, connection matrix and out-degree matrix of the three-dimensional communication topology respectively.

8. A three-dimensional multi-agent formation consensus control method based on self-organizing topology according to claim 1, It is characterized in that The controller in step 4 needs to be designed based on factors such as the specific model of the intelligent agent, the state quantity of control and the external environment.

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