A distributed topology time-varying formation control method and system

Abstract

The application relates to a kind of distributed topology time-varying formation control method and system, and relates to the field of agent formation control, method includes: according to the communication relationship of each node in multi-agent formation, construct initial undirected complete graph;Each node is agent;Based on the initial undirected complete graph, according to distributed algorithm, generate global optimal rigid communication topology;Based on the global optimal rigid communication topology, according to the communication relationship of each node, the corresponding edge of each node is directed, and the in-degree of each node is less than or equal to 3, obtain optimal persistent communication topology;The optimal persistent communication topology is used to carry out communication control to multi-agent formation.The application reduces the complexity of multi-agent communication.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of multi-agent formation control, and particularly relates to a distributed topology time-varying formation control method and system. BACKGROUND

[0002] In recent years, multi-agent cooperation has been widely applied in industry, national defense and life. Compared with a single agent, a multi-agent system, especially a distributed multi-agent system, has many obvious advantages. The multi-agent system has a wider perception range and a wider activity range, has better fault tolerance and robustness due to its greater redundancy, has lower requirements for individual performance, has lower cost and is more economical. Therefore, in the past decade, the multi-agent system has developed into an important research direction in the fields of control and robotics.

[0003] Multi-agent systems have a wide range of directions. In the control direction, there are multi-robot formation control, swarm motion, consensus, etc. Existing research mainly focuses on the stability of formation, and there is less research on formation communication topology (such as optimization, reconstruction, etc.).

[0004] Persistent communication topology can effectively reduce communication complexity and communication energy consumption. In the study of persistent formation topology, rigid graph theory plays an important role as a foundation. For communication topology, Smith et al. proposed a minimum rigid graph and a minimum stable graph generation algorithm based on graph operations. Fang Bin et al. studied the maintenance conditions of rigid formation under the operations of node addition and deletion, formation gathering and separation based on rigid graph. Although rigid communication topology reduces the cost and complexity of communication to a certain extent, rigid communication topology is a bidirectional topology, and persistent communication is directional on the basis of rigid communication, obtaining persistent communication topology, further reducing the cost and complexity of communication. Hendrickx et al. analyzed and studied the specific operations of vertices and edges in the minimum rigid graph and the minimum persistent graph from the perspective of graph theory, but did not give the minimum persistent formation generation algorithm. Luo et al. proposed an optimal persistent formation generation algorithm, but the algorithm is only applicable to special structures of formation. Wang et al. studied the information interaction and topology optimization of persistent formation for "formation leader constraints" and "fault constraints".

[0005] When the number of intelligent agents is large, the communication complexity between intelligent agents will be high, and designing a reasonable communication link will not only be a huge workload, but also be prone to errors. At present, most of the researches on communication topology direction need global information, but in practical applications such as target reconnaissance tracking, communication relay, environmental monitoring and map surveying, the system is difficult to obtain global information due to the limitations of distance and weather and other factors. At the same time, due to communication interference, control failure and other unexpected situations, the communication topology will be damaged. In order to cope with complex application environment, distributed topology generation algorithm and communication topology fault-tolerant control method need to be researched. SUMMARY

[0006] The purpose of the present application is to provide a distributed topology time-varying formation control method, which reduces the complexity of multi-agent communication.

[0007] In order to achieve the above purpose, the present application provides the following scheme:

[0008] A distributed topology time-varying formation control method, comprising:

[0009] An initial undirected complete graph is constructed according to the communication relationship of each node in the multi-agent formation; each node is an intelligent agent;

[0010] Based on the initial undirected complete graph, a globally optimal rigid communication topology is generated according to a distributed algorithm;

[0011] Based on the globally optimal rigid communication topology, the corresponding edges of each node are directed and the in-degree of each node is less than or equal to 3 according to the communication relationship of each node, to obtain an optimal persistent communication topology;

[0012] The optimal persistent communication topology is used for communication control of the multi-agent formation.

[0013] Optionally, the initial undirected complete graph is represented as G U (V, E, W, S), wherein V represents the set of all nodes in the initial undirected complete graph G U , E represents the set of links of each node in G U , W represents the weighted adjacency matrix in G U , and S represents the set of positions of the nodes in G U .

[0014] Optionally, the globally optimal rigid communication topology is generated according to a distributed algorithm based on the initial undirected complete graph, and specifically comprises:

[0015] The local optimal rigid communication topology of each node is obtained by traversing each node;

[0016] The intersection R of the local optimal rigid communication topologies of each node is obtained.

[0017] deleting edges of each node v i to obtain a local optimal rigid communication topology R i in which satisfies and e kl ∈G j , obtaining a global optimal rigid communication topology;

[0018] wherein, e kl represents an edge from node v k to node v l , and node v k to node v l are nodes in G i , and node v k to node v l are nodes in G j , and G i represents a local weighted undirected complete graph of node v i , and G j represents a local weighted undirected complete graph of node v j , and i≠j.

[0019] Optionally, the obtaining of the local optimal rigid communication topology of each node by traversing each node comprises:

[0020] when node v i is traversed:

[0021] obtaining a neighbor set N i of node v i , and obtaining a local weighted undirected complete graph G i corresponding to the neighbor set N i ;

[0022] calculating a weight of an edge e i in the local weighted undirected complete graph G ij according to a formula ;

[0023] wherein, e ij represents an edge from node v i to node v j , S ij represents a value after s ij is normalized, s ij represents a length of the edge e ij , P loss represents a path loss, E ti represents energy consumed by node v i for receiving data, and E rj represents energy consumed by node v i for sending data; a irepresenting the initial energy of node v i a j representing the initial energy of node v j ;

[0024] Sort all edges in the edge set E i of the local weighted undirected complete graph G i in ascending order of weight, and obtain an updated edge set E i ;

[0025] Construct a stiffness matrix M according to the updated edge set E i , the stiffness matrix M being a |E i | row 3|V i | column stiffness matrix constructed according to the coordinates corresponding to each node in G i , V i representing the set of all nodes in G i ; wherein in the stiffness matrix M, the 3(i-1)+1 column element is x i -x j , the 3(i-1)+2 column element is y i -y j , the 3i column element is z i -z j , the 3(j-1)+1 column element is -(x i -x j ), the 3(j-1)+2 column element is -(y i -y j ), the 3 j column corresponding element is -(z i -z j ), and the remaining columns are 0;

[0026] Initialize j=0, the set E R , the set W R , and the matrix Mc are all empty; the set W R is the weighted adjacency matrix of the edge set E R ;

[0027] Let the matrix Mc'=[Mc;M(j,:)], [Mc;M(j,:)] representing the matrix obtained by placing the jth row of the stiffness matrix M into the matrix Mc;

[0028] If the matrix Mc' is a rank-deficient matrix, let the value of j be increased by 1, and return to the step of "Let the matrix Mc'=[Mc;M(j,:)], [Mc;M(j,:)] representing the matrix obtained by placing the jth row of the stiffness matrix M into the matrix Mc";

[0029] If the matrix Mc' is a full-rank matrix, add the edge e ij to E RAccording to the current E R Update W R ;

[0030] If the rank of the matrix Mc is less than 3|V|-6, let j value add 1, return to the step "let the matrix Mc'= [Mc; M(j,:)]", [Mc; M(j,:)] represents the matrix obtained by putting the jth row of the stiffness matrix M into the matrix Mc";

[0031] If the rank of the matrix Mc is equal to 3|V|-6, R i =(V i ,E R ,W R ,S i ) is the local optimal rigid communication topology of the node v i .

[0032] Optionally, based on the global optimal rigid communication topology, the corresponding edges of each node are directed and the in-degree of each node is less than or equal to 3 according to the communication relationship of each node, to obtain an optimal persistent communication topology, specifically including:

[0033] Obtain the connection matrix of the global optimal rigid communication topology and the connectivity of each node in the global optimal rigid communication topology;

[0034] Initialize i=1, set P is empty, and the flag is 1;

[0035] Determine whether the connectivity of the node v i is 1, 2 or 3,

[0036] If the connectivity of the node v i is 1, 2 or 3, the corresponding edge of the node v i is directed as e xi , e xi is added to the set P, and the corresponding edge of the node v i in the current global optimal rigid communication topology is deleted, while the connectivity and in-degree of each node in the current global optimal rigid communication topology are updated, and the flag is 0;

[0037] If i is less than N, the value of i is added by 1, and the step "determine whether the connectivity of the node v i is 1, 2 or 3" is returned

[0038] If i is equal to N and the flag is 0, let i=1, the flag is 1, and the step "determine whether the connectivity of the node v i is 1, 2 or 3" is returned;

[0039] If i is equal to N and the flag is 1, it is determined whether there is a node with a connectivity equal to 4 in the current global optimal rigid communication topology;

[0040] If there is a node with connectivity equal to 4, the edge corresponding to the node with connectivity equal to 4 is directed as e xi xi is added to the set P, the connectivity and in-degree of each node in the current global optimal rigid communication topology are updated, i is set to 1, flag is set to 1, and the step of "judging whether the connectivity of node v i is 1, 2 or 3" is returned.

[0041] If there is no node with connectivity equal to 4, an optimal persistent communication topology P is output according to the directed graph P composed of the set P.

[0042] Optionally, the optimal persistent communication topology P output according to the directed graph P composed of the set P specifically includes the following steps.

[0043] It is judged whether there is a node with in-degree equal to 4 in the directed graph P composed of the set P.

[0044] If there is a node with in-degree equal to 4 in the directed graph P, the path of the node with in-degree equal to 4 is negated, and the directed graph P after the path negation operation is taken as the optimal persistent communication topology and is output.

[0045] If there is no node with in-degree equal to 4 in the directed graph P, the directed graph P is taken as the optimal persistent communication topology and is output.

[0046] Optionally, the method further includes the following steps. If there is a communication arc failure in the optimal persistent communication topology, a directed weighted complete topology of the optimal persistent communication topology is obtained, the communication arc with failure in the directed weighted complete topology is deleted to obtain a communication topology G De ; the communication arc is a unidirectional communication link between nodes.

[0047] If the intersection of the edge set of the optimal persistent communication topology and the edge set of the communication topology G D is not empty, the communication arc in the communication topology G De is converted into a corresponding weighted undirected topology G e .

[0048] Based on the weighted undirected topology G e , a current global optimal rigid communication topology R e is generated according to the distributed algorithm.

[0049] Based on the current global optimal rigid communication topology R e , the corresponding edge of each node is directed and the in-degree of each node is less than or equal to 3 according to the communication relationship of each node, and a current optimal persistent communication topology P e is obtained.

[0050] The current optimal persistent communication topology P​e Communication control is performed on the multi-agent formation.

[0051] The application discloses a distributed topology time-varying formation control system, comprising:

[0052] An initial undirected complete graph construction module is configured to construct an initial undirected complete graph according to the communication relationship of each node in the multi-agent formation.

[0053] A globally optimal rigid communication topology generation module is configured to generate a globally optimal rigid communication topology according to a distributed algorithm based on the initial undirected complete graph.

[0054] An optimal persistent communication topology determination module is configured to obtain an optimal persistent communication topology by directing the corresponding edges of each node and making the in-degree of each node less than or equal to 3 according to the communication relationship of each node based on the globally optimal rigid communication topology.

[0055] An optimal persistent communication topology application module is configured to perform communication control on the multi-agent formation by using the optimal persistent communication topology.

[0056] According to the embodiments of the application, the following technical effects are achieved:

[0057] The application discloses a distributed topology time-varying formation control method, which comprises the following steps: constructing an initial undirected complete graph according to the communication relationship of each node in the multi-agent formation; generating a globally optimal rigid communication topology according to a distributed algorithm based on the initial undirected complete graph; and obtaining an optimal persistent communication topology by directing the corresponding edges of each node and making the in-degree of each node less than or equal to 3 according to the communication relationship of each node based on the globally optimal rigid communication topology. BRIEF DESCRIPTION OF DRAWINGS

[0058] In order to more clearly illustrate the technical solutions of the embodiments of the application or the prior art, the following will briefly introduce the drawings needed in the embodiments. Obviously, the drawings in the following description are only some embodiments of the application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0059] Figure 1 The application discloses a distributed topology time-varying formation control method, which comprises the following steps: constructing an initial undirected complete graph according to the communication relationship of each node in the multi-agent formation; generating a globally optimal rigid communication topology according to a distributed algorithm based on the initial undirected complete graph; and obtaining an optimal persistent communication topology by directing the corresponding edges of each node and making the in-degree of each node less than or equal to 3 according to the communication relationship of each node based on the globally optimal rigid communication topology.

[0060] Figure 2 The application discloses a distributed topology time-varying formation control method, which comprises the following steps: constructing an initial undirected complete graph according to the communication relationship of each node in the multi-agent formation; generating a globally optimal rigid communication topology according to a distributed algorithm based on the initial undirected complete graph; and obtaining an optimal persistent communication topology by directing the corresponding edges of each node and making the in-degree of each node less than or equal to 3 according to the communication relationship of each node based on the globally optimal rigid communication topology.

[0061] Figure 3 Fig. 6 is a schematic diagram of the degree operation on the globally optimal rigid topology according to an embodiment of the present application;

[0062] Figure 4 Fig. 7 is a schematic diagram of the path negation operation on node v1 according to an embodiment of the present application;

[0063] Figure 5 Fig. 8 is a schematic diagram of the path negation operation on node v3 according to an embodiment of the present application;

[0064] Figure 6 Fig. 9 is a schematic diagram of the optimal persistent communication topology according to an embodiment of the present application;

[0065] Figure 7 Fig. 10 is a schematic diagram of the optimal persistent communication topology with a fault according to an embodiment of the present application;

[0066] Figure 8 Fig. 11 is a schematic diagram of the optimal persistent communication topology after reconstruction according to an embodiment of the present application;

[0067] Figure 9 Fig. 12 is a schematic diagram of the structure of a distributed topology time-varying formation control system according to an embodiment of the present application. DETAILED DESCRIPTION

[0068] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the scope of the present application.

[0069] The purpose of the present application is to provide a distributed topology time-varying formation control method, which reduces the complexity of multi-agent communication.

[0070] In order to make the above-mentioned purposes, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0071] Figure 1 Fig. 13 is a schematic diagram of the flow of a distributed topology time-varying formation control method according to an embodiment of the present application, as shown in the figure, a distributed topology time-varying formation control method comprises the following steps: Figure 1

[0072] Step 101: constructing an initial undirected complete graph according to the communication relationship of each node in the multi-agent formation; each node is an agent.

[0073] The initial undirected complete graph is denoted as G U (V, E, W, S), wherein V represents the initial undirected complete graph G U ​A set of all nodes in G, E represents G U A set of links (a set of edges or a set of links) of each node in G, W represents G U A weighted adjacency matrix in G, S represents G U A set of positions of nodes.

[0074] Step 102: generating a global optimal rigid communication topology according to a distributed algorithm based on the initial undirected complete graph.

[0075] Wherein, step 102 specifically comprises:

[0076] By traversing each node, respectively obtaining the local optimal rigid communication topology of each node;

[0077] Obtaining the intersection R of the local optimal rigid communication topologies of each node;

[0078] Deleting each node v i in the local optimal rigid communication topology R i of the node v kl that satisfies and the edge e j ∈G kl , obtaining the global optimal rigid communication topology;

[0079] Wherein, e k represents an edge from node v l to node v k , and node v l to node v i are nodes in G k , and node v l to node v j are nodes in G i , G i represents the local weighted undirected complete graph of node v j , G j represents the local weighted undirected complete graph of node v i , and i≠j.

[0080] Wherein, by traversing each node, respectively obtaining the local optimal rigid communication topology of each node, specifically comprising:

[0081] When traversing to node v i :

[0082] Obtaining the neighbor set N i of node v i , and obtaining the local weighted undirected complete graph G i corresponding to the neighbor set N

[0083] According to the formula , the local weighted undirected complete graph G iMiddle edge e ij ;

[0084] wherein e ij represents an edge between node v i and node v j , S ij represents a value after normalization processing of s ij , s ij represents a length of edge e ij , P loss represents a path loss, E ti represents energy consumed by node v i to receive data, E rj represents energy consumed by node v i to send data; a i represents initial energy of node v i , a j represents initial energy of node v j ;

[0085] all edges in edge set E i of local weighted undirected complete graph G i are sorted according to weights from small to large, to obtain updated edge set E i ;

[0086] a stiffness matrix M is constructed according to updated edge set E i , the stiffness matrix M is a stiffness matrix with |E i | rows and 3|V i | columns, which is constructed according to coordinates corresponding to each node in G i , V i represents a set of all nodes in G i , and E i represents an edge set of each node in G i ; wherein in the stiffness matrix M, the element in the 3(i-1)+1 column is x i -x j , the element in the 3(i-1)+2 column is y i -y j , the element in the 3i column is z i -z j , the element in the 3(j-1)+1 column is -(x i -x j ), the element in the 3(j-1)+2 column is -(y i -y j ), and the element in the 3 j column is -(z i -z j ), and the elements in the other columns are 0;

[0087] initialize j=0, and set ER Set W R Both the matrix Mc and the set W are empty. R Let E be the set of edges R The weighted adjacency matrix;

[0088] Let matrix Mc' = [Mc; M(j,:)], where [Mc; M(j,:)] represents the matrix obtained by inserting the j-th row of the stiffness matrix M into matrix Mc;

[0089] If matrix Mc' is a non-full-rank matrix, increment the value of j by 1 and return to the step "Let matrix Mc' = [Mc; M(j,:)], where [Mc; M(j,:)] represents the matrix obtained by inserting the j-th row of stiffness matrix M into matrix Mc".

[0090] If matrix Mc' is a full-rank matrix, then edge e ij Join E R And according to the current E R Update W R ;

[0091] If the rank of matrix Mc is less than 3|V|-6, increment the value of j by 1 and return to the step "Let matrix Mc' = [Mc; M(j,:)], where [Mc; M(j,:)] represents the matrix obtained by inserting the j-th row of stiffness matrix M into matrix Mc".

[0092] If the rank of matrix Mc is equal to 3|V|-6, then R i =(V i E R W R ,S i ) is node v i The locally optimal rigid communication topology.

[0093] Step 103: Based on the globally optimal rigid communication topology, according to the communication relationship of each node, the corresponding edges of each node are directed and the in-degree of each node is less than or equal to 3, so as to obtain the optimal persistent communication topology.

[0094] Step 103 specifically includes:

[0095] Obtain the connection matrix of the globally optimal rigid communication topology and the connectivity of each node in the globally optimal rigid communication topology;

[0096] Initialize i = 1, set P to empty, and set flag to 1;

[0097] Determine node v i Is the connectivity 1, 2, or 3?

[0098] If node v i If the connectivity is 1, 2, or 3, then node v will be...i The corresponding edge is directed as e xi xi is added to the set P, and the connectivity and in-degree of node v i in the current global optimal rigid communication topology are updated, and flag is set to 0.

[0099] If i is less than N, the value of i is increased by 1, and the step of “judging whether the connectivity of node v i is 1, 2 or 3” is returned to.

[0100] If i is equal to N and flag is 0, i is set to 1, flag is set to 1, and the step of “judging whether the connectivity of node v i is 1, 2 or 3” is returned to.

[0101] If i is equal to N and flag is 1, it is judged whether there is a node with a connectivity equal to 4 in the current global optimal rigid communication topology.

[0102] If there is a node with a connectivity equal to 4, the corresponding edge of the node with the connectivity equal to 4 is directed as e xi , e xi is added to the set P, the connectivity and in-degree of each node in the current global optimal rigid communication topology are updated, i is set to 1, flag is set to 1, and the step of “judging whether the connectivity of node v i is 1, 2 or 3” is returned to.

[0103] If there is no node with a connectivity equal to 4, an optimal persistent communication topology is output according to the directed graph P composed of the set P.

[0104] The optimal persistent communication topology output according to the directed graph P composed of the set P specifically includes:

[0105] It is judged whether there is a node with an in-degree equal to 4 in the directed graph P composed of the set P.

[0106] If there is a node with an in-degree equal to 4 in the directed graph P, the path of the node with the in-degree equal to 4 is negated (using a path negation algorithm), and the directed graph P after the path negation operation is taken as the optimal persistent communication topology and output.

[0107] If there is no node with an in-degree equal to 4 in the directed graph P, the directed graph P is taken as the optimal persistent communication topology and output.

[0108] The input of the path negation algorithm is a node with an in-degree equal to 4 and the directed graph P, and the output is the updated directed graph P, i.e., the directed graph P after the path negation.

[0109] ​Step 104: Use the optimal persistent communication topology to perform communication control on the multi-agent formation.

[0110] A distributed topology time-varying formation control method further includes: if a communication arc in the optimal persistent communication topology fails, obtaining a directed weighted complete topology of the optimal persistent communication topology, and deleting the failed communication arc in the directed weighted complete topology to obtain a communication topology G. De The communication arc is a link for one-way communication between nodes;

[0111] If the edge set in the optimal persistent communication topology and the communication topology G D If the intersection of the edge sets is not empty, then the communication topology G will be... De The communication arc is transformed into the corresponding weighted undirected topology G. e ;

[0112] Based on the weighted undirected topology G e The current globally optimal rigid communication topology R is generated based on the distributed algorithm. e ;

[0113] Based on the current globally optimal rigid communication topology R e Based on the communication relationships between nodes, the edges corresponding to each node are directed, and the in-degree of each node is less than or equal to 3, thus obtaining the current optimal persistent communication topology P. e ;

[0114] Using the current optimal persistent communication topology P e Communication control for multi-agent formations.

[0115] The implementation process of the distributed topology time-varying formation control method of the present invention includes a distributed global optimal rigid topology generation algorithm, a path inversion algorithm, a distributed persistent topology generation algorithm, and a distributed persistent communication topology fault-tolerant control algorithm. These four algorithms are briefly described below.

[0116] Algorithm 1: Distributed Global Optimal Rigid Topology Generation Algorithm

[0117] Input: Undirected complete graph G U (V,E,W,S);

[0118] Among them, the undirected complete graph G U Let V be the set of all communication links within the communication range; where V = V(G) = {v1, v2, ..., v...} N} represents an undirected graph G U The set of all nodes in v i This represents the i-th node; Represents graph G U The set of lines connecting each point in the equation represents the communication links between agents, where eij (i≠j) represents a communication link; in an undirected graph, e ij represents a bidirectional link between nodes v i and v j , v i and v j are neighbors, in a directed graph, e ij represents a unidirectional link from node v i to node v j , v i is called a neighbor of v j ; represents the weighted adjacency matrix of graph G U , w ij is the weight of edge e ij , if e ij ∈E, w ji >0, otherwise w ji =0; S(G) = {s i} represents the position set of nodes, where s i is represented by (x i , y i , z i ).

[0119] Step 1: let i = 1;

[0120] Step 2: search the neighbor set N i of node v i , get the local weighted undirected complete graph G i (V i , E i , W i , S i );

[0121] Step 3: calculate the corresponding weight value through the weight function w ij

[0122] The weight function formula is;

[0123]

[0124] P loss = kP-rss (2)

[0125]

[0126]

[0127] wherein, P loss represents path loss; S ij represents the result after normalizing s ij ; E ti ​and E rj These represent the energy consumed in sending and receiving data between nodes; a i and a j They are v i and node v j The initial energy; k = (rss) max -rss min ) / (P max -P min P represents the node's transmit power, and rss represents the power of the signal received by the node. max and RSS min These are the maximum and minimum values ​​of the signal strength received by the node, respectively; P is the node's transmit power, P max ,P min These are the maximum and minimum values ​​of the node's transmit power, respectively; s ij The length of the communication link, s safe This is the safe distance between nodes; if the distance is less than the safe distance, there is a risk of collision between nodes. range E represents the maximum communication distance between nodes. elec E represents the energy consumption per unit bit sent and received. amp This represents the energy consumption per unit bit amplification, where l represents the number of bits in the data packet;

[0128] Step 4: Transfer edge set E i Sort all edges by weight in ascending order and update edge set E. i And construct the stiffness matrix M;

[0129] The stiffness matrix is ​​defined as: G i The coordinates of each node in the array are (x, y, y). i ,y i ,z i Construct a stiffness matrix with |E| rows and 3|V| columns. The k-th edge in E corresponds to the k-th row in M, and the elements in its 3(i-1)+1, 3(i-1)+2, and 3i columns are x. i -x j ,y i -y j and z i -z j The corresponding elements in columns 3(j-1)+1, 3(j-1)+2, and 3j are -(x i -x j ),-(y i -y j ) and -(z i -z j ), and the rest of the columns are 0.

[0130] Step5: Let j = 1, E R = [], W R = [], Mc = [];

[0131] Step6: Let Mc' = [Mc; M(j,:)];

[0132] Step7: If Mc' is not full rank, let j = j + 1, go to Step6;

[0133] If Mc' is full rank, add the corresponding edge e ij to E R , update W R , and go to Step8;

[0134] Step8: If rank(Mc) is less than 3|V|-6, let j = j + 1, go to Step6;

[0135] If rank(Mc) is equal to 3|V|-6, then R i = (V i , E R , W R , S i ) is a locally optimal rigid topology for v i ; where rank() denotes the rank of a matrix;

[0136] Step9: If i < N, let i = i + 1, and go to Step2,

[0137] If i = N, go to Step10;

[0138] Step10: Let R = R1∪...∪R N , i = 1, j = 1;

[0139] Step11: Remove all edges in R i that satisfy the condition k, l ∈ G i , G j , and , e kl ∈ G j , and update R;

[0140] Step12: If i < N, let i = i + 1, go to Step11;

[0141] If i = N, j < N, let i = 1, j = j + 1, go to Step11;

[0142] If i = N, j = N, end the algorithm;

[0143] Output: the globally optimal rigid topology R(V, E R , W R , S);

[0144] Algorithm 2: Path Inversion Algorithm

[0145] Input: The node v whose in-degree needs to be inverted. i Communication topology G;

[0146] Step 1: Search for node v in G i The set of neighboring nodes N i ;

[0147] Step 2: If in N i There exists a node v j The condition deg(v) is satisfied j If the value is less than 3, proceed to Step 3; otherwise, proceed to Step 4.

[0148] Step 3: Let edge e in G be... ji The opposite is e ij The algorithm terminates, and the current communication topology G is output.

[0149] Step 4: Let v j =N i (1) Let the edge e in G be ji The opposite is e ij If i = j, proceed to Step 1;

[0150] Output: The reversed communication topology G (current communication topology G).

[0151] In Algorithm 2, i and j are both node labels.

[0152] Note: (1) The degree of a node is deg(v) i () is for undirected graphs and represents the number of edges of a given node in the undirected graph;

[0153] (2) The in-degree of a node (deg) in (v i () is for directed graphs, indicating a path starting from another node and pointing to node v. i The number of edges;

[0154] (3) Out-degree of a node (deg) out (v i () is for directed graphs, representing a graph consisting of nodes v i The number of edges originating from other nodes;

[0155] Algorithm 3: Distributed Persistent Topology Generation Algorithm

[0156] Input: Optimal rigidity graph R(V,E,W,S);

[0157] Step 1: Calculate the adjacency matrix W(G) = {wij} and the degree deg(v i ) of the node;

[0158] Step2: Let P = [], i = 1, flag = 1;

[0159] Step3: If the degree deg(v i ) of the node = 3, 2, 1, jump to Step4;

[0160] Otherwise, jump to Step5;

[0161] Step4: Direct all edges corresponding to the node v i to e xi , delete the corresponding edges in R, add the directed edges to P, update the degrees deg(v i ),...,deg(v x ) of the nodes, update the in-degrees deg in (v i ),...,deg in (v x ) of the nodes, and let flag = 0;

[0162] Step5: If i < N, let i = i + 1, and jump to Step3;

[0163] If i = N and flag = 0, let i = 1, flag = 1, and jump to Step3;

[0164] If i = N and flag = 1, jump to Step6;

[0165] Step6: Determine whether there exists a node v j such that deg(v j ) = 4;

[0166] If yes, direct the edges corresponding to the node v i to e xi , add them to P, update the degrees deg(v i ),...,deg(v x ) of the nodes and the in-degrees deg in (v i ),...,deg in (vx) of the nodes, let i = 1, flag = 1, and jump to Step3;

[0167] If no, jump to Step7;

[0168] Step7: According to the in-degrees deg in (v i), and determine whether there are nodes satisfying deg in (v i ) == 4, if so, execute algorithm 2 on all nodes satisfying the condition as input respectively, and reverse the corresponding path in P;

[0169] Output: Optimal persistent communication topology P(V, E, W, S).

[0170] Algorithm 4: Distributed fault-tolerant control algorithm for persistent communication topology

[0171] Input: Persistent communication topology P(V P ,E P ,W P ,S P ) before failure, directed and weighted complete topology G D (V, E, W, S), and failed communication arc E e ;

[0172] Step 1: delete the failed communication arc in G D to obtain G De (V De ,E De ,W De ,S De );

[0173] Step 2: If E P ∩ E e == [], then let P e = P, and end the algorithm;

[0174] Step 3: Convert the arcs in G De into the corresponding weighted undirected topology G e (V e ,E e ,W e ,S e );

[0175] Step 4: Take G e as input to execute algorithm 1 to generate three-dimensional optimal rigid communication topology R e (V Re ,E Re ,W Re ,S Re );

[0176] Step 5: Take R e as input to execute algorithm 3 to generate three-dimensional optimal persistent communication topology P e (V Pe ,E Pe ,W Pe ,S Pe );

[0177] Step 6: If it exists With v j and P e As input, execute Algorithm 2 to update P. e Conversely, execute P. e This is the optimal persistent communication topology;

[0178] Output: The reconstructed optimal persistent communication topology P e .

[0179] The following simulation illustrates a distributed topology time-varying formation control method of the present invention using specific embodiments.

[0180] Assume a multi-agent formation has 16 nodes, each with a communication range of Δ = 35m. The globally optimal rigid communication topology generated by the distributed algorithm is as follows: Figure 2 As shown. Solid lines represent edges in the globally optimal rigid communication topology, and dashed lines represent edges deleted during the delete edge operation. There are a total of 9 edges that satisfy the delete edge operation, namely e... 15 ,e 26 ,e 210 ,e 37 ,e 313 ,e 410 ,e 414 ,e 814 ,e 1213 Ultimately, the globally optimal rigid communication topology R can be obtained.

[0181] Using R as input, Algorithm 3 is executed to perform a directed operation on the rigid communication topology. After performing the degree operation, the following can be obtained: Figure 3 Nodes v1 and v3 are nodes with an in-degree of 4, marked with a diamond shape in the graph. All other nodes have an in-degree less than 3. Therefore, Algorithm 2, i.e., path inversion, needs to be performed on nodes v1 and v3, as follows: Figure 4 and Figure 5 These are the path inversion operations for nodes v1 and v3, respectively. The dashed lines represent the directed paths to be inverted. Figure 6 This is the globally optimal persistent communication topology obtained after performing the inversion operation.

[0182] To address link failures under fault conditions, Algorithm 4 is executed to verify the proposed communication topology fault-tolerant control algorithm. The initial communication topology is as follows: Figure 7 As shown, the faulty link is set to e. 14 ,e 17 ,e 34 ,e 37 The solid and dashed lines represent communication arcs in the optimal persistent communication topology, and the dashed lines represent directed links e. 14 ,e 17For the failed directed link in the current communication topology, the structure of the communication topology changes, and the link e 34 37 For the failed directed link not in the communication topology, it has no effect on the current communication topology.

[0183] After the failure, algorithm 4 is executed to reconstruct the communication topology, and the reconstructed communication topology is as shown in Figure 8

[0184] The application is based on a distributed communication topology switching fault-tolerant control method of a persistent graph. The link weight function is designed by comprehensively considering the link quality and energy consumption factors, and the optimal persistent communication topology in three-dimensional space is generated, which improves the communication quality and prolongs the network life. Combined with the characteristics of the persistent graph, the degree operation and the path inversion operation of the persistent graph are proposed to rigidify the graph and direct it, and the corresponding theoretical proof is given. A distributed topology optimization algorithm based on the optimal persistent graph is proposed, and the globally optimal persistent communication topology is obtained. An active distributed communication topology fault-tolerant control algorithm is proposed, which realizes the recovery of the connectivity of the communication network under fault conditions and improves the stability of the communication topology. Finally, the simulation of the algorithm proposed in the application verifies the effectiveness of the algorithm.

[0185] Figure 9 The application is a distributed topology time-varying formation control system structure diagram, as shown in Figure 9 The application is a distributed topology time-varying formation control system, comprising:

[0186] An initial undirected complete graph construction module 201 is used to construct an initial undirected complete graph according to the communication relationship of each node in the multi-agent formation; each node is an agent;

[0187] A global optimal rigid communication topology generation module 202 is used to generate a global optimal rigid communication topology based on the initial undirected complete graph according to a distributed algorithm;

[0188] An optimal persistent communication topology determination module 203 is used to direct the edges of each node based on the global optimal rigid communication topology according to the communication relationship of each node, and the in-degree of each node is less than or equal to 3, to obtain an optimal persistent communication topology;

[0189] An optimal persistent communication topology application module 204 is used to control the communication of the multi-agent formation by using the optimal persistent communication topology.

[0190] ​​The various embodiments described in this specification are presented for the purpose of illustrating the principles of the present application and its best mode of operation. Each of the embodiments described in this specification has been provided for the purpose of illustration only and the various embodiments are not intended to limit the present application in any way unless otherwise specifically indicated. The same parts and / or features of the various embodiments described in this specification can be referenced using the same reference numerals for the ease of understanding of the present application.

[0191] The principles and implementations of the present application have been described in the above embodiments, which are only used to help understand the method of the present application and its core idea. Meanwhile, for those skilled in the art, the specific implementation and application range of the present application can be changed according to the idea of the present application. In summary, the content of the specification should not be understood as a limitation of the present application.

Claims

1. A distributed topology time-varying formation control method, characterized in that, include: An initial undirected complete graph is constructed based on the communication relationships among the nodes in the multi-agent formation; each node is an agent. Based on the initial undirected complete graph, a globally optimal rigid communication topology is generated according to a distributed algorithm. Based on the global optimal rigid communication topology, according to the communication relationship of each node, the corresponding edges of each node are directed and the in-degree of each node is less than or equal to 3, so as to obtain the optimal persistent communication topology. The optimal persistent communication topology is used for communication control of multi-agent formations; The optimal persistent communication topology, based on the globally optimal rigid communication topology, is obtained by directing the edges of each node according to their communication relationships, ensuring that the in-degree of each node is less than or equal to 3. Specifically, this includes: Obtain the connection matrix of the globally optimal rigid communication topology and the connectivity of each node in the globally optimal rigid communication topology; Initialize i = 1, set P is empty, and flag is set to 1; Determine node v i Is the connectivity 1, 2, or 3? If node v i If the connectivity is 1, 2, or 3, then node v will be... i The corresponding edge is directed to e. xi , will e xi Add to set P, and include node v in the current globally optimal rigid communication topology. i The corresponding edge is deleted, and the connectivity and in-degree of each node in the current globally optimal rigid communication topology are updated, and the flag is set to 0. If i is less than N, increment i by 1 and return to step "determine node v". i Is the connectivity 1, 2 or 3? If i equals N and flag is 0, let i = 1, set the flag bit to 1, and return to step "determine node v". i Is the connectivity 1, 2, or 3? If i equals N and flag is 1, then determine whether there are nodes with a connectivity of 4 in the current globally optimal rigid communication topology. If there exists a node with a connectivity of 4, then the edges corresponding to that node with a connectivity of 4 are directed to e. xi , will e xi Add to set P, update the connectivity and in-degree of each node in the current globally optimal rigid communication topology, let i = 1, flag = 1, and return to step "determine node v". i Is the connectivity 1, 2, or 3? If there are no nodes with a connectivity of 4, then output the optimal persistent communication topology based on the directed graph P formed by set P. The distributed topology time-varying formation control method further includes: if a communication arc in the optimal persistent communication topology fails, obtaining a directed weighted complete topology of the optimal persistent communication topology, and deleting the failed communication arc in the directed weighted complete topology to obtain a communication topology G. De The communication arc is a link for one-way communication between nodes. If the edge set in the optimal persistent communication topology and the communication topology G De If the intersection of the edge sets is not empty, then the communication topology G will be... De The communication arc is transformed into the corresponding weighted undirected topology G. e ; Based on the weighted undirected topology G e The current globally optimal rigid communication topology R is generated based on the distributed algorithm. e ; Based on the current globally optimal rigid communication topology R e Based on the communication relationships between nodes, the edges corresponding to each node are directed, and the in-degree of each node is less than or equal to 3, thus obtaining the current optimal persistent communication topology P. e ; Using the current optimal persistent communication topology P e Communication control for multi-agent formations.

2. The distributed topology time-varying formation control method according to claim 1, characterized in that, The initial undirected complete graph is denoted as G. U (V,E,W,S), where V represents the initial undirected complete graph G. U The set of all nodes in G, where E represents G. U The set of connections between all nodes in G, where W represents G. U The weighted adjacency matrix, S represents G U The set of positions of the nodes in the middle.

3. The distributed topology time-varying formation control method according to claim 1, characterized in that, The step of generating a globally optimal rigid communication topology based on the initial undirected complete graph using a distributed algorithm specifically includes: By traversing each node, the local optimal rigid communication topology of each node is obtained; Obtain the intersection R of the locally optimal rigid communication topologies of each node; Delete each node v i The local optimal rigid communication topology R i China satisfies And e kl ∈G j By finding the edges, we can obtain the globally optimal rigid communication topology; Among them, e kl Represents node v k to node v l Edge, node v k to node v l All are G i Middle node, node v k to node v l All are G j Middle node, G i Represents node v i A locally weighted undirected complete graph, G j Represents node v j A locally weighted undirected complete graph, i ≠ j.

4. The distributed topology time-varying formation control method according to claim 3, characterized in that, The process of traversing each node to obtain the locally optimal rigid communication topology for each node specifically includes: When traversing to node v i hour: Get node v i The neighbor set N i And obtain the neighbor set N i The corresponding locally weighted undirected complete graph G i ; According to the formula Compute locally weighted undirected complete graph G i Middle edge e ij The weights; Among them, e ij Represents node v i and node v j The edge, S ij Indicates s ij The value after normalization, s ij Representing edge e ij The length of P loss E represents path loss. ti Represents node v i Energy consumed in receiving data, E rj Represents node v i Energy consumed in sending data; a i Represents node v i The initial energy, a j Represents node v j The initial energy; The locally weighted undirected complete graph G i edge set E i Sort all edges in the set E according to their weights in ascending order to obtain the updated edge set E. i ; According to the updated edge set E i Construct the stiffness matrix M, which is based on G. i A |E| is constructed from the coordinates of each node. i |Line 3|V i | The stiffness matrix of the column, V i G represents i The set of all nodes in M; where the element in the 3(i-1)+1th column of the stiffness matrix M is x. i -x j The element in the 3(i-1)+2th column is y. i -y j The element in the 3ith column is z. i -z j The element in the 3(j-1)+1th column is -(x i -x j ), 3(j-1)+2 columns of elements are -(y i -y j The element corresponding to column 3j is -(z) i -z j ), and the rest of the columns are 0; Initialize j = 0, set E R Set W R Both the matrix Mc and the set W are empty. R Let E be the set of edges R The weighted adjacency matrix; Let matrix Mc' = [Mc; M(j,:)], where [Mc; M(j,:)] represents the matrix obtained by inserting the j-th row of the stiffness matrix M into matrix Mc; If matrix Mc' is a non-rank matrix, increment the value of j by 1 and return to the step "Let matrix Mc' = [Mc; M(j,:)], where [Mc; M(j,:)] represents the matrix obtained by inserting the j-th row of stiffness matrix M into matrix Mc". If matrix Mc' is a full-rank matrix, then edge e ij Join E R And according to the current E R Update W R ; If the rank of matrix Mc is less than 3|V|-6, increment the value of j by 1 and return to the step "Let matrix Mc' = [Mc; M(j,:)], where [Mc; M(j,:)] represents the matrix obtained by inserting the j-th row of stiffness matrix M into matrix Mc". If the rank of matrix Mc is equal to 3|V|-6, then R i =(V i E R W R ,S i ) is node v i The locally optimal rigid communication topology.

5. The distributed topology time-varying formation control method according to claim 1, characterized in that, The step of outputting the optimal persistent communication topology based on the directed graph P formed by the set P specifically includes: Determine whether there exists a node with an in-degree of 4 in the directed graph P formed by the set P. If there is a node with an in-degree of 4 in a directed graph P, then the path of the node with an in-degree of 4 is inverted, and the directed graph P after the path inversion operation is output as the optimal persistent communication topology. If there is no node with an in-degree of 4 in the directed graph P, then the directed graph P will be output as the optimal persistent communication topology.

6. A distributed topology time-varying formation control system, characterized in that, The distributed topology time-varying formation control system applies the distributed topology time-varying formation control method of claim 1, and the distributed topology time-varying formation control system includes: An initial undirected complete graph construction module is used to construct an initial undirected complete graph based on the communication relationships of each node in a multi-agent formation; each node is an agent. A global optimal rigid communication topology generation module is used to generate a global optimal rigid communication topology based on the initial undirected complete graph and according to a distributed algorithm. The optimal persistent communication topology determination module is used to obtain the optimal persistent communication topology based on the global optimal rigid communication topology and according to the communication relationship of each node, to make the corresponding edges of each node directed and the in-degree of each node less than or equal to 3. The optimal persistent communication topology application module is used to perform communication control on a multi-agent formation using the optimal persistent communication topology.

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