CN114895703A - Distributed fault-tolerant time-varying formation control method and system based on topology optimization reconstruction - Google Patents
Distributed fault-tolerant time-varying formation control method and system based on topology optimization reconstruction Download PDFInfo
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Abstract
The invention discloses a distributed fault-tolerant time-varying formation control method and system based on topology optimization reconstruction, and relates to the technical field of multi-agent systems, wherein the method comprises the following steps: searching a local undirected graph of each node according to the undirected graph; determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters; obtaining the local optimal rigid communication performance topology of each node according to the weight; obtaining a global optimal communication topology according to the local optimal rigid communication performance topology; performing formation control according to the global optimal communication topology; and when the global optimal communication topology is judged to have faults, eliminating fault edges and fault nodes in the undirected graph according to fault information, and returning to the step of searching the local undirected graph of each node according to the undirected graph. The invention can automatically generate the global optimal communication topology of the multi-agent system and automatically generate a new global optimal communication topology after the communication topology fails, thereby ensuring the stable formation structure of the multi-agent system.
Description
Technical Field
The invention relates to the technical field of multi-agent systems, in particular to a distributed fault-tolerant time-varying formation control method and system based on topology optimization reconstruction.
Background
The multiple intelligent synergies have wide application in the fields of industry, national defense, life and the like, and have developed into an important research direction in the control field and the robot field. Compared to single agents, multi-agent systems, and in particular distributed multi-agent systems, have a number of distinct advantages. The multi-agent system has wider sensing range and moving range, better fault tolerance and robustness due to larger redundancy, lower requirement on individual performance, lower cost and more economic benefit.
The multi-agent system has wide directions, and has multi-robot formation control, cluster movement, consistency and the like in the control direction, and coverage strategy, topology generation, topology optimization, reconstruction and the like in the aspect of topology. The existing research mainly focuses on the stability problem of formation, and the research on the communication topology (such as optimization, reconstruction and the like) of the formation is less. The following problems exist in the research of the existing multi-agent system:
(1) the existing topology mostly adopts a fixed communication topology, the fixed communication topology needs to be designed in advance, the complexity of the communication topology is high, and a proper communication topology cannot be adopted when a formation flying task is executed.
(2) In the process of executing the task, the method is easily limited by the environment, and global information is difficult to obtain.
(3) In the process of executing tasks, due to the unexpected situations of communication interference, control failure and the like of the multi-agent system, the communication topology of the multi-agent system is damaged, and thus the tasks cannot be completed.
In summary, how to automatically generate the global optimal communication topology of the multi-agent system, and automatically generate a new global optimal communication topology after the communication topology fails, so as to ensure the stable formation structure of the multi-agent system becomes a problem to be urgently solved by the technical staff in the field.
Disclosure of Invention
The invention aims to provide a distributed fault-tolerant time-varying formation control method and system based on topology optimization reconstruction, which can automatically generate a global optimal communication topology of a multi-agent system and automatically generate a new global optimal communication topology after the communication topology fails, so that the stability of the formation structure of the multi-agent system is ensured.
In order to achieve the purpose, the invention provides the following scheme:
a distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction comprises the following steps:
constructing an undirected graph of the multi-agent system; the undirected graph comprises a plurality of nodes and a plurality of edges; the node is an agent; the edges are communication links between nodes;
searching a local undirected graph of each node according to the undirected graph;
determining the weight of each edge by using a weight function according to the local undirected graph and related parameters of the multi-agent system;
obtaining the local optimal rigid communication performance topology of each node according to the weight;
obtaining a global optimal communication topology of the multi-agent system according to the local optimal rigid communication performance topology;
performing formation control according to the global optimal communication topology;
judging whether the globally optimal communication topology has a fault;
if so, acquiring fault information; the fault information comprises fault edges and fault nodes;
removing the fault edge and the fault node in the undirected graph according to the fault information, and returning to the step of searching the local undirected graph of each node according to the undirected graph;
and if not, continuing the formation control according to the global optimal communication topology.
Optionally, the determining, according to the local undirected graph and the relevant parameters of the multi-agent system, the weight of each edge by using a weight function specifically includes:
acquiring relevant parameters of the multi-agent system; the relevant parameters include: the method comprises the following steps of (1) the bit number of a data packet, the transmitting power of nodes, the maximum value of the transmitting power of the nodes, the minimum value of the transmitting power of the nodes, the distance between the nodes, the safety distance between the nodes, the maximum communication distance of the nodes, a distance adjusting coefficient, the energy consumption of transmitting and receiving unit bits, the energy consumption of amplifying unit bits, the maximum value of the intensity of a signal received by the nodes, the minimum value of the intensity of a signal received by the nodes, the power value of the signal received by the nodes and the initial energy of the nodes;
and determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters.
Optionally, the obtaining a local optimal rigid communication performance topology of each node according to the weight specifically includes:
according to the weight, all the edges in the undirected graph are sorted from small to large according to the weight to obtain an edge set;
constructing a rigidity matrix according to the edge set;
obtaining the rank of the matrix according to the rigidity matrix;
and obtaining the local optimal rigid communication performance topology of each node according to the rank of the matrix.
Optionally, the obtaining a globally optimal communication topology of the multi-agent system according to the locally optimal rigid communication performance topology specifically includes:
and taking a union set of all the local optimal rigid communication performance topologies to obtain a global optimal communication topology of the multi-agent system.
Optionally, the performing formation control according to the globally optimal communication topology specifically includes:
establishing a kinetic model of the multi-agent system;
obtaining a Laplace matrix of the multi-agent system according to the global optimal communication topology and the dynamic model;
obtaining a control input of the multi-agent system according to the Laplace matrix and the dynamic model;
and performing formation control according to the control input.
The invention also provides the following scheme:
a distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction, the system comprising:
the undirected graph constructing module is used for constructing an undirected graph of the multi-agent system; the undirected graph comprises a plurality of nodes and a plurality of edges; the node is an agent; the edges are communication links between nodes;
the local undirected graph searching module is used for searching the local undirected graph of each node according to the undirected graph;
a weight determining module, configured to determine a weight of each edge by using a weight function according to the local undirected graph and related parameters of the multi-agent system;
the local optimal topology obtaining module is used for obtaining the local optimal rigid communication performance topology of each node according to the weight;
the global optimal topology obtaining module is used for obtaining a global optimal communication topology of the multi-agent system according to the local optimal rigid communication performance topology;
the formation control module is used for performing formation control according to the global optimal communication topology;
the fault judgment module is used for judging whether the global optimal communication topology has faults or not;
the fault information acquisition module is used for acquiring fault information when the output result of the fault judgment module is yes; the fault information comprises fault edges and fault nodes;
the fault removing and returning module is used for removing the fault edge and the fault node in the undirected graph according to the fault information and returning the fault edge and the fault node to the local undirected graph searching module;
and the continuous formation control module is used for continuously performing formation control according to the global optimal communication topology when the output result of the fault judgment module is negative.
Optionally, the weight determining module specifically includes:
a relevant parameter acquiring unit for acquiring relevant parameters of the multi-agent system; the relevant parameters include: the method comprises the following steps of (1) the bit number of a data packet, the transmitting power of nodes, the maximum value of the transmitting power of the nodes, the minimum value of the transmitting power of the nodes, the distance between the nodes, the safety distance between the nodes, the maximum communication distance of the nodes, a distance adjusting coefficient, the energy consumption of transmitting and receiving unit bits, the energy consumption of amplifying unit bits, the maximum value of the intensity of a signal received by the nodes, the minimum value of the intensity of a signal received by the nodes, the power value of the signal received by the nodes and the initial energy of the nodes;
and the weight determining unit is used for determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters.
Optionally, the local optimal topology obtaining module specifically includes:
the weight value sorting unit is used for sorting all the edges in the undirected graph from small to large according to the weight value to obtain an edge set;
the rigidity matrix construction unit is used for constructing a rigidity matrix according to the edge set;
the rank obtaining unit of the matrix is used for obtaining the rank of the matrix according to the rigidity matrix;
and the local optimal topology obtaining unit is used for obtaining the local optimal rigid communication performance topology of each node according to the rank of the matrix.
Optionally, the global optimal topology obtaining module specifically includes:
and the global optimal topology obtaining unit is used for taking a union set of all the local optimal rigid communication performance topologies to obtain a global optimal communication topology of the multi-agent system.
Optionally, the formation control module specifically includes:
a dynamics model establishing unit for establishing a dynamics model of the multi-agent system;
a laplacian matrix obtaining unit, configured to obtain a laplacian matrix of the multi-agent system according to the globally optimal communication topology and the dynamical model;
a control input obtaining unit, configured to obtain a control input of the multi-agent system according to the laplacian matrix and the dynamical model;
and the formation control unit is used for performing formation control according to the control input.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention discloses a distributed fault-tolerant time-varying formation control method and a system based on topology optimization reconstruction, determining the weight of each edge by using a weight function according to the local undirected graph of each node in the undirected graph of the multi-agent system and the related parameters of the multi-agent system, obtaining the local optimal rigid communication performance topology of each node according to the weight, obtaining the global optimal communication topology of the multi-agent system by synthesizing the local optimal rigid communication performance topologies of all the nodes, performing formation control according to the global optimal communication topology, removing fault edges and fault points when the global optimal communication topology has faults, regenerating the global optimal communication topology, therefore, the global optimal communication topology of the multi-agent system is automatically generated, a new global optimal communication topology is automatically generated after the communication topology breaks down, and the stability of the formation structure of the multi-agent system is ensured.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flowchart of an embodiment of a distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction according to the present invention;
FIG. 2 is a three-dimensional deformable view and a three-dimensional rigid view;
FIG. 3 is G i (V i ,E i ,W i ) And G j (V j ,E j ,W j ) A relationship graph;
FIG. 4 shows a node v i A local optimal communication topology diagram of (a);
FIG. 5 is a diagram of a globally optimal rigid topology;
FIG. 6 is a schematic diagram of communication topology reconfiguration;
fig. 7 is a schematic diagram of node positions where t is 0s, t is 4s, t is 10.2s, and t is 10.5 s;
FIG. 8 is a diagram of a queuing error;
FIG. 9 is a structural diagram of an embodiment of a distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a distributed fault-tolerant time-varying formation control method and system based on topology optimization reconstruction, which can automatically generate a global optimal communication topology of a multi-agent system and automatically generate a new global optimal communication topology after the communication topology fails, thereby ensuring the stable formation structure of the multi-agent system.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Fig. 1 is a flowchart of an embodiment of a distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction according to the present invention. Referring to fig. 1, the distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction includes:
step 101: constructing an undirected graph of the multi-agent system; the undirected graph comprises a plurality of nodes and a plurality of edges; the node is an agent; edges are inter-node communication links.
Step 102: and searching the local undirected graph of each node according to the undirected graph.
Step 103: and determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters of the multi-agent system.
The step 103 specifically includes:
acquiring relevant parameters of the multi-agent system; the relevant parameters include: the method comprises the steps of the number of bits of a data packet, the transmitting power of nodes, the maximum value of the transmitting power of the nodes, the minimum value of the transmitting power of the nodes, the distance between the nodes, the safety distance between the nodes, the maximum communication distance of the nodes, a distance adjusting coefficient, the energy consumption of transmitting and receiving unit bits, the energy consumption of amplifying unit bits, the maximum value of the strength of a signal received by the nodes, the minimum value of the strength of a signal received by the nodes, the power value of the signal received by the nodes and the initial energy of the nodes.
And determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters.
Step 104: and obtaining the local optimal rigid communication performance topology of each node according to the weight.
The step 104 specifically includes:
and according to the weight, sequencing all edges in the undirected graph from small to large according to the weight to obtain an edge set.
And constructing a rigidity matrix according to the edge set.
And obtaining the rank of the matrix according to the rigidity matrix.
And obtaining the local optimal rigid communication performance topology of each node according to the rank of the matrix.
Step 105: and obtaining the global optimal communication topology of the multi-agent system according to the local optimal rigid communication performance topology.
The step 105 specifically includes:
and (4) taking a union set of all the local optimal rigid communication performance topologies to obtain a global optimal communication topology of the multi-agent system.
Step 106: and performing formation control according to the global optimal communication topology.
The step 106 specifically includes:
and establishing a dynamic model of the multi-agent system.
And obtaining a Laplace matrix of the multi-agent system according to the global optimal communication topology and the dynamic model.
And obtaining the control input of the multi-agent system according to the Laplace matrix and the dynamic model.
And performing formation control according to the control input.
Step 107: and judging whether the globally optimal communication topology has a fault.
If the output result of step 107 is yes, step 108 is executed: acquiring fault information; the failure information includes failed edges and failed nodes.
Step 109: and removing the fault edges and the fault nodes in the undirected graph according to the fault information, and returning to the step 102.
If the output result of step 107 is no, execute step 110: and continuing the formation control according to the global optimal communication topology.
The technical solution of the present invention is illustrated by a specific example below:
for further explanation of the present invention, the formation control of the unmanned clustering system is taken as an embodiment, and this embodiment is only for explaining one implementation method of the present invention, and does not represent a limitation on the applicable scenarios of the present invention. The invention discloses a distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction, which is essentially a distributed fault-tolerant time-varying formation control method based on network topology optimization reconstruction, and comprises the following steps:
the dynamics formula of the agent system (dynamics model of the multi-agent system) is as follows:
wherein the content of the first and second substances,
the status is represented by a number of time slots,
representing the control inputs of the multi-agent system,
represents the system matrix, B ∈ R n×p Representing the input matrix. If formula (5) satisfies
(i ═ 1, 2.. multidot.n), then the formation is said to implement a formation form h (t), where r (t) is a state formation reference function, h (t) · i (t) represents a formation, and h i (t) (i ═ 1, 2.., N) segments are continuously differentiable.
Set finite set
Represents a set of topologies, and the topologies are all connected,
for switching signals, G σ(t) And L σ(t) Respectively representing the corresponding interaction topology and laplacian matrix.
Aiming at the formation control problem of communication topology switching, the following control protocol is adopted:
wherein, i is 1,2 1 ,K 2 ,K 3 Is a constant gain matrix of appropriate dimensions, N i (t) denotes a set of neighbors, v i (t)∈R m Indicating an external command signal, w ij Representing the weight of the edge. The system can be written as follows:
wherein N is the node of the multi-agent systemThe number of points, L ═ D-W, D (g) ═ diag { deg ], denotes the laplacian matrix of the multi-agent system in (v i ) I 1, 2.., N represents a degree matrix of the system, w (g) { w ═ N } represents a degree matrix of the system, and w (g) } represents a degree matrix of the system ij Denotes the weighted adjacency matrix of the system, deg in (v i ) Representing a node v i The degree of entry of (c). If e ij E is then w ji > 0, otherwise w ji 0. If and only if for any v i ,v j Having a value of e ij ,e ji ∈E,w ji ＝w ij G is called an undirected graph.
(Algorithm 1) the control algorithm performs the steps of:
step 1: according to
And
obtaining a matrix
And
order to
Step 2: according to the result obtained in step 1
And
is obtained to satisfy
External command signal v i (t) wherein K 1 A constant gain matrix of appropriate dimensions;
and step 3: design K 2 So that A + BK 1 +BK 2 The eigenvalues of (a) are at the negative half axis of the complex plane;
and 4, step 4: according to L σ(t) Obtain its minimum eigenvalue lambda min Calculate P o (A+BK 1 +BK 2 )+(A+BK 1 +BK 2 ) T P o -P o BB T P o Positive definite solution P of + I ═ 0 o Let us order
The motion track of the multi-agent in the three-dimensional space is X, the communication topology of the formation nodes is an undirected graph, and the undirected graph is used for any node v i ,v j With | | x i -x j ||＝d ij (d ij Is a constant value, representing v i And v j Distance of (d) is said to be a rigid topology, otherwise is said to be a deformable graph. If any edge of a three-dimensional rigid graph cannot maintain the rigidity after being deleted, the rigid graph is called a three-dimensional minimum rigid graph. If the sum of the weight values of all the edges of one three-dimensional rigid graph is the minimum of all the rigid graphs with the same node, the three-dimensional minimum rigid graph is called a three-dimensional optimal rigid graph. As shown in fig. 2, (a) is a three-dimensional deformable graph, and fig. 2, (b) and 2, (c) and 2, (d) are different three-dimensional rigid graphs having the same node. Here, part (c) in fig. 2 and part (d) in fig. 2 are three-dimensional minimum rigidity diagrams, and part (d) in fig. 2 is a three-dimensional optimum rigidity diagram.
Due to the fact that actual tasks are complex and changeable, not only the connectivity of a network needs to be guaranteed, but also the communication quality of a link needs to be optimized when topology generation and optimization are carried out. In the process of optimizing network connectivity by using a rigid graph theory, a link weight function comprehensively considering link communication quality and energy consumption is designed, so that the communication quality can be effectively improved, the load among nodes can be balanced, and the overall service life of the network can be prolonged.
(Algorithm 2) an algorithm for generating a rigid topology with optimal three-dimensional link quality is as follows:
inputting: complete communication topology (undirected graph of multi-agent system) G, relevant parameters of multi-agent system (including bit number of data packet l; transmission power of node P; transmission power of node)Maximum and minimum values P of rate max ,P min (ii) a Distance d between nodes ij Safety distance d between nodes safe Maximum communication distance d of nodes range (ii) a A distance adjustment coefficient γ; energy consumption E for transmitting and receiving unit bit elec Amplifying energy consumption E per bit amp (ii) a Maximum and minimum rss of node received signal strength max ,rss min (ii) a A power value rss of a signal received by a node; node v i And node v j Initial energy a of i ,a j )。
And 5: calculating the weight w of each edge i,j The function for calculating the weight (weight function) is as follows:
wherein, P loss Represents the path loss, D ij ＝(d ij -d safe )/(d range -d safe ) γ ，d ij Representing the distance between nodes, d safe Indicating the safe distance between nodes, d range Represents the maximum communication distance of the node, E ti And E rj Respectively representing the energy consumed by the nodes for transmitting and receiving data, a ═ a i +a j ，a i ,a j Are each v i And node v j The initial energy of (a). P loss 、E ti 、E rj The expression of (a) is as follows:
P loss ＝kP-rss (5)
wherein rss represents a power value of a signal received by a node; k ═ s (rss) max -rss min )/(P max -P min )，rss max ,rss min Respectively, the maximum and minimum values of the received signal strength of the node, P max ,P min The maximum value and the minimum value of the node transmitting power are respectively; p isThe transmit power of the node; gamma is a distance adjustment coefficient; e elec Representing the energy consumption of transmitting and receiving a unit bit, E amp Representing the power consumption of the unit bit of amplification, l representing the number of bits of the data packet, d ij Representing the distance between the nodes.
And 6: and (4) according to the weight calculated in the step (5), sequencing all communication edges in the step (G) from small to large according to the weight to obtain an edge set E. Constructing a stiffness matrix M epsilon R of | E | row and 3| V | column |E|×nr 。
Wherein, the kth side in E corresponds to the kth row in M, and the elements corresponding to the 3(i-1) +1 column, the 3(i-1) +2 column and the 3i column are x i -x j ,y i -y j And z i -z j The corresponding element in column 3(j-1) +1, column 3(j-1) +2, and column 3j is- (x) i -x j ),-(y i -y j ) And- (z) i -z j ) And the remaining columns are 0, wherein (x) i ,y i ,z i ) For the coordinates corresponding to each node.
And 7: adding the row of the M constructed in the step 6 into the Mc, and if the M is added to the full rank of the rear matrix Mc, adding the corresponding edge e ij Adding E R If the matrix Mc is not of full rank, the row just added to Mc is deleted and the process is repeated for the next row in M until E R There are 3| V | 6 rows or execution until all rows in matrix M have been added to matrix Mc.
And 8: obtaining the rank of the matrix Mc according to the matrix Mc obtained in the step 7, and if the rank of the matrix Mc is equal to 3| V | -6, then R (V, E) R ,W R ) For a three-dimensional optimal rigid topology (local optimal rigid communication performance topology of each node) of G, if the rank of the matrix Mc is less than 3| V | -6, then a three-dimensional optimal rigid graph does not exist in G.
And (3) outputting: optimal rigid communication performance topology (local optimal rigid communication performance topology per node) R (V, E) R ,W R )。
Wherein the communication topology of the multi-agent system is represented by the graph G (V, E, W), where V (G) ═ V 1 ,v 2 ,...,v N Represents the set of nodes of diagram G,
set of communication edges representing G, w (G) { w ═ c ij Denotes a weighted adjacency matrix of G, w ij Represents an edge e ij The weight of (2).
The method is a related theory of optimal rigid communication topology in a distributed three-dimensional space, analyzes the relationship between global rigidity and local rigidity, demonstrates the problems of local rigidity substitution and the like, and provides a three-dimensional distributed communication topology generation algorithm.
Theorem 1: graph G with n (n > 3) nodes in three-dimensional plane n Is a least rigid graph, and if and only if the graph has 3n-6 edges, and each has a derived sub-graph G 'of i (i ≦ n) nodes' i Containing at most 3| V i -6 edges.
And (3) proving that: the necessity: from theory 1, the three-dimensional minimum stiffness map has 3| V i I-6 sides, the Haniberg sequence is a least rigid sequence, i.e. each G i Are all a minimum stiffness map, each minimum stiffness map G i (i > 4) are all available as a result of a certain Haniberg sequence. Then | E i |≤3|V i |-6。G n Each of which has a | V i Sub-graph G 'of | nodes' i Can be regarded as G i Is a sub-diagram of
The necessity is verified.
The sufficiency: when i is 4, there is | V 4 |＝9，G 4 Is a complete graph, satisfying the condition that each derived sub-graph G 'has i (i ≦ 4) nodes' i Contains at most 3i-6 sides and is the least rigid graph. G i-1 Is a minimum stiffness map, | E i-1 |＝3V i-1 -6, as can be seen from the necessity of theorem 1
To ensure G i Having | E i |＝3|V i I-6 edges, need to execute the operation of adding nodes or separating edges, and execute the new graph G obtained after the operation i Again, from the rigid diagram, it is necessary to understand from theorem 1 that G is i Each derived subgraph ofG' i ≤3|V' i And l-6. By analogy, a derived subgraph G 'with i (i ≦ n) nodes' i The graph containing at most 3i-6 sides is a rigid graph, and sufficiency is confirmed.
Theorem 2: for graph G (V, E, W), if any node V i E is equal to V and exists in i K is not less than 3 neighbors and N is the neighbor of the neighbor i Composition diagram G i (V i ,E i ,W i ) Is a rigid figure in which
G (V, E, W) is a stiffness map.
And (3) proving that: n is a radical of i ,N j And G i ,G j Are respectively a node v i And v j V of (a) neighbor set i ∈N j ,v j ∈N i And a rigidity map, and (v) i ,v j )∈E i ,E j Thus G i All nodes in relation to v i With constant relative distance of G j All nodes in relation to v j Is constant. And because of v i ∈N j ,v j ∈N i Therefore v is i And v j Is constant, i.e. from G i And G j Drawing G of the constitution ij Is a rigid graph. By analogy, v i The graph with all its neighbor nodes is rigid and the resulting graph G is rigid. After the syndrome is confirmed.
Since the optimal stiffness map belongs to a stiffness map, the following can be deduced:
inference 1: for graph G (V, E, W), if any node V i E is equal to V and exists in i K is not less than 3 neighbors and N is the neighbor of the neighbor i Composition diagram G i (V i ,E i ,W i ) Is an optimal stiffness map, wherein V i ＝{i,N i },
Then G ═ V, E, W is the stiffness map.
Theorem 3: rigidity for any one of rigidity subgraphs G '(V', E ', W') in rigidity diagram G (V, E, W)Panel G '(V', E ', W') was replaced, resulting in new panel G new (V new ,E new ,W new ) Still a rigid map.
And (3) proving that: respectively with G m (V,E m ,W m )，G′ m (V′,E′ m ,W′ m )，G″′ m (V′,E″′ m ,W″ m ) A minimum stiffness diagram of diagrams G (V, E, W), G '(V', E ', W'), G '(V', E ', W') is shown. Since each rigid graph can be generated by adding edges to the corresponding minimum rigid graph, so long as G '″ is certified' m (V′,E″ m ,W″ m ) Replacement G' m (V′,E′ m ,W′ m ) Can still maintain G m (V,E m ,W m ) Being rigid, theorem 3 can be proved to hold.
G new (V new ,E new ,W new ) Denotes by G ″) m (V′,E″ m ,W″ m ) Alternative picture G' m (V′,E′ m ,W′ m ) The new picture obtained then is E' m ＝E″ m 3| V' | -6 and E ex If 3| V | -6, G is to be certified new (V new ,E new ,W new ) Still a rigid map, only G has to be proved new (V new ,E new ,W new ) Any subfigure G of sub (V sub ,E sub ,W sub ) Satisfy | E sub |≤3|V sub I.e. | -6, and the graph obtained after the replacement is proved to be a rigid graph in three cases.
(1) If G is sub (V sub ,E sub ,W sub ) Satisfy the requirement of
From theorem 1, | E sub |≤3|V sub |-6；
(2) If G is sub (V sub ,E sub ,W sub ) Satisfy the requirement of
From theorem 1, | E sub |≤3|V sub |-6；
(3) If G is sub Satisfy the requirements of
Obviously:
|E sub |≤(2|V sub1 +V″ m |-3)-2|V″ m -V sub2 |＝2|V sub1 +V sub2 |-3
the three cases include graph G new (V new ,E new ,W new ) All subgraphs of (1), thus G new (V new ,E new ,W new ) Any subgraph of
Satisfy | E sub |≤3|V sub L-6, and E new 3| V | -6, G is obtained by theorem 1 new (V new ,E new ,W new ) Is the minimum stiffness map, so that any one of the stiffness subgraphs G '(V', E ', W') in the stiffness map G (V, E, W) is replaced by a stiffness map G '(V', E ', W'), resulting in a new map G new (V new ,E new ,W new ) Still, the rigid graph, theorem 3 proves.
Inference 2: any subgraph G '(V', E ', W') in rigid graph G (V, E, W) is replaced by rigid graph G '(V', E ', W'), and a new graph G is obtained new (V new ,E new ,W new ) Still a rigid graph.
And (3) proving that: if G '(V', E ', W') is a rigid graph, G can be seen from theorem 3 new (V new ,E new ,W new ) Is a rigid graph;
if G '(V', E ', W') is not a rigid pattern, the rigid pattern G 'can be obtained by adding edges' a (V' a ,E' a ,W' a ) From G' a (V' a ,E' a ,W' a ) Substitution of G ' (V ', E ', W ') gave a new graph G ' new (V' new ,E' new ,W' new ) G 'is known from theorem 3' new (V' new ,E' new ,W' new ) Is rigidityThe new graph G is obtained by replacing G '(V', E ', W') with G '(V', E ', W') new (V new ,E new ,W new ) Since the add edge operation is performed in G '(V', E ', W'), it can be seen that G is performed new ＝G' new Then G is new (V new ,E new ,W new ) Still a rigid map.
Theorem 4: g i (i 1.. n.) denotes a node v i Optimal rigid graph formed by all the neighbor nodes, G ═ G 1 ∪…∪G n Deleting all the elements satisfying k, l e G in G i ,G j And is provided with
e kl ∈G j Edge e of kl Obtaining a global optimal rigid graph G gop 。
And (3) proving that: the pair G is denoted by G '(V', E ', W') i ∪G j The graph obtained after the edge deletion operation in theorem 4 is executed, where V ═ V 1 ∪V 2 ，E'＝E i +E j -E ij . By G ij (V ij ,E ij ,W ij ) Represents G i (V i ,E i ,W i ) And G j (V j ,E j ,W j ) A graph of common points of (1), wherein V ij ＝V i ∩V j ，E ij Indicates that both nodes are at V ij The edge of (1) is
Let E ij ＝c+p i +p j C represents G i And G j Common edges of (1), pi and p j Shows diagram G ij (V ij ,E ij ,W ij ) In only G i And G j The relationship is shown in fig. 3.
Delete G ij (V ij ,E ij ,W ij ) P in (1) i And p j Then obtaining picture G' ij (V ij ,E' ij ,W' ij ) Only G 'needs to be proved' ij (V ij ,E' ij ,W' ij ) Each sub-graph G' sub (V' sub ,E' sub ,W' sub ) Satisfy the condition of | E' sub |≤3|V' sub -6, i.e. it can be verified that any subgraph of G ' (V ', E ', W ') satisfies the condition | E ' sub1 |≤3|V' sub1 And l-6. If G' ij (V ij ,E' ij ,W' ij ) Sub-picture | E' sub |≥3|V' sub L-6, then G i Or G j Is greater than | E i |≥3|V i 6 or E j |≥3|V j L-6, and G i And G j Is a condition of the optimum rigidity map, so G' ij (V ij ,E' ij ,W' ij ) G 'is absent' sub (V sub ,E' sub ,W' sub ) So that | E' sub |＞3|V' sub L-6, so G' ij Satisfy | E' sub |≤3|V' sub L-6, then l E' sub1 |≤3|V' sub1 |-6。
By inference 1, G is known gop Is a rigid graph, and assumes that there is an edge e satisfying the condition of theorem 4 kl Then e is U.G i Also a rigid map. Then, by inference 2, the available G is known i In place of G i ∪G j In (e $ G @ G @ i The rigidity of the graph is not changed, so the deletion of edges in theorem 4 is performed without changing the rigidity of the graph, and E' is equal to or greater than 3V-6.
In conclusion, | E' sub1 |≤3|V' sub1 I-6 and i E '| 3| V' | 6, it can be known from theorem 1 that G '(V', E ', W') is the optimal stiffness map.
Therefore, the operation of deleting edges in theorem 4 is repeatedly performed until G ═ G 1 ∪…∪G n The edge satisfying the condition of theorem 4 does not exist, and the global optimal rigid graph G can be obtained gop (V,E gop ,W gop )。
(Algorithm 3) the three-dimensional distributed globally optimal communication topology generation algorithm is as follows:
inputting: a full communication topology G of the unmanned cluster system; the bit number l of the data packet; the transmitting power P of the node; maximum and minimum values P of node transmitting power max ,P min (ii) a Distance d between nodes ij Safety distance between nodesDistance d safe Maximum communication distance d of nodes range (ii) a A distance adjustment coefficient gamma; energy consumption E of transmitting and receiving unit bit elec Amplifying energy consumption E per bit amp (ii) a Maximum and minimum rss of node received signal strength max ,rss min (ii) a A power value rss of a signal received by a node; node v i And node v j Initial energy a of i ,a j 。
And step 9: let i equal 1, N i ＝[]；
Step 10: searching for each node v according to a full communication topology G i Partial full topology (local undirected graph per node) G of i ；
Step 11: will be partially complete topology G i As input, each node v is computed using Algorithm 2 i Obtaining a local optimal rigid graph R of each node (local optimal rigid communication performance topology of each node) i ；
Step 12: deleting all local optimal rigid maps R i In accordance with the condition k, l ∈ G i ,G j And is
e kl ∈G j Edge e of kl ；
Step 13: let R ═ R 1 ∪...∪R N ；
Step 14: updating the control protocol according to R and the algorithm 1;
and (3) outputting: a globally optimal rigid communication topology (globally optimal communication topology of a multi-agent system) R and a control protocol (team control according to the globally optimal communication topology).
Based on research, the invention provides a distributed fault-tolerant algorithm based on optimal rigid topology switching. When a node fails, firstly, whether the connectivity of the topological network is influenced by the fault edge is judged, and if the node v fails, the node v is judged to be in a state of being connected with the topological network i Is not in its locally optimal rigid topology R i If the connectivity of the topology is not damaged, maintaining the current communication topology; calculating if the communication topology connectivity of the system is damagedAnd (4) reconstructing the local optimal communication topology of the related nodes, and restoring the connectivity of the system.
From theorem 4, the following can be deduced:
inference 3: r ═ R k1 ∪...∪R kr Wherein R is kr Representing the optimal rigid graph consisting of the node and all the neighbor nodes thereof, and deleting all the nodes satisfying k in R, and belonging to R i ,R j And is
e kl ∈G j Edge e of kl Obtaining a global optimal rigid graph G gop 。
(algorithm 4) distributed communication topology switching fault-tolerant control method based on rigid graph, the algorithm is as follows:
inputting: rigid topology before failure R, Global topology G gop (ii) a Neighbor information N i Fault edge E e And a failed node V e ；
Step 15: according to E e Judging whether the fault edge is in the rigid topology R or not, and if the fault edge is not in the rigid topology R, enabling the fault edge R to be in the rigid topology R r If the fault edge is in the rigid topology R, the next step is carried out;
step 16: according to E e Delete G gop Relative fault edge, local weighted undirected complete graph G of all nodes i ；
And step 17: let G r For all involved fault edges E e To make the rest nodes in the local optimal rigid topology R i Is R r1 ＝{R i I belongs to N }, wherein i is E e Numbering of the locally optimal rigid graph of the nodes not involved;
step 18: g is to be r Algorithm 3 is executed as input, yielding R r2 ＝{R i I belongs to N, wherein i is E e Numbering of the local optimal rigid graph of the involved nodes;
step 19: satisfies the condition k, l ∈ G i ,G j And is
e kl ∈G j Edge e of kl To R, to R r1 ,R r2 Performing a delete edge operation results in R r ；
Step 20: according to R r And equation (6) updating the control protocol;
and (3) outputting: reconstructed topology R r And a control protocol.
The invention provides a distributed communication topology switching fault-tolerant control method based on a rigid graph. The link quality and energy consumption factors are comprehensively considered, a weight function of the link is designed, an optimal rigid communication topology in a three-dimensional space is generated, the communication quality is improved, and the service life of the network is prolonged. The method analyzes the relation between global rigidity and local rigidity by combining the characteristics of the rigid graph, demonstrates the subgraph replacement theory maintained by the rigid graph, and provides a theoretical basis for realizing the distributed optimal rigid communication topology through edge operation. The feasibility of the formation control problem under topology switching conditions is then demonstrated. On the basis, a distributed communication topology fault-tolerant control algorithm is provided, and connectivity recovery of a communication network is realized and the stability of a communication topology is improved through active topology fault-tolerant control.
And according to the algorithm flow, carrying out simulation verification on the distributed global optimal rigid topology generation algorithm. Suppose that a multi-agent is formed with 16 nodes, and the communication range is 35 m. A locally optimal rigid topology of all nodes is first generated as shown in fig. 4.
Performing the global optimal rigid topology generation algorithm on the formation may obtain part (b) in fig. 5, part (b) in fig. 5 represents the generated global optimal rigid topology, and part (a) in fig. 5 represents the generated distributed global optimal rigid topology. As can be seen from fig. 5, the sides of the communication topology generated by the proposed distributed communication topology generation algorithm are the same, as shown in part (a) of fig. 5 and part (b) of fig. 5. The communication topology weight generated by executing the distributed algorithm is as follows: 1624.7572, executing the global optimal rigid communication topology generation algorithm to generate the communication topology weight as: 1624.7572, the weights of the two algorithms are the same, and the communication topology generated by the distributed global optimal rigid topology generation algorithm provided by the invention is verifiedIs a globally optimal rigid communication topology. Executing edge deletion operation, deleting edges which do not belong to the global optimal rigid topology, wherein the number of the edges which accord with the edge deletion operation is 9, and the steps are as follows: e.g. of the type 15 ,e 210 ,e 37 ,e 313 ,e 410 ,e 414 ,e 814 ,e 1213 . Such as the edge e therein 15 Satisfy condition v of deleting edge 1 ,v 5 ∈R 1 ,R 3 And condition e 15 ∈R 1 ,
Therefore delete edge e 15 . And finally, obtaining the globally optimal rigid communication topology R.
And according to the algorithm flow, carrying out simulation verification on the distributed fault-tolerant time-varying formation control method. Initial communication topology (communication topology before failure) as shown in part (a) of fig. 6, a failure occurring is set to a link e 14 ,e 17 ,e 34 ,e 37 ,e 79 And (4) failing. Wherein e 34 ,e 79 Not belonging to the current communication topology, having no influence on the current communication topology, e 14 ,e 17 ,e 37 In the current communication topology, deletion is required, and if the deleted failed link is shown as a dotted link in part (a) of fig. 6, the communication topology needs to be reconstructed. The result of performing a distributed fault-tolerant time-varying formation control method on a communication topology (communication topology after failure) is shown in part (b) of fig. 6, in which the dashed edge e 23 ,e 56 To perform the delete edge operation, part (c) of fig. 6 is a globally optimal rigid communication topology generated by global information (the globally optimal rigid topology generated by algorithm 1). As can be seen from fig. 6, the distributed fault-tolerant time-varying formation control method and the optimal rigid communication topology generated by means of the global information have the same communication links, and the weights are 130.7179 and are the same. The communication topology reconstructed by the distributed fault-tolerant time-varying formation control method is a globally optimal rigid communication topology.
In order to verify the effectiveness of the fault-tolerant control algorithm, simulation is carried out aiming at the fault distributed topology fault-tolerant control problem. Assume an initial communication topology of formation in this embodimentR is shown as part (a) in fig. 6, when the t is 10, a fault occurs, the fault type is shown as part (a) in fig. 6, an algorithm distributed fault-tolerant time-varying formation control method is executed to reconstruct the communication topology, and the communication topology R is generated r As shown in part (b) of fig. 6.
After reconstruction of the communication topology, using topology R r In fig. 7, instead of the original communication topology R, the positions of the nodes at time points t ═ 0s, t ═ 4s, t ═ 10.2s, and t ═ 10.5s are shown in parts (a), (b), (c), and (d), respectively, and fig. 8 shows the errors in formation.
As can be seen from fig. 8, the fault-tolerant control algorithm provided by the present invention has a good control effect, the formation error finally converges to 0 under the topology switching condition, the expected formation can be realized, and after the communication topology of the formation is switched t-10, the formation form is not affected.
The invention solves the problems that the fixed communication topology is mostly adopted in the existing topology, the fixed communication topology needs to be designed in advance, the complexity of the communication topology is higher, and the proper communication topology can not be adopted when the formation flying task is executed in the research of the existing multi-agent system based on the algorithm 2, solves the problems that the environment is easy to limit and the global information is difficult to obtain in the task executing process in the research of the existing multi-agent system based on the algorithm 3, and solves the problem that the communication topology of the multi-agent system is damaged and the task can not be completed due to the unexpected conditions of communication interference, control failure and the like in the task executing process of the multi-agent system in the research of the existing multi-agent system based on the algorithm 4. The algorithm 1 is a control algorithm, the algorithms 2, 3 and 4 are topology-related algorithms, the algorithm 3 is executed first, the algorithm 3 calls the algorithm 2 and the algorithm 1, the algorithm 4 is executed under the condition of a fault, the algorithm 4 calls the algorithm 3 and the algorithm 1, and the algorithm 3 calls the algorithm 2.
The invention provides a distributed communication topology switching fault-tolerant control algorithm based on a rigid graph. The method comprises the steps of firstly considering the quality and energy consumption of communication links, generating a local optimal rigid communication topology based on an optimal rigid graph theory, reducing the number of the communication links on the premise of ensuring the stable communication, and reducing the communication complexity. In order to solve the situation that global information is difficult to obtain in practice, the relation between global rigidity and local rigidity is analyzed, and the problem that the local rigidity can be replaced is proved, a three-dimensional distributed communication topology generation algorithm is provided. On the basis, the problem that communication topological structures are changed due to communication interference, control failure and other accidents can be solved, an active distributed communication topological fault-tolerant control algorithm for rigid topological switching is provided, and stability of a formation structure is guaranteed.
Compared with the prior art, the distributed fault-tolerant time-varying formation control method based on network topology optimization reconstruction provided by the invention has the following advantages:
(1) the algorithm 2 generates a rigid communication topology based on a rigid graph correlation theory, and automatically generates the communication topology of the multi-agent system according to the position relationship among nodes in the multi-agent system, so that the problems of high communication complexity among agents and automatic generation of the topology when the number of agents is large are solved, and the communication complexity of the multi-agent system is effectively reduced.
(2) The algorithm 3 can adopt a distributed method, and under the condition that global information is difficult to obtain, a global optimal rigid communication topology is generated according to local information, so that the problem that the system is difficult to obtain the global information due to the limitation of factors such as distance and weather in practical applications such as target reconnaissance and tracking, communication relay, environment monitoring and mapping is solved.
(3) The communication topology can be damaged due to communication interference, control failure and other accidents, in order to cope with complex application environments, the topology generation algorithm (algorithm 4) adopted by the invention can automatically generate a new communication topology after the communication topology fails, the reconstruction problem of the communication topology after the communication topology fails in the task execution process is solved, the formation control of an intelligent cluster can be realized when the communication topology of the system fails, and ideal time-varying formation flight is completed under the conditions of node failure and link failure of the communication topology.
FIG. 9 is a structural diagram of an embodiment of a distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction. Referring to fig. 9, the distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction includes:
an undirected graph construction module 901, configured to construct an undirected graph of a multi-agent system; the undirected graph comprises a plurality of nodes and a plurality of edges; the node is an agent; edges are inter-node communication links.
And a local undirected graph searching module 902, configured to search a local undirected graph of each node according to the undirected graph.
And a weight determining module 903, configured to determine a weight of each edge by using a weight function according to the local undirected graph and related parameters of the multi-agent system.
The weight determination module 903 specifically includes:
a relevant parameter acquiring unit for acquiring relevant parameters of the multi-agent system; the relevant parameters include: the method comprises the following steps of data packet bit number, node transmitting power maximum value, node transmitting power minimum value, distance between nodes, safety distance between nodes, node maximum communication distance, distance adjusting coefficient, unit bit transmitting and receiving energy consumption, unit bit amplifying energy consumption, node received signal strength maximum value, node received signal strength minimum value, node received signal power value and node initial energy.
And the weight determining unit is used for determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters.
And a local optimal topology obtaining module 904, configured to obtain a local optimal rigid communication performance topology of each node according to the weight.
The local optimal topology obtaining module 904 specifically includes:
and the weight value sorting unit is used for sorting all edges in the undirected graph from small to large according to the weight values to obtain an edge set.
And the rigidity matrix constructing unit is used for constructing a rigidity matrix according to the edge set.
And the rank obtaining unit of the matrix is used for obtaining the rank of the matrix according to the rigidity matrix.
And the local optimal topology obtaining unit is used for obtaining the local optimal rigid communication performance topology of each node according to the rank of the matrix.
And a global optimal topology obtaining module 905, configured to obtain a global optimal communication topology of the multi-agent system according to the local optimal rigid communication performance topology.
The global optimal topology obtaining module 905 specifically includes:
and the global optimal topology obtaining unit is used for taking a union set of all local optimal rigid communication performance topologies to obtain a global optimal communication topology of the multi-agent system.
And a queuing control module 906, configured to perform queuing control according to the globally optimal communication topology.
The formation control module 906 specifically includes:
and the dynamic model establishing unit is used for establishing a dynamic model of the multi-agent system.
And the Laplace matrix obtaining unit is used for obtaining the Laplace matrix of the multi-agent system according to the global optimal communication topology and the dynamic model.
And the control input obtaining unit is used for obtaining the control input of the multi-agent system according to the Laplace matrix and the dynamic model.
And the formation control unit is used for performing formation control according to the control input.
And a fault determining module 907 configured to determine whether the globally optimal communication topology has a fault.
A fault information obtaining module 908, configured to obtain fault information when an output result of the fault determining module 907 is yes; the failure information includes failed edges and failed nodes.
And a failure removing and returning module 909, configured to remove the failure edge and the failure node in the undirected graph according to the failure information, and return to the local undirected graph searching module 902.
And a queuing continuing control module 910, configured to continue queuing control according to the globally optimal communication topology when the output result of the failure determining module 907 is negative.
In the present specification, the embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction is characterized by comprising the following steps:
constructing an undirected graph of the multi-agent system; the undirected graph comprises a plurality of nodes and a plurality of edges; the node is an agent; the edges are communication links between nodes;
searching a local undirected graph of each node according to the undirected graph;
determining the weight of each edge by using a weight function according to the local undirected graph and related parameters of the multi-agent system;
obtaining the local optimal rigid communication performance topology of each node according to the weight;
obtaining a global optimal communication topology of the multi-agent system according to the local optimal rigid communication performance topology;
performing formation control according to the global optimal communication topology;
judging whether the globally optimal communication topology has a fault;
if so, acquiring fault information; the fault information comprises fault edges and fault nodes;
removing the fault edge and the fault node in the undirected graph according to the fault information, and returning to the step of searching the local undirected graph of each node according to the undirected graph;
and if not, continuing the formation control according to the global optimal communication topology.
2. The distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction as claimed in claim 1, wherein the determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters of the multi-agent system specifically comprises:
acquiring relevant parameters of the multi-agent system; the relevant parameters include: the method comprises the following steps of (1) the bit number of a data packet, the transmitting power of nodes, the maximum value of the transmitting power of the nodes, the minimum value of the transmitting power of the nodes, the distance between the nodes, the safety distance between the nodes, the maximum communication distance of the nodes, a distance adjusting coefficient, the energy consumption of transmitting and receiving unit bits, the energy consumption of amplifying unit bits, the maximum value of the intensity of a signal received by the nodes, the minimum value of the intensity of a signal received by the nodes, the power value of the signal received by the nodes and the initial energy of the nodes;
and determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters.
3. The distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction according to claim 1, wherein the obtaining of the local optimal rigid communication performance topology of each node according to the weight specifically includes:
according to the weight, all the edges in the undirected graph are sorted from small to large according to the weight to obtain an edge set;
constructing a rigidity matrix according to the edge set;
obtaining the rank of the matrix according to the rigidity matrix;
and obtaining the local optimal rigid communication performance topology of each node according to the rank of the matrix.
4. The distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction as claimed in claim 1, wherein the obtaining of the globally optimal communication topology of the multi-agent system according to the locally optimal rigid communication performance topology specifically includes:
and taking a union set of all the local optimal rigid communication performance topologies to obtain a global optimal communication topology of the multi-agent system.
5. The distributed fault-tolerant time-varying formation control method based on topology optimization reconstruction according to claim 1, wherein the formation control according to the globally optimal communication topology specifically includes:
establishing a kinetic model of the multi-agent system;
obtaining a Laplace matrix of the multi-agent system according to the global optimal communication topology and the dynamic model;
obtaining a control input of the multi-agent system according to the Laplace matrix and the dynamic model;
and performing formation control according to the control input.
6. A distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction is characterized by comprising:
the undirected graph construction module is used for constructing an undirected graph of the multi-agent system; the undirected graph comprises a plurality of nodes and a plurality of edges; the node is an agent; the edges are communication links between nodes;
the local undirected graph searching module is used for searching the local undirected graph of each node according to the undirected graph;
a weight determining module, configured to determine a weight of each edge by using a weight function according to the local undirected graph and related parameters of the multi-agent system;
the local optimal topology obtaining module is used for obtaining the local optimal rigid communication performance topology of each node according to the weight;
the global optimal topology obtaining module is used for obtaining a global optimal communication topology of the multi-agent system according to the local optimal rigid communication performance topology;
the formation control module is used for performing formation control according to the global optimal communication topology;
the fault judgment module is used for judging whether the global optimal communication topology has a fault;
the fault information acquisition module is used for acquiring fault information when the output result of the fault judgment module is yes; the fault information comprises fault edges and fault nodes;
the fault removing and returning module is used for removing the fault edge and the fault node in the undirected graph according to the fault information and returning the fault edge and the fault node to the local undirected graph searching module;
and the continuous formation control module is used for continuously performing formation control according to the global optimal communication topology when the output result of the fault judgment module is negative.
7. The distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction as claimed in claim 6, wherein the weight determination module specifically comprises:
a relevant parameter acquiring unit for acquiring relevant parameters of the multi-agent system; the relevant parameters include: the method comprises the following steps of (1) the bit number of a data packet, the transmitting power of nodes, the maximum value of the transmitting power of the nodes, the minimum value of the transmitting power of the nodes, the distance between the nodes, the safety distance between the nodes, the maximum communication distance of the nodes, a distance adjusting coefficient, the energy consumption of transmitting and receiving unit bits, the energy consumption of amplifying unit bits, the maximum value of the intensity of a signal received by the nodes, the minimum value of the intensity of a signal received by the nodes, the power value of the signal received by the nodes and the initial energy of the nodes;
and the weight determining unit is used for determining the weight of each edge by using a weight function according to the local undirected graph and the related parameters.
8. The distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction as claimed in claim 6, wherein the local optimal topology obtaining module specifically comprises:
the weight value sorting unit is used for sorting all the edges in the undirected graph from small to large according to the weight value to obtain an edge set;
the rigidity matrix construction unit is used for constructing a rigidity matrix according to the edge set;
the rank obtaining unit of the matrix is used for obtaining the rank of the matrix according to the rigidity matrix;
and the local optimal topology obtaining unit is used for obtaining the local optimal rigid communication performance topology of each node according to the rank of the matrix.
9. The distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction as claimed in claim 6, wherein the global optimal topology obtaining module specifically comprises:
and the global optimal topology obtaining unit is used for taking a union set of all the local optimal rigid communication performance topologies to obtain a global optimal communication topology of the multi-agent system.
10. The distributed fault-tolerant time-varying formation control system based on topology optimization reconstruction as claimed in claim 6, wherein the formation control module specifically comprises:
a dynamics model establishing unit for establishing a dynamics model of the multi-agent system;
a laplacian matrix obtaining unit, configured to obtain a laplacian matrix of the multi-agent system according to the globally optimal communication topology and the dynamical model;
a control input obtaining unit, configured to obtain a control input of the multi-agent system according to the laplacian matrix and the dynamical model;
and the formation control unit is used for performing formation control according to the control input.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
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| CN116149372A (en) * | 2023-04-17 | 2023-05-23 | 西北工业大学 | Method, system and application for eliminating fault single machine |
| CN116321192A (en) * | 2023-02-28 | 2023-06-23 | 燕山大学 | Submersible vehicle networking formation method based on optimal rigidity graph |
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| CN116321192A (en) * | 2023-02-28 | 2023-06-23 | 燕山大学 | Submersible vehicle networking formation method based on optimal rigidity graph |
| CN116321192B (en) * | 2023-02-28 | 2023-09-19 | 燕山大学 | Submersible vehicle networking formation method based on optimal rigidity graph |
| CN116149372A (en) * | 2023-04-17 | 2023-05-23 | 西北工业大学 | Method, system and application for eliminating fault single machine |
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