Multi-agent system pure angle positioning method and system under malicious measurement condition

Abstract

The invention discloses a pure angle positioning method and system for a multi-agent system under an intentional measurement condition. The method comprises the following steps: initializing multi-agent position distribution; calling a drawing function, and marking each agent in a node form; establishing a triangular relationship for each agent to form a topological graph, and defining an interior angle range of a triangle; based on the triangular geometrical relationship constraint, the effectiveness of the triangular relationship established by each agent is judged, if the triangular relationship established by each agent is effective, the corresponding agent continues to keep the triangular relationship, and if the triangular relationship is ineffective, the triangular relationship is replaced; after the replacement is completed, verifying the effectiveness of each triangular relationship, and constructing a triangular relationship set by triangles which are combined with the geometrical relationship constraint; checking the angle rigidity of the topological graph, and determining whether to execute the triangular relation replacement process again or not according to a checking result; according to the invention, accurate positioning can be realized under the condition that malicious measurement exists.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-agent positioning, and specifically to a pure angle positioning method and system for a multi-agent system under malicious measurement conditions. Background Art

[0002] With the rapid development of information technology and network systems, multi-agent systems (MAS) have gradually become an important research direction in the field of modern control. The cooperative positioning and dynamic control problems of multi-agent systems are widely applied in fields such as unmanned aerial vehicle formations, autonomous driving vehicle fleets, and underwater robot swarms. These systems achieve complex tasks such as environmental perception, target positioning, path planning, and cluster formation through the collaboration of multiple agents.

[0003] In cooperative positioning, a multi-agent system constructs the relative position information of the entire system through mutual observation and information interaction among individual agents, and then realizes positioning. Most of the existing cluster cooperative positioning methods rely on multi-source information fusion to obtain accurate position information of the target, so they have relatively high requirements for the completeness of information collection.

[0004] Considering the complexity of the actual operating environment and the practical experience in the research of unmanned systems, unmanned systems may encounter weak information environments when performing tasks. Under weak information conditions, due to the complex environment or limited information acquisition channels, the communication and observation of the system may be affected by noise and occlusion, and these factors will reduce the information accuracy obtained by the agents. At the same time, in practical applications, there are also situations where malicious incorrect information is received. Therefore, in the face of a complex environment in practical applications, an actual multi-agent system often can only obtain partial correct information, and there may be missing and incorrect possibilities in the scenario observation data, thus bringing many challenges in the process of cooperative positioning.

[0005] In the prior art, the invention patent with the patent publication number CN118244794A discloses an unmanned system cluster formation control method under angle measurement. This invention patent considers two working conditions of cluster formation, namely, the situation where the sensor can sense other agents and the situation where it cannot sense other agents due to the limitation of the sensing range, which is more comprehensive and has application value. In the case of being unable to sense other agents, such as when the cluster cannot receive GPS signals, 1 - 3 agents in the cluster act as leaders and implement a control method for relative position measurement, and a formation control method under only angle measurement is designed for 4 - N agents in the cluster. However, this patent improves the problem that when the unmanned system formation control encounters the situation where the distance or relative position cannot be measured, each agent can only measure the relative angle with its adjacent agent in its local coordinate system.

[0006] The invention patent with the publication number CN114339989A discloses a distributed positioning method for multi-agent systems based on azimuth angles. This patent comprehensively considers the estimation of angle information and the estimation of position information as a cascaded system, enabling accurate positioning effects in more complex network environments. However, most of the current distributed positioning methods based on azimuth angle information in this patent are based on global coordinate information, and the few methods that consider local coordinate systems require the communication topology between agents to be an undirected topology, which increases the energy consumption of agents and is not applicable to complex network environments.

[0007] In an uncertain environment and with limited information, achieving efficient and accurate cooperative positioning and control is of great significance for improving the robustness of the system and the autonomous decision-making ability of agents. Therefore, how to perform precise cooperative positioning under weak information conditions and in the presence of malicious measurements has become a difficult problem in the research of multi-agent systems. Summary of the Invention

[0008] The technical problem to be solved by the present invention is: how to perform precise cooperative positioning under weak information conditions and in the presence of malicious measurements.

[0009] To solve the above technical problem, the present invention provides the following technical solution:

[0010] A pure angle positioning method for multi-agent systems under malicious measurement conditions, including:

[0011] Initialize the position distribution of multi-agents;

[0012] Call the drawing function to mark each agent in the form of a node;

[0013] Establish triangular relationships among agents to form a topological graph, and define the range of interior angles of the triangle;

[0014] Based on the constraints of triangular geometric relationships, judge the validity of the triangular relationships established by each agent. If valid, the corresponding agent continues to maintain the triangular relationship. If invalid, replace the triangular relationship;

[0015] After replacement, verify the validity of each triangular relationship, and construct a set of triangular relationships for the triangles that meet the composite geometric relationship constraints;

[0016] Check the angle rigidity of the topological graph, and decide whether to execute the triangular relationship replacement process again according to the check result;

[0017] After completing the angle rigidity check of the topological graph, position the positions of each agent.

[0018] In an embodiment of the present invention, the basis for determining whether the triangle relationships established by each agent are valid is as follows:

[0019] According to the geometric operation of the sum of interior angles of a triangle, if a measured angle value β ijk is damaged, then β ijk + β jik + β ikj ≠ 180° ± A°, then this measured value is considered malicious, and it is determined that the triangle relationship is invalid; if β ijk + β jik + β ikj = 180° ± A°, then the measurement result is normal and it is determined that the triangle relationship is valid; where β ijk , β jik , β ikj are respectively the three interior angles of the triangle established by the agent, and A° represents the angle limit value.

[0020] In an embodiment of the present invention, if it is invalid, then replace the triangle relationship, including:

[0021] Obtain the set X = {1, 2,... q} of all nodes;

[0022] Define the fixed array set and the array to be replaced; among them, the fixed array set is defined as where each f i = {x i , y i , z i} represents a triple, and the elements in the triple can be exchanged in order; in the fixed array set, the total number of fixed arrays is set to m, and i ∈ m; the array to be replaced is represented as o = {o 1 , o 2 , o 3};

[0023] Select all possible triple combinations from the set X to form the set C;

[0024] Then, from the set C, remove the array o to be replaced and the fixed array set Obtain the new candidate set C ′ ;

[0025] Select a combination r = {r 1 , r 2 , r 3} from the candidate set according to the screening conditions;

[0026] Define the current covered point set and check whether all points are covered after adding the combination r;

[0027] If the coverage condition is satisfied, then select the combination r as the new combination to replace the replaced array o. At the same time, record the value of the new combination r into the storage matrix;

[0028] If the coverage condition is not satisfied, then select a combination from the candidate set C′ again and continue to judge the coverage condition until a combination that can be used as a replacement group is selected.

[0029] In an embodiment of the present invention, the combination r can be used as a replacement group and satisfies the following conditions:

[0030]

[0031] s.t. r ∈ C′ and |X covered ∪ r| = q;

[0032]

[0033] Wherein, X covered represents the current covered point set, find_replacement represents the combination replacement function with coverage constraints, q represents the total number of nodes, and s.t. represents the constraint condition.

[0034] In an embodiment of the present invention, the coverage condition is: |X′ covered | = q; and, X′ covered = X covered ∪ r; where, X′ covered represents the set after adding the combination r to the current covered point set, X covered represents the current covered point set, and q represents the total number of nodes.

[0035] In an embodiment of the present invention, after the replacement is completed, verify the effectiveness of each triangle relationship, including:

[0036] Reuse the method of judging whether the triangle relationship established by each agent is effective to judge the effectiveness of each triangle relationship after the replacement is completed;

[0037] If there are some ineffective triangle relationships, then reuse the method of replacing the triangle relationship to replace the ineffective triangle relationship again.

[0038] In an embodiment of the present invention, decide whether to execute the triangle relationship replacement process again according to the inspection result, including:

[0039] Divide the nodes into two categories, including the anchor point set and the unknown position node set;

[0040] Define the positions p of all agents according to the anchor point set and the unknown position node set;

[0041] Assume that each node i measures the angles of adjacent nodes k and j in the counterclockwise direction as Define as a set of angles, each element of which is a triple. In the given set of angles , (i, j, k) can be freely changed to (k, j, i); where the vertex set V = {1, 2, …, n}; the anchor point set includes the vertex set;

[0042] Combined with the two-dimensional rotation matrix, and based on the anchor point set and the positions of all agents, obtain the triangular network and obtain the triangular network the coefficient matrix of nodes i, k, and j in;

[0043] According to the coefficient matrix of nodes i, k, and j, obtain the matrix weighted vector function of the positions of nodes i, k, and j;

[0044] Similarly, obtain the matrix weighted vector function of the positions of all nodes in the triangular network and the angular stiffness function;

[0045] According to the angular stiffness function, set the angular rigidity rule;

[0046] When setting any number of nodes y and substituting it into the angular rigidity rule for calculation, if the formula of the angular rigidity rule holds, it indicates the triangular angular rigidity of the topological graph; otherwise, execute the triangular relationship replacement process again.

[0047] In an embodiment of the present invention, the angular rigidity rule is:

[0048]

[0049] In the formula, represents the triangular stiffness matrix, represents the angular stiffness function, and the specific form of the triangular network is represented by ; T is the transpose.

[0050] In an embodiment of the present invention, obtaining the coefficient matrix of nodes i, k, and j in the triangular network includes:

[0051]

[0052] In the formula, respectively represent the matrix weighted vector functions of the positions of nodes i, k, and j, Δijk represents the triangle formed by nodes i, k, and j, and I 2 represents the identity matrix, represents the two-dimensional rotation matrix with a rotation angle of θ, and T represents the matrix transpose.

[0053] The present invention also provides a pure angle positioning system for a multi-agent system under malicious measurement conditions, which applies the pure angle positioning method for a multi-agent system under malicious measurement conditions described above, and includes:

[0054] An initial position distribution module, which is used to initialize the position distribution of multi-agents;

[0055] An initial topology graph module, which is used to call a drawing function, mark each agent in the form of a node, and mark the coordinates of each node;

[0056] An angle range constraint module, which is used to establish a triangular relationship among agents to form a topology graph and define the angle range of the triangle;

[0057] A replacement judgment module, which is used to judge the validity of the triangular relationship established by each agent based on the geometric relationship constraints of the triangle. If it is valid, the corresponding agent continues to maintain the triangular relationship. If it is invalid, the triangular relationship is replaced;

[0058] A triangular relationship set module, which is used to verify the validity of each triangular relationship after replacement and construct a set of triangular relationships for the triangles that meet the geometric relationship constraints;

[0059] An angle rigidity module, which is used to check the angle rigidity of the topology graph and decide whether to execute the triangular relationship replacement process again according to the check result;

[0060] A positioning module, which is used to position the positions of each agent after the angle rigidity check of the topology graph is completed.

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] The present invention provides a pure angle positioning method for a multi-agent system that can perform autonomous error correction under malicious measurement conditions. By using a combined replacement function with coverage constraints and adding a pre-error correction and replacement function to the angle positioning algorithm, it can achieve accurate positioning even in the presence of malicious measurement, and solve or at least partially solve the deficiencies in the existing angle positioning technology.

[0063] Aiming at the working limitation that the robot is restricted by the traditional angle positioning method and cannot be correctly positioned when there is malicious measurement at present, the combined replacement function with coverage constraints in the present invention can enable the algorithm to achieve autonomous error correction and replacement in the early stage, and can achieve accurate positioning in the presence of malicious measurement.

[0064] In view of the possible situation that the triangular topology cannot be located after actual autonomous modification, the code innovatively realizes the dynamic optimization design of the triangular graph. For subgraphs that do not meet the stiffness conditions, the program can prompt for adjustment. This method not only reduces the subjectivity of manual design, but also provides a systematic topology reconstruction mechanism, ensuring that the finally generated network has high robustness and stability, and is suitable for the positioning and cooperative control requirements of multi-agent systems.

[0065] The fixed-point navigation described in the present invention has excellent flexibility in actual operation. The application of the combination replacement and topology reconstruction method in the present invention provides a new idea for the geometric topology optimization of large-scale networks. This method can be suitable for various scenarios in multi-agent cooperation tasks, including positioning and tracking based on geometric stiffness, dynamic encirclement, sensor layout optimization, etc. Brief Description of the Drawings

[0066] Figure 1 It is a flowchart of a pure angle positioning method for a multi-agent system under malicious measurement conditions according to an embodiment of the present invention.

[0067] Figure 2 It is the first malicious triangle schematic diagram of the triangle replacement step according to an embodiment of the present invention.

[0068] Figure 3 It is the first malicious triangle schematic diagram of the random replacement according to an embodiment of the present invention.

[0069] Figure 4 It is the second malicious triangle schematic diagram of the triangle replacement step according to an embodiment of the present invention.

[0070] Figure 5 It is the second malicious triangle schematic diagram of the random replacement according to an embodiment of the present invention.

[0071] Figure 6 It is the actual malicious triangle topology diagram according to an embodiment of the present invention.

[0072] Figure 7 It is the triangle topology diagram after actual replacement according to an embodiment of the present invention.

[0073] Figure 8 It is the position estimation error change diagram in the continuous case according to an embodiment of the present invention.

[0074] Figure 9 It is a block diagram of a pure angle positioning system for a multi-agent system under malicious measurement conditions according to an embodiment of the present invention. Detailed Embodiment

[0075] To facilitate those skilled in the art to understand the technical solution of the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings of the specification.

[0076] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of this application, "a plurality of" means two or more unless otherwise specifically defined.

[0077] Please refer to Figure 1 As shown, the present invention provides a pure angle positioning method for a multi-agent system under malicious measurement conditions, including:

[0078] S10. Initialize the position distribution of multi-agents.

[0079] In an embodiment of the present invention, in this part, through data initialization operations, a set of random coordinate points are generated to simulate the distribution of multi-agents in a two-dimensional plane. These nodes represent the specific positions of multiple agents in the two-dimensional plane. Each coordinate point is defined by two values (x, y), and these points are stored in the variable position matrix and uniformly managed in matrix form for subsequent geometric calculations and collaborative analysis. In this embodiment, the number of agents is set to 27 through code, and the plane range is specified as x, y ∈ [-30, 30], providing boundary conditions for the drawing of the multi-agent positions.

[0080] S20. Call the drawing function to label each agent in the form of a node.

[0081] In an embodiment of the present invention, when calling the drawing function, all nodes are labeled in the form of dots, and a numbered label is added next to each point for easy observation and distinction of the positions of each node. The overall spatial layout of the multi-agent system is visually reflected through the drawing effect, laying a spatial framework for the entire research and providing a starting point for subsequent calculations based on geometric relationships. By visualizing the node distribution, the possible collaboration patterns or conflict relationships are initially analyzed to facilitate the design of more accurate algorithms later. The hold on function is used to keep the drawing area available for subsequent overlay drawing of geometric structures.

[0082] S30. Establish triangular relationships among the agents to form a topological graph and define the range of interior angles of the triangles.

[0083] In an embodiment of the present invention, the range of interior angles of the triangle is defined as {θ min , θ max}, where θ min represents the minimum angle of the interior angle of the triangle, and θ max represents the maximum angle of the interior angle of the triangle. In this embodiment, θ min = 10°, θ max= 170°, ensuring that the triangle is neither too flat nor too sharp. This is the basis of geometric constraints, ensuring that the generated triangles are suitable for practical scenarios.

[0084] S40. Based on the geometric relationship constraints of the triangle, the agents that establish the triangle relationship are used to judge the validity of the triangle relationships established by each agent. If valid, the corresponding agent continues to maintain the triangle relationship. If invalid, the triangle relationship is replaced.

[0085] In an embodiment of the present invention, geometric operations of the sum of interior angles of a triangle are performed. If an angle measurement value β ijk is disrupted by an opponent, then β ijk + β jik + β ikj ≠ 180° ± A°. This measurement value is considered malicious, and the triangle relationship is judged to be invalid. Otherwise, if β ijk + β jik + β ikj = 180° ± A°, then the measurement result is normal, and the triangle relationship is judged to be valid. Among them, β ijk 、β jik 、β ikj are the three interior angles of the triangle established by the agent respectively, and A° represents the angle limit value. Since the angle set is set as a triple composed of three vertices, as long as there is one wrong angle in the triangle composed of the triple, the entire angle set is determined to be wrong.

[0086] In this embodiment, since the angles are all measured by sensors in actual applications, there will definitely be a small error when the sum of the three angles is 180°. In the program design, we set a small error range for the sum of the three measurement values, that is, the angle limit value A° is set. Actually, it is verified whether the sum of the interior angles of the triangle differs too much from 180°. If it differs too much, the entire angle set is determined to be wrong.

[0087] In this embodiment, if some node groups do not meet the angle range, the replacement algorithm adjusts them. The core of the replacement algorithm is a combinatorial replacement function with coverage constraints.

[0088] In this embodiment, first, the set X = {1, 2,... q} of all nodes is obtained.

[0089] Define the fixed array set and the array to be replaced. Among them, the fixed array set is defined as where each f i = {x i , y i , z i} represents a triple, and the elements in the triple can be swapped in order. Therefore, if two triples have the same elements but different orders, they are considered the same. The total number of fixed arrays is set to m, and i ∈ m. The replaced array is represented as: o = {o 1 , o 2 , o 3}, where the replaced array can be understood as the triple for which the measured value is considered malicious in step S30.

[0090] Next, find new combinations. Select all possible triple combinations from set X to form set C. From all possible triple combination sets C, exclude the replaced array o and the fixed array set to obtain a new candidate set C'. Among them, A\B represents the difference set, which contains elements that belong to set A but not to set B. Let C' be the set obtained by excluding the non - allowable combinations from all possible combinations, representing the final available candidate solution space, which can be expressed by the formula:

[0091]

[0092] Randomly select a combination r = {r 1 , r 2 , r 3} from C', satisfying the following conditions:

[0093] Condition 1: The combination r is not the same as the replaced array o, that is, r ≠ 180°.

[0094] Condition 2: The combination r is not the same as any element in the fixed array set, that is

[0095] Finally, check the coverage condition. Define the current set of covered points as:

[0096]

[0097] Check whether all points are covered after adding the combination r:

[0098] X' covered = X covered ∪ r;

[0099] If it satisfies: |X' covered | = q;

[0100] Then select the combination r as the new combination to replace the replaced array o. At the same time, record the value of the new combination r into the storage matrix. If the coverage condition is not satisfied, that is: |X' covered | ≠ q, then select another combination from the candidate set C' and continue to judge the coverage condition until a combination that can be used as a replacement group is selected.

[0101] In this embodiment, the operations in this step are summarized into a combined replacement function with constraints. The complete function expression is written as follows:

[0102]

[0103] s.t. r∈C′and|X covered ∪r|=q;

[0104] In the formula, find_replacement represents the combined replacement function with coverage constraints, q represents the total number of nodes, and ∪ represents the union set

[0105] In this embodiment, in practical applications, due to the limited AC distance of the sensor, after screening out the replacement triples that meet the composite conditions, it is necessary to further check whether the three points are within each other's communication range.

[0106] In the experiment of replacing triangles, there is also the situation of whether there are isolated points after removing malicious triangles. The explanation is as follows:

[0107] (1) After removing the malicious triangle, a certain point is isolated and this point needs to be protected

[0108] As Figure 2 shown, the combination r = {1, 7, 22} is removed and node 22 is isolated. Node 22 needs to actively find neighbors within its communication range, that is, divide the large area near node 22 and find a combination that contains node 22 and meets the conditions in the neighborhood. After random replacement, as Figure 3 shown.

[0109] (2) After removing the malicious triangle, no point is isolated

[0110] As Figure 4 shown, the combination r = {12, 13, 19} is removed. Nodes 12, 13, and 19 are all in other triangles. At this time, new triangles can be randomly selected as long as the three selected points are within each other's communication range. After random replacement, as Figure 5 shown.

[0111] S50. After the replacement is completed, verify the validity of the relationships of each triangle, and construct a triangle relationship set for the triangles that meet the composite geometric relationship constraints.

[0112] In an embodiment of the present invention, the construction and maintenance of the triangle relationship set are accompanied by strict geometric verification. To verify the correctness of the screening results, the code performs angle detection on each triangle again to ensure that its geometric structure meets the validity requirements. The specific steps are as follows:

[0113] First, reuse the method of judging whether the triangle relationships established by each agent are valid to judge the validity of each triangle relationship after replacement. For each triangle combination, in order to prevent incorrect sensor information in the new triangle from causing malicious measurements to still exist in the replaced topology graph, all triangles need to be detected again through geometric verification of whether the sum of interior angles is 180°. Without a doubt, in actual operation, we have defined a range for detection and allow for a small error.

[0114] If some triangles are invalid, the code will detect the error in time and search for new replacement triples to maintain the continuity of the entire geometric model. Here, the geometric relationship of the interior angles of the triangle is used to search for new replacement triples. This replacement mechanism is the key to ensuring the stability of the system in a dynamic environment. In a dynamic environment, the triangle set can be adjusted according to the node state changes to ensure the flexibility and adaptability of the topological structure.

[0115] S60, check the angular rigidity of the topology graph and decide whether to execute the triangle relationship replacement process again according to the check result.

[0116] In an embodiment of the present invention, after the triangle detection and visual drawing, and after the replacement of the triangle and the reconstruction of the topology graph, check the angular rigidity of the entire topology graph and decide whether to loop to execute the work according to the result to ensure that the topology graph meets the requirements. Among them, the method used to check the angular rigidity of the entire topology graph is not limited by the present invention, but a checking method is specifically given.

[0117] In this embodiment, first, consider a network with N agents, and the position of agent i is represented by p i . Divide all agents into two categories. It can be understood that all nodes are divided into two categories, including the anchor point set and the unknown position node set. The positions of the anchor points are already given, and the positions of the unknown position nodes need to be estimated.

[0118] In this embodiment, the anchor point set includes the first anchor point set and the second anchor point set. Define the first anchor point set as the vertex set V = {1, 2,..., n}, and the second anchor point set V e = {1, 2,... n e}, where the second anchor point set can be understood as the set of the three points in the triangle and the second known point. The unknown position node set is V w = {n e + 1,... n}. Correspondingly, the position set of the anchor points is represented as The position set of the unknown position nodes is represented as Use I 2 to represent the 2×2 identity matrix, use to represent the two-dimensional rotation matrix with a rotation angle of θ, and T represents the matrix transpose.

[0119] Then the position representation form of all agents:

[0120] For the vertex set V = {1, 2,..., n}, define as an angle set, each element of which is a triple, and define the three-vertex triple (i, j, k) to describe the angle constraint α ijk , the angle constraint α ijk is equivalent to the angle constraint α kji , and in the given angle set , (i, j, k) can be freely changed to (k, j, i). Use to represent the two-dimensional triangle localization network, indicating that each vertex i ∈ V e is mapped to its point p i .

[0121] Combined with the two-dimensional rotation matrix, assume that each node i measures in the counterclockwise direction, that is, the angles of adjacent nodes k and j are For the triangle network represented by Given Define the matrix weighted vector function of the positions p of nodes i, k, and j as: i 、p j 、p k to be:

[0122]

[0123] The coefficient matrix of nodes i, k, and j is:

[0124]

[0125] In the formula, respectively represent the matrix weighted vector functions of the positions of nodes i, k, and j, and Δijk represents the triangle formed by nodes i, k, and j. Similarly, in the triangle network, obtain the matrix weighted vector functions of the positions of all nodes and combine them to form the angle stiffness function. Among them, the angle stiffness function is:

[0126]

[0127] Among them is defined as the triangle stiffness matrix, is the infinitesimal motion of p.

[0128] When setting y as the number of nodes, if and only if where the positions p of all agents are in an arbitrary general configuration, the topological graph is triangle angle rigid. In this experiment, y can be understood as the number of vertices in the anchor points is 27, correspondingly, n in the anchor pointse is 2.

[0129] In this embodiment, the detected topology graph can be considered locatable. The topology graph before replacement in this experiment is as Figure 6 shown, with two malicious triangles appearing. After self-correction and replacement, the finally formed topology graph is as Figure 7 shown.

[0130] In this embodiment, after the triangle detection is completed, the code presents these geometric shapes through drawing to form a clear two-dimensional plane graph. Each triangle is represented by the edges connected by its vertices. After being superimposed with the node position graph, it intuitively shows the geometric relationship of the system. This visualization not only helps researchers quickly understand and analyze the spatial layout of the system, but also can identify potential problems, such as uneven distribution or abnormal angles.

[0131] S70. After completing the angle rigidity check of the topology graph, the positions of each agent are located.

[0132] In an embodiment of the present invention, after the topology graph meets the requirements and the drawing is completed, next, precise positioning is performed through an angle positioning algorithm. In this embodiment, the specific angle positioning algorithm is not limited, but a specific embodiment is given.

[0133] In this embodiment, locating the positions of each agent includes:

[0134] Let Divide the triangle stiffness matrix into the anchor point part matrix and the free node part matrix Then the matrix D(α * ) can be written as Here When and only when D ww is non-singular, the number of anchor points is not less than 2 and the positions p of all agents are generic, and the triangle network is locatable, the true positions of the free nodes can be calculated through .

[0135] In this embodiment, the change of the position estimation error in the continuous case is as Figure 8 shown. Among them, is expressed as the estimation of p w .

[0136] Please refer to Figure 9As shown in the figure, the present invention also provides a pure angle positioning system for a multi-agent system under malicious measurement conditions, which applies the pure angle positioning method for a multi-agent system under malicious measurement conditions described above, and includes:

[0137] An initial position distribution module, which is used to initialize the position distribution of multi-agents.

[0138] An initial topology graph module, which is used to call a drawing function to label each agent in the form of a node.

[0139] An angle range constraint module, which is used to establish a triangular relationship among agents to form a topology graph and define the angle range of the triangle.

[0140] A replacement judgment module, which is used to judge the validity of the triangular relationship established by each agent based on the geometric relationship constraints of the triangle. If it is valid, the corresponding agent continues to maintain the triangular relationship. If it is invalid, the triangular relationship is replaced.

[0141] A triangular relationship set module, which is used to verify the validity of each triangular relationship after replacement and construct a set of triangular relationships for the triangles that meet the geometric relationship constraints.

[0142] An angle rigidity module, which is used to check the angle rigidity of the topology graph and decide whether to execute the triangular relationship replacement process again according to the inspection result.

[0143] A positioning module, which is used to position the positions of each agent after the angle rigidity check of the topology graph is completed.

[0144] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention, and any reference signs in the claims should not be regarded as limiting the claims involved.

[0145] The above-described embodiments only represent the implementation manners of the invention. The protection scope of the present invention is not limited to the above embodiments. For those skilled in the art, without departing from the concept of the present invention, several deformations and improvements can be made, and these all belong to the protection scope of the present invention.

Claims

1. A pure angle positioning method for a multi-agent system under malicious measurement conditions, characterized in that: include: Initialize multi-agent position distribution; Call the drawing function to mark each agent as a node; Establish triangle relationships among the agents, form a topological graph, and define the range of the triangle's internal angles; Each intelligent agent that establishes a triangle relationship based on the triangle geometric relationship constraint determines the validity of the triangle relationship established by each intelligent agent. If it is valid, the corresponding intelligent agent continues to maintain the triangle relationship. If it is invalid, the triangle relationship is replaced; After the replacement is completed, the validity of each triangle relationship is verified, and the triangles constrained by the composite geometric relationship are used to construct a triangle relationship set; Check the angular rigidity of the topology graph and decide whether to execute the triangle relationship replacement process again based on the check results; After completing the angular rigidity check of the topology graph, the position of each intelligent body is located.

2. The pure angle positioning method of a multi-agent system under malicious measurement conditions according to claim 1 is characterized in that: The basis for judging whether the triangle relationship established by each agent is valid is: According to the geometric operation of the sum of the interior angles of a triangle, if an angle measurement value β ijk is destroyed, then β ijk +β jik +β ikj ≠180°±A ° , then this measurement value is considered malicious, and the triangle relationship is invalid; if β ijk +β jik +β ikj =180°±A ° , if the measurement result is normal, the triangle relationship is considered valid; where β ijk , β jik , β ikj are the three inner angles of the triangle established by the agent, A ° Indicates the angle limit value.

3. The pure angle positioning method of a multi-agent system under malicious measurement conditions according to claim 1 is characterized in that: If invalid, replace the triangle relationship, including: Get the set of all nodes X = {1, 2, ... q}; Define a fixed array set and a replaced array; where the fixed array set is defined as Each f i ={x i ,y i ,z i } represents a triple, and the elements in the triple can be interchanged; in the fixed array set, the total number of fixed arrays is set to m, i∈m; the replaced array is represented by o={o1,o2,o3}; Select all possible triple combinations from set X to form set C; Then remove the replaced array o and the fixed array set from set C Get a new candidate set C ′ ; From the candidate set, select a combination r = {r1, r2, r3} according to the screening conditions; Define the current set of covered points and check whether all points are covered after adding combination r; If the coverage condition is met, then select combination r as the new combination to replace the replaced array o, and at the same time, record the value of the new combination r into the storage matrix; If the coverage condition is not met, then select ′ Select a combination again and continue to cover the condition judgment until a combination that can be used as a replacement group is selected.

4. The pure angle positioning method for a multi-agent system under malicious measurement conditions according to claim 3, characterized in that: The combination r can be used as a replacement group if the following conditions are met: s.t.r∈C′and|X covered ∪r|=q; Where, X covered Represents the current set of covered points, find_replacement represents the combined replacement function with coverage constraints, q represents the total number of nodes, and st represents the constraint condition.

5. The pure angle positioning method for a multi-agent system under malicious measurement conditions according to claim 3 is characterized in that: The coverage condition is: |X′ covered | = q; and, X′ covered =X covered ∪r; where X′ covered It represents the set after the current set of coverage points is added to the set of combination r, X covered It represents the current set of covered points, and q represents the total number of nodes.

6. The pure angle positioning method of a multi-agent system under malicious measurement conditions according to claim 1 is characterized in that: After the replacement is completed, verify the validity of each triangle relationship, including: Reuse the method of judging whether the triangle relationship established by each agent is valid, and judge the validity of each triangle relationship after the replacement is completed; If some triangle relationships are invalid, the method of replacing the triangle relationship is reused to replace the invalid triangle relationship again.

7. The pure angle positioning method of a multi-agent system under malicious measurement conditions according to claim 1 is characterized in that: Determine whether to execute the triangle relationship replacement process again based on the inspection results, including: The nodes are divided into two categories, including anchor point set and unknown position node set; Define the position p of all agents based on the anchor point set and the unknown position node set; Assume that each node i measures the angle of the adjacent node k, j in the counterclockwise direction as definition is an angle set, each element is a triplet, in a given angle set (i,j,k) can be freely changed to (k,j,i); where the vertex set V = {1,2,…,n}; the anchor point set includes the vertex set; Combine the two-dimensional rotation matrix and obtain the triangle network based on the anchor point set and the positions of all agents. And get the triangle network The coefficient matrix of nodes i, k, j; According to the coefficient matrix of nodes i, k, j, the matrix weighted vector function of the position of nodes i, k, j is obtained; Similarly, get the triangle network , a matrix-weighted vector function of all node positions, and an angular stiffness function; According to the angular stiffness function, the angular stiffness rule is set; When any number of nodes y is set, it is substituted into the angle rigidity rule for calculation. If the formula of the angle rigidity rule holds, it indicates that the triangle angle of the topological graph is rigid. Otherwise, the triangle relationship replacement process is executed again.

8. The pure angle positioning method of a multi-agent system under malicious measurement conditions according to claim 7 is characterized in that: The angular rigidity rule is: In the formula, Expressed as a triangular stiffness matrix, Expressed as an angular stiffness function, the triangle network The specific form of Represents; T is the transpose.

9. The pure angle positioning method of a multi-agent system under malicious measurement conditions according to claim 8, characterized in that: Get the coefficient matrix of nodes i, k, j in the triangle network, including: In the formula, They are represented as matrix-weighted vector functions of the positions of nodes i, k, and j, △ijk is represented as a triangle composed of nodes i, k, and j, and I2 is represented as the unit matrix. It is represented as a two-dimensional rotation matrix with a rotation angle of θ, and T represents the matrix transpose.

10. A pure angle positioning system for a multi-agent system under malicious measurement conditions, characterized in that: The method for purely angular positioning of a multi-agent system under malicious measurement conditions according to any one of claims 1 to 9 comprises: The initial position distribution module is used to initialize the multi-agent position distribution; The initial topology diagram module is used to call the drawing function, mark each agent as a node, and annotate the coordinates of each node; Angle range constraint module, used to establish triangle relationships between agents, form a topological graph, and define the triangle angle range; A replacement judgment module is used for each intelligent agent that establishes a triangle relationship based on the triangle geometric relationship constraint, and judges the validity of the triangle relationship established by each intelligent agent. If it is valid, the corresponding intelligent agent continues to maintain the triangle relationship; if it is invalid, the triangle relationship is replaced; The triangle relationship set module is used to verify the validity of each triangle relationship after the replacement is completed, and to construct a triangle relationship set for the triangles constrained by the composite geometric relationship; Angle rigidity module, used to check the angle rigidity of the topology diagram and decide whether to execute the triangle relationship replacement process again based on the check results; The positioning module is used to locate the position of each intelligent body after completing the angular rigidity check of the topological map.

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