Distributed construction method for affine formation hierarchical topology of multi-agent system
By constructing a hierarchical affine formation topology for a multi-agent system in a distributed manner, nodes autonomously select neighbors and solve stress values, solving the problem of real-time node joining and leaving in existing technologies, and achieving efficient communication cost and optimized control performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-22
- Publication Date
- 2026-03-10
AI Technical Summary
Existing multi-agent system formation control methods rely on centralized solutions from a central processing unit, which cannot handle real-time joining and leaving of nodes, and cannot optimize communication costs and control performance in highly dynamic scenarios.
A distributed construction method based on a hierarchical topology of affine formations in a multi-agent system is adopted. Each node autonomously selects its neighbors and solves the stress value in a distributed manner, generating the optimal interaction topology in real time. By designing a hierarchical directed topology and a distributed neighbor selection criterion, a local topology is constructed and the stress value is optimized, thereby achieving the autonomy and efficiency of the system.
It optimizes communication costs and control performance in highly dynamic scenarios, improves computational efficiency, is suitable for real-time node joining and leaving, and has autonomy and intelligence in topology construction, making it highly adaptable.
Smart Images
Figure CN121635472A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of cooperative control technology, specifically relating to a distributed construction method for a hierarchical topology of an affine formation of a multi-agent system and a distributed control system for an affine formation of a multi-agent system determined based on the distributed construction method. Background Technology
[0002] With the rapid development of wireless communication and networking technologies, the control of multi-agent systems has been extensively studied. Interaction and coordination among agents enable tasks that a single agent cannot accomplish. Formation control is one of the core technologies of multi-agent cooperation, aiming to enable a group of agents to form a desired formation. Formation changes can enhance the flexibility and maneuverability of the formation.
[0003] In affine formation methods, the desired formation information is encoded into a stress matrix, which represents the interaction topology and interaction gain between nodes, significantly impacting the overall network performance. Due to limited communication and sensing range, agents typically only acquire information from their neighbors. Traditional formation research focuses more on the design of backend controllers and less on the construction and optimization of the frontend interaction topology. Existing topology construction methods rely on centralized solutions from a central processing unit, which cannot handle highly dynamic scenarios such as real-time node additions and departures, and are not scalable. Summary of the Invention
[0004] In view of this, this invention proposes a distributed construction method for hierarchical topology of affine formation in multi-agent systems, which addresses the problem of multi-agent cooperative control. Each node autonomously selects its neighbors and solves for stress values in a distributed manner, which can generate a better interactive topology in real time, greatly improving computational efficiency and optimizing system communication costs and control performance.
[0005] The technical solution for implementing the present invention is as follows: A distributed method for constructing hierarchical topologies of affine formations in multi-agent systems is described below. Based on the affine formation configuration, a hierarchical directed topology is designed, and the hierarchical directed topology is selected as d+1-spanning tree, so that the topology of the affine formation satisfies the condition that any target configuration can be reached with the fewest interaction edges. The distributed neighbor selection criterion is designed as follows: each node calculates all neighbor nodes within its own communication range. Error from its desired position The d+1 neighbors with the smallest error among the higher-level nodes are selected as parent nodes; based on the dynamically changing node errors, each node selects its own parent node according to the distributed neighbor selection criteria, forming the local topology of each node, thereby constructing a d+1-spanning tree. For each node's local topology, the stress values between nodes are solved using the local topology stress balance condition to obtain the optimal interaction topology in real time.
[0006] Preferably, the local topological stress equilibrium condition is: For the case where d=2, for the node The parent node that satisfies the distributed neighbor selection criterion is ,node With nodes The stress values between Then the node The corresponding stress equilibrium condition for the local topology is:
[0007] in For nodes The target location.
[0008] Preferably, the stress value of the neighbor node is: Given a node based on the desired convergence rate. i Total neighbor stress , Define as a node i Interaction edge stress values between it and all its neighboring nodes The sum; According to the node i Total neighbor stress Combining the stress equilibrium conditions of the local topology and the total stress of the neighboring units and Define the relationship and calculate the stress value of neighboring nodes. .
[0009] Preferably, the method further includes: determining whether the calculated stress values of neighboring nodes are all within the set stress value boundaries; if not, establishing a constrained linear programming model to solve for the optimal stress value.
[0010] Preferably, the constraints of the linear programming model include: stress value boundary constraints, and the total stress value of neighboring stresses. The definition of stress equilibrium conditions in local topology.
[0011] Preferably, the linear programming model is constructed as follows:
[0012] in, These are the upper and lower limits of the stress value, and the optimization objective is to maximize the system convergence rate. Represents the real number field. Total stress of neighboring units Definition, The stress equilibrium condition for the local topology; For nodes i Its neighboring nodes The stress values of the interaction edges between them; For nodes Target location; select based on the required convergence rate. The optimization objective is to maximize the system convergence speed.
[0013] Preferably, at each time step, it is determined whether the set of parent nodes of each node has changed according to the distributed neighbor selection criterion. If it has changed, the directed edges are reconnected and the stress value is calculated to update the affine formation topology at the current time.
[0014] Preferably, when a node joins or leaves in real time, it triggers a change in the set of parent nodes, reconnects the directed edges, calculates the stress value, and updates the affine formation topology at the current moment.
[0015] This invention also provides a distributed control system for a multi-agent system affine formation, which uses the aforementioned distributed construction method of hierarchical topology for multi-agent system affine formations to determine stress values; the distributed controller is designed as follows:
[0016] in, For nodes i The controller, For affine formation configurations, the interaction edge set; For nodes i and nodes t The stress values of the interaction edges between them are obtained using the distributed construction method of the hierarchical topology of the affine formation of the multi-agent system. and They are nodes i and nodes t The actual location; For the leader, the controller is ,in Additional control inputs imposed on the leader:
[0017] in, For nodes i Target location; A positive coefficient is given.
[0018] Preferably, the coefficient .
[0019] Beneficial effects: 1. This invention is an intelligent topology construction method. Given a desired configuration and corresponding optimization indicators, it can automatically generate an interactive topology while optimizing communication costs and overall system performance, thereby achieving affine formation control of multi-agent systems. Compared to traditional methods that require adjacency matrices or numerical calculations, this method has higher autonomy, intelligence, and environmental adaptability.
[0020] 2. This invention selects a hierarchical directed topology, ensuring the system satisfies the condition that it can reach any target configuration. Therefore, the Laplace matrix under this topology has a lower triangular structure, and the main diagonal elements are... This achieves decoupling between elements, making It can be used as a separate optimization objective. However, existing topology construction methods use feature values as optimization objectives, and these feature values are obtained based on global information. This invention utilizes local information for distributed topology design, making it impossible to obtain global feature values. Furthermore, it employs... This perfectly solves the problem of not being able to obtain eigenvalues. It is the d+1 smallest eigenvalue of the stress matrix, which is minimized. This allows the affine formation to converge the fastest.
[0021] 3. The topology construction of this invention is completely distributed. Each node only needs to interact with its neighbors within its communication range and can autonomously decide its own connections. Compared with centralized solution methods that rely on global information and a central processing unit, this method has low computational complexity, strong scalability, and is suitable for highly dynamic scenarios such as real-time joining and leaving of nodes. Attached Figure Description
[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0023] Figure 1 Flowchart of real-time distributed stress matrix optimization algorithm.
[0024] Figure 2 Add an operation diagram to the node.
[0025] Figure 3 This is a graph showing the formation error.
[0026] Figure 4 This is a simulation trajectory diagram for an affine formation. Detailed Implementation
[0027] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0028] This invention proposes a distributed construction method for hierarchical topology of affine formations in multi-agent systems, such as... Figure 1 As shown, its detailed implementation method is as follows: Step 1: Establish the node hierarchy and analyze the topological conditions that can be achieved by affine formation.
[0029] The specific process is as follows: This invention considers In 3D space An affine formation system consisting of intelligent agents with first-order integrator dynamics has a dynamic model that is a first-order integrator model, i.e.
[0030] in Represents intelligent agents Location coordinates, For intelligent agents Control input.
[0031] Using a leader-follower control framework, additional control input is applied to the leader. The leaders are driven to move to their desired positions. The remaining agents engage in localized interactions.
[0032] The diagram of the affine formation is as follows: Represents a set of nodes. Represents an edge set. For intelligent agents and The stress value of the interaction edges between them.
[0033] The closed-loop dynamic representation of the system is as follows:
[0034] in, , The stress matrix is the topology of the affine formation, consisting of the stress values of each interacting edge.
[0035] Assume a set of leaders Given known quantities, and that there is no interaction between leaders. Define the communication range of the agents as having a radius of [missing information]. The circle, for each intelligent agent j ,only At that time, it was called for The neighbors, that is , Represents a node i The neighbor set. In this invention, each follower communicates only with its own neighbors, determines its own topological connections in a distributed manner, calculates the stress values on the interaction edges, and improves system performance while ensuring the stability of the overall formation.
[0036] The stress matrix based on directed topology is derived from It means that among them The elements satisfy
[0037] Hierarchical topology is a special type of directed topology where nodes are organized in a hierarchical structure. Each node is connected only to its adjacent upper / lower level nodes, forming a directed acyclic graph consisting of several levels of nodes and directed edges between adjacent levels. Specifically, a hierarchical topology must satisfy the following conditions: 1. Hierarchical structure: In a hierarchical topology, each node has its own level. There are only directed edges between nodes with different levels, from higher level (lower level) to lower level (higher level). There are no directed edges in opposite directions. Therefore, there are no cycles in the topology. The level of a node can be arbitrarily specified.
[0038] 2. Node connections: In a hierarchical topology, each node is only connected to nodes at a lower (higher) level. There are no connections between nodes at the same level. If there is a directed edge between two nodes, it is an incoming edge (outgoing edge) for the lower-level node and an outgoing edge (incoming edge) for the higher-level node. 3. Number of levels: The position of each node in a hierarchical topology can be represented by the number of levels, which is a non-negative integer. Usually, the highest level is defined as 0, and the levels increase sequentially.
[0039] If and only if the figure for - When the root graph is in use, the graph Affine formation control is feasible. Therefore, - Root diagram The roots, acting as leaders in an affine formation, are defined as the highest level, with a level number of 0. Each follower interacts only with its higher-level neighbors, and directed edges point from the current node to higher-level nodes. Therefore, the Laplace matrix in this type of topology has a lower triangular structure, i.e. (1) Therefore, for a hierarchical directed topology , - A spanning tree is a topology that minimizes the number of interactive edges while ensuring that affine grouping is feasible. ,in For nodes The set of parent nodes, This indicates the number of elements in the set.
[0040] In conclusion, if and only if the diagram for - When the root graph is in use, the graph Affine formation control is achievable by selecting a hierarchical directed topology. The "root graph" is the condition for the realization of affine formation control. The Laplace matrix under this type of topology conforms to the form of equation (1), which facilitates the solution of the following text. Furthermore, A spanning tree is a topology that minimizes the number of interacting edges while ensuring that affine arrays are feasible. Therefore, by minimizing... The interaction of neighboring nodes can achieve the affine transformation of the entire formation.
[0041] The following proposes a topology construction operation that guarantees the feasibility of affine formations. Assume... That is, considering motion in a two-dimensional plane.
[0042] Node addition: Given a hierarchical directed topology that satisfies the conditions for affine formation realizability, add a new node to it. Select 3 existing nodes (at higher levels). Add 3 directed edges ,like Figure 2 As shown, the newly generated topology also satisfies the conditions for affine array realization, and the entire topology is the topology with the fewest interactive edges under the conditions.
[0043] The operation is fully distributed, meaning that each node only needs to interact with its neighbors within its communication range and can decide its own connections independently.
[0044] Step 2: Distributed Neighbor Selection The criteria for optimizing neighbor selection are derived through dynamic analysis of node errors. For nodes... Its candidate parent node is The corresponding stress value is Then the node The control law is
[0045] And because Adding the two equations together, we get
[0046] Make each intelligent agent The error from its desired position is The error dynamics are then...
[0047] In the above formula, Partially driven intelligent agents Move to its desired location, and It is considered a perturbation term in the system. When the candidate parent node... When all reach the desired position, intelligent agent It will proceed directly to the desired location; otherwise, due to the disturbance term... The role of intelligent agents i This will result in an unwanted state of motion, deviating from the fastest convergence path. For the sake of brevity, we will use... express Let Lyapunov function Then there is
[0048] because and For numbers of the same order, there exists a positive real number. , making Therefore, there is
[0049] From the above formula, it can be seen that if The value should be as small as possible. The smaller the value of , the less the system will be affected by unwanted disturbance terms. According to the properties of vector norms, we have...
[0050]
[0051]
[0052] Based on the above formula, the error of the candidate parent node is... As an indicator for selecting neighboring nodes, the criterion for selecting the optimal neighbor is: each node calculates the neighboring nodes within its own communication range. Error from its desired position Select the three neighbors with the smallest error within the communication range as the parent node.
[0053] Step 3: Stress value solution and optimization For nodes Based on the three parent nodes selected in step 2 , in the set The stress values on the three interactive edges are calculated, and the stress matrix that satisfies the affine formation stability condition is solved based on the stress equilibrium condition.
[0054] node The stress equilibrium condition is (2) Rewriting the above equation in matrix form, we have:
[0055] in , Therefore, the above equation does not have a unique solution. This is because the stress matrix satisfies the following definition: (3) therefore (4) If determined Then there exists a Vectors in null space , making That is, each stress value has a unique solution.
[0056] Because the stress matrix of a hierarchical directed topology has a lower triangular structure, the elements on the diagonal are the eigenvalues of the matrix. This ensures... Under these conditions, the stress matrix obtained by solving the problem must satisfy the system stability condition.
[0057] Therefore, by giving The value of can be configured for each eigenvalue of the stress matrix to achieve the desired performance metrics. For example, all eigenvalues of the stress matrix can be configured to achieve the desired performance metrics. Setting the values of to be the same yields the stress matrix with the optimal condition number. However, due to limitations of real physical systems, the stress value of each edge, as the control gain for the interaction, cannot be infinitely large. If directly given... The value of , the stress value obtained by solving The system constraints may not be met. Therefore, it is assumed that the stress value of each edge has upper and lower limits. When given The stress values obtained from the solution do not satisfy the requirements. At that time, run the linear programming algorithm: (5) in, represents the upper and lower limits of the stress value, and the optimization objective is to maximize the system convergence rate. , , Due to scope limitations, for Definition, This is the stress equilibrium condition.
[0058] Based on the above principles, the real-time topology construction process of this invention is as follows: Figure 1 As shown: At each time step, it is determined whether the set of parent nodes of each node has changed according to the distributed neighbor selection criteria. If it has changed, the directed edges are reconnected according to the parent nodes of each node determined in real time. First, the local topological stress balance condition (Equation 2) and the total stress value of the neighbors are used. The definition (Formula 3) combined with the given node i Total neighbor stress Solve for the stress values between nodes. To obtain the optimal interaction topology in real time. The convergence speed can be set according to the desired convergence speed.
[0059] Judgment obtained Does it meet the requirements? and Define the stress value boundary; if it is within the boundary, then utilize the obtained... Update the topology; if it is not within the stress value boundary, use the constrained linear programming model of formula (5) to solve for the optimal stress value, and use the optimal stress value to update the topology.
[0060] Based on the distributed construction method of the hierarchical topology of affine formation in multi-agent systems described above, stress values are obtained. Therefore, the distributed controller for the affine formation is:
[0061] In a two-dimensional plane, according to the relevant theory of affine formation, controlling at least three leader agents can achieve control over the entire formation.
[0062] For the selected leader, the controller is External control input In a preferred embodiment, .
[0063] Finally, simulation experiments were conducted to demonstrate the proposed affine formation distributed topology construction and control method. The simulation considered the 2D planar motion of nine agents, with each agent's communication range being a radius. A disk is constructed, and the 1st, 2nd, and 3rd agents are selected as leaders. Their initial positions are randomized, and their desired positions are given as follows:
[0064] Let the time interval The total running time is The upper and lower limits of the stress value are set as follows: Given that the expected feature values are all At every moment, it runs as follows: Figure 1 The distributed stress matrix construction and optimization algorithm shown employs a real-time dynamic stress matrix and interaction topology. Each agent distributes its interactions by selecting the neighbor that minimizes its own error and calculating the stress value. The convergence and historical trajectories of the affine formation system are shown below. Figure 3 and Figure 4 As shown, the total convergence error over the running period is 129.8651. The appearance of a bend in the convergence error curve indicates that the agent's neighbor set has changed, and the entire system can converge at a faster speed.
[0065] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for constructing a distributed affine formation hierarchical topology of a multi-agent system, characterized in that, The specific process is: According to the affine formation configuration, a hierarchical directed topology is designed, and the hierarchical directed topology is selected as a d+1-generated tree, so that the topology of the affine formation satisfies the condition of the minimum interaction edges under the condition of reaching any target configuration; The distributed neighbor selection criterion is designed as follows: each node calculates the error of each neighbor node in its communication range from the expected position of the node to itself , selects d+1 neighbors with the smallest error from the higher level nodes as the parent nodes; according to the dynamically changing node error, each node selects the parent node according to the distributed neighbor selection criterion, forms the local topology of each node, and thus constructs a d+1-spanning tree. For the local topology of each node, the stress values between nodes are solved by using the local topology stress balance condition, so as to obtain the optimal interaction topology in real time.
2. The method of claim 1, wherein, The local topology stress balance condition is: For d = 2, for node , the parent node satisfying the distributed neighbor selection criterion is , the stress value between node and node is ; then the stress balance condition of the local topology corresponding to node is: wherein is the target position of the node .
3. The method of claim 2, wherein, The stress value of the neighbor node is solved by: Given a node based on the desired convergence rate. i Total neighbor stress , Define as a node i Interaction edge stress values between it and all its neighboring nodes The sum; According to the node i Total neighbor stress Combining the stress equilibrium conditions of the local topology and the total stress of the neighboring units and Define the relationship and calculate the stress value of neighboring nodes. .
4. The method of claim 3, wherein, The method further comprises: judging whether the calculated stress values of the neighbor nodes are all within the set stress value boundary, and if not, establishing a linear programming model with constraints to solve the optimal stress value.
5. The method of claim 4, wherein, The constraints of the linear programming model include: stress value boundary constraints, neighbor stress total value definition, stress balance conditions of local topology.
6. The method of claim 5, wherein, The linear programming model is constructed as: wherein, is the upper and lower limit of the stress value, the optimization objective is to maximize the system convergence speed; represents the real number field, is the total value of the neighbor stress definition, is the stress balance condition of the local topology; is the stress value of the interaction edge between the node i and its neighbor node ; is the target position of the node ; is selected according to the required convergence speed , the optimization objective is to maximize the system convergence speed.
7. The method of claim 1, wherein, At each time step, it is determined according to the distributed neighbor selection criterion whether the parent node set of each node changes, and when the change occurs, the directed edge is reconnected and the stress value is calculated, and the affine formation topology at the current time is updated.
8. The method of claim 1, wherein, When a node joins or leaves in real time, the parent node set is triggered to change, the directed edge is reconnected and the stress value is calculated, and the affine formation topology at the current time is updated.
9. A multi-agent system affine formation distributed control system, characterized in that, The stress value is determined by using the distributed construction method of the hierarchical topology of the affine formation of the multi-agent system according to any one of claims 1-6; and a distributed controller is designed as: wherein, is a controller of the node i , is an interaction edge set of the affine formation configuration; is a stress value of an interaction edge between the node i and the node t , which is obtained by using a distributed construction method of the affine formation hierarchical topology of the multi-agent system; and are actual positions of the node i and the node t , respectively. For the leader, the controller is where extra control input imposed on the leader: wherein is the target position of the node i ; is a given positive coefficient.
10. The control system of claim 9, wherein, The coefficients .