Multi-agent distributed formation control method based on projection controller

Abstract

The application discloses a kind of multi-agent distributed plane formation control method based on projection controller, belong to multi-agent cooperative control field, including: according to the position vector of each agent in target formation formation, the network communication topology graph between agent is constructed;Wherein, in network communication topology graph, agent is classified and marked as 1 leader, 1 deputy leader and several non-leaders, the out-degree of leader, deputy leader, non-leader is respectively 0, 1, 2;According to the relative position vector of leader relative to deputy leader, the following speed of deputy leader is calculated to control deputy leader;For each non-leader, according to the projection of non-leader on orthogonal vector group, the relative position of successor neighbor relative to the non-leader, the following speed of non-leader is calculated to control non-leader.Guarantee global stability on the basis of not increasing control complexity.

Description

Technical Field

[0001] This invention belongs to the field of multi-agent cooperative control, and more specifically, relates to a multi-agent distributed planar formation control method based on a projection controller. Background Technology

[0002] Multi-agent formation control refers to controlling the behavior of multiple agents to form a specific formation in space and maintain its stability during movement. Compared to centralized formation, distributed formation can respond more flexibly, intelligently, and efficiently to external changes and disturbances, and has greater application value.

[0003] Traditional distributed formation control methods can be categorized as follows: Distributed formation methods based on a combination of distance controllers and rigid graph theory can only guarantee local convergence stability and lack effective initial formation generation for multi-agent clusters with random initial positions. Consistent distributed formation methods based on relative displacement require that the coordinate systems of each agent be aligned, which is difficult to implement under communication constraints. Methods combining distance controllers and collision avoidance controllers can address the problems of the above two methods; however, this method is limited to equilateral triangle formations and is not applicable to other formations, potentially leading to non-convergence or formation ambiguity. Introducing angle control into distance-based rigid formation control methods can avoid flip ambiguity, or increasing the number of edges to form a globally rigid formation can also avoid flip ambiguity. However, the introduction of additional control variables (angles or edges) complicates the control law and increases communication costs, making it difficult to implement in practical applications.

[0004] In summary, given the inconsistent coordinate systems of each agent, achieving stable and reliable distributed formation with different initial positions for multiple agents to avoid flip ambiguity without increasing controller complexity is of significant research importance. Furthermore, current two-dimensional distributed formation control methods rarely address the formation repair problem when agents malfunction due to deliberate attacks. Summary of the Invention

[0005] To address the shortcomings and improvement needs of existing technologies, this invention provides a multi-agent distributed planar formation control method based on a projection controller. Its purpose is to achieve stable and reliable distributed formation with different initial positions of multiple agents without increasing the complexity of the controller, so as to avoid flip ambiguity, especially when the coordinate system orientation of each agent is inconsistent.

[0006] To achieve the above objectives, according to one aspect of the present invention, a multi-agent distributed planar formation control method based on a projection controller is provided, comprising: constructing a network communication topology graph between agents based on the position vectors of each agent in a target formation; wherein, in the network communication topology graph, agents are classified and labeled as one leader, one deputy leader, and several non-leaders, with out-degrees of 0, 1, and 2 for the leader, deputy leader, and non-leaders, respectively, the out-degree representing the number of successor neighbor agents of the agent, and the agent communicating unidirectionally with its successor neighbor agents and being able to obtain the position of its successor neighbor agents, the leader being a deputy leader, deputy leader, and non-leader. The leader's successor neighbor agents; based on the relative position vector of the leader relative to the deputy leader and the target formation, the follow speed of the deputy leader is calculated to control the deputy leader; based on the target formation, the projection of each non-leader onto an orthogonal vector group is determined, where one vector in the orthogonal vector group is aligned with the relative direction between the two successor neighbor agents of the non-leader; for each non-leader, based on the projection and the relative position vector of the two successor neighbor agents of the non-leader relative to the non-leader, the follow speed of the non-leader is calculated to control the non-leader.

[0007] Furthermore, the formation position controller of the deputy leader takes the form of:

[0008]

[0009] d=||x1 * -x2 * ||

[0010] in, Let x1 be the following speed of the secondary leader, x2 be the current position vector of the leader, c be a set positive real parameter, and d be the expected distance between the leader and the secondary leader in the target formation. * Let x2 be the position vector of the leader in the target formation. * Let ||•|| be the position vector of the deputy leader in the target formation, and ||•|| denote the 2-norm of the orientation quantity.

[0011] Furthermore, the non-leader formation position controller takes the form of:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] in, x represents the following speed of non-leader i. i Let x be the current position vector of non-leader i. j x k Let be the current position vectors of the two successor neighbor agents j and k of non-leader i, respectively. Let x be the unit relative direction vector of k relative to j. i * Let x be the position vector of the non-leader i in the target formation. j * x k * Let s1 and s2 be the position vectors of j and k in the target formation, respectively. Let s1 be the projection of the non-leader i in the target formation onto the first vector. The first vector is in the same direction as the relative position vector of k with respect to j. Let s2 be the projection of the non-leader i in the target formation onto the second vector. The second vector is obtained by rotating the first vector counterclockwise by 90 degrees. c is a set positive real parameter. R is the rotation matrix. ||•|| represents the 2-norm of the orientation vector.

[0018] Furthermore, the construction of the network communication topology graph between agents specifically includes: generating an initial triangulation graph with the agents as nodes based on the position vectors of each agent in the target formation; selecting an agent as a leader, selecting an initial triangle containing the leader in the initial triangulation graph, designating another agent in the initial triangle as a deputy leader, directionally simplifying the edges of the initial triangle so that the out-degrees of the leader and deputy leader are 0 and 1 respectively, and marking the nodes in the initial triangle; traversing all unmarked nodes, if an unmarked node has two or more marked neighbor nodes in the initial triangulation graph, directionally simplifying the edges connecting any two marked neighbor nodes to the unmarked node, making the marked nodes the successor neighbors of the unmarked node, and marking the unmarked node, until all nodes are marked; deleting the undirected edges in the initial triangulation graph to obtain the network communication topology graph.

[0019] Furthermore, when an agent malfunctions, the method further includes: deleting the malfunctioning agent and constructing a new network communication topology based on the classification of the malfunctioning agent; and controlling the malfunction-free agents based on the new network communication topology and the target formation.

[0020] Furthermore, when the malfunctioning agent is the leader: delete the leader and its connected directed edges, transform the deputy leader into the new leader, transform the non-leaders that are directed to both the deleted leader and the new leader into the new deputy leader; add a non-repeating directed edge to the new leader or the new deputy leader for the non-leaders that are directed to the deleted leader, and obtain a new network communication topology.

[0021] Furthermore, when the agent that malfunctions is a deputy leader: delete the deputy leader and the directed edges connected to it, and transform the non-leaders that are directed to both the leader and the deleted deputy leader into new deputy leaders; add a non-repeating directed edge to the leader or the new deputy leader for the non-leaders that are directed to the deleted deputy leader, and obtain a new network communication topology.

[0022] Furthermore, when the failed agent is a non-leader: obtain the set V1 of all predecessor neighbor agents and the set V2 of successor neighbor agents for the failed agent; iterate through each agent V in the set V1 of predecessor neighbor agents. 1j Search for V from the set of successor neighbor agents V2 1j A non-neighbor intelligent agent V 2j , with V 1j Starting from V 2j The directed edges are removed; the faulty agent and its connected directed edges are deleted to obtain a new network communication topology.

[0023] According to another aspect of the present invention, a multi-agent distributed planar formation control system based on a projection controller is provided, comprising: a processor; and a memory storing a computer-executable program, wherein when executed by the processor, the program causes the processor to perform the multi-agent distributed planar formation control method based on a projection controller as described above.

[0024] According to another aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the multi-agent distributed planar formation control method based on a projection controller as described above.

[0025] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0026] (1) A multi-agent distributed planar formation control method based on projection controller is provided. The out-degree of each agent is designed to be no greater than 2. A persistent network communication topology with the minimum number of directed communication channels is constructed. The agents only need to communicate in one direction to obtain relative position information. This can ensure that the formation can remain stable even when the coordinate systems of the agents are not aligned.

[0027] For each agent, a distributed controller is designed to control its own motion according to the classification of leader, deputy leader, and non-leader. A projection controller is designed for the non-leader. The projection controller projects onto a specific set of orthogonal vectors, which retains the advantage of translation and rotation invariance. Therefore, it is also applicable to the case where the coordinate system of the agents is not aligned. Moreover, the controller does not introduce additional control variables. Without increasing the complexity of the controller, it can achieve stable and reliable distributed formation under different initial positions of multiple agents to avoid flip ambiguity and achieve reliable and stable control.

[0028] (2) When an agent suddenly experiences an unrepairable fault, the vertices and edges corresponding to the faulty agent in the communication network are deleted, and as few directed edges as possible are added locally, so that the reconstructed network communication topology remains persistent, ensuring that the stability and anti-interference of the formation after reconstruction will not be weakened due to the removal of nodes, and realizing the reliable and stable movement of the multi-agent system. Attached Figure Description

[0029] Figure 1 A flowchart of a multi-agent distributed planar formation control method based on a projection controller provided in an embodiment of the present invention;

[0030] Figure 2 The positional relationship of the target formation and the corresponding network communication topology diagram in the reference coordinate system provided in the embodiments of the present invention;

[0031] Figure 3 This is a schematic diagram comparing the generation effects based on the projection controller and the distance controller under the initial position distribution 1.

[0032] Figure 4 This is a schematic diagram comparing the generation effects based on the projection controller and the distance controller under the initial position distribution 2.

[0033] Figure 5 This is a schematic diagram illustrating the use of projection positivity to distinguish the flipping ambiguity of formations in an embodiment of the present invention;

[0034] Figure 6A , Figure 6B These are the initial triangulation diagram and the network communication topology diagram provided in the embodiments of the present invention;

[0035] Figure 7 This is a network communication topology diagram for reconstructing a faulty intelligent agent, provided in an embodiment of the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0037] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0038] Figure 1 A flowchart illustrating a multi-agent distributed planar formation control method based on a projection controller, provided in an embodiment of the present invention. (See also...) Figure 1 , combined Figures 2-7 The multi-agent distributed planar formation control method based on the projection controller in this embodiment is described in detail. The method includes operations S1-S4.

[0039] Operation S1 constructs a network communication topology graph between agents based on the position vectors of each agent in the target formation. In the network communication topology graph, agents are classified and labeled as 1 leader, 1 deputy leader, and several non-leaders. The out-degrees of the leader, deputy leader, and non-leaders are 0, 1, and 2, respectively. The out-degree represents the number of successor neighbor agents of an agent. Agents can communicate unidirectionally with their successor neighbor agents and can obtain the position of their successor neighbor agents. The leader is the successor neighbor agent of the deputy leader.

[0040] First, let's explain the basic terminology for network graphs in this embodiment. An inter-agent communication network can be represented by a graph G = (V, E), where the vertex set V = {v1, v2, v3, ..., v...} n} represents the agents in a multi-agent system, and the edge set E = {e1, e2, e3, ..., e...} m} represents all pairwise communication links between agents. If G is an undirected graph, then the agents corresponding to the two vertices of an undirected edge e can communicate with each other; these two vertices are called neighbor vertices. If G is a directed graph, then the directed edge e = (v i v j ) represents a v i Point to v j A one-way edge, in this communication network, vertex v i Only with v j To perform one-way communication, i.e., v i Can obtain v j Relative position information, and v j Unable to obtain v iRelative position information, where v i Called the starting point, v j This is called the endpoint, v i Called v j The former neighbor, v j Called v i The successor neighbor, e is v i Go beyond the edge.

[0041] When the coordinate systems of multiple agents are not aligned, the network communication topology graph must meet the following conditions to maintain the stability of the formation: The undirected network communication topology graph should be rigid, that is, the graph will not deform while ensuring that the length of each edge remains unchanged. This graph is called a rigid graph. Otherwise, it is a non-rigid graph. The directed network communication topology graph should be durable, that is, the durable graph is the directed version of the rigid graph and the corresponding undirected graph is still a rigid graph after deleting the number of out-edges of all nodes with an out-degree greater than 3 to 2. In addition, the minimum durable graph is the durable graph with the minimum number of edges, and the out-degree of each node is less than or equal to 2.

[0042] Once the above conditions are met, a suitable controller can be designed to ensure the stability of the multi-agent formation, allowing only overall movement and turning. Furthermore, directed networks require only one-way communication, thus saving communication resources compared to undirected networks. The objective of this invention is to construct a directed persistent network communication topology with the minimum number of directed edges (i.e., the number of communication channels).

[0043] According to an embodiment of the present invention, operation S1 specifically includes: sub-operation S11-sub-operation S14.

[0044] In sub-operation S11, an initial triangulation diagram with agents as nodes is generated based on the position vectors of each agent in the target formation. The resulting initial triangulation diagram is as follows: Figure 6A As shown.

[0045] Since the target formation is known, a reference coordinate system is constructed and the position vector of each agent in the target formation is given. Then, the Delaunay triangulation algorithm is implemented to obtain the initial triangulation map. It is assumed that all nodes are unlabeled initially.

[0046] In suboperation S12, select an agent as the leader, select an initial triangle containing the leader in the initial triangulation graph, designate another agent in the initial triangle as the deputy leader, directionify the edges of the initial triangle so that the out-degrees of the leader and deputy leader are 0 and 1 respectively, and mark the nodes in the initial triangle.

[0047] In sub-operation S13, traverse all unmarked nodes. If an unmarked node has two or more marked neighbor nodes in the initial triangulation graph, arbitrarily select two marked neighbor nodes and the unmarked node to perform directed processing on the edges. The marked node becomes the successor neighbor of the unmarked node. Mark the unmarked node. Repeat the above operations in sub-operation S13 until all nodes are marked.

[0048] In suboperation S14, undirected edges in the initial triangulation graph are deleted to obtain a minimum directed persistent graph as the network communication topology graph of the multi-agent system.

[0049] In this embodiment, for example, select Figure 6A Nodes 1, 2, and 3 are used as the three vertices of the initial triangle, and the triangle is gradually expanded to eventually obtain the following: Figure 6B The network communication topology diagram shown in the diagram represents the node labeling order, where node 1 is the leader and node 2 is the deputy leader.

[0050] In this embodiment, the target formation is processed using a triangulation algorithm to obtain an initial triangulation graph. Subsequently, no operations specific to equilateral triangle formation, such as deleting boundaries or splitting edges, are performed. Instead, the graph is directly directed while redundant edges are deleted to obtain a minimum directed persistent network communication topology graph.

[0051] Operation S2 calculates the follow speed of the secondary leader based on the relative position vector of the leader and the target formation to control the secondary leader.

[0052] After the network communication topology is constructed, agents are categorized into leader, deputy leader, and non-leader based on the out-degree of the corresponding nodes. For example... Figure 2 As shown, agent 1 is the leader with an out-degree of 0 and no successor neighbor nodes; agent 2 is the deputy leader with an out-degree of 1 and a successor neighbor that is the leader; the remaining agents are non-leaders with an out-degree of 2 and two distinct successor neighbors. The resulting minimal directed persistent network has exactly one leader and one deputy leader, with the rest being non-leaders. Because the different number of successor neighbor nodes leads to different control inputs for the agents, a distributed formation controller needs to be designed for each type of agent.

[0053] The distributed formation controller adjusts the speed of each agent by controlling the input to make them more consistent, and ensures that the distance between each agent is the same as the target formation, so as to achieve the purpose of forming and maintaining the stability of the formation.

[0054] Since the leader has no successor neighbor nodes, a controller needs to be designed based on the specific movement path of the multi-agent system formation. To simplify the analysis, this embodiment assumes that the leader's speed remains constant.

[0055] For the secondary leader, the constraint is only from the distance to the leader; therefore, a distance-based gradient controller can be directly used to guarantee global convergence. The specific controller form is as follows:

[0056]

[0057] d=||x1 * -x2 * ||

[0058] in, Let x1 be the following speed of the secondary leader, x2 be the current position vector of the leader, c be the set positive real parameter, and d be the expected distance between the leader and secondary leader in the target formation. * Let x2 be the position vector of the leader in the target formation. * Let c be the position vector of the deputy leader within the target formation, and ||•|| denote the 2-norm of the orientation vector. The value of c can be freely adjusted; a larger value of c results in faster formation speed, but also increases fuel consumption. 21 =x1-x2 is the relative position vector of the leader relative to the deputy leader.

[0059] Operation S3 determines the projection of each non-leader onto the orthogonal vector group according to the target formation. One vector in the orthogonal vector group is aligned with the relative direction between the two successor neighbor agents of the non-leader.

[0060] Operation S4: For each non-leader, calculate the following speed of the non-leader based on the projection and the relative position vectors of the two successor neighbor agents of the non-leader relative to the non-leader, in order to control the non-leader.

[0061] like Figure 5 The target formation shown is composed of four agents i, j, k, and m. If the positions of agents j, k, and m are already determined, and a distance-based controller is used, requiring only that the distance between agents and their neighboring nodes tends to the target value, then agent i has two possible equilibrium positions i and i′ in the plane. This phenomenon is also called flip ambiguity, which may lead to the generation of incorrect formations.

[0062] The projection controller proposed in this embodiment of the invention first uses a rotation matrix R to transform the direction vectors x between neighboring nodes j and k. jk Rotate 90 degrees counterclockwise to obtain vector Rx jk x jk With Rx jkA pair of orthogonal vectors in a plane is constructed using only relative position information. Then, the agent i is controlled by projecting its image onto specific real numbers s1 and s2 in the two directions of the orthogonal vectors. Here, s1 and s2 are uniquely determined by the target formation in operation S3. Unlike distance-based controllers, projection-based controllers avoid flip ambiguity, such as... Figure 5 As shown. At the two ambiguous flip positions i and i′ of the balance based on the distance controller, although at x jk The directional projection is the same, but in Rx jk The directional projection values ​​have opposite signs. When parameters s1 and s2 are determined, the relative positions of the agents are also uniquely determined. Therefore, the projection-based controller has global convergence stability. Furthermore, compared to distance-based controllers, the projection-based controller retains the advantage of rotation invariance and achieves global convergence stability without increasing the number of control variables or network edges, thus solving the formation generation problem under random initial positions.

[0063] According to an embodiment of the present invention, a projection-based controller, rather than a distance-based controller, is used for the non-leader. Under the control of the projection controller, the following speed of the non-leader is:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] in, x represents the following speed of non-leader i. i Let x be the current position vector of non-leader i. j x k Let be the current position vectors of the two successor neighbor agents j and k of non-leader i, respectively. Let x be the unit relative direction vector of k relative to j. i * Let x be the position vector of the non-leader i in the target formation. j * x k *Let be the position vectors of j and k in the target formation, respectively. s1 is the projection of the non-leader i in the target formation onto the first vector, which is in the same direction as the relative position vector of k with respect to j. s2 is the projection of the non-leader i in the target formation onto the second vector, which is obtained by rotating the first vector counterclockwise by 90 degrees. c is a set positive real parameter; R is a rotation matrix used to rotate the vector counterclockwise by 90 degrees; ||•|| represents the 2-norm of the orientation vector. Figure 2 In the agent system shown, if i is agent 3, then j is one of agents 2 and 5, and k is the other one of agents 2 and 5.

[0070] Once configured, the multi-agent system can form the target formation after a period of time and maintain the current formation stably. If the target formation needs to be changed due to a change in task, operation S1 needs to be re-executed to construct the directed network communication topology and the controller needs to be reset. The aforementioned distributed controller is flexible; when a change in task requires a change in the target formation, the new formation can be achieved by modifying the successor neighbors of some agents and the corresponding controller parameters s1 and s2.

[0071] Considering potential malicious attacks and drastic environmental changes in real-world applications, a critical agent in a multi-agent system may experience an unrecoverable malfunction, disrupting the persistence of the multi-agent network communication topology and affecting the stability and anti-interference capabilities of the formation. To ensure that the formation stability and anti-interference capabilities remain unaffected by agent failures, this invention proposes a network reconstruction algorithm. First, the vertices and edges corresponding to the failed agent in the communication network are deleted. Then, as few directed edges as possible are added locally, ensuring the persistence of the reconstructed network communication topology. By modifying the controller parameters of a few agents whose successor neighbors change, the stability and anti-interference capabilities of the formation can be maintained.

[0072] Specifically, according to an embodiment of the present invention, when a multi-agent system moves according to a target formation, the method further includes the following steps (1)-(2) when an agent malfunctions.

[0073] Step (1): Based on the classification of the faulty agents, delete the faulty agents and construct a new network communication topology.

[0074] When the agent that malfunctions is the leader: delete the leader and all directed edges connected to it, make the deputy leader the new leader, and make the non-leaders that are directed to both the deleted leader and the new leader the new deputy leader; add a non-repeating directed edge to the new leader or the new deputy leader for the non-leaders that are directed to the deleted leader, and obtain a new network communication topology.

[0075] When the agent that malfunctions is a deputy leader: delete the deputy leader and the directed edges connected to it; change the non-leaders that are directed to both the leader and the deleted deputy leader into new deputy leaders; add a non-repeating directed edge to the leader or the new deputy leader for the non-leaders that are directed to the deleted deputy leader, and obtain a new network communication topology.

[0076] When the failed agent is a non-leader: Obtain the set V1 of all predecessor neighbors and the set V2 of successor neighbors of the failed agent; iterate through each agent V in the set V1 of predecessor neighbors. 1j Search for V from the set of successor neighbor agents V2 1j A non-neighbor intelligent agent V 2j , with V 1j Starting from V 2j The directed edges are removed; the faulty agent and its connected directed edges are deleted to obtain a new network communication topology.

[0077] Figure 7 This is an illustrative example of network communication topology reconstruction when an agent fails. Agent 10 is the failed agent. First, based on its out-degree of 2, it is determined to be a non-leader. Then, agent 10 and all its connected edges are deleted. Next, a new non-repeating directed edge is added to each of agent 10's predecessor neighbor agents (agents 11 and 12), pointing to either agent 10 or agent 8. The newly added edges are as follows: Figure 7 As shown by the thick dashed line, the reconstructed network graph is the new directed network communication topology.

[0078] Step (2): Control the fault-free intelligent agent according to the new network communication topology and target formation.

[0079] The control principles for the leader, deputy leader, and non-leader in the new network communication topology are the same as those for the leader, deputy leader, and non-leader in operations S2-S4 above, and will not be repeated here.

[0080] by Figure 2 Taking the five-agent system shown as an example, two different initial position distributions of multi-agents, 1 and 2, are selected. With other conditions being the same, the target formation generation task is completed by using a distance controller and, in this embodiment, a projection controller.

[0081] Figure 3From left to right, the figures represent: initial position distribution 1; the motion paths and final position states of each agent during formation generation using a distance controller; and the motion paths and final position states of each agent during formation generation using a projection controller. It can be seen that under initial position distribution 1, both controllers can ultimately form the target formation.

[0082] Figure 4 From left to right, the figures show: initial position distribution 2; motion paths and final position states of each agent during formation generation using a distance controller; and motion paths and final position states of each agent during formation generation using a projection controller. It can be seen that, under the distance controller approach, the final position state of the multi-agent system does not meet the target formation requirements, making it impossible to complete the task; under the projection controller approach, the motion paths and final position states of each agent are consistent with the target formation, meeting the requirements of the formation generation task.

[0083] contrast Figure 3 and Figure 4 It is known that although distance-based controllers can complete formation control tasks under conditions where the coordinate systems of multi-agent systems are not aligned, the initial position distribution of the multi-agents is required in the formation generation task. In this embodiment of the invention, the projection controller does not require the coordinate systems of the multi-agents to be aligned, nor does it impose any restrictions on the initial positions of the multi-agents; furthermore, it does not require the addition of additional control variables, thus reducing the difficulty of controller implementation.

[0084] The multi-agent distributed planar formation control method based on projection controllers proposed in this invention first establishes a reference coordinate system for the target formation, used for subsequent calculation of controller parameters and construction of the multi-agent system network communication topology. Then, a motion controller is set for each agent according to the node type in its corresponding communication topology, thus completing the generation and maintenance of the target formation. If an agent malfunctions, a network reconstruction algorithm is immediately used to repair the communication topology and modify the controller parameters of some agents, ensuring that the remaining agents can maintain the stability of the current formation. This method can solve the distributed formation control problem of multi-agent systems in two-dimensional scenarios, as well as the formation repair problem when agents malfunction under deliberate attacks. It can be applied to formation control and group movement in various planar multi-agent systems such as unmanned vehicle swarms and unmanned surface vessel swarms.

[0085] This invention provides a multi-agent distributed planar formation control system based on a projection controller, comprising: a processor; and a memory storing a computer-executable program, wherein when the program is executed by the processor, the processor performs the aforementioned multi-agent distributed planar formation control method based on a projection controller.

[0086] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned multi-agent distributed planar formation control method based on a projection controller.

[0087] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 multi-agent distributed planar formation control method based on a projection controller, characterized in that, include: Based on the position vectors of each agent in the target formation, a network communication topology graph is constructed between agents. In the network communication topology graph, agents are classified and labeled as 1 leader, 1 deputy leader, and several non-leaders. The out-degrees of the leader, deputy leader, and non-leaders are 0, 1, and 2, respectively. The out-degree represents the number of successor neighbor agents of an agent. An agent can communicate unidirectionally with its successor neighbor agents and can obtain the position of its successor neighbor agents. The leader is the successor neighbor agent of the deputy leader. The following speed of the deputy leader is calculated based on the relative position vector of the leader relative to the deputy leader and the target formation to control the deputy leader; Based on the target formation, the projection of each non-leader on the orthogonal vector group is determined, and one vector in the orthogonal vector group is in the same direction as the relative direction between the two successor neighbor agents of the non-leader. For each non-leader, the following speed of the non-leader is calculated based on the projection and the relative position vectors of the non-leader's two successor neighbor agents relative to the non-leader, in order to control the non-leader. The non-leader formation position controller takes the form of: in, as a non-leader The following speed, as a non-leader The current position vector, , Non-leaders Two successor neighbor intelligent agents , The current position vector, for relatively The unit relative direction vector, as a non-leader Position vector within the target formation , They are respectively , Position vector within the target formation Non-leadership members in target formation The projection onto the first vector, the first vector and Compared to The relative position vectors are in the same direction. Non-leadership members in target formation The projection onto the second vector, which is obtained by rotating the first vector counterclockwise by 90 degrees. To set the positive real parameter, For rotation matrix, The 2-norm of the orientation quantity is represented.

2. The multi-agent distributed planar formation control method based on a projection controller as described in claim 1, characterized in that, The deputy leader's formation position controller takes the form of: in, The following speed of the deputy leader, Let this be the leader's current position vector. Let be the current position vector of the deputy leader. To set the positive real parameter, The desired distance between the leader and deputy leader in the target formation. Let be the position vector of the leader within the target formation. Let be the position vector of the deputy leader within the target formation. The 2-norm of the orientation quantity is represented.

3. The multi-agent distributed planar formation control method based on a projection controller as described in claim 1, characterized in that, The construction of the network communication topology diagram between intelligent agents specifically includes: Based on the position vectors of each agent in the target formation, an initial triangulation diagram is generated with the agents as nodes. Select an agent as the leader, select an initial triangle containing the leader in the initial triangulation graph, designate another agent in the initial triangle as the deputy leader, directionally shape the edges of the initial triangle such that the out-degrees of the leader and deputy leader are 0 and 1 respectively, and mark the nodes in the initial triangle. Traverse all unmarked nodes. If an unmarked node has two or more marked neighbor nodes in the initial triangulation graph, randomly select two marked neighbor nodes and the unmarked node and direct the edges between them. The marked nodes are the successor neighbors of the unmarked node. Mark the unmarked node until all nodes have been marked. The network communication topology graph is obtained by deleting the undirected edges in the initial triangulation graph.

4. The multi-agent distributed planar formation control method based on a projection controller as described in any one of claims 1-3, characterized in that, When an agent malfunctions, the method further includes: Based on the classification of the malfunctioning agents, delete the malfunctioning agents and construct a new network communication topology. Based on the new network communication topology and the target formation, control the fault-free intelligent agent.

5. The multi-agent distributed planar formation control method based on a projection controller as described in claim 4, characterized in that, When the agent that malfunctions is the leader: Delete the leader and its connected directed edges, transform the deputy leader into the new leader, and transform the non-leaders that are directed to both the deleted leader and the new leader into the new deputy leaders. Add a non-repeating directed edge to the new leader or the new deputy leader from the non-leader that is connected to the deleted leader, and obtain a new network communication topology.

6. The multi-agent distributed planar formation control method based on a projection controller as described in claim 4, characterized in that, When the agent that malfunctions is the deputy leader: Delete the deputy leader and its connected directed edges, and transform the non-leaders that are both directed to the leader and the deleted deputy leader into new deputy leaders; Add a non-repeating directed edge to the leader or the new deputy leader from the non-leader that is connected to the deleted deputy leader, and obtain a new network communication topology.

7. The multi-agent distributed planar formation control method based on a projection controller as described in claim 4, characterized in that, When the agent that malfunctions is a non-leader: Obtain the set of all predecessor neighbor agents V1 and successor neighbor agents V2 of the agent that failed; Iterate through each agent V in the set of predecessor neighbor agents V1 1j Search for V from the set of successor neighbor agents V2 1j A non-neighbor intelligent agent V 2j , with V 1j Starting from V 2j The directed edges; Delete the faulty agent and its connected directed edges to obtain a new network communication topology.

8. A multi-agent distributed planar formation control system based on a projection controller, characterized in that, include: processor; A memory storing a computer-executable program, which, when executed by the processor, causes the processor to perform the multi-agent distributed planar formation control method based on a projection controller as described in any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the multi-agent distributed planar formation control method based on a projection controller as described in any one of claims 1-7.

Images