A cluster formation trajectory planning method based on submatrix selection

Abstract

The present invention discloses a cluster formation trajectory planning method based on submatrix selection, comprising: abstracting the cluster formation into a graph structure, where the nodes of the graph are the agents in the cluster, the edges are the connection constraints between the agents, and the edge weights are the squares of the Euclidean distances between the two agents, thereby constructing a Laplace matrix of the graph; based on the maximum trace of the matrix, selecting several columns from the Laplace matrix to form an optimal submatrix of the Laplace matrix; based on the optimal submatrix, re-determining the connection relationship between each agent and other agents, thereby constructing the expected subgraph of each agent; and performing cluster formation trajectory planning based on the expected subgraph of each agent. This improves the current distributed fully connected formation algorithm, aiming to reduce connection constraints by selecting submatrices of the fully connected Laplace matrix, improve optimization efficiency, and achieve larger-scale distributed cluster formation while ensuring formation performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of cluster formation trajectory planning, and in particular relates to a cluster formation trajectory planning method based on submatrix selection. Background Art

[0002] Swarm formation flying has applications in a variety of fields, including cargo handling and formation performances. To alleviate the drawbacks of centralized swarm formations, such as high computational complexity and poor fault tolerance, numerous distributed swarm formation research and inventions have emerged. However, most currently use fully connected graphs to describe cluster relationships, requiring drones to consider the trajectories of all other drones for coordination. This results in exponentially increasing formation planning complexity with increasing swarm size, making it impossible to achieve real-time, distributed, large-scale, high-performance formation planning.

[0003] There are currently some methods to sparse the connection graph, such as a single agent only coordinating with some neighboring agents. However, this sparse connection loses too many features of the entire formation shape, and the formation coordination effect is poor in an environment with obstacles.

[0004] For large-scale formation systems, traditional methods use centralized strategies for coordination. However, this method was difficult to meet the requirements of formation coordination in environments with dense obstacles. Moreover, this centralized computing method has poor robustness and is extremely dependent on the central computer.

[0005] In a distributed cluster formation system, each agent receives the position information of other agents and autonomously calculates its own trajectory. The entire system is highly robust. However, in most studies, a single agent redundantly considers the constraints of all other agents, which greatly reduces the efficiency of trajectory optimization.

[0006] Existing research only considers the algorithm research of the position information of neighboring intelligent agents. However, the information obtained by this sparse strategy is too local, and the global characteristics of the entire cluster are excessively lost, resulting in poor formation maintenance effect in dense obstacle environments. Summary of the Invention

[0007] In response to the problems existing in the prior art, the purpose of the embodiments of the present application is to provide a cluster formation trajectory planning method based on sub-matrix selection, to improve the current distributed fully connected formation algorithm, and to reduce connection constraints by selecting sub-matrices of the fully connected Laplace matrix, thereby improving optimization efficiency and achieving larger-scale distributed cluster formations while ensuring formation performance.

[0008] According to a first aspect of an embodiment of the present application, a cluster formation trajectory planning method based on submatrix selection is provided, comprising:

[0009] The cluster formation is abstracted into a graph structure, where the nodes of the graph are the agents in the cluster, the edges are the connection constraints between the agents, and the edge weight is the square of the Euclidean distance between the two agents, thereby constructing the Laplace matrix of the graph;

[0010] Selecting a plurality of columns of the Laplacian matrix based on the maximum trace of the matrix to form an optimal submatrix of the Laplacian matrix;

[0011] Re-determine the connection relationship between each agent and other agents based on the optimal submatrix, so as to construct the expected subgraph of each agent;

[0012] Cluster formation trajectory planning is performed based on the desired subgraph of each agent.

[0013] Furthermore, for a cluster formation with n agents, the graph formed is is a set of nodes, and the edges of the graph are The i-th node has a position vector The edge weight w ij =||p i -p j || 2 ,||.|| is the Euclidean distance metric;

[0014] The Laplacian matrix of a graph is L = D – A, where D is the degree matrix of the graph and A is the adjacency matrix of the graph:

[0015]

[0016] Furthermore, based on the maximum trace of the matrix, several columns of the Laplacian matrix are selected to form an optimal submatrix of the Laplacian matrix, including:

[0017] Determine the number of columns of the submatrix selected n is the number of columns of the Laplacian matrix;

[0018] Constructing the first objective problem in It represents the submatrix formed by selecting specific m columns in the Laplace matrix L, namely the optimal submatrix, R L is the set of column labels selected from L;

[0019] The maximum trace of the matrix is ​​used as the metric for selecting the optimal submatrix, thereby transforming the first objective problem into the second objective problem where f s is the trace of the matrix;

[0020] The second objective problem is solved by using a genetic algorithm to obtain a set of index numbers of the selected columns in the Laplace matrix, that is, to obtain the optimal submatrix.

[0021] Furthermore, a genetic algorithm is used to solve the second objective problem to obtain a set of index numbers of the selected columns in the Laplace matrix, that is, to obtain the optimal submatrix, specifically:

[0022] Set the optimization variable to an n-dimensional vector:

[0023] x[i]=0or1

[0024] Where x[i] indicates whether the i-th column in the selected matrix is ​​selected, and the optimization variable is the set of x[i];

[0025] Set constraints on the number of selected columns

[0026]

[0027] Based on the above settings, the second objective problem is solved using a genetic algorithm to determine whether each column in the Laplace matrix is ​​selected, thereby obtaining the optimal submatrix.

[0028] Furthermore, based on the optimal submatrix, the connection relationship between each agent and other agents is re-determined, thereby constructing the expected subgraph of each agent, including:

[0029] According to the optimal submatrix Re-determine the connection relationship between each agent and other agents:

[0030]

[0031] For the i-th agent, according to the connection relationship between agents, the expected subgraph is:

[0032]

[0033] Where a[i] represents the adjacency matrix of the desired subgraph of the i-th agent, represents the element in the αth row and βth column in the Laplace matrix, d[i] represents the degree matrix of the expected subgraph of the i-th agent, and m is the number of columns of the optimal submatrix.

[0034] According to a second aspect of an embodiment of the present application, a cluster formation trajectory planning device based on submatrix selection is provided, comprising:

[0035] The graph construction module is used to abstract the cluster formation into a graph structure. The nodes of the graph are the agents in the cluster, the edges are the connection constraints between the agents, and the edge weight is the square of the Euclidean distance between the two agents, thereby constructing the Laplace matrix of the graph;

[0036] a submatrix selection module, configured to select a plurality of columns of the Laplace matrix based on the maximum trace of the matrix to form an optimal submatrix of the Laplace matrix;

[0037] An expected subgraph construction module is used to redetermine the connection relationship between each agent and other agents based on the optimal submatrix, thereby constructing an expected subgraph for each agent;

[0038] The trajectory planning module is used to perform cluster formation trajectory planning based on the desired subgraph of each agent.

[0039] According to a third aspect of an embodiment of the present application, a computer program product is provided, comprising a computer program / instruction, which implements the method described in the first aspect when executed by a processor.

[0040] According to a fourth aspect of the embodiments of the present application, there is provided an electronic device, including:

[0041] one or more processors;

[0042] a memory for storing one or more programs;

[0043] When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in the first aspect.

[0044] According to a fourth aspect of an embodiment of the present application, a computer-readable storage medium is provided, on which computer instructions are stored. When the instructions are executed by a processor, the steps of the method described in the first aspect are implemented.

[0045] The technical solutions provided by the embodiments of the present application may have the following beneficial effects:

[0046] Most existing distributed formation algorithms use fully connected graphs. Each agent considers the positional constraints of all other agents, introducing redundant constraints during trajectory optimization. As the cluster size increases, optimization efficiency decreases dramatically, limiting scalability. Simple methods for reducing connections, such as nearest neighbor connections, lose too much global information, resulting in poor formation performance.

[0047] This invention uses a submatrix selection method to sparsify connections, significantly improving efficiency while accurately capturing global information. This method strikes a good balance between trajectory optimization efficiency and formation performance. Compared to fully connected graphs, cluster trajectory planning efficiency on sparse graphs is exponentially improved, and this efficiency advantage becomes even more pronounced as the cluster size increases. This makes it suitable for larger-scale cluster formation obstacle avoidance navigation in complex environments.

[0048] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0050] Figure 1 The figure is a flowchart of a cluster formation trajectory planning method based on sub-matrix selection according to an exemplary embodiment.

[0051] Figure 2 The block diagram of a cluster formation trajectory planning device based on sub-matrix selection is shown according to an exemplary embodiment.

[0052] Figure 3 The figure is a schematic diagram of an electronic device according to an exemplary embodiment. DETAILED DESCRIPTION

[0053] Exemplary embodiments are described in detail herein, with examples illustrated in the accompanying drawings. When the following description refers to the drawings, identical numerals in different drawings represent identical or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with this application.

[0054] The terms used in this application are for the purpose of describing specific embodiments only and are not intended to limit this application. The singular forms "a," "the," and "the" used in this application are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" as used herein refers to and includes any or all possible combinations of one or more of the associated listed items.

[0055] This application proposes a cluster formation trajectory planning method based on submatrix selection. This algorithm can better capture the characteristics of the entire cluster, minimize the number of connections, and improve the efficiency of intelligent agent trajectory optimization. It is suitable for large-scale, low-computing distributed cluster formation obstacle avoidance flight in complex environments.

[0056] like Figure 1 As shown, this method includes the following steps:

[0057] Step S1: Abstract the cluster formation into a graph structure, where the nodes of the graph are the agents in the cluster, the edges are the connection constraints between the agents, and the edge weight is the square of the Euclidean distance between the two agents, thereby constructing the Laplace matrix of the graph;

[0058] Specifically, the agents in the cluster (including fixed-wing aircraft, multi-rotor aircraft, hybrid-wing aircraft, ships, vehicles and other unmanned or manned vehicles) are regarded as nodes, and the connection constraints are regarded as edges of the graph, so that the entire cluster formation can be abstracted as a graph structure. In order to analyze this structure, it is necessary to use the adjacency matrix, degree matrix and Laplace matrix of graph theory as analysis tools. In this invention, the square of the Euclidean distance between two agents is used as the weight of the adjacency matrix element. Assuming there are n agents, the graph formed is is a set of nodes, and the edges of the graph are The i-th node has a position vector The edge weight w ij =||p i -p j || 2 , ‖.‖ is the Euclidean distance metric. Therefore, the adjacency matrix A and degree matrix D of the graph can be determined.

[0059]

[0060] Therefore, the Laplace matrix is ​​L = DA, and the normalized Laplace matrix is

[0061] In the optimization problem, the loss function of formation coordination is set as in The Laplacian matrix representing the desired formation, with the Frobenius norm used as the distance metric. F .

[0062] Step S2: Based on the maximum trace of the matrix, select several columns in the Laplace matrix to form an optimal submatrix of the Laplace matrix, thereby achieving sparseness of the Laplace matrix;

[0063] According to the empirical formula Determine the number of columns m of the submatrix to be selected, and use the matrix maximum trace (maxtrace) as the metric for selecting the optimal submatrix. Because the formation gradient is transmitted through the Laplacian matrix during trajectory optimization, and each element of the Laplacian matrix except the diagonal elements represents the connection relationship between nodes, the Laplacian matrix is ​​selected as the matrix. This step is to find a The norm of the difference between the submatrix and the original matrix is Minimum, ξ=2or F represents the type of matrix norm, where ξ=F represents the F norm, Indicates that specific m columns are selected from L as submatrices, and the set of column labels selected from L is R L , R L There are m elements in

[0064]

[0065] Solution This is an NP-hard problem. An approximate solution can be obtained by using the matrix submodularity. The maximum trace of the submatrix is ​​selected as the submodular metric, that is, the maximum trace of the submatrix is ​​solved. where f s is the trace of the matrix.

[0066] A genetic algorithm is used to solve this problem, and the optimization variable is set to an n-dimensional vector:

[0067] x[i]=0or1

[0068] Where x[i] indicates whether the i-th column in the selected matrix is ​​selected, and the optimization variable is the set of x[i];

[0069] At the same time, in order to ensure that the number of selected columns is the same as the number selected at the beginning, add the following equality constraints:

[0070]

[0071] Step S3: Based on the optimal submatrix, redetermine the connection relationship between each agent and other agents, thereby constructing the expected subgraph of each agent;

[0072] When the algorithm solves an optimal solution R L * , according to R L * The sparse Laplace matrix is ​​obtained Here we are not directly Participate in the subsequent trajectory optimization, because directly using non-full rank This may cause gradient discontinuity during subsequent trajectory optimization.

[0073] In this application, according to Understand which agents the i-th agent is connected to (i.e. which agents’ trajectories are optimized):

[0074]

[0075] According to these relationships, when the i-th agent optimizes its trajectory, it only accepts the trajectories of connected agents. For the i-th agent, there is a new expected sub-formation. The geometry of this expected sub-formation is the i-th agent and the agents that it considers receiving the trajectory. Then, for the i-th agent, according to the selected submatrix structure, its expected subgraph can be obtained as:

[0076]

[0077] Where a[i] represents the adjacency matrix of the desired subgraph of the i-th agent, represents the element in the αth row and βth column of the original Laplace matrix, d[i] represents the degree matrix of the expected subgraph of the i-th agent, and m is R L The number of elements in .

[0078] Step S4: Based on the desired subgraph of each agent, cluster formation trajectory planning is performed.

[0079] Based on the expected subgraph of each agent, cluster formation trajectory planning can be performed based on any trajectory planning method that relies solely on the distance between agents to maintain formation. Specifically, for a formation of n drones, the fully connected Laplacian matrix corresponding to the expected formation is L des , the desired sparse matrix L is obtained by submatrix selection spr , according to L spr The connection relationship corresponding to each UAV can be obtained, that is, the trajectory information of other UAVs that each UAV should consider collecting. Compared with the fully connected graph, the number of trajectories that each UAV should consider is reduced. At the same time, the structure of the original fully connected graph can be retained as much as possible through sub-matrix selection, so that when the formation performs overall obstacle avoidance planning, the impact of the environment on the entire formation can be considered more.

[0080] Corresponding to the aforementioned embodiment of the cluster formation trajectory planning method based on sub-matrix selection, the present application also provides an embodiment of a cluster formation trajectory planning device based on sub-matrix selection.

[0081] Figure 2 The figure is a block diagram of a cluster formation trajectory planning device based on sub-matrix selection according to an exemplary embodiment.

[0082] Reference Figure 2 , the apparatus may include:

[0083] A graph construction module 21 is used to abstract the cluster formation into a graph structure, where the nodes of the graph are the agents in the cluster, the edges are the connection constraints between the agents, and the edge weight is the square of the Euclidean distance between two agents, thereby constructing the Laplace matrix of the graph;

[0084] a submatrix selection module 22 for selecting a plurality of columns in the Laplacian matrix based on the maximum trace of the matrix to form an optimal submatrix of the Laplacian matrix;

[0085] An expected subgraph construction module 23 is used to redetermine the connection relationship between each agent and other agents based on the optimal submatrix, thereby constructing an expected subgraph for each agent;

[0086] The trajectory planning module 24 is used to perform cluster formation trajectory planning based on the desired subgraph of each agent.

[0087] Regarding the apparatus in the above embodiment, the specific manner in which each module performs operations has been described in detail in the embodiment of the method, and will not be elaborated here.

[0088] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial description of the method embodiments. The device embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the present application scheme. A person of ordinary skill in the art can understand and implement it without paying any creative work.

[0089] Accordingly, the present application also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the above-mentioned cluster formation trajectory planning method based on sub-matrix selection.

[0090] Accordingly, the present application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned cluster formation trajectory planning method based on sub-matrix selection. Figure 3 As shown in FIG. 1 , a hardware structure diagram of a cluster formation trajectory planning device based on submatrix selection provided by an embodiment of the present invention is provided in any device with data processing capability, except Figure 3 In addition to the processor, memory, and network interface shown, any device with data processing capabilities in which the apparatus in the embodiment is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0091] Accordingly, the present application also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the cluster formation trajectory planning method based on submatrix selection as described above. The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities as described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (Flash Card), etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or is to be output.

[0092] Those skilled in the art will readily conceive of other embodiments of the present application after considering the specification and practicing the contents disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of this application and include common knowledge or customary techniques in the art that are not disclosed in this application.

[0093] It will be understood that the present application is not limited to the exact construction that has been described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof.

Claims

1. A cluster formation trajectory planning method based on submatrix selection, characterized in that: include: The cluster formation is abstracted into a graph structure, where the nodes of the graph are the agents in the cluster, the edges are the connection constraints between the agents, and the edge weight is the square of the Euclidean distance between the two agents, thereby constructing the Laplace matrix of the graph; Selecting a plurality of columns of the Laplacian matrix based on the maximum trace of the matrix to form an optimal submatrix of the Laplacian matrix; Re-determine the connection relationship between each agent and other agents based on the optimal submatrix, so as to construct the expected subgraph of each agent; Perform cluster formation trajectory planning based on the desired subgraph of each agent; The method of selecting a plurality of columns of the Laplacian matrix based on the maximum trace of the matrix to form an optimal submatrix of the Laplacian matrix includes: Determine the number of columns m selected by the submatrix = , is the number of columns of the Laplacian matrix; Constructing the first objective problem ,in It indicates that the submatrix formed by selecting specific m columns in the Laplace matrix L is the optimal submatrix, is the set of column labels selected from L; The maximum trace of the matrix is ​​used as the metric for selecting the optimal submatrix, thereby transforming the first objective problem into the second objective problem ,in is the trace of the matrix; The second objective problem is solved by using a genetic algorithm to obtain a set of index numbers of the selected columns in the Laplace matrix, that is, to obtain the optimal submatrix.

2. The method according to claim 1, characterized in that For a cluster formation with n agents, the graph formed is , is a set of nodes, and the edges of the graph are , the i-th node has position vector , where the edge weight , is the Euclidean distance metric; Laplacian matrix of a graph , where D is the degree matrix of the graph and A is the adjacency matrix of the graph: ， 。 3. The method according to claim 1, characterized in that The second objective problem is solved using a genetic algorithm to obtain a set of index numbers of the selected columns in the Laplace matrix, that is, to obtain the optimal submatrix, specifically: Set the optimization variable to an n-dimensional vector: ， in Indicates whether the i-th column in the selected matrix is ​​selected, and the optimization variable is A collection of Set constraints on the number of selected columns , Based on the above settings, the second objective problem is solved using a genetic algorithm to determine whether each column in the Laplace matrix is ​​selected, thereby obtaining the optimal submatrix.

4. The method according to claim 1, wherein Based on the optimal submatrix, the connection relationship between each agent and other agents is re-determined, thereby constructing the expected subgraph of each agent, including: According to the optimal submatrix , redefine the connection relationship between each agent and other agents: ， ， For the i-th agent, according to the connection relationship between agents, the expected subgraph is: ， ， Where a[i] represents the adjacency matrix of the desired subgraph of the i-th agent, represents the element in the αth row and βth column in the Laplace matrix, d[i] represents the degree matrix of the expected subgraph of the i-th agent, and m is the number of columns of the optimal submatrix.

5. A cluster formation trajectory planning device based on submatrix selection, characterized in that: include: The graph construction module is used to abstract the cluster formation into a graph structure. The nodes of the graph are the agents in the cluster, the edges are the connection constraints between the agents, and the edge weight is the square of the Euclidean distance between the two agents, thereby constructing the Laplace matrix of the graph; a submatrix selection module, configured to select a plurality of columns of the Laplace matrix based on the maximum trace of the matrix to form an optimal submatrix of the Laplace matrix; An expected subgraph construction module is used to redetermine the connection relationship between each agent and other agents based on the optimal submatrix, thereby constructing an expected subgraph for each agent; The trajectory planning module is used to plan cluster formation trajectories based on the desired subgraph of each agent; The method of selecting a plurality of columns of the Laplacian matrix based on the maximum trace of the matrix to form an optimal submatrix of the Laplacian matrix includes: Determine the number of columns m selected by the submatrix = , is the number of columns of the Laplacian matrix; Constructing the first objective problem ,in It indicates that the submatrix formed by selecting specific m columns in the Laplace matrix L is the optimal submatrix, is the set of column labels selected from L; The maximum trace of the matrix is ​​used as the metric for selecting the optimal submatrix, thereby transforming the first objective problem into the second objective problem ,in is the trace of the matrix; The second objective problem is solved by using a genetic algorithm to obtain a set of index numbers of the selected columns in the Laplace matrix, that is, to obtain the optimal submatrix.

6. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the method according to any one of claims 1 to 4 is implemented.

7. An electronic device, characterized in that: include: one or more processors; a memory for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to any one of claims 1 to 4.

8. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the instruction is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

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