Cluster formation trajectory planning method based on submatrix selection

Abstract

The invention discloses a cluster formation trajectory planning method based on submatrix selection, and the method comprises the steps: abstracting a cluster formation into a graph structure, enabling nodes of the graph to be intelligent agents in a cluster, enabling edges to be connection constraints between the intelligent agents, enabling the weight of the edges to be the square of the Euclidean distance between the two intelligent agents, and constructing a Laplacian matrix of the graph; based on the maximum trace of the matrix, selecting a plurality of columns in the Laplacian matrix to form an optimal sub-matrix of the Laplacian matrix; according to the optimal sub-matrix, re-determining a connection relationship between each agent and other agents, so as to construct an expected sub-graph of each agent; and performing cluster formation trajectory planning based on the expected sub-graph of each agent. The present distributed full-connection formation algorithm is improved, and the purpose is to realize larger-scale distributed cluster formation under the conditions of reducing connection constraints, improving optimization efficiency and ensuring formation performance by selecting sub-matrixes of a full-connection Laplacian matrix.

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 many fields such as cargo handling and formation performances. In order to alleviate the drawbacks of high computational complexity and poor fault tolerance of centralized swarm formations, many distributed swarm formation studies and inventions have emerged. However, most of them currently use fully connected graphs to describe cluster relationships, that is, drones need to consider the trajectories of all other drones for coordination, resulting in exponential growth in formation planning complexity as the size of the cluster increases, 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, for example, a single agent only collaborates with some neighboring agents, but 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, but the information obtained by this sparse strategy is too local and excessively loses the global characteristics of the entire cluster, resulting in poor formation maintenance effect in dense obstacle environments. Summary of the invention

[0007] In view of 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, including:

[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 weight of the edge is the square of the Euclidean distance between the two agents, thereby constructing the Laplace matrix of the graph;

[0010] Based on the maximum trace of the matrix, a number of columns in the Laplacian matrix are selected to form an optimal submatrix of the Laplacian matrix;

[0011] Re-determine the connection relationship between each agent and other agents according to 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 resulting graph 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 the 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] Further, based on the maximum trace of the matrix, several columns in the Laplace matrix are selected to form an optimal submatrix of the Laplace matrix, including:

[0017] Determine the number of columns to select from the submatrix n is the number of columns of the Laplacian matrix;

[0018] Constructing the first objective problem in represents the submatrix formed by selecting specific m columns from 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, 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, which is 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, according to the optimal submatrix, the connection relationship between each agent and other agents is re-determined, so as to construct 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 Laplacian matrix, d[i] represents the degree matrix of the expected subgraph of the ith 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, including:

[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 weight of the edge is the square of the Euclidean distance between two agents, so as to construct the Laplace matrix of the graph;

[0036] A submatrix selection module, used for selecting a number of columns in 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 intelligent agent and other intelligent agents according to the optimal submatrix, so as to construct an expected subgraph for each intelligent 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 an embodiment 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, and when the instructions are executed by a processor, the steps of the method described in the first aspect are implemented.

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

[0046] Most existing distributed formation algorithms use fully connected graphs, where a single agent considers the position constraints of all other agents, which brings redundant constraints when optimizing trajectories. As the size of the cluster increases, the optimization efficiency drops sharply, limiting the scale increase. Some simple methods to reduce connections, such as the nearest neighbor connection method, lose too much global information, resulting in poor formation performance.

[0047] The present invention adopts the method of submatrix selection to perform connection sparseness, which greatly improves efficiency while accurately grasping global information, and well balances trajectory optimization efficiency and formation performance. Compared with the fully connected graph, the cluster trajectory planning efficiency under the sparse graph is improved by multiples, and as the cluster size increases, the efficiency advantage becomes more obvious. It is 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 present invention is a flowchart of a cluster formation trajectory planning method based on sub-matrix selection according to an exemplary embodiment.

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

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

[0053] Here, exemplary embodiments are described in detail, and examples thereof are shown in the accompanying drawings. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The implementations described in the following exemplary embodiments do not represent all implementations consistent with the present application.

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

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

[0056] like Figure 1 As shown, the method comprises 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 weight of the edge is the square of the Euclidean distance between 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 the 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 the present 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 to in The Laplacian matrix representing the desired formation, with the Frobenius norm used in 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, so as to achieve 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 ​​used as the selected matrix. This step is to find a The norm of the difference between the submatrix and the original matrix is minimum, ξ=2or F indicates the type of matrix norm, where ξ=F indicates 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 number selected at the beginning, add the following equality constraints:

[0070]

[0071] Step S3: re-determine the connection relationship between each agent and other agents according to the optimal submatrix, so as to construct the expected subgraph of each agent;

[0072] When the algorithm solves an optimal solution R L * , according to R L * The sparse Laplacian 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 received for optimization):

[0074]

[0075] According to these relationships, when the ith agent optimizes the trajectory, it only accepts the trajectories of the connected agents. For the ith agent, there is a new expected sub-formation. The geometry of this expected sub-formation is the ith agent and the agents that it considers receiving the trajectory. Then, for the ith agent, according to the selected sub-matrix structure, its expected sub-graph 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 ith agent, and m is R L The number of elements in .

[0078] Step S4: Perform cluster formation trajectory planning based on the desired subgraph of each agent.

[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 Laplace 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 overall 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 present invention 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 device 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 weight of the edge is the square of the Euclidean distance between two agents, so as to construct the Laplace matrix of the graph;

[0084] A submatrix selection module 22, configured to select a number 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 according to the optimal submatrix, so as to construct an expected subgraph for each agent;

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

[0087] Regarding the device 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 embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only 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 cluster formation trajectory planning method based on sub-matrix selection as described above.

[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, 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 capability 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 capability, 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 capability 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 capability. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, 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 appreciate other embodiments of the present application after considering the specification and practicing the contents disclosed herein. The present application is intended to cover any variations, uses or adaptations of the present application, which follow the general principles of the present application and include common knowledge or customary technical means in the art that are not disclosed in the present application.

[0093] It should 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 weight of the edge is the square of the Euclidean distance between the two agents, thereby constructing the Laplace matrix of the graph; Based on the maximum trace of the matrix, a number of columns in the Laplacian matrix are selected to form an optimal submatrix of the Laplacian matrix; Re-determine the connection relationship between each agent and other agents according to the optimal submatrix, so as to construct the expected subgraph of each agent; Cluster formation trajectory planning is performed based on the desired subgraph of each agent.

2. The method according to claim 1, characterized in that For a cluster formation with n agents, the resulting graph 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; The Laplacian matrix of the graph is L = D – A, 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 Based on the maximum trace of the matrix, a number of columns in the Laplacian matrix are selected to form an optimal submatrix of the Laplacian matrix, including: Determine the number of columns to select from the submatrix n is the number of columns of the Laplacian matrix; Constructing the first objective problem in represents the submatrix formed by selecting specific m columns from the Laplace matrix L, namely the optimal submatrix, R L 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. where f s 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.

4. The method according to claim 3, characterized in that 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, which is specifically: Set the optimization variable to an n-dimensional vector: x[i]=0or1 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]; 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.

5. The method according to claim 1, characterized in that According to the optimal submatrix, the connection relationship between each agent and other agents is re-determined, so as to construct the expected subgraph of each agent, including: According to the optimal submatrix Re-determine 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 Laplacian matrix, d[i] represents the degree matrix of the expected subgraph of the ith agent, and m is the number of columns of the optimal submatrix.

6. 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 weight of the edge is the square of the Euclidean distance between two agents, so as to construct the Laplace matrix of the graph; A submatrix selection module, used for selecting a number of columns in 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 intelligent agent and other intelligent agents according to the optimal submatrix, so as to construct an expected subgraph for each intelligent agent; The trajectory planning module is used to perform cluster formation trajectory planning based on the desired subgraph of each agent.

7. 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 5 is implemented.

8. 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 5.

9. 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 5 are implemented.

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