A distributed optimal formation method of a cluster unmanned system

Abstract

The application discloses a kind of distributed optimal formation methods of cluster unmanned system, it is related to control and information technology field.The method comprises: establishing the undirected graph corresponding to cluster unmanned system, and establishing first optimal formation problem according to undirected graph;Based on the preset formation shape, the first optimal formation problem is converted into the second optimal formation problem containing two optimization variables;Two optimization variables are respectively the matching relationship of unmanned platform and formation configuration vertex, center point;The second optimal formation problem is decomposed into formation matching problem and center point positioning problem;The optimal matching relationship is obtained according to formation matching problem solution, and the optimal center point is obtained according to center point positioning problem solution.The application can solve optimal formation problem under complex conditions, so that the system state of all unmanned platforms finally converges to optimal solution, and ideal formation structure is formed in optimal formation position with optimal formation matching relationship.

Description

Technical Field

[0001] This invention relates to the fields of control and information technology, and in particular to a distributed optimal formation method for swarm unmanned systems. Background Technology

[0002] Swarm unmanned systems are widely used in fields such as collaborative transportation, regional patrol, and environmental monitoring. The optimal formation problem of swarm unmanned systems refers to a group of unmanned platforms cooperating to form and maintain a specific geometric configuration in their positional relationships.

[0003] Traditional optimal formation methods assume that the position of each unmanned platform in the formation is predetermined. However, in large-scale formation tasks, it is impractical to manually assign the role of each unmanned platform in the formation beforehand. Therefore, it is necessary to consider the allocation of unmanned platforms to the formation positions, i.e., the formation matching problem. When the specific position of the target formation is unknown, the optimal formation problem also needs to find the optimal center point position (also known as the optimal center point), i.e., the center point localization problem.

[0004] Most current optimal formation methods only consider a single subproblem of the optimal formation problem, making it difficult to quickly and effectively obtain the optimal solutions to the formation matching problem and the center point location problem.

[0005] Therefore, existing technologies still need improvement and development. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a distributed optimal formation method for clustered unmanned systems, addressing the aforementioned deficiencies of existing technologies. This method aims to solve the problem that most existing optimal formation methods only consider a single subproblem of the optimal formation problem, making it difficult to quickly and effectively obtain the optimal solutions to the formation matching problem and the center point location problem.

[0007] The technical solution adopted by this invention to solve the problem is as follows:

[0008] This invention provides a distributed optimal formation method for a clustered unmanned system, the method comprising:

[0009] An undirected graph is pre-established to characterize the network communication topology of the cluster unmanned system. Based on the undirected graph, a first optimal formation problem of the cluster unmanned system is established. The overall optimization objective of the first optimal formation problem is to minimize the sum of the distances from all unmanned platforms to their respective matching vertices.

[0010] Based on the preset formation shape, the first optimal formation problem is transformed into a second optimal formation problem with two optimization variables; the two optimization variables are the matching relationship between the unmanned platform and the vertex of the formation configuration, and the center point;

[0011] The second optimal formation problem is decomposed into a center point localization problem and a formation matching problem. The decomposition method includes: based on the matching relationship between the unmanned platform and the vertices of the formation configuration, the second optimal formation problem is transformed into an optimization problem only about the center point, thus obtaining the center point localization problem; based on the Caro-Kuhn-Tucker condition and the center point localization problem, the optimal solution satisfying condition of the center point localization problem is determined; and based on the optimal solution satisfying condition of the center point localization problem and the second optimal formation problem, the formation matching problem is obtained.

[0012] The optimal matching relationship is obtained by solving the formation matching problem, and the optimal center point is obtained by solving the center point positioning problem.

[0013] The beneficial effects of this invention are as follows: In this embodiment, an undirected graph representing the network communication topology of a cluster of unmanned systems is pre-established. A first optimal formation problem for the cluster of unmanned systems is then established based on this undirected graph. The overall optimization objective of the first optimal formation problem is to minimize the sum of distances from all unmanned platforms to their respective matching vertices. Based on a preset formation shape, the first optimal formation problem is transformed into a second optimal formation problem with two optimization variables: the matching relationship between the unmanned platform and the vertices of the formation configuration, and the center point. The second optimal formation problem is decomposed into a center point location problem and a formation matching problem. The decomposition method includes: based on the matching relationship between the unmanned platform and the vertices of the formation configuration, the second optimal formation problem is transformed into an optimization problem only concerning the center point, resulting in the center point location problem; based on the Cartesian-Kun-Tucker condition and the center point location problem, the optimal solution condition for the center point location problem is determined; based on the optimal solution condition for the center point location problem and the second optimal formation problem, the formation matching problem is obtained; the optimal matching relationship is obtained by solving the formation matching problem, and the optimal center point is obtained by solving the center point location problem. This invention can solve the optimal formation problem under complex conditions, enabling the system state of all unmanned platforms to eventually converge to the optimal solution, and forming an ideal formation structure at the optimal formation position with the optimal formation matching relationship. Attached Figure Description

[0014] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0015] Figure 1 This is a basic flowchart illustrating the distributed optimal formation method for clustered unmanned systems provided in this embodiment of the invention.

[0016] Figure 2 This is a complete flowchart of the distributed optimal formation method for clustered unmanned systems provided in this embodiment of the invention.

[0017] Figure 3 This is a schematic diagram of forming two concentric circle formations provided in an embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram of the convergence trajectory when forming a concentric circle formation configuration, provided in an embodiment of the present invention.

[0019] Figure 5 This is a schematic diagram of the formation of the three letters BIT provided in an embodiment of the present invention.

[0020] Figure 6 This is a schematic diagram of the convergence trajectory when forming the three letters BIT in the formation configuration provided in the embodiment of the present invention.

[0021] Figure 7 This is a schematic diagram illustrating the solution to the mismatch phenomenon provided by an embodiment of the present invention. Detailed Implementation

[0022] This invention discloses a distributed optimal formation method for swarm unmanned systems. To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention.

[0023] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that when we say an element is “connected” or “coupled” to another element, it can be directly connected or coupled to the other element, or there may be intermediate elements. Furthermore, “connected” or “coupled” as used herein can include wireless connections or wireless coupling. The term “and / or” as used herein includes all or any units and all combinations of one or more associated listed items.

[0024] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless specifically defined as herein.

[0025] To address the aforementioned shortcomings of existing technologies, this invention provides a distributed optimal formation method for clustered unmanned systems, such as... Figure 1 As shown, the method includes:

[0026] Step S100: First, establish an undirected graph in advance to characterize the network communication topology of the cluster unmanned system, and establish the first optimal formation problem of the cluster unmanned system based on the undirected graph; the overall optimization objective of the first optimal formation problem is to minimize the sum of the distances from all unmanned platforms to their respective matching vertices.

[0027] Specifically, the first step is to establish the network topology of the clustered unmanned system. This is done using an undirected graph. Characterizes the network communication topology of a cluster of unmanned systems, where Represents a set of nodes. Represents the number of unmanned platforms. Denotes the set of edges. It is a node The neighborhood group, It is a node The degree. Representing an undirected graph The adjacency matrix of , where the is the adjacency matrix of . The first line The elements are denoted as If the side ,but =1, otherwise =0. Representing Euclidean space, express 3D space, undirected graph The Laplace matrix is ​​defined as , of which The first line The elements are denoted as The value is and , .

[0028] Secondly, it is necessary to construct the optimal formation problem for the clustered unmanned system. In this embodiment, the initially constructed optimal formation problem is defined as the first optimal formation problem. For the first optimal formation problem, consider the formation process... It consists of several unmanned platforms, and its goal is to form a collaborative system. A formation configuration with predetermined positions, where each unmanned platform occupies one of the positions. Definition The initial position of the unmanned platform. , The vector formed, where yes The One element, represent transpose, yes 3D space yes 3D space It means any element in . yes The desired positions for the unmanned platforms to form an ideal formation configuration, among which , It is the apex of the formation configuration. yes The Transpose of an element It means any element in .

[0029] The expression for the first optimal formation problem of a swarm unmanned system is as follows:

[0030] ;

[0031] in Therefore The cost function for the variable, For unmanned platforms and formation configuration vertices The matching relationship between them Represents unmanned platforms Matching vertices ,otherwise . It is an unmanned platform The decision variables, among which yes The One element, yes 3D space It represents the overall matching relationships. yes The Transpose of each element.

[0032] Furthermore, the local objective function of the first optimal formation problem Represents unmanned platforms initial position and its matching vertex The overall optimization objective is to minimize the sum of the distances from all unmanned platforms to their matching vertices.

[0033] Furthermore, the equality constraints of the first optimal formation problem are used to reflect that each vertex matches only one unmanned platform, and each unmanned platform matches only one vertex. Specifically, the equality constraints... and Each vertex represents a vertex. Only one unmanned platform can be matched. and each unmanned platform Only one vertex can be matched. .

[0034] Furthermore, the inequality constraints of the first optimal formation problem are used to reflect the state constraints on the desired formation configuration. Specifically, the inequality constraints... , It is a state constraint on the desired formation configuration, where It is a differentiable convex function. yes The Each element.

[0035] Step S200: Based on the preset formation shape, the first optimal formation problem is transformed into a second optimal formation problem with two optimization variables; the two optimization variables are the matching relationship between the unmanned platform and the vertex of the formation configuration, and the center point.

[0036] Specifically, set It is the center point of the desired formation configuration. .make , Represents vertices To the center point The relative position. Although the expected formation position The relative positions of the vertices are unknown, but the formation shape is predetermined, and therefore the relative positions of the vertices are also known. And the relative position of the vertex to the center point This is known. Therefore, the first optimal formation problem can be reformulated as the second optimal formation problem, as shown in the following expression:

[0037] ;

[0038] The optimization variables for the second optimal formation problem include: binary matching relationships. and center point The matching relationship here. Specifically, it refers to the matching relationship between unmanned platforms and the vertices of the formation configuration.

[0039] Step S300: Decompose the second optimal formation problem into a center point localization problem and a formation matching problem; the decomposition method includes: based on the matching relationship between the unmanned platform and the vertices of the formation configuration, transform the second optimal formation problem into an optimization problem only about the center point, thus obtaining the center point localization problem; based on the Caro-Kun-Tucker condition and the center point localization problem, determine the optimal solution satisfaction condition of the center point localization problem; and based on the optimal solution satisfaction condition of the center point localization problem and the second optimal formation problem, obtain the formation matching problem.

[0040] The second-optimal formation problem is broken down into two sub-problems: formation matching and center point localization. Specifically, for any given matching relationship... The second optimal formation problem degenerates into a problem only concerning the center point under this matching relation. The optimization problem, namely the center point location problem. It can be used to find the optimal center point, and the expression is as follows:

[0041] ;

[0042] in In the matching relationship Unmanned platform The relative positions of the matched vertices to the center point. Represents vertices To the center point The relative position.

[0043] Center point location problem The Lagrange function is shown below:

[0044] ;

[0045] in , ; yes The element transpose, These are the dual variables of the inequality constraints. The set of non-negative real numbers.

[0046] Based on the Karush–Kuhn–Tucker conditions (KKT conditions), the problem of center point location can be understood. The optimal solution satisfies the following conditions:

[0047] ;

[0048] Among them, the center point location problem The optimal solution includes , ; It is the optimal center point. It is the optimal dual variable. Pointer function pairs Find the gradient of the partial derivative.

[0049] The problem of center point location Substituting the expression for the optimal solution satisfying the condition into the expression for the second optimal formation problem, and ignoring constants irrelevant to the optimization variables, we obtain another expression that only relates to the matching relationship. The optimization problem, namely the formation matching problem. . The expression used to solve the matching relationship between unmanned platforms and the vertices of the formation configuration is as follows:

[0050] ;

[0051] in Describes unmanned platform With the apex of the formation The matching cost.

[0052] Step S400: Solve the formation matching problem to obtain the optimal matching relationship, and solve the center point positioning problem to obtain the optimal center point.

[0053] Specifically, the formation matching problem is used to solve the matching relationship between the unmanned platform and the vertices of the formation configuration, and the solution is the optimal matching relationship; the center point location problem is used to solve the center point of the formation, and the solution is the optimal center point.

[0054] In one implementation, the optimal matching relationship is obtained by solving the formation matching problem, including:

[0055] By replacing the binary constraints with box constraints, the formation matching problem is relaxed to obtain the relaxed formation matching problem.

[0056] Construct a distributed dual problem based on the relaxed formation matching problem;

[0057] Based on the distributed dual problem, a formation matching algorithm is established using the consistent alternating vector multiplier method, and the optimal matching relationship is obtained by solving the algorithm.

[0058] Specifically, due to Binary constraints, formation matching problem Since it is non-convex, finding its optimal or even feasible solution is extremely difficult. Therefore, box constraints are needed. Alternate binary constraints Regarding the formation matching problem Relaxation is applied to facilitate the solution. The relaxed formation matching problem. The expression is as follows:

[0059] ;

[0060] Relaxed formation matching problem This is a convex optimization problem. Let's define them separately. The optimal solution set is , The optimal solution set is They satisfy the relationship It should be noted that when the matching cost... When it is a special value, The optimal solution does not belong to the binary set. This special case is called a mismatch phenomenon.

[0061] Relaxed formation matching problem The equivalent expression is:

[0062] ;

[0063] in , yes transpose, yes The One element, It is a set of all elements that are 1. 3D column vector, yes The transpose of .

[0064] Relaxed formation matching problem The equivalent expression of the Lagrange function for:

[0065] ;

[0066] in and , It is the dual variable of the equality constraint. yes The transpose of .

[0067] set up ,in yes The The dual problem is established based on the equivalent expression of the formation matching problem, using 1 element. Its expression is:

[0068] ;

[0069] in:

[0070] ;

[0071] represent Individual box constraints Cartesian product; It is a mathematical process, referring to Minimize the variables.

[0072] To implement the distributed algorithm, this embodiment assigns a local dual variable to each unmanned platform. In order to obtain the dual problem The corresponding distributed dual problem Its expression is:

[0073] ;

[0074] It has been redefined , yes The Transpose of an element yes 3D space. Assuming the undirected graph of the network topology of a clustered unmanned system is connected (an undirected graph that is connected can also be called an undirected connected graph), then... Equivalent to This establishes the distributed dual problem of the formation matching problem. .against A distributed dual consistent alternating vector multiplier method (DC-ADMM algorithm) is designed using the Consistent Alternating Vector Multiplier Method (CADMM), which yields a formation matching algorithm that can be used to solve for optimal matching relationships.

[0075] In one implementation, the formation matching algorithm includes:

[0076] Each unmanned platform is pre-defined to include four state variables: the original variable of the current iteration, the dual variable of the equality constraint, the Lagrange multiplier of the equality constraint, and the Lagrange multiplier of the consistency constraint.

[0077] Each unmanned platform receives the dual variables of the equality constraints from its neighboring nodes, uses them to iteratively update its own four state variables, and broadcasts the iteratively updated dual variables of the equality constraints to all neighboring nodes until a preset convergence target or a preset number of iterations is reached, thus obtaining the optimal matching relationship.

[0078] Specifically, each unmanned platform has four state variables. , respectively representing the The unmanned platform in the first The original variables of the next iteration Dual variables of equality constraints (Also known as the formation matching problem) Dual variables), Lagrange multipliers of equality constraints Lagrange multipliers with consistency constraints .

[0079] The iterative steps of the formation matching algorithm are as follows:

[0080] ;

[0081] in , These are intermediate variables introduced to simplify the expression of the algorithm.

[0082] ;

[0083] ;

[0084] , , , , , These are all sub-steps of the formation matching algorithm; , It is a constant step size. In the formation matching algorithm, each unmanned platform... From neighboring nodes Receiving Update all of its own state variables, and then iterate through the updated variables. The algorithm broadcasts to all neighboring nodes, making it a fully distributed algorithm. Furthermore, it only transmits one variable per iteration, resulting in low communication costs. While many existing algorithms involve solving sub-optimization problems during their iterative processes, this algorithm updates the state using only simple algebraic operations, leading to lower computational complexity.

[0085] For example, the overall process of the formation matching algorithm mainly includes the following steps:

[0086] 1. Configure each unmanned platform With variables ;

[0087] 2. Initialization , , , , ;

[0088] 3. Each unmanned platform Parallel execution: from neighboring nodes Receiving , , , , ;

[0089] 4. Send to neighboring nodes broadcast ;

[0090] 5. Order This continues until the algorithm converges or the number of iterations reaches a preset value.

[0091] In one implementation, after the steps of reaching a preset convergence target or a preset number of iterations are completed, the following steps are also included:

[0092] If there is a matching relationship between an unmanned platform and a vertex in the formation configuration that is in the open interval between 0 and 1, then a random value is applied to the matching cost of the matching relationship until all matching relationships are 0 or 1; wherein, a matching relationship of 1 indicates that the unmanned platform matches the vertex, and a matching relationship of 0 indicates that the unmanned platform does not match the vertex.

[0093] Specifically, this embodiment also addresses the formation matching problem. And the problem of grouping after relaxation A perturbation-based formation matching algorithm (PDC-ADMM algorithm) was proposed to solve the mismatch problem. The steps of the perturbation-based formation matching algorithm are as follows:

[0094] When executing the formation matching algorithm, continue looping through each unmanned platform until the algorithm converges or the number of iterations reaches a preset value. implement:

[0095] If elements exist , , then execute , until all elements All are either 0 or 1. Among them... It is a random value.

[0096] In one implementation, the optimal center point is obtained by solving the center point localization problem, including:

[0097] Construct an equivalent saddle point problem based on the distributed form of the central point localization problem;

[0098] A center point localization algorithm is established based on the equivalent saddle point problem, and the optimal center point is obtained by solving the algorithm.

[0099] Specifically, the problem of center point location The distributed form can be expressed as:

[0100] ;

[0101] It has been redefined , yes The Transpose of an element yes The One variable, yes The One variable, Indicates unmanned platform The cost function.

[0102] Center point location problem The distributed form of the Lagrange function can be expressed as:

[0103] ;

[0104] in It is the dual variable of the consistency constraint; yes transpose, It is an array where all elements are 1. Dimensional column vector.

[0105] set up Then the problem of center point location The distributed form can be equivalently expressed as the following saddle point problem, thus obtaining the equivalent saddle point problem. :

[0106] ;

[0107] Addressing the problem of center point location Equivalent saddle point problem We designed a distributed optimistic gradient ascent and descent algorithm (D-OGDA), which is a center point localization algorithm that can be used to solve for the optimal center point.

[0108] In one implementation, the center point localization algorithm includes:

[0109] Each unmanned platform is defined to include three state variables, which represent the central point of the current iteration, the dual variable of the consistency constraint, and the dual variable of the inequality constraint, respectively.

[0110] Each unmanned platform receives the current iteration's center point and the dual variable of the consistency constraint from its neighboring nodes to iteratively update its three state variables. It then broadcasts the iteratively updated center point and the iteratively updated dual variable of the consistency constraint to all neighboring nodes until a preset convergence target or a preset number of iterations is reached, thus obtaining the optimal center point.

[0111] Specifically, each unmanned platform is configured to have three state variables. , respectively representing the The unmanned platform in the first The center point of the next iteration Dual variables of consistency constraints Dual variables of inequality constraints The center point localization algorithm can be described as follows:

[0112] ;

[0113] ;

[0114] ;

[0115] in , , These are all sub-steps of the center point localization algorithm; It is a fixed step size. , It is a bounded constant. Represents projection onto a set Above. In the center point localization algorithm, each unmanned platform... From neighboring nodes Receiving and Two state variables are used to update all state variables of themselves, and then the updated state variables are iterated over. , The algorithm broadcasts to all neighboring nodes, making it a fully distributed algorithm.

[0116] For example, the overall process of the center point localization algorithm mainly includes the following steps:

[0117] 1. Configure each unmanned platform With variables ;

[0118] 2. Initialization: , , , ;

[0119] 3. Cycle through each unmanned platform Parallel execution: from neighboring nodes Receiving , , , , ;

[0120] 4. Send to neighboring nodes broadcast , ;

[0121] 5. Order This continues until the algorithm converges or the number of iterations reaches a preset value.

[0122] Figure 2 The following is a complete flowchart of the method in this embodiment. The method in this embodiment will be further explained below with three simulation examples. The first two examples consider the case where the algorithm forms different formation configurations with different numbers of unmanned platforms. The third example verifies the case where the algorithm solves the mismatch phenomenon.

[0123] The first example involves 24 unmanned platforms performing a formation task, with the desired formation configuration consisting of two concentric circles. The network topology of the swarm unmanned system is a randomly generated undirected connected graph, and nonlinear inequality constraints represent obstacle avoidance. The constraint function is... ,in It is the center of the obstacle. It is the safe distance from obstacles. Figure 3 The diagram illustrates the formation of unmanned platforms, where red dots represent the randomly generated initial positions of the unmanned platforms, green dots represent the desired final formation configuration of the unmanned platforms, and black dashed lines represent the matching relationship between the unmanned platforms and the vertices of the formation. Figure 4 The left side shows the matching relationships calculated by the formation matching algorithm as the number of iterations increases. and the optimal solution relative error between The right side shows the center point calculated by the center point localization algorithm. and the optimal solution relative error The overall result reflects the convergence of the formation matching algorithm and the center point localization algorithm.

[0124] The second example involves 34 unmanned platforms performing a formation task, forming a desired formation configuration resembling the letters BIT. The network topology of the swarm unmanned system is a randomly generated undirected connected graph, employing linear constraint functions. ,in It is a constant vector. Figure 5 This demonstrates the formation of unmanned platforms. Figure 6 The convergence of the formation matching algorithm and the center point localization algorithm is demonstrated.

[0125] The third example is five unmanned platforms performing a formation mission. Figure 7 This demonstrates how the perturbation-based formation matching algorithm, after introducing a perturbation strategy, improves performance in specific matching costs. , The convergence results verified that the algorithm can solve the mismatch problem.

[0126] In summary, this invention presents a distributed optimal formation method for swarm unmanned systems under complex constraints, primarily composed of a perturbation-based formation matching algorithm and a center point localization algorithm. It can solve optimal formation problems with coupled equality constraints, nonlinear inequality constraints, and binary set constraints, ensuring that the system states of all unmanned platforms eventually converge to the optimal solution, forming an ideal formation structure at the optimal formation position with the optimal formation matching relationship. The specific technical contributions and beneficial effects include:

[0127] 1. The optimal formation problem for swarm unmanned systems considered in this invention addresses the situation where the matching relationship between unmanned platforms and the vertices of the formation configuration, as well as the formation positions, are unknown. Compared to the case where the roles of unmanned platforms are predetermined, it requires additional solving for the matching relationship. The optimal formation problem solved by this implementation method not only involves linear equality constraints but also includes nonlinear inequality constraints and binary set constraints. Compared to the case containing only equality constraints, solving the nonlinear inequality constraints is more difficult, and the non-convex binary set constraints make the problem particularly complex.

[0128] 2. The algorithm proposed in this invention is fully distributed, involves only simple algebraic operations, does not require solving sub-optimization problems, has low computational complexity and communication cost, and does not increase with the scale of the unmanned platform.

[0129] 3. The algorithm designed in this invention can handle mismatch phenomena and ensure that the optimal integer solution to the formation matching problem is obtained.

[0130] In summary, this invention discloses a distributed optimal formation method for swarm unmanned systems, relating to the fields of control and information technology. The method includes: pre-establishing an undirected graph to characterize the network communication topology of a cluster of unmanned systems; establishing a first optimal formation problem for the cluster of unmanned systems based on the undirected graph; the overall optimization objective of the first optimal formation problem is to minimize the sum of distances from all unmanned platforms to their respective matching vertices; based on a preset formation shape, transforming the first optimal formation problem into a second optimal formation problem with two optimization variables; the two optimization variables are the matching relationship between the unmanned platforms and the vertices of the formation configuration, and the center point; decomposing the second optimal formation problem into a center point location problem and a formation matching problem; the decomposition method includes: based on the matching relationship between the unmanned platforms and the vertices of the formation configuration, transforming the second optimal formation problem into an optimization problem only concerning the center point, obtaining the center point location problem; based on the Cartesian-Kun-Tucker condition and the center point location problem, determining the optimal solution condition for the center point location problem; obtaining the formation matching problem based on the optimal solution condition for the center point location problem and the second optimal formation problem; solving the formation matching problem to obtain the optimal matching relationship, and solving the center point location problem to obtain the optimal center point. This invention can solve the optimal formation problem under complex conditions, enabling the system state of all unmanned platforms to eventually converge to the optimal solution, and forming an ideal formation structure at the optimal formation position with the optimal formation matching relationship.

[0131] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A distributed optimal formation method for a clustered unmanned system, characterized in that, The method includes: An undirected graph is pre-established to characterize the network communication topology of the cluster unmanned system. Based on the undirected graph, a first optimal formation problem of the cluster unmanned system is established. The overall optimization objective of the first optimal formation problem is to minimize the sum of the distances from all unmanned platforms to their respective matching vertices. Based on the preset formation shape, the first optimal formation problem is transformed into a second optimal formation problem with two optimization variables; the two optimization variables are the matching relationship between the unmanned platform and the vertex of the formation configuration, and the center point; The second optimal formation problem is decomposed into a center point localization problem and a formation matching problem. The decomposition method includes: based on the matching relationship between the unmanned platform and the vertices of the formation configuration, the second optimal formation problem is transformed into an optimization problem only about the center point, thus obtaining the center point localization problem; based on the Caro-Kuhn-Tucker condition and the center point localization problem, the optimal solution satisfying condition of the center point localization problem is determined; and based on the optimal solution satisfying condition of the center point localization problem and the second optimal formation problem, the formation matching problem is obtained. The optimal matching relationship is obtained by solving the formation matching problem, and the optimal center point is obtained by solving the center point positioning problem.

2. The distributed optimal formation method for a clustered unmanned system according to claim 1, characterized in that, The first optimal formation problem also includes: equality constraints to reflect that each vertex matches only one unmanned platform and each unmanned platform matches only one vertex.

3. The distributed optimal formation method for a clustered unmanned system according to claim 1, characterized in that, The first optimal formation problem also includes: inequality constraints, which reflect the state constraints on the desired formation configuration.

4. The distributed optimal formation method for a clustered unmanned system according to claim 1, characterized in that, The optimal matching relationship is obtained by solving the formation matching problem, including: By replacing the binary constraints with box constraints, the formation matching problem is relaxed to obtain the relaxed formation matching problem. Construct a distributed dual problem based on the relaxed formation matching problem; Based on the distributed dual problem, a formation matching algorithm is established using the consistent alternating vector multiplier method, and the optimal matching relationship is obtained by solving the algorithm.

5. The distributed optimal formation method for a clustered unmanned system according to claim 4, characterized in that, The formation matching algorithm includes: Each unmanned platform is pre-defined to include four state variables: the original variable of the current iteration, the dual variable of the equality constraint, the Lagrange multiplier of the equality constraint, and the Lagrange multiplier of the consistency constraint. Each unmanned platform receives the dual variables of the equality constraints from its neighboring nodes, uses them to iteratively update its own four state variables, and broadcasts the iteratively updated dual variables of the equality constraints to all neighboring nodes until a preset convergence target or a preset number of iterations is reached, thus obtaining the optimal matching relationship.

6. The distributed optimal formation method for a clustered unmanned system according to claim 5, characterized in that, After the preset convergence target or preset number of iterations is reached, the following steps are also included: If there is a matching relationship between an unmanned platform and a vertex in the formation configuration that is in the open interval between 0 and 1, then a random value is applied to the matching cost of the matching relationship until all matching relationships are 0 or 1; wherein, a matching relationship of 1 indicates that the unmanned platform matches the vertex, and a matching relationship of 0 indicates that the unmanned platform does not match the vertex.

7. The distributed optimal formation method for a clustered unmanned system according to claim 1, characterized in that, The optimal center point is obtained by solving the center point location problem, including: Construct an equivalent saddle point problem based on the distributed form of the central point localization problem; A center point localization algorithm is established based on the equivalent saddle point problem, and the optimal center point is obtained by solving the algorithm.

8. The distributed optimal formation method for a clustered unmanned system according to claim 7, characterized in that, The center point localization algorithm includes: Each unmanned platform is defined to include three state variables, which represent the central point of the current iteration, the dual variable of the consistency constraint, and the dual variable of the inequality constraint, respectively. Each unmanned platform receives the current iteration's center point and the dual variable of the consistency constraint from its neighboring nodes to iteratively update its three state variables. It then broadcasts the iteratively updated center point and the iteratively updated dual variable of the consistency constraint to all neighboring nodes until a preset convergence target or a preset number of iterations is reached, thus obtaining the optimal center point.

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