Cluster unmanned aerial vehicle multi-target interception decision-making method

Abstract

The invention relates to the field of multi-target interception decision making, in particular to a cluster unmanned aerial vehicle multi-target interception decision making method, which comprises the following steps: constructing an attack and defense game model of an unmanned aerial vehicle cluster in a three-dimensional space, decomposing the attack and defense game of the unmanned aerial vehicle cluster into a plurality of multi-defense games from a many-to-many game, and setting a game value function to represent targets of two game parties; wherein convex optimization conversion is carried out on a game value function to obtain an optimal interception point in real time, maximum interception matching of multiple multi-prevention-one games is achieved through maximum matching of the conflict bipartite graph with the weight, and meanwhile the maximum matching problem of the conflict bipartite graph with the weight is solved based on integer programming. The method can be effectively applied to various types of target interception scenes including the unmanned aerial vehicle, can be expanded to a large-scale target interception scene, adopts convex optimization to perform decision solution and can perform matching solution in polynomial time, and can be used for a high-speed target interception scene with a high real-time requirement.

Description

Technical Field

[0001] The present invention relates to the field of multi-target interception decision-making, and in particular to a multi-target interception decision-making method for clustered unmanned aerial vehicles. Background Art

[0002] Existing work on cluster interception mainly focuses on point capture and homogeneous attack and defense, and lacks in-depth collaborative analysis. At present, research on differential games of many-to-many collaborative regional attack and defense in three-dimensional space is very limited, and only stays at the stage of problem modeling and numerical solution. At the same time, due to the high dimensionality of the game decision problem of cluster collaborative confrontation in three-dimensional scenes, the solution efficiency is low. For large-scale cluster interception scenarios, the increase in the number of clusters will lead to an increase in the dimensionality of strategy variables, resulting in a further reduction in the efficiency of decision optimization solution; and due to its high-speed motion characteristics, the drone system has high real-time requirements. Therefore, for large-scale interception tasks in three-dimensional scenes, the current solution still needs to be improved. Summary of the invention

[0003] In order to solve the problem that the existing drone cluster interception method cannot guarantee real-time performance when facing large-scale scenarios, the present invention proposes a cluster drone multi-target interception decision method, which can be effectively applied to various types of target interception scenarios including drones, and can be expanded to large-scale target interception scenarios. At the same time, since this method uses convex optimization for decision solving and can perform matching solutions in polynomial time, it can be used in high-speed target interception scenarios with high real-time requirements. Its specific technical solution is as follows:

[0004] A multi-target interception decision method for swarm UAVs includes the following contents:

[0005] Construct an attack and defense game model of drone swarms in three-dimensional space, decompose the attack and defense game of drone swarms from many-to-many games into multiple many-to-one defense games, and set the game value function to represent the goals of both parties in the game;

[0006] Among them, the game value function is transformed into a convex optimization to obtain the optimal interception point in real time, and the maximum interception matching of multiple multi-defense-one games is achieved through the maximum matching of the weighted conflict bipartite graph. At the same time, the maximum matching problem of the weighted conflict bipartite graph is solved based on integer programming.

[0007] Furthermore, the construction of the attack and defense game model specifically includes:

[0008] Step 10: Get the spatial coordinate information of the drone;

[0009] Step 11: Treat the UAV as a mass point and simplify its dynamic model into a single integrator kinematic model to construct an attack and defense game model in a convex bounded region;

[0010] Step 12: Represent the convex bounded region, i.e., the game space, as the intersection of half-spaces partitioned by multiple hyperplanes.

[0011] Furthermore, the step 11 specifically includes: in a convex bounded three-dimensional Euclidean space Including N d Defender and N a Attacker Each participant sets the position information of the attacker and defender according to Current value, decide the optimal control input under the current state The drone follows a single integrator kinematic model:

[0012]

[0013] in

[0014] Furthermore, the step 12 specifically includes: representing the game space as the intersection of half spaces divided by multiple hyperplanes Then we get the representation form of linear inequality:

[0015]

[0016] There is one plane Euclidean space It is divided into two non-intersecting sub-areas. The half space on the side that does not contain the game area is called the target area. A is the hyperplane coefficient matrix, and b is a constant term. The exit is defined as the point x on the plane. o is a bounded circle with a center and a radius of l, and the target area Ω goal , game area Ω game 、Export Ω exit The expression is as follows:

[0017]

[0018] Define the capture / capture radius of the drone as r i ≥0, define the current position of the drone as the center of the circle and the radius as r i The sphere is the capture domain. When the attacker A i With at least one defender D j When the distance is less than or equal to the corresponding capture radius, the attacker A i D j capture, then the attacker's capture set is:

[0019]

[0020] Furthermore, the goals of both parties in the game are set and expressed as a game value function. Specifically, the defender's goal is to prevent the attacker from reaching the exit. Even if the attacker fails in the attack, he still tries to approach the exit. This game goal can be expressed as the following value function:

[0021]

[0022] Where V is a terminal set The HJI equation; the attacker still tries to get as close to the exit as possible even if the attack fails, and the objective function is:

[0023]

[0024] Furthermore, the game value function is subjected to convex optimization transformation to obtain the optimal interception point in real time, specifically including:

[0025] Building an offensive advantage domain The offensive advantage domain It refers to the attacker's position in Euclidean space in a three-dimensional scene. Chinese defender D s First arrived area; definition The surface boundary is the boundary of the attack domain; define the potential function for:

[0026]

[0027] Where r represents the capture radius, α represents the velocity ratio, and its gradient can be calculated as follows:

[0028]

[0029] The potential function actually describes the degree of interception, f ij ≤0 indicates successful defense;

[0030] According to the potential function definition, the attack domain is also expressed as:

[0031]

[0032] The closure of the attack domain is And the closure is bounded and strictly convex; by definition, if This means that in Ω goal There is no point in the attack cluster A j Can reach undefended cluster D s Captured, at this point, means a successful defense;

[0033] Based on the offensive advantage domain, the optimal interception point of the defender is defined and proved through the optimal feedback strategy calculation method;

[0034] definition A critical point in is the interception point: and if The interception point Is in Ω game Distance Ω inside the convex hull exit The closest unique point;

[0035] Based on the definition of the interception point, if the defender successfully intercepts, that is, If the defender D i Adopting state feedback strategy So Will not approach Ω goal ,Right now In addition, if and only if A j Adopt a feedback strategy hour,

[0036] Convert the game value function into a convex optimization problem;

[0037] According to the potential function definition and the game task requirements, for the state So that the game value function shown in formula (5) Differentiable, then It can be calculated by the following convex optimization problem:

[0038]

[0039] Consider only the status Make the value function The differentiable part, so the value function satisfies the HJI equation relative to the subgame as follows:

[0040]

[0041] Since neither the terminal set Ψ nor the cost function J depends on time, For any two different time points t1,t2≥0, if x s (t1) = x s (t2) and Then the value function for these moments satisfies Therefore, the above formula (18) can also be equivalently expressed as:

[0042]

[0043] Note x I is the solution of (19), and assumes The interception point x ISatisfy the KKT condition of the convex optimization problem (17):

[0044]

[0045] but:

[0046]

[0047] You can get:

[0048]

[0049] According to the definition of potential function, the left side of equation (23) is the same as equation (8). Combining (21) and (22), we can get:

[0050]

[0051] In the maximum and minimum operations, the feedback strategy is adopted as well as Therefore, the value function Satisfies HJI formulas (8) and (19); According to the definition of Ψ, at the end of the game, there is a defender D s Make mean Contains the only point That is, there exists f ij (x)≥0 such that Therefore, the convex optimization problem has a unique solution The value function satisfies

[0052] Finally, the NLOPT library is used to quickly solve and calculate the optimal interception point x * and u:

[0053]

[0054] Furthermore, the attack and defense game of the drone cluster is decomposed from a many-to-many game into a plurality of many-to-one defense games, specifically:

[0055] It can be broken down into several sub-games in which no more than 3 defenders intercept 1 attacker, that is, for any and if Then there exists a subgame combination such that I(s1,j)=I(s,j) and s1≤3.

[0056] Furthermore, the maximum interception matching of multiple multi-defense-one games is achieved by the maximum matching of the weighted conflict bipartite graph, specifically:

[0057] In the case of N defenders and M attackers, A defensive cluster, where each sub-cluster represents 1, 2, and 3 drones intercepting 1 attacking drone;

[0058] Define an undirected bipartite graph Each node in U1 represents a defensive combination. Each node in U2 represents an attacker ε represents the undirected edge connecting U1 and U2, which indicates the relationship between the two parties; the node will only be connected if the following conditions are met: defensive combination Able to successfully intercept attacker A j When the defensive combination In the absence of any defender, the remaining defenders cannot guarantee the success of the defense; weights are imposed on the edges of the bipartite graph according to the minimum distance to the interception point:

[0059]

[0060] The conflict constraint is set such that each defender can only appear in one defense cluster node during the matching process, that is, two defense cluster nodes containing at least one common defender cannot coexist in the matching process; the above constraints are implemented through an undirected conflict graph To describe, The nodes of the graph are The edge set And satisfy the following formula:

[0061]

[0062] Furthermore, the method for solving the maximum matching problem of the weighted conflicting bipartite graph based on integer programming is as follows:

[0063] For an undirected weighted bipartite graph and conflict graph Redefine the maximum matching of the weighted conflict bipartite graph and transform it into the following integer programming problem:

[0064]

[0065] where x i,j =1 means defensive cluster Assigned to intercept attacker A j , x i,j =0 means not participating in matching;

[0066] Use the branch and bound method to solve this integer programming problem.

[0067] The beneficial effects of the present invention are:

[0068] 1. The collaborative attack and defense game method in a three-dimensional environment of the present invention can solve the optimal interception point for multiple drones to intercept one drone within milliseconds, has theoretical completeness and meets the real-time requirements of the drone deployment method.

[0069] 2. The present invention can decompose large-scale cluster problems into multiple sub-game problems, solve the sub-game problems using a collaborative attack and defense game method in a three-dimensional environment, and then use a weighted conflict bipartite graph maximum matching method to achieve maximum interception matching, and convert it into an integer programming problem to be solved in polynomial time. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Attached Figure 1 It is a schematic diagram of a convex bounded region game with an exit of the present invention;

[0071] Attached Figure 2 is a schematic diagram of a cross section of the attacking domain of three defenders of the present invention;

[0072] Attached Figure 3 is a schematic cross-sectional view of the attacking domain of four defenders of the present invention;

[0073] Attached Figure 4 It is a schematic diagram of a weighted conflict bipartite graph of the present invention;

[0074] Attached Figure 5 It is a schematic diagram of the conflict constraint diagram in the maximum matching of the game of the present invention. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical scheme and technical effect of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0076] This embodiment provides a swarm drone multi-target interception decision-making method, constructs a many-to-many collaborative attack and defense game model in a three-dimensional environment; for the heterogeneous attack and defense problem in a three-dimensional bounded convex confrontation area with an exit, the many-to-many game that is difficult to analyze directly is decomposed into multiple many-to-one defense games, and for the many-to-one defense game, a three-dimensional heterogeneous attack domain is proposed, and a defense victory strategy based on the three-dimensional heterogeneous attack domain and the maximum required number of members of the defense combination in the heterogeneous attack and defense are given; for the large-scale cluster confrontation game problem, a weighted conflict bipartite graph maximum matching problem with the game cost as the measurement standard is constructed, and it is converted into an integer programming problem for solution, and finally the large-scale cluster game problem of many-to-many defense is converted into a sub-game problem of multiple defense drones not exceeding 3 intercepting one attack drone.

[0077] In view of the above content, the present invention designs two major modules: a collaborative attack and defense game module in a three-dimensional environment and a weighted conflict bipartite graph maximum matching module.

[0078] The collaborative attack and defense game module in the three-dimensional environment considers the game process of the attack and defense in the three-dimensional scene, and can give the optimal interception point for multiple drones to intercept one drone, providing reference information for subsequent multi-target interception problems. The methods used by this module specifically include the following:

[0079] Step 10: Obtain the spatial coordinate information of the drone based on the relevant position capture equipment and algorithms. Drones are divided into defenders and attackers.

[0080] Step 11: Treat the UAV as a point mass and simplify its dynamic model into a single integrator kinematic model to construct an attack and defense game model in a convex bounded region.

[0081] Consider a system with N a +N d Convex bounded area attack and defense differential game with exit for N drones d Defender and N a Attacker In order to make real-time decisions, a state feedback information structure is adopted, that is, each participant sets the position information of the attacker and the defender according to the Current value, decide the optimal control input under the current state For the differential game problem, the drone follows the single integrator kinematic model:

[0082]

[0083] in

[0084] First, we solve the following attack-defense differential game problem in a convex bounded region: and attack cluster Given the current state, how to determine whether the attacker or defender wins. On this basis, further study the winning strategy of the defender, that is, if the defensive cluster Can win the game, then What strategies should the defenders in the game adopt to ensure victory?

[0085] Step 12: Represent the game space as the intersection of half-spaces partitioned by multiple hyperplanes.

[0086] Cluster attack and defense game in convex bounded three-dimensional Euclidean space The convex bounded region is called the game space. For the convenience of optimization, the game space is represented as the intersection of half spaces divided by multiple hyperplanes. Then we get the representation form of linear inequality:

[0087]

[0088] There is one plane Euclidean space The half space that does not contain the game area is called the target area. A is the hyperplane coefficient matrix and b is a constant term. The exit is defined as the point x on the plane. o is a bounded circle with a center and a radius of l. According to the description, the target area Ω goal , game area Ω game 、Export Ω exit The expression is as follows:

[0089]

[0090] Define the capture / capture radius of the drone as r i ≥0, which corresponds to the radius of the drone in the actual experiment or the safety distance threshold set to prevent drone collision. Define the current position of the drone as the center of the circle and the radius as r i The sphere is the capture domain. i With at least one defender D j When the distance is less than or equal to the corresponding capture radius, the attacker A i D j Capture. According to this description, the attacker's capture set is:

[0091]

[0092] The goal of the attacking drone swarm is to get as many attackers as possible out of exit Ω exit Enter the target areaΩ goal , and the defender's goal is to goal Capture as many attackers as possible before. In order to more conveniently verify the proposed game planning method, the uncertainty caused by perception and positioning is abandoned here, and it is assumed that the current states of both parties are known to each other.

[0093] Step 13: Construct the value function of the differential game problem.

[0094] Different from defense based on trajectory prediction, in the differential game system, each individual strives to achieve victory for his own side, so the representation of its value function satisfies the maximum and minimum optimization problem.

[0095] The goal of the defender is to prevent the attacker from reaching the exit. Even if the attacker fails, he still tries to get as close to the exit as possible. This game goal can be expressed as the following value function:

[0096]

[0097] Where V is a terminal set Considering the most conservative case, that is, the attacker still tries to get as close to the exit as possible even if the attack fails, the objective function is:

[0098]

[0099] This is a maximum-minimum optimization problem, which will be transformed into a standard convex optimization problem later. After solving it, the optimal feedback strategy can be calculated, that is, the control input is u s , Then calculate the optimal interception point x * .

[0100] Step 14: Convert the above maximum and minimum optimization problem into a standard convex optimization problem to obtain the optimal interception point within a limited time and meet the real-time requirements of the UAV system. It includes the following sub-steps:

[0101] Step 141: construct an offensive advantage domain for the differential game problem. The offensive advantage domain refers to the area that the attacker reaches before the defender in the Euclidean space in a three-dimensional scene, also known as an advantageous reachable domain.

[0102] In order to facilitate the representation of the game process, the offensive advantage domain is introduced: given any defender and attackers Regardless of D s Control input, attack advantage area In Euclidean space Middle A j Can be reached without being D s A collection of captured locations.

[0103] In order to facilitate the subsequent calculation of the optimal interception point, define The surface boundary is the boundary of the attack domain. In order to represent the interception process, the potential function is defined for:

[0104]

[0105] Where r represents the capture radius, α represents the velocity ratio, and its gradient can be calculated as follows:

[0106]

[0107] This explicit gradient form can be conveniently used in subsequent optimization.

[0108] The potential function actually describes the degree of interception, f ij ≤0 indicates successful defense. According to the potential function definition, the attack domain can also be expressed as:

[0109]

[0110] The closure of the attack domain is And the closure is bounded and strictly convex, as shown in the attached visualization Figure 1 According to the definition, if This means that in Ω goal There is no point in the attack cluster A j Can reach undefended cluster D s Captured means the defense is successful. Since the speed ratio and capture radius are introduced here, the method of the present invention can also handle heterogeneous drones with different speeds and capture radii.

[0111] In case of successful defense, further defense cluster D s Come up with the best feedback strategy to ensure victory. Definition A critical point in is the interception point: and if The interception point Is in Ω game Distance Ω inside the convex hull exit The closest unique point, such as Figure 1 As shown in point I.

[0112] Step 142: Proof of the optimal interception strategy based on the optimal interception point. Based on the offensive advantage domain, the relevant definition of the defender's optimal interception point is given, and further the optimal feedback strategy calculation method is given and the effectiveness of the interception strategy is proved.

[0113] Based on the definition of the interception point, if the defender successfully intercepts, that is, If the defender D i Adopting state feedback strategy So Will not approach Ω goal ,Right now In addition, if and only if A j Adopt a feedback strategy hour,

[0114] Proof: According to the definition of interception point and the convex hull lemma of attack domain, the following convex optimization problem can be obtained:

[0115]

[0116] stf ij (x)≥0

[0117] Ax≤b (10),

[0118] The proof that the convex optimization problem can represent the game value function will be discussed in step 144, and it is assumed here that it holds. exit The definition of divides the exit into two cases: inside the center of the circle and outside the center of the circle. This makes it difficult to solve the optimization problem. Therefore, the objective function here simplifies the exit to the center of the circle. It is a convex optimization solution. Since the exit of the present invention is located on a certain boundary, it is necessary to discuss whether the feedback strategy can represent the interception point in the following two cases.

[0119] Case 1: If Located in Ω play Internally, Since the line segment from the start point to the end point must be located in the convex hull, the boundary constraint can be omitted here. It satisfies the following Karush-Kuhn-Tucker (KKT) condition:

[0120]

[0121] in is a Lagrange multiplier, and then:

[0122]

[0123] Case 2: If Located in Ω play External, then I (i,j) becomes the solution of problem (9), at this time I (i,j) Located in Ω game For simplicity, the boundary condition in formula (9) is defined as g ij (x)≥0, so:

[0124]

[0125] According to the KKT conditions:

[0126]

[0127]

[0128] It can be seen that in the above two cases, formula (11) is valid. Then, consider Taking the derivative of t, we can get:

[0129]

[0130] According to the single integral kinematic model (1) and formula (15) used in the game, we can know that:

[0131]

[0132] According to formulas (11) and (16), when hour, In addition, when the state feedback hour Get the certificate.

[0133] Step 143: Proof of uniqueness of optimal interception point. The premise of the optimal feedback strategy is to calculate the optimal interception point, and its uniqueness is further proved.

[0134] In step 142, the definition of interception point is introduced, the calculation method of optimal feedback strategy is given and its effectiveness is proved. The premise of optimal feedback strategy is to calculate the optimal interception point, and its uniqueness needs to be further clarified. In this step, its uniqueness is proved. Here, the definition of the uniqueness of the optimal interception point is clarified again: for any defender and attackers if The estimated intercept point I (i,j) only.

[0135] Proof: Define region Λ as defender D s Relative to attacker A j Offensive Domain With border Convex hull The intersection area, due to and are all convex regions, and according to the intersection theorem of convex sets, Λ is also convex. By definition, the interception point I (i,j) is the distance Ω in Λ exit The nearest point is then proved by contradiction. Suppose there are two different nearest points x in Λ m ,x n ∈Λ, for any point x∈Λ, ‖x m -x o ‖2=‖x n -x o ‖2>‖xx o ‖2. According to the properties of convex sets, the line segment connecting two points in a convex set must be in the convex set, denoted by Combined with ‖x m -x o ‖2=‖x n -x o ‖2 shows that the target point x o On line segment The median line of There must be a midpoint x on the line segment v Make the distance to the target point smaller than the endpoint of the line segment, that is This is contrary to the assumption, so the estimated intercept point I (i,j) The uniqueness of is proved.

[0136] Step 144: Convex transformation of the game value function. In order to quickly solve the highly non-convex and nonlinear maximum and minimum optimization problem, the game value function is transformed into a convex optimization problem.

[0137] According to the potential function definition and the game task requirements, for the state So that the game value function shown in formula (5) Differentiable, then It can be calculated by the following convex optimization problem:

[0138]

[0139] Proof: Since we only consider the state Make the value function The differentiable part, so the value function satisfies the HJI equation for this subgame as follows:

[0140]

[0141] Since neither the terminal set Ψ nor the cost function J depends on time, For any two different time points t1,t2≥0, if x s (t1) = x s (t2) and Then the value function for these moments satisfies Therefore, the above formula can also be equivalently expressed as:

[0142]

[0143] Next, we prove that the optimal solution of the convex optimization problem (17) satisfies (19). I is the solution of (19), and assumes Since the intercept point x I Satisfy the KKT condition of the convex optimization problem (17):

[0144]

[0145] but:

[0146]

[0147] Similar to the proof process of the optimal feedback strategy, we can obtain:

[0148]

[0149] According to the definition of potential function, the left side of equation (23) is the same as equation (8). Combining (21) and (22), we can get:

[0150]

[0151] In the maximum and minimum operations, the feedback strategy is adopted as well as Therefore, the value function Satisfies HJI formulas (8) and (19). According to the definition of Ψ, at the end of the game, there is a defender D s Make mean Contains the only point That is, there exists f ij (x)≥0 such that Therefore, the convex optimization problem has a unique solution The value function satisfies Get the certificate.

[0152] In summary, it is proved that the attack and defense game HJI equation described by the game value function can be transformed into a convex optimization problem. The optimal strategy of the game can be obtained by solving the optimal solution of the convex optimization problem, thereby greatly reducing the computational complexity. For this convex optimization problem, the NLOPT library can be used to quickly solve it, and finally calculate the optimal interception point x * and u:

[0153]

[0154] Steps 10 to 144 are completed in milliseconds. The optimal interception points under different attack and defense matching pairs are obtained as prior information and passed to the weighted conflict bipartite graph maximum matching module.

[0155] The weighted conflict bipartite graph maximum matching module, for large-scale cluster confrontation game problems, constructs a weighted conflict bipartite graph maximum matching problem with game cost as the measurement standard, and converts it into an integer programming problem for solution. Finally, the large-scale cluster game problem of multiple defenses is converted into a sub-game problem of multiple defense drones intercepting one attacking drone. The methods used in this module mainly include the following:

[0156] Step 20: Decompose the large-scale clustering problem into sub-game problems, where the maximum number of defenders in the sub-game set does not exceed 3.

[0157] For the multi-defense-multi cluster interception problem, on the basis of solving the multi-defense-one optimal interception strategy, it is decomposed into several game sub-problems of no more than 3 defenders intercepting 1 attacker, providing a theoretical basis for the subsequent solution of large-scale cluster interception problems.

[0158] Its complete definition is as follows: For any and if Then there exists a subgame combination such that I(s1,j)=I(s,j) and s1≤3.

[0159] Proof: Here combined with the attached Figure 2 and Figure 3 Proof. If |s|≤3, then the conclusion is obviously true, so here we discuss the case of |s|≥4. First, select |s1|=3, and further deduce based on this. Assume that I(s1,j) depends on all D s ,but The following discusses the two cases where the sub-game combinations are coplanar and non-coplanar.

[0160] Case 1: A j , D1, D2, and D3 are not coplanar. I(s1, j) is one of the intersection points of two strictly convex closed curves in a plane, and there are at most four intersection points. Here, it is assumed that the direction of the arrow is the direction of the target position, so H3 is the interception point. Then add defender D4. If I(s, j) depends on all four defenders, it must be one of H1, H2, H3, and H4. If I(s, j) = H3, then D4 is redundant. If I(s, j) = H2, the arrow of the new curve must decrease from the inside to the outside at H2; conversely, if the new curve increases from the inside to the outside, then H2 cannot be an interception point. Therefore, D2 is redundant. Similarly, if I(s, j) = H4, then D1 is redundant. Since both curves at H1 and I(s, j) are downward, I(s, j) cannot be H1. In summary, introducing a new defender does not increase the number of defenders that the interception point must depend on.

[0161] Case 2: A j , D1, D2, and D3 are coplanar. Combining formulas (2) and (7), the intercept point is converted into polar coordinates as follows:

[0162]

[0163] in The above formula (25) can be written as follows:

[0164]

[0165] in Because A j , D1, D2, and D3 are coplanar, so vectors m1, m2, and m3 are linearly independent. If formula (26) has a solution, then m3 can be derived from m1 and m2. In other words, and All intersection points between Therefore, D3 can be ignored. If (26) has no solution, then there exists D i , so that Therefore, D can be ignored i And continue to consider The remaining defenders in the. In summary, the above two situations are proved.

[0166] Step 21: After decomposing into sub-game problems, the maximum interception matching is realized based on the maximum matching problem of the weighted conflict bipartite graph.

[0167] In order to solve the large-scale cluster attack and defense game problem, a matching method considering the game situation is introduced. Step 20 has proved that the defense combination only needs no more than 3 drones to intercept 1 attacker. Therefore, the many-to-many attack and defense game problem can be decomposed into the sub-problem of no more than 3 defensive drones intercepting 1 offensive drone. In the case of N defenders and M attackers, there is There are 1, 2 and 3 defensive clusters, each of which represents 1, 2 and 3 drones intercepting 1 attacking drone. In the present invention, the above matching problem is modeled as a weighted conflict bipartite graph maximum matching problem, as shown in the attached figure. Figure 4 shown.

[0168] The problem is described as follows: Define an undirected bipartite graph Each node in U1 represents a defensive combination. Each node in U2 represents an attacker ε represents the undirected edge connecting U1 and U2, which indicates the relationship between the two parties. The nodes will only establish a connection if the following conditions are met: Able to successfully intercept attacker A j When the defensive combination When any defender is missing, the remaining defenders cannot guarantee the success of the defense. In order to improve the interception efficiency, weights are applied to the edges of the bipartite graph according to the minimum distance to the interception point:

[0169]

[0170] Unlike the traditional bipartite graph maximum matching problem, this problem contains conflict constraints. Each defender can only appear in at most one defending cluster node during the matching process, that is, two defending cluster nodes that contain at least one common defender cannot coexist in the matching. The above constraints can be implemented through an undirected conflict graph To describe, combined with the Figure 3 The nodes and edges of the conflict graph are attached. Figure 5 shown. The nodes of the graph are The edge set And satisfy the following formula:

[0171]

[0172] Step 22: Efficiently solve the maximum matching problem based on integer programming. The difficult-to-solve maximum matching of the weighted conflict bipartite graph is transformed into an integer programming problem and solved in a finite time using the SCIP solver.

[0173] For an undirected weighted bipartite graph and conflict graph Redefine the maximum matching of the weighted conflict bipartite graph and transform it into the following integer programming problem:

[0174]

[0175] where x i,j =1 means defensive cluster Assigned to intercept attacker A j , x i,j = 0 means not participating in the matching. The integer programming problem is solved using the branch and bound method. Thus, the maximum matching problem of the bipartite graph with weighted conflicts that is difficult to solve can be solved efficiently.

[0176] Steps 20 to 22 are completed in polynomial time immediately after the multi-to-multi coordinated attack and defense game module 1 in the three-dimensional environment. The entire decision-making process can meet the requirement of a decision-making frequency of 20 Hz, and meet the real-time requirements of the method deployed on the drone.

[0177] The above is only a preferred implementation case of the present invention and does not limit the present invention in any form. Although the implementation process of the present invention is described in detail above, for those familiar with the art, they can still modify the technical solutions recorded in the above examples, or replace some of the technical features therein with equivalents. All modifications, equivalent replacements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-target interception decision method for swarm UAVs, characterized by: Construct an attack and defense game model of drone swarms in three-dimensional space, decompose the attack and defense game of drone swarms from many-to-many games into multiple many-to-one defense games, and set the game value function to represent the goals of both parties in the game; Among them, the game value function is transformed into a convex optimization to obtain the optimal interception point in real time, and the maximum interception matching of multiple multi-defense-one games is achieved through the maximum matching of the weighted conflict bipartite graph. At the same time, the maximum matching problem of the weighted conflict bipartite graph is solved based on integer programming.

2. A multi-target interception decision method for swarm drones as claimed in claim 1, characterized in that: The construction of the attack and defense game model specifically includes: Step 10: Get the spatial coordinate information of the drone; Step 11: Treat the UAV as a mass point and simplify its dynamic model into a single integrator kinematic model to construct an attack and defense game model in a convex bounded region; Step 12: Represent the convex bounded region, i.e., the game space, as the intersection of half-spaces partitioned by multiple hyperplanes.

3. A swarm UAV multi-target interception decision method as claimed in claim 2, characterized in that: The step 11 specifically includes: in a convex bounded three-dimensional Euclidean space Including N d Defender and N a Attacker Each participant sets the position information of the attacker and defender according to Current value, decide the optimal control input under the current state The drone follows a single integrator kinematic model: in 4. A swarm UAV multi-target interception decision method as claimed in claim 3, characterized in that: The step 12 specifically includes: representing the game space as the intersection of half spaces divided by multiple hyperplanes Then we get the representation form of linear inequality: There is one plane Euclidean space It is divided into two non-intersecting sub-areas. The half space on the side that does not contain the game area is called the target area. A is the hyperplane coefficient matrix, and b is a constant term. The exit is defined as the point x on the plane. o is a bounded circle with a center and a radius of l, and the target area Ω goal , game area Ω game 、Export Ω exit The expression is as follows: Define the capture / capture radius of the drone as r i ≥0, define the current position of the drone as the center of the circle and the radius as r i The sphere is the capture domain. When the attacker A i With at least one defender D j When the distance is less than or equal to the corresponding capture radius, the attacker A i D j capture, then the attacker's capture set is:

5. A swarm UAV multi-target interception decision method as claimed in claim 4, characterized in that: The goals of both parties in the game are set and expressed as a game value function. Specifically, the defender's goal is to prevent the attacker from reaching the exit. Even if the attacker fails in the attack, he still tries to approach the exit. This game goal can be expressed as the following value function: Where V is a terminal set The HJI equation; the attacker still tries to get as close to the exit as possible even if the attack fails, and the objective function is:

6. A swarm UAV multi-target interception decision method as claimed in claim 4, characterized in that: The game value function is subjected to convex optimization transformation to obtain the optimal interception point in real time, specifically including: Building an offensive advantage domain The offensive advantage domain It refers to the attacker's position in Euclidean space in a three-dimensional scene. Chinese defender D s Area to reach first; definition The surface boundary is the boundary of the attack domain; define the potential function for: Where r represents the capture radius, α represents the velocity ratio, and its gradient can be calculated as follows: The potential function actually describes the degree of interception, f ij ≤0 indicates successful defense; According to the potential function definition, the attack domain is also expressed as: The closure of the attack domain is And the closure is bounded and strictly convex; by definition, if This means that in Ω goal There is no point in the attack cluster A j Can reach undefended cluster D s Captured, at this point, means a successful defense; Based on the offensive advantage domain, the optimal interception point of the defender is defined and proved through the optimal feedback strategy calculation method; definition A critical point in is the interception point: and if The interception point Is in Ω game Distance Ω inside the convex hull exit The closest unique point; Based on the definition of the interception point, if the defender successfully intercepts, that is, If the defender D i Adopting state feedback strategy So Will not approach Ω goal ,Right now In addition, if and only if A j Adopt a feedback strategy hour, Convert the game value function into a convex optimization problem; According to the potential function definition and the game task requirements, for the state So that the game value function shown in formula (5) Differentiable, then It can be calculated by the following convex optimization problem: Consider only the status Make the value function The differentiable part, so the value function satisfies the HJI equation relative to the subgame as follows: Since neither the terminal set Ψ nor the cost function J depends on time, For any two different time points t1,t2≥0, if x s (t1) = x s (t2) and Then the value function for these moments satisfies Therefore, the above formula (18) can also be equivalently expressed as: Note x I is the solution of (19), and assumes The interception point x I Satisfy the KKT condition of the convex optimization problem (17): but: You can get: According to the definition of potential function, the left side of equation (23) is the same as equation (8). Combining (21) and (22), we can get: In the maximum and minimum operations, the feedback strategy is adopted as well as Therefore, the value function Satisfies HJI formulas (8) and (19); According to the definition of Ψ, at the end of the game, there is a defender D s Make mean Contains the only point That is, there exists f ij (x)≥0 such that Therefore, the convex optimization problem has a unique solution The value function satisfies Finally, the NLOPT library is used to quickly solve and calculate the optimal interception point x * and u:

7. A swarm UAV multi-target interception decision method as claimed in claim 6, characterized in that: The attack and defense game of the drone cluster is decomposed from a many-to-many game into multiple many-to-one defense games, specifically: It can be broken down into several sub-games in which no more than 3 defenders intercept 1 attacker, that is, for any and if Then there exists a subgame combination such that I(s1,j)=I(s,j) and s1≤3.

8. A swarm UAV multi-target interception decision method as claimed in claim 7, characterized in that: The maximum interception matching of multiple multi-defense-one games is achieved by maximum matching of the weighted conflict bipartite graph, specifically: In the case of N defenders and M attackers, A defensive cluster, where each sub-cluster represents 1, 2, and 3 drones intercepting 1 attacking drone; Define an undirected bipartite graph Each node in U1 represents a defensive combination. Each node in U2 represents an attacker ε represents the undirected edge connecting U1 and U2, which indicates the relationship between the two parties; the node will only be connected if the following conditions are met: defensive combination Able to successfully intercept attacker A j When the defensive combination In the absence of any defender, the remaining defenders cannot guarantee the success of the defense; weights are imposed on the edges of the bipartite graph according to the minimum distance to the interception point: Set the conflict constraint that each defender can only appear in at most one defending cluster node during the matching process, that is, two defending cluster nodes containing at least one common defender cannot coexist in the matching; The above constraints are expressed through an undirected conflict graph To describe, The nodes of the graph are The edge set And satisfy the following formula:

9. A swarm UAV multi-target interception decision method as claimed in claim 8, characterized in that: The method of solving the maximum matching problem of the weighted conflicting bipartite graph based on integer programming is as follows: For an undirected weighted bipartite graph and conflict graph Redefine the maximum matching of the weighted conflict bipartite graph and transform it into the following integer programming problem: where x i,j =1 means defensive cluster Assigned to intercept attacker A j , x i,j =0 means not participating in matching; Use the branch and bound method to solve this integer programming problem.

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