An aircraft formation position reconstruction analytical optimization method

Abstract

The application discloses a kind of aircraft formation position reconstruction analytical optimization method, it is related to aircraft cooperative guidance and control technical field.Combining the distance between the original position of aircraft and new position, velocity vector front angle two factors, the individual benefit of single aircraft from original position to reach new position is evaluated, preliminary screening scheme is obtained according to individual benefit to scheme, and the individual benefit of scheme is calculated, the time difference value of last aircraft to new position and first aircraft to new position is multiplied by proportionality coefficient, as the time cooperative benefit of scheme, the number of trajectory intersection in the flight trajectory of each aircraft flying to new position is used to evaluate the trajectory intersection benefit of scheme.According to time cooperative benefit and trajectory intersection benefit, the cooperative benefit of scheme is calculated.The comprehensive benefit is obtained by weighted summation of scheme individual benefit and cooperative benefit, and the scheme with maximum comprehensive benefit is selected as the final aircraft formation position reconstruction scheme.

Description

Technical Field

[0001] This invention relates to the field of aircraft cooperative guidance and control technology, specifically to an analytical optimization method for aircraft formation position reconstruction. Background Technology

[0002] In the problem of aircraft formation reconfiguration and transformation, a crucial issue is assigning a position to each aircraft in the original formation within the reconfigured formation. Several related technologies exist for the reconstruction and optimization of multi-agent formation positions. In the paper "Target Task Allocation for Unmanned Vessel Swarm Formation Reconfiguration" by Lü Guanghao, Peng Zhouhua, Wang Dan, and Dou Weitao, a distance-based reward function is generated based on the current positions of each unmanned vessel, and an auction termination mechanism based on the maximum number of iterations is proposed to address the target allocation problem in unmanned vessel formation reconfiguration. In the paper "Optimal role and position assignment in multi-robot-freely reachable formations" by Mosteo AR, Montijano E, and Tardioli D, the role assignment problem during multi-robot formation transformation is addressed by decomposing the desired formation position relative to the robots' initial positions and poses into translation and rotation. The combined parameters of translation, rotation, and assignment are optimized with the goal of minimizing the total displacement. In the paper "Optimal Formation Method for Multi-Robots Based on Two-Layer Path Optimization Algorithm" proposed by Zhou Jiajia, Zhang Qiang, Wang Hongjian, Zhang Hongquan, and Wang Yingying, a method for solving the optimal formation assembly point based on the PSO algorithm was designed. The path planning was transformed into an assignment problem based on the total energy consumption constraint, and the optimal allocation path was searched based on CHNN to achieve optimal formation assembly. In the paper "Research on UAV Formation Cooperative Control Technology Based on Distributed Architecture" proposed by Zeng Xu, the optimal solution problem of aircraft formation transformation was transformed into the problem of finding the correspondence between aircraft when the formation transformation time is minimized, and the Hungarian algorithm was used for the solution.

[0003] Current research on the multi-aircraft formation reconfiguration and position allocation problem mainly considers minimizing the total time or total distance for each aircraft to reach its designated position, while neglecting the coordination factors among aircraft during formation changes. For example, minimizing the time difference between aircraft completing the transformation (i.e., almost simultaneous formation changes) and minimizing trajectories crossing each other during formation changes to reduce the risk of collisions are crucial considerations. Furthermore, current technologies rely on intelligent optimization algorithms such as genetic algorithms to solve the formation reconfiguration problem, resulting in slow solution speeds that are difficult to meet the requirements of online applications. Summary of the Invention

[0004] In view of this, the present invention provides an analytical optimization method for reconstructing the position of aircraft formations. This method not only considers the individual benefits of a single aircraft during the reconstruction of the aircraft formation position, but also the collaborative benefits of multiple aircraft trajectory intersections and simultaneous arrival as much as possible. This enables a fast and online-implementable method for reconstructing the position of multiple aircraft formations to find the optimal solution.

[0005] To achieve the above objectives, the technical solution of this invention is an analytical optimization method for reconstructing aircraft formation positions. Taking the position before the formation as the original position and the position after the formation as the new position, with n aircraft in n original positions and n desired new positions after formation, each of the n original positions corresponds to one of the n desired new positions. The following steps are used for analytical optimization of the reconstructed positions:

[0006] Step 1: Evaluate the gains for a single aircraft moving from its original position to its new position by combining the distance between the aircraft's original and new positions, and the velocity vector lead angle. Each original position pair A matrix of individual payoffs for each desired new position.

[0007] Step 2: After obtaining the individual payoff matrix, the schemes are initially screened based on the individual payoffs between the original and new positions of the aircraft to obtain the initial screening schemes, and the individual payoff matrix of the initial screening schemes is calculated.

[0008] Step 3: For each initial screening scheme, the time difference between the time it takes for the last aircraft to travel from its original position to its new position and the time it takes for the first aircraft to travel from its original position to its new position is multiplied by a certain proportional coefficient to obtain the time synergy benefit of the initial screening scheme.

[0009] For each initial screening scheme, the trajectory crossover benefit of the initial screening scheme is evaluated based on the number of trajectory crossovers in the flight trajectories of each aircraft from its original position to its new position.

[0010] The collaborative benefits of each initial screening scheme are calculated based on the time synergy benefits and trajectory crossover benefits.

[0011] Step 4: Based on the individual and collaborative benefits of each initial screening scheme, the weighted sum is used to obtain the comprehensive benefit. Based on the comprehensive benefit, the scheme with the largest comprehensive benefit is selected as the final aircraft formation position reconstruction scheme.

[0012] Furthermore, by combining the distance between the aircraft's original position and its new position, and the velocity vector lead angle, the individual gains of a single aircraft in moving from its original position to its new position are evaluated, yielding... Each original position pair The individual payoff matrix for each desired new position is as follows:

[0013] The distance between the original position i and the new position j of the aircraft is r ij .

[0014] The angle between the aircraft's velocity vector and the line connecting the original position and the new position is the velocity lead angle, including the longitudinal velocity vector lead angle. and lateral velocity vector lead angle .

[0015] The distance and velocity lead angle between the original and new positions of the aircraft are normalized and scaled down to the specified values. The interval is calculated, weights are assigned, and the weighted sum is used to obtain the individual profit of the current aircraft from its original position i to its new position j.

[0016] From this, we can obtain Each original position pair A matrix of individual payoffs for each desired new position.

[0017] Furthermore, after obtaining the individual payoff matrix, the schemes are initially screened based on the individual payoffs for the desired new position from the original position of the aircraft, resulting in a preliminary selection of schemes, specifically:

[0018] In the scheme, the n original positions are M1~M n Prioritize the original position The aircraft is assigned the desired new position, and then... In the order of priority, assign new positions with better expected returns to the corresponding original positions according to certain rules; when priority is given to... After the allocation scheme is selected, priority will be given to the original position. Distribute, then according to Assign them in that order; continue in this manner, finally prioritizing the original position. Distribute, and then according to The allocation is carried out in the following order, for From the perspective of each original position, their opportunities are equal, thus obtaining the initial screening plan.

[0019] Furthermore, for each initial screening scheme, the time difference between the time it takes for the last aircraft to travel from its original position to its new position and the time it takes for the first aircraft to travel from its original position to its new position is multiplied by a certain proportional coefficient to represent the time synergy benefit of the initial screening scheme, specifically:

[0020] No. The aircraft flew from its original position to the... The formula for predicting the flight time at a new location is:

[0021]

[0022] In the formula, r ijThis represents the distance between the i-th original position and the j-th new position. To approach the speed.

[0023] No. Time-coordinated benefits corresponding to each initial screening scheme for .

[0024] In the formula, The time it takes for the first aircraft to fly from its original position to its new position. The time it takes for the last aircraft to fly from its original position to its new position; This is the proportionality coefficient. .

[0025] Furthermore, for each initial screening scheme, the trajectory crossover benefit of the initial screening scheme is evaluated based on the number of trajectory crossovers in the flight trajectories of each aircraft from its original position to its new position, specifically as follows:

[0026] Set trajectory cross factor The complexity of trajectory intersections is represented by the following formula: The flight trajectory of the aircraft from its original position to its new position is projected onto the lateral plane and the longitudinal plane, respectively. Trajectory intersections in the lateral plane are defined as lateral trajectory intersections, and trajectory intersections in the longitudinal plane are defined as longitudinal trajectory intersections. The longitudinal trajectory intersection factor is calculated as follows: and lateral trajectory cross factor .

[0027] For each new location allocation scheme, take the corresponding original location. coordinate Arrange them in ascending order from smallest to largest; the original positional order matrix is... Then obtain the corresponding new attack position. The coordinates, corresponding to the new position order matrix are as follows , respectively

[0028]

[0029] The number of times the data is not sorted in ascending order is the number of vertical trajectory intersections; if If the longitudinal trajectory crosses once, the number of intersections is counted as 1; otherwise, there is no intersection. This process is repeated sequentially. The intersection cases are counted, and the number of intersections is used as the longitudinal trajectory intersection factor. .

[0030] For each new location allocation scheme, take the corresponding original location. coordinate Arrange them in ascending order from smallest to largest, the order matrix is ​​as follows: Then obtain the corresponding information about the aircraft flying to the new location. Coordinates, corresponding matrix is , respectively

[0031]

[0032] The number of times the data is not sorted in ascending order is the number of vertical trajectory intersections. If the longitudinal trajectory crosses once, the number of intersections is counted as 1; otherwise, there is no intersection. This process is repeated sequentially. The intersection situation is determined, and the number of intersections is counted as the lateral trajectory intersection factor. .

[0033] Calculate the sum of the longitudinal and lateral trajectory intersections for each initial screening scheme. ; For the plan The number of longitudinal trajectory intersections, For the plan The number of lateral trajectory intersections, For the plan The total number of trajectory intersections.

[0034] The trajectory crossover payoff for each option is then... ; For the plan Trajectory crossover benefits, This is the cross-return ratio coefficient. .

[0035] Beneficial effects:

[0036] 1. This invention provides an analytical optimization method for aircraft formation position reconfiguration. This method not only considers the individual benefits of a single aircraft during formation position reconfiguration but also the collaborative benefits of intersecting flight trajectories and achieving simultaneous arrival as much as possible, making it more practically significant. Based on the distance and velocity vector lead angle of each aircraft reaching its designated position, this invention designs an individual benefit calculation method and allocates schemes according to individual benefits. Then, considering the time synergy and trajectory intersection of the aircraft reaching their designated positions in each scheme, a collaborative benefit calculation method is designed. Finally, combining individual and collaborative benefits, the scheme with the largest overall benefit is selected, resulting in a formation reconfiguration position allocation model. Compared to existing technologies, this method considers the collaborative benefits of each aircraft reaching its designated position, coordinates the changing relationships between aircraft in the formation, and avoids interference and collisions.

[0037] 2. This invention does not involve slow algorithms such as intelligent optimization. It obtains a better solution based on an analytical method that first screens out the best individual benefit schemes and then further optimizes the selection by combining collaborative benefits. The calculation speed is fast and it can be applied online. Attached Figure Description

[0038] Figure 1 A schematic diagram illustrating the scenario of reconfiguring position allocation for formation;

[0039] Figure 2 To analyze and optimize the allocation scheme diagram of the algorithm;

[0040] Figure 3 A graph showing the objective function values ​​of the population in each generation of the genetic algorithm;

[0041] Figure 4 A diagram illustrating the allocation scheme for the genetic algorithm;

[0042] Figure 5 The flowchart of an analytical optimization method for reconstructing aircraft formation positions is provided by the present invention. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0044] This invention transforms the aircraft formation position reconstruction optimization problem into a missile-target allocation problem when a missile attacks a target. That is, the positions of the missiles in the required new formation are considered as targets. Therefore, the missile formation position reconstruction problem can be viewed as... missile attack The problem of missile-target allocation is solved when there are multiple targets, with missiles corresponding to the original position of the aircraft and targets corresponding to the new position the aircraft flies to. This paper proposes an analytical optimization method for aircraft formation position reconstruction that considers both the individual and collaborative benefits of missiles attacking targets as they move from their original positions to new positions.

[0045] Taking the position before the formation of the aircraft as the original position and the position after the formation as the new position, with n aircraft in n original positions and n expected new positions after formation, each of the n original positions corresponds to one of the n expected new positions. Each of these scenarios represents a possible solution, and the following approach is adopted: Figure 5 The steps shown are for refactoring, parsing, and optimization:

[0046] Step 1: Individual Income Calculation

[0047] Individual gain refers to the gain of a single aircraft when flying from its original position to a new position, taking into account factors such as the distance between the original and new positions and the deviation between the speed and the flight trajectory. The impact of these two factors on individual gain will be analyzed below.

[0048] (1) Distance between the original position and the new position

[0049] In missile target allocation, considering factors such as fuel consumption, it is generally desirable for missiles to attack targets that are relatively close to the target. Therefore, individual benefits can be set based on the distance between the missile and the target (referred to as "missile-target distance"). A smaller missile-target distance results in a larger individual benefit, and vice versa.

[0050] Therefore, when calculating the individual benefits of aircraft formation repositioning, the distance between the original position and the new position should also be considered. A smaller distance results in a larger individual benefit, and vice versa.

[0051] The method for calculating the distance between the original location and the new location is as follows:

[0052] (1)

[0053] In the formula, Original position and new location The distance between them Original position In the ground coordinate system Position coordinates on the axis For the new position In the ground coordinate system Position coordinates on the axis.

[0054] (2) Velocity vector lead angle

[0055] The maneuverability of an aircraft is represented by its available overload. In the missile target allocation problem, it is also necessary to consider that the missile's trajectory should be as straight as possible and the required overload should be as small as possible when flying towards the target, so as to meet the constraints of available overload. Generally speaking, when the angle between the missile's velocity vector and the missile-target line of sight (line of sight) is small (velocity lead angle), the missile's required overload is small and the individual benefit is large; conversely, the required overload is large and the individual benefit is small.

[0056] Based on the consideration of velocity vector angle in the above missile-target allocation problem, the calculation method for the leading velocity angle of aircraft formation is as follows:

[0057] (2)

[0058] in

[0059] (3)

[0060] In the formula, These are the longitudinal velocity vector lead angle and the lateral velocity vector lead angle along the line connecting the original position and the new position, respectively. The tilt and yaw angles of the aircraft's flight path from its original position to a new position. (Subscript "") " indicates the first The aircraft reached the first [position]. The quantity at a new position. , These are the line-of-sight angles of the aircraft as it flies from its original position to a new position, both longitudinally and laterally.

[0061] (3) Total individual payout matrix

[0062] The distances and velocity lead angles between each original position and different new positions are normalized and scaled down to the specified values. The interval is defined, and weights are assigned. Based on the preceding analysis, let the formula for calculating individual returns be:

[0063] (4)

[0064] in

[0065] (5)

[0066] For individual benefit, For the weights, and .

[0067] From this, we can obtain Each original position pair The individual payoff matrix for each desired new position is as follows:

[0068] (6)

[0069] Step 2: Initial screening of solutions based on individual benefits

[0070] After obtaining the individual payoff matrix, the proposed solutions are initially screened. The number of original positions and the number of new positions are both [number missing]. The original location number was , , , The new location number is , , , The initial screening approach involves selecting multiple options with higher individual returns according to certain principles as initial screening options, and then calculating the individual returns for each initial screening option. The individual return for each initial screening option is the sum of the individual returns for all individuals who move from the original position to the new position within that option.

[0071] In this embodiment of the invention, when selecting the optimal solution for individual benefits, the question arises as to which original position of the aircraft should be prioritized. The method of this invention is as follows: First, priority is given to the original position... The aircraft were allocated at the location, and then... In order, each aircraft at its original position is assigned a new position with better individual benefits according to certain rules; when priority is given to... After the allocation scheme is selected, priority will be given to the original position. The aircraft were allocated, and then according to... Assign them in that order; continue in this manner, finally prioritizing the original position. The aircraft were allocated, and then according to... The allocation is carried out in the order specified. Therefore, for For each aircraft in its original position, the chances are equal.

[0072] Specifically:

[0073] set up , It is a fixed integer, and , The specific allocation includes the following steps:

[0074] Step 1: Based on the individual payoff matrix, in the original position Prioritize the original position and take the queue to be allocated as follows. Execute S101~S104 to assign new positions;

[0075] Use the current priority original position as the current allocation original position. All original positions are initialized and marked as unallocated;

[0076] S101: Based on the individual payoff matrix, retrieve the original position of the current allocation. The individual gains generated when flying to different new locations are sorted in descending order of individual gains, and the top few are retained. A new location, in the reserved Randomly select a new position from the new positions as the current original position. allocation object That is, the current allocation of the original position The aircraft flew to a new location. ; Current allocation in original position and its allocation objects The marker is changed to "allocated", and the original position of the "allocated" item is moved to the corresponding position in the individual payoff matrix. and new location Delete the row and column it belongs to;

[0077] S102: Update the current allocation location Find the next original position in the queue to be allocated; determine if the number of new positions marked as unallocated is greater than 1. a If yes, return to S101; otherwise, execute S103.

[0078] S103: Reset the current assignment to its original position. Randomly select a new location from the remaining unassigned locations as its assignment target. That is, the current allocation of the original position The aircraft flew to a new location. ; Current allocation in original position and its allocation objects The marker is changed to "allocated", and the original position of the "allocated" item is moved to the corresponding position in the individual payoff matrix. and new location Delete the row and column it belongs to;

[0079] S104: Update the current allocation location To sort to the next original position after it; check if the number of new positions marked as unassigned is 0. If it is not 0, return to S103; if the number of new positions marked as unassigned is 0, then... The allocation results of all original positions have been obtained. At this point, each aircraft at its original position has one and only one new position to be allocated, thus completing the allocation of the scheme for the priority original position.

[0080] Perform the above steps to obtain the priority original position. Allocation scheme;

[0081] Step 2: Retrieve the original position Prioritize the original position and take the queue to be allocated as follows. Execute steps S101~S104;

[0082] And so on, finally taking the original position. Prioritize the original position and take the queue to be allocated as follows. Execute steps S101~S104;

[0083] Each time generated The allocation scheme ultimately yields A preliminary screening program.

[0084] Step 3: With other The original position takes priority, and each time it is also generated. There are various allocation schemes, and eventually there will be... Initial screening protocol;

[0085] Specifically, priority should be given to the original position. The spacecraft was assigned a new location, and then given Taking allocation as an example, let's illustrate the process of priority allocation in each round. , It is a fixed integer, and , The specific allocation process is as follows:

[0086] ① Based on the individual payoff matrix, prioritize allocating resources to the original position. The aircraft is assigned a new position. First, based on the original position... The individual gains generated when a spacecraft flies to different new locations, eliminating the competition. For new positions with lower individual returns, only those with lower returns are retained. A new location with higher individual gains. (Assuming retention is maintained.) One pair The new position offers greater individual benefit, then the original position is left untouched. The aircraft in the area are preserved A new position is randomly selected from the given positions as the allocation target. The corresponding allocation combination is: That is, the original position The aircraft flew to a new location. This is taken as the allocation result for the first aircraft. Once an aircraft is assigned a new position, it cannot be assigned another new position, and this new position cannot be assigned to another aircraft that was originally in that position. Therefore, the original position is removed from the individual payoff matrix. The aircraft and new location After removing the row and column, return it to its original position. The aircraft was assigned a new location.

[0087] ② Give priority to After assigning the new positions, proceed according to the original position order. The aircraft was assigned a new position. Based on its original position... The aircraft flew towards the location Individual gains generated when in different new positions outside the original location, retaining the previous... One pair Move the aircraft to a new location where it can gain more benefit, and then leave the original location. The aircraft is in the preservation Randomly select one from the original positions as its allocation target; the corresponding allocation combination is: This is used as the allocation result for the aircraft at the second original position. Then, following this allocation rule, the original positions are allocated sequentially. , , , The aircraft was assigned a new location.

[0088] ③ When giving After allocation, return to the original position. The aircraft is assigned a new position. When the original position... The aircraft flew towards the location , , , , When a new position is created outside the given location, the number of remaining new positions is: At this point, retain the total number of remaining new positions, and let The aircraft at the location will randomly select one of the reserved new locations as the allocation target, and the corresponding allocation combination is as follows: , thus as the first Original position The allocation results of the aircraft at the location.

[0089] ④ When giving After allocation, return to the original position. The aircraft is assigned a new position. When the original position... The aircraft flew towards the location , , , , When a new position is created outside the given location, the number of remaining new positions is: Retain the remaining number of new positions. Then, let the aircraft randomly select one of the retained new positions as the allocation target. The corresponding allocation combination is: , thus as the first Original position The allocation results of the aircraft at the location. Then, according to this allocation rule, the aircraft at the original location are allocated sequentially. , , The aircraft was assigned a new location.

[0090] ⑤ When giving After allocation, return to the original position. The aircraft is assigned a new position. When the original position... The aircraft flew towards the location When a new position is created outside the given position, the number of remaining new positions is 1. At this point, the remaining new positions are... The allocation target of the spacecraft, and the corresponding allocation combination are: , thus as the first The allocation results for the aircraft at their original positions. At this point, each aircraft has one and only one new position, completing one allocation cycle.

[0091] As can be seen from the above, priority should be given to the original position. The spacecraft was assigned a new location, and then given During the allocation of aircraft, except for the last original position in the allocation sequence Apart from the aircraft in their original positions, all other aircraft will be randomly assigned to a relatively better new position from among the reserved new positions. Therefore, assuming priority is given to... The allocation scheme for assigning new positions to aircraft is as follows: Different allocation schemes are generated according to the given allocation rules. Other The original position takes priority, and each time it is also generated. There are several options, and eventually there will be... A preliminary screening program.

[0092] The total number of screening and allocation schemes is , recorded as Let the first... The individual benefit of each solution is The calculation method is as follows:

[0093] (7)

[0094] In the formula, For the plan The Middle The aircraft, originally in its original position, flew towards the... Individual gains at a new location The sum of the individual payoffs for each aircraft moving from its original position to its new position is the individual payoff for this scheme. The individual payoffs for each selected scheme are:

[0095] (8)

[0096] At this point, the preliminary screening and allocation plan is complete.

[0097] Step 3: Calculation of Synergistic Benefits for Initial Screening Schemes

[0098] During the allocation process, coordination must also be considered, such as minimizing the time difference in arrival at the target, i.e., ensuring that all missiles arrive at the target as simultaneously as possible. In addition to considering the aforementioned arrival time coordination issue, this invention also considers minimizing the risk of collision and avoiding trajectory intersections during the flight of the aircraft from its original position to a new position. The impact of two factors will be analyzed next.

[0099] (1) Time-related benefits

[0100] During the allocation process, the time difference between each aircraft's flight from its original position to its new position needs to be as small as possible. The smaller the time difference, the greater the time coordination benefit. The time coordination benefit is defined as: the time difference between the last aircraft's arrival time at its new position and the first aircraft's arrival time at its new position, multiplied by a certain proportional coefficient. The aircraft flew from its original position to the... The formula for predicting the flight time at a new location is:

[0101] (9)

[0102] In the formula, To approximate the velocity, the solution formula is as follows:

[0103] (10)

[0104] No. Time-coordinated benefits corresponding to each initial screening scheme for

[0105] (11)

[0106] In the formula, The time it takes for the first aircraft to travel from its original position to its new position. The time it takes for the last aircraft to travel from its original position to its new position (obtained from (9)). The greater the time difference between the arrival times of each aircraft from its original position to its new position in each scheme, the smaller the time coordination benefit; therefore, the coefficient... .

[0107] (2) Trajectory Crossover Benefits

[0108] During the flight of each aircraft from its original position to a new position, in order to reduce the risk of mutual interference or collision, the flight paths of each aircraft need to avoid intersecting as much as possible. Define a trajectory intersection factor. This indicates the complexity of trajectory intersections. The aircraft's flight trajectory is projected onto both the lateral and longitudinal planes. Trajectory intersections in the lateral plane are defined as lateral trajectory intersections, and those in the longitudinal plane are defined as longitudinal trajectory intersections. The longitudinal trajectory intersection factor is described in detail below. and lateral trajectory cross factor The calculation method.

[0109] (a) Longitudinal trajectory intersection

[0110] For the allocation scheme of each new position, take the position corresponding to the original position of each aircraft. coordinate Arrange them in ascending order from smallest to largest. The original position order matrix of the aircraft is as follows: Then obtain the corresponding arrival at the new location. The coordinates, corresponding to the new position order matrix are as follows , respectively

[0111] (12)

[0112] The number of times the elements are not arranged in ascending order is the number of vertical trajectory intersections. If...

[0113] (13)

[0114] If the longitudinal trajectory intersects once, it is counted as one intersection; otherwise, it is counted as no intersection. This process is repeated sequentially. The intersection cases are counted, and the number of intersections is used as the longitudinal trajectory intersection factor. .

[0115] (b) Lateral trajectory intersection

[0116] For each new position allocation scheme, take the position corresponding to the original position of each aircraft. coordinate Arrange them in ascending order from smallest to largest, the order matrix is ​​as follows: Then obtain the corresponding arrival at the new location. Coordinates, corresponding matrix is , respectively

[0117] (14)

[0118] The number of times the lateral trajectory intersects is calculated by counting the number of times the trajectories are not in ascending order. If

[0119] (15)

[0120] If the lateral trajectory crosses once, it is counted as one; otherwise, it is counted as no crossover. This process is repeated sequentially. The intersection situation is determined, and the number of intersections is counted as the lateral trajectory intersection factor. .

[0121] (c) Trajectory Cross-Benefit Calculation Method

[0122] Calculate the sum of the number of longitudinal and lateral trajectory intersections for each scheme.

[0123] (16)

[0124] In the formula, For the plan The number of longitudinal trajectory intersections, For the plan The number of lateral trajectory intersections, For the plan The total number of trajectory intersections.

[0125] The trajectory crossover payoff for each option is then...

[0126] (17)

[0127] In the formula, For the plan Trajectory crossover benefits, This represents the cross-trajectory benefit ratio. Generally, the more times the aircraft trajectories cross paths in each scheme, the smaller the trajectory cross-trajectory benefit; therefore, it is usually taken as... .

[0128] (3) Calculation of synergistic benefits

[0129] After calculating the time-coordination benefit and trajectory-crossing benefit separately, the coordinating benefit of each scheme is calculated. The calculation method is as follows:

[0130] (18)

[0131] Therefore, the synergistic benefit matrix for each scheme can be obtained as follows:

[0132] (19)

[0133] Step 4: Calculation of comprehensive benefits based on individual and collaborative benefits

[0134] Based on equations (8) and (19), the allocation scheme can be calculated. Individual benefits and synergistic benefits Then the allocation scheme The overall benefit is

[0135] (20)

[0136] In the formula, These are the weighting coefficients for the individual returns of the scheme. The combined collaborative weighting coefficient for time synchronization revenue and trajectory crossover revenue, and has

[0137] (twenty one)

[0138] Based on the overall returns, the maximum value of the overall returns is selected as the final allocation scheme.

[0139] Example 1

[0140] The following is a verification of the analytical optimization method based on aircraft formation position reconstruction.

[0141] (1) Simulation condition settings

[0142] Common formations for multi-aircraft formations include line formation, square formation, trapezoidal formation, and triangular formation. This invention uses the square formation as an example to compare analytical optimization methods and genetic algorithms, verifying the performance of the analytical algorithm.

[0143] Let the number of aircraft be... The numbers are M1, M2, ..., M12, and the desired positions in the reconstructed formation are T1, T2, ..., T12. Assuming the formation is transformed from a horizontal line to a square formation, the scenario for reconstructing the formation and allocating positions is as follows: Figure 1 As shown.

[0144] The initial conditions for a multi-aircraft formation are shown in Table 1. In the table, These represent the initial coordinates of the spacecraft in the ground coordinate system. Position in direction Indicates the initial launch velocity. This represents the initial trajectory inclination angle and trajectory deflection angle.

[0145] Table 1 Initial conditions for each aircraft in the formation

[0146]

[0147] The expected positional distribution of the square formation is shown in Table 2.

[0148] Table 2 Expected Location Distribution of Square Formation

[0149]

[0150] The weighting coefficients for individual income, collaborative income, and comprehensive income are set as shown in Table 3.

[0151] Table 3. Weighting Coefficients of Individual Income, Collaborative Income, and Comprehensive Income

[0152]

[0153] Let the number of solutions of the analytical optimization algorithm be . K =1200, there are 12 possible new aircraft position allocation orders, and each allocation order has 100 possible schemes. a =3, m =10.

[0154] For comparison, the genetic algorithm described in Jiang Lai's paper "Multi-Objective Allocation Strategy Based on Genetic Algorithm" is used to solve the above problem. In this case, the original-new position allocation matrix is ​​used as the design variable, and the objective function is set as follows: The relevant parameter settings for the genetic algorithm are shown in Table 4.

[0155] Table 4. Parameters related to the improved genetic algorithm

[0156]

[0157] (2) Comparative simulation analysis

[0158] Based on the simulation conditions in Tables 1, 2, 3, and 4, the formation was transformed from a line formation to a square formation. The analytical optimization method and the genetic algorithm were used to simulate and analyze the reconfiguration of the aircraft's position allocation.

[0159] The final allocation scheme of the parsing algorithm is as follows: Figure 2 As shown.

[0160] The objective function is solved using a genetic algorithm, and the objective function value for each generation of the population is as follows: Figure 3As shown, the allocation scheme is as follows: Figure 4 As shown.

[0161] Depend on Figure 3 It can be seen that the objective function value gradually decreases and eventually converges to the minimum value, which is... The corresponding maximum comprehensive return is .

[0162] The aircraft position allocation results of the analytical optimization algorithm and the genetic algorithm are shown in Table 5.

[0163] Table 5. Aircraft Position Allocation Table

[0164]

[0165] As can be seen from Table 5, except for the aircraft at their original positions M7 and M8, the expected positions that all aircraft need to reach are the same for both the analytical optimization algorithm and the genetic algorithm.

[0166] The performance of the analytical optimization algorithm and the genetic algorithm across various metrics is compared, and the comparison results are shown in Table 6.

[0167] Table 6. Parameters related to the improved genetic algorithm

[0168]

[0169] Table 6 shows that the individual returns, collaborative returns, and maximum returns of the analytical optimization algorithm and the genetic algorithm are not significantly different. However, in terms of time, the simulation time of the analytical optimization algorithm is 0.0748s, while that of the genetic algorithm is 10.1401s, making the analytical optimization algorithm about 140 times faster than the genetic algorithm, demonstrating a significant advantage in computational speed. In engineering applications, methods that take a long time to obtain the optimal solution are not feasible; methods that can quickly obtain a near-optimal solution are more valuable. A comparison of the performance indicators of the analytical optimization algorithm and the genetic algorithm shows that in the multi-aircraft formation position reconstruction problem, the analytical optimization algorithm can obtain a near-optimal solution very quickly, meeting engineering needs and possessing broad prospects for military applications.

[0170] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analytical optimization of aircraft formation position reconstruction, characterized in that, Taking the position before the formation of the aircraft as the original position and the position after the formation as the new position, with n aircraft in n original positions and n expected new positions after formation, each of the n original positions corresponds to one feasible solution for reaching the n expected new positions. The following steps are used for reconstruction analysis and optimization: Step 1: Evaluate the gains for a single aircraft moving from its original position to its new position by combining the distance between the aircraft's original and new positions, and the velocity vector lead angle. Each original position pair A matrix of individual payoffs for each desired new position; Step 2: After obtaining the individual payoff matrix, the schemes are initially screened based on the individual payoffs of the aircraft at the original position and the desired new position, and the individual payoffs of the initial screened schemes are calculated. Step 3: For each initial screening plan, multiply the difference between the time taken for the last aircraft to travel from its original position to its new position and the time taken for the first aircraft to travel from its original position to its new position by a certain proportional coefficient to obtain the time synergy benefit of the initial screening plan; Time-coordinated benefits corresponding to each initial screening scheme for In the formula, The time it takes for the first aircraft to travel from its original position to its new position. This represents the time it takes for the last aircraft to travel from its original position to its new position. The greater the time difference between the arrival times of each aircraft in each scenario, the smaller the time coordination benefit; therefore, the coefficient... ; For each initial screening scheme, the trajectory crossover benefit is evaluated based on the number of trajectory crossovers in the flight paths of each aircraft from its original position to its new position; the trajectory crossover benefit for each scheme is... In the formula, For the plan Trajectory crossover benefits, This is the cross-return ratio coefficient. For the plan The overall number of trajectory intersections is considered. For each scheme, the more trajectory intersections the aircraft undergoes, the smaller the benefit of trajectory intersections. ; Calculate the synergistic benefits of each initial screening scheme based on the time synergy benefits and trajectory crossover benefits; After calculating the time-coordinated benefit and trajectory-crossing benefit separately, the coordinated benefit of each scheme is calculated; the calculation method is as follows: The synergistic benefit matrix of each scheme is obtained as follows: ; Step 4: Based on the individual benefits and collaborative benefits of the initial screening schemes, the weighted sum is obtained to get the comprehensive benefit. According to the comprehensive benefit, the scheme with the largest comprehensive benefit is selected as the final aircraft formation position reconstruction scheme. Allocation scheme Individual benefits and synergistic benefits Then the allocation scheme The overall benefit is In the formula, These are the weighting coefficients for the individual returns of the scheme. The combined collaborative weighting coefficient for time synchronization revenue and trajectory crossover revenue, and has Based on the comprehensive returns, the maximum value of the comprehensive returns is selected as the final allocation scheme.

2. The analytical optimization method for reconstructing aircraft formation positions as described in claim 1, characterized in that, The method combines the distance between the aircraft's original and new positions, as well as the velocity vector lead angle, to evaluate the individual gains of a single aircraft as it moves from its original position to its new position. Each original position pair The individual payoff matrix for each desired new position is as follows: The distance between the original position i and the new position j of the aircraft is r ij ; The angle between the aircraft's velocity vector and the line connecting the original position and the new position is the velocity lead angle, including the longitudinal velocity vector lead angle. and lateral velocity vector lead angle ; The distance and velocity lead angle between the original and new positions of the aircraft are normalized and scaled down to the specified values. The interval is calculated, weights are assigned, and the weighted sum is used to obtain the individual benefit of the current aircraft from its original position i to its new position j; From this, we can obtain Each original position pair A matrix of individual payoffs for each desired new position.

3. The analytical optimization method for reconstructing aircraft formation positions as described in claim 1, characterized in that, After obtaining the individual payoff matrix, the proposed schemes are initially screened based on the individual payoffs for the desired new position from the original position of the aircraft, resulting in a preliminary selection of schemes. Specifically: In the scheme, the n original positions are M1~M n Prioritize the original position The aircraft is assigned the desired new position, and then... In the order of priority, assign new positions with better expected returns to the corresponding original positions according to certain rules; when priority is given to... After the allocation scheme is selected, priority will be given to the original position. Distribute, then according to The order in which they are assigned; This process continues, with priority ultimately given to those in their original positions. Distribute, and then according to The allocation is carried out in the following order, for From the perspective of each original position, their opportunities are equal, thus obtaining the initial screening plan.

4. The analytical optimization method for reconstructing aircraft formation positions as described in any one of claims 1 to 3, characterized in that, For each initial screening scheme, the time difference between the time it takes for the last aircraft to travel from its original position to its new position and the time it takes for the first aircraft to travel from its original position to its new position is multiplied by a certain proportional coefficient to obtain the time synergy benefit of the initial screening scheme. Specifically: No. The aircraft flew from its original position to the... The formula for predicting the flight time at a new location is: In the formula, r ij This represents the distance between the i-th original position and the j-th new position. Approximate speed; No. Time-coordinated benefits corresponding to each initial screening scheme for ; In the formula, The time it takes for the first aircraft to fly from its original position to its new position. The time it takes for the last aircraft to fly from its original position to its new position; This is the proportionality coefficient. .

5. The analytical optimization method for reconstructing aircraft formation positions as described in any one of claims 1 to 3, characterized in that, For each initial screening scheme, the trajectory crossover benefit of the initial screening scheme is evaluated based on the number of trajectory crossovers in the flight trajectories of each aircraft from its original position to its new position. Specifically: Set trajectory cross factor The complexity of trajectory intersections is represented by the following formula: The flight trajectory of the aircraft from its original position to its new position is projected onto the lateral plane and the longitudinal plane, respectively. Trajectory intersections in the lateral plane are defined as lateral trajectory intersections, and trajectory intersections in the longitudinal plane are defined as longitudinal trajectory intersections. The longitudinal trajectory intersection factor is calculated as follows: and lateral trajectory cross factor ; For each new location allocation scheme, take the corresponding original location. coordinate Arrange them in ascending order from smallest to largest; the original positional order matrix is... Then obtain the corresponding new attack position. The coordinates, corresponding to the new position order matrix are as follows , respectively The number of times the data is not sorted in ascending order is the number of vertical trajectory intersections; if If the longitudinal trajectory crosses once, the number of intersections is counted as 1; otherwise, there is no intersection. This process is repeated sequentially. The intersection cases are counted, and the number of intersections is used as the trajectory intersection factor. ; For each new location allocation scheme, take the corresponding original location. coordinate Arrange them in ascending order from smallest to largest, the order matrix is ​​as follows: Then obtain the corresponding information about the aircraft flying to the new location. Coordinates, corresponding matrix is , respectively The number of times the trajectory is not sorted in ascending order is the number of lateral trajectory intersections. If the crossover occurs, it counts as one; otherwise, it counts as no crossover. This process is repeated sequentially. The intersection situation is determined, and the number of intersections is counted as the lateral trajectory intersection factor. ; Calculate the sum of the longitudinal and lateral trajectory intersections for each initial screening scheme. ; For the plan The number of longitudinal trajectory intersections, For the plan The number of lateral trajectory intersections, For the plan The total number of trajectory intersections; The trajectory crossover payoff for each option is then... ; For the plan Trajectory crossover benefits, This is the cross-return ratio coefficient. .

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