Multi-form cooperative penetration trajectory planning and voyage adjustment method based on geometric curve

Abstract

The application discloses a multi-form cooperative penetration path planning and voyage adjustment method based on geometric curves, and comprises the following steps: acquiring aircraft performance parameter information, path constraint information and target situation information; setting the required path planning form for each aircraft individual; selecting a cooperative penetration strategy; converting the arrival time requirement into a voyage constraint according to the task requirement, and performing voyage adjustment; and if the voyage adjustment cannot be performed, re-planning the path. The application flexibly combines a circle and a straight line, adopts three path planning modes to design a penetration strategy based on the task requirements of simultaneous attack and sequential attack, and constructs a voyage adjustment method for different path planning modes.

Description

Technical Field

[0001] This invention relates to the field of aircraft trajectory planning application technology, and in particular to a method for multi-form collaborative penetration trajectory planning and range adjustment based on geometric curves. Background Technology

[0002] In recent years, with the gradual improvement of defense systems, penetration techniques and online trajectory planning technologies have played a greater role, highlighting the necessity of developing penetration strategies. Adopting reasonable strategies can effectively circumvent enemy defense equipment and increase the difficulty for the enemy to predict flight trajectories. Because high-speed aircraft possess rapid maneuverability, higher demands are placed on algorithm processing time. To efficiently complete attack missions, it is necessary to use more efficient algorithms that do not consume excessive computational resources in the design of penetration methods.

[0003] Compared to single-vehicle attacks, swarm attacks have significant advantages in scale and coordination, which can significantly improve mission completion efficiency and increase the success rate of penetration attacks. However, the trajectory planning problem for multi-vehicles is more complex than that for single-vehicles. To meet the requirements of coordinated attacks, the arrival time requirements of different aircraft need to be considered. If the aircraft speed is fixed, the arrival time can be converted into a range constraint. Therefore, a range adjustment method that meets the arrival time requirement is needed. Hence, a penetration trajectory planning and range adjustment method that solves the above problems is required. Summary of the Invention

[0004] This invention aims to at least partially solve one of the technical problems in related technologies. To this end, one objective of this invention is to propose a multi-form cooperative penetration trajectory planning and range adjustment method based on geometric curves, constructing an online range adjustment method that meets arrival time requirements.

[0005] According to the present invention, a multi-form cooperative penetration trajectory planning and range adjustment method based on geometric curves is proposed, the method steps are as follows:

[0006] S1: Acquire aircraft performance parameters, trajectory constraints, and target situation information. S and E represent the aircraft's state information at the starting and target points, respectively. S y S ) and (x E y E θ represents the coordinates of the starting point and the target point, respectively. S and θ E These represent the velocity directions of the aircraft at the starting point and the target point, respectively, and De represents the location information of the defense facility. de y de () represents the location coordinates of the defensive facilities;

[0007]

[0008] S2: Set the required trajectory planning format for each individual aircraft;

[0009] S3: Select a coordinated penetration strategy;

[0010] S4: Based on mission requirements, convert arrival time requirements into flight range constraints and adjust the flight range accordingly;

[0011] S5: If the route adjustment in step S4 cannot be executed, return to step S2 to replan the route.

[0012] Preferably, the trajectory planning forms in step S2 include the basic mode, the feint mode, and the multi-circle mode;

[0013] S21: The basic mode achieves maneuvering and turning trajectory planning through circular arc trajectory, and controls the speed direction through two circles. The trajectory form is circular arc-straight line-circular arc.

[0014] S22: The feint attack mode is divided into single feint attack and double feint attack. It adopts a combination of circular arc and straight line trajectory. By hiding the relationship between the current course of the aircraft and the final target, it achieves tactical deception and reduces the accuracy of the enemy's tactical reaction.

[0015] S23: The multi-circle mode uses the connection of pure circular arc trajectories to form the overall track.

[0016] Preferably, the method steps for the basic mode of flight planning in step S21 are as follows:

[0017] S211: Calculate the coordinates of the center of the two maneuvering circles based on the aircraft's status information at the starting point and target point;

[0018]

[0019] Among them, (x Si y Si (i = 1, 2) are the coordinates of the centers of the circles on either side of the initial position, and (x... Ei y Ei ), (i = 1, 2) are the coordinates of the centers of the circles on either side of the target point, and α S Indicates the initial directional maneuver, α E Indicates the direction of the terminal attack, r s and r e These are the radii of the initial circle and the final circle, respectively.

[0020] S212: Calculate the equation of the tangent line connecting the initial circle and the final circle;

[0021]

[0022] in, Represents the straight-line distance between the centers of the two circles. λ and μ represent the angles between the line connecting the point of tangency and the center of the circle and the line connecting the centers of the two circles, respectively; μ represents the angle between the line connecting the centers and the x-axis; r s and r e The radii of the initial circle and the final circle are respectively used to solve the equations of the tangents and the positions of the tangent points to form the straight line segments and circular arc segments of the track.

[0023] Preferably, the method steps for flight planning in the single feint attack mode in step S22 are as follows:

[0024] S221: Calculate the coordinates of the center of the two maneuvering circles based on the aircraft's state information at the starting point and target point;

[0025] S222: Calculate the tangent point between the feint target and the initial maneuver circle, and solve the tangent equation and the position of the tangent point to form the straight line segment and circular arc segment track;

[0026] The coordinates of the center of the end-effector circle (x E y E The solution formula is:

[0027]

[0028] Where y = a1x + b1 is the expression for the feint target and the tangent of the initial circle, and y = a2x + b2 is the expression for the line pointing to the target, (x j y j Let y be the intersection of the two lines, y = ax + b be the analytical expression for the angle bisector of the two lines, and r be the radius of the end circle.

[0029] Preferably, the double feint attack mode in step S22 is to repeat steps S221 and S222 once to complete the switching of the feint attack target.

[0030] Preferably, the method steps for multi-circle mode range planning in step S23 are as follows:

[0031] S231: Calculate the coordinates of the center of the two maneuvering circles based on the aircraft's state information at the starting point and the target point;

[0032] S232: Calculate the center (x) of the circumcircle. o y o );

[0033]

[0034] in, The point of tangency on the circle (x i y i ) and center (x)r y r The vector formed by (x) o y o ) represents the coordinates of the center of the circumcircle, and R is the radius of the circumcircle.

[0035] Preferably, the cooperative penetration strategy in step S3 includes a simultaneous attack strategy of multiple aircraft arriving at the same time and attacking from multiple directions, and a sequential attack strategy of multiple aircraft conducting continuous attacks in the same direction with time intervals.

[0036] S31: The simultaneous attack strategy requires mission negotiation to negotiate the attack direction of each aircraft towards the target, thereby determining the optimal attack direction for each aircraft.

[0037] Perform trajectory pre-planning and form different mission combinations. Calculate the range of an individual aircraft under a set trajectory pattern and different attack directions, forming multiple combination methods. In each combination, the same aircraft selects different attack directions, and establish a mission allocation matrix D. k :

[0038]

[0039] Where n represents the number of aircraft, m represents the selectable attack direction, and D k The matrix contains information about the attack direction chosen by the aircraft in the k-th combination, d ij This indicates whether the i-th aircraft chooses the j-th attack direction; if d is selected... ij =1, do not select d ij =0;

[0040] For each combination, task negotiation is performed to establish the objective function:

[0041]

[0042]

[0043] L j J1 represents the initial range of each aircraft, J2 represents the minimum maximum range in each combination, and J2 represents the minimum range adjustment within the combination when attacking simultaneously. The combination with the minimum range adjustment and the minimum maximum range is selected as the task allocation method.

[0044] Select the value L with the largest range in the optimal combination. max Used for adjusting the aircraft's range;

[0045] L max =max{L1, L2, ..., L n} (9)

[0046] S32: When adopting a sequential attack strategy, the routes under different trajectory planning forms are reordered to ensure that the adjustment of each route is minimized while meeting the sequential arrival requirements. L is the set of all routes.

[0047] L = {L1, L2, ..., L} n}, (L1>L2>...>L n (10)

[0048] Preferably, based on mission requirements, the arrival time requirement is converted into a flight range constraint, and the flight range is adjusted accordingly:

[0049] S41: In the basic mode, the original flight path consists of two circular arcs and one straight line. The flight path is adjusted by adding a circular arc, as shown in equation (11). B Original range in base mode, θ ex To increase the curvature of the arc segment, L max This is the maximum range among all aircraft.

[0050] R ex θ ex =L max -L B (11)

[0051] S42: In feint attack mode, it is necessary to ensure that the attack direction is pointing towards the feint target. Therefore, a three-segment circular arc is used to adjust the flight path without changing the velocity direction after the extended trajectory, as shown in equation (12). f For the original range in feint attack mode, R exi θ exi (i = 1, 2, 3) are the radius of the circle and the central angle of the corresponding arc trajectory, respectively. exi θ exi (i = 1, 2, 3) are the lengths of the three circular arcs, l s L is the length of the original straight line segment. max This represents the maximum range among all aircraft.

[0052] R ex1 θ ex1 +R ex2 θ ex2 +R ex3 θ ex3 -l s =L max -L f (12)

[0053] S43: The range in multi-circle mode is the sum of the lengths of multiple circular arcs. The range is calculated using the method shown in equation (13), and the range is adjusted by adjusting the curvature of each circular arc. L R For the original range in feint attack mode, Ri θ i These are the radius of the circle and the central angle of the corresponding arc trajectory, respectively.

[0054]

[0055] The beneficial effects of this invention are:

[0056] (1) Using geometric curves with arcs and straight lines as the main components for combined planning consumes less computational resources and has a faster calculation speed, which meets the requirements of online planning.

[0057] (2) Three trajectory planning modes are adopted, combined with the ideas of feint attack and multiple maneuvers. By adjusting the turning radius, feint attack target and other elements, multiple trajectory combinations are formed to increase the difficulty for the enemy to predict the trajectory.

[0058] (3) A range adjustment method for different flight path patterns is proposed. The adjustment method is designed based on the characteristics of geometric trajectory, which can meet the performance constraints of the aircraft and does not affect the setting of penetration strategies such as feint attacks, and fully meets the arrival time requirements.

[0059] (4) Combine simultaneous and sequential attacks to improve the success rate of penetration by leveraging the advantages of collaboration and scale. Attached Figure Description

[0060] In the attached diagram:

[0061] Figure 1 This is a schematic diagram of the overall planning process proposed in this invention;

[0062] Figure 2 This is a schematic diagram of the basic mode trajectory proposed in this invention;

[0063] Figure 3 This is a schematic diagram of the flight path for the single feint attack mode proposed in this invention;

[0064] Figure 4 This is a schematic diagram of the flight path for the dual feint attack mode proposed in this invention;

[0065] Figure 5 This is a schematic diagram of the multi-circle mode track proposed in this invention;

[0066] Figure 6 This is a schematic diagram of the collaborative strategy proposed in this invention;

[0067] Figure 7 This invention provides a basic mode range adjustment method.

[0068] Figure 8 This invention provides a method for adjusting the flight range in a feint attack mode.

[0069] Figure 9This is a simulation example 1 of the simultaneous attack proposed in this invention;

[0070] Figure 10 This is a simulation example 2 of the simultaneous attack proposed in this invention;

[0071] Figure 11 Simultaneous attack simulation example 3 proposed in this invention

[0072] Figure 12 This is a simulation example 1 of the sequential attack proposed in this invention;

[0073] Figure 13 This is simulation example 2 of the sequential attack proposed in this invention;

[0074] Figure 14 This is simulation example 3 of the sequential attack proposed in this invention. Detailed Implementation

[0075] To better illustrate the purpose and advantages of this invention, the following description, in conjunction with the accompanying drawings and simulation examples, further explains the invention. The overall planning process is as follows: Figure 1 As shown.

[0076] Step 1: Set initial flight parameters and environmental constraints

[0077] Set flight parameters and target situation information. As shown in equation (1), S and E are the state information of the aircraft at the starting point and the target point, respectively. S y S ) and (x E y E θ represents the coordinates of the starting point and the target point, respectively. S and θ E These represent the velocity directions of the aircraft at the starting point and the target point, respectively, and De represents the location information of the defense facility. de y de () represents the location coordinates of the defensive facility.

[0078]

[0079] Step 2: Set the trajectory planning format

[0080] The collaborative trajectory planning method proposed in this invention sets a trajectory planning form for each individual aircraft, which includes three trajectory forms: basic mode trajectory, feint mode trajectory, and multi-circle feint mode trajectory.

[0081] (1) The basic pattern adopts a combination of circular arcs and straight lines in the flight path, such as Figure 2As shown, the velocity direction is controlled by two circular arc trajectories. This trajectory planning method has various forms, fast online calculation speed, fewer constraints, and is easy to obtain a trajectory that meets the mission requirements. First, based on the aircraft's state information at the starting point and the target point, the coordinates of the center of the two maneuvering circles are calculated using equation (2).

[0082]

[0083] Among them, (x S y S ) and (x E y E ) are respectively, (x Si y Si (i = 1, 2) are the coordinates of the centers of the circles on either side of the initial position, and (x... Ei y Ei ), (i = 1, 2) are the coordinates of the centers of the circles on either side of the target point, and α S Indicates the initial directional maneuver, α E Indicates the direction of the terminal attack, r s and r e These are the radii of the initial circle and the final circle, respectively.

[0084]

[0085] The equation of the tangent connecting the initial circle and the final circle is calculated using equation (3). Represents the straight-line distance between the centers of the two circles. λ and μ represent the angles between the line connecting the point of tangency and the center of the circle and the line connecting the centers of the two circles, respectively; μ represents the angle between the line connecting the centers and the x-axis; r s and r e The radii of the initial circle and the final circle are respectively used to solve the equations of the tangents and the positions of the tangent points to form the straight line segments and circular arc segments of the track.

[0086] (2) The feint attack mode can be divided into single feint attack and double feint attack. By hiding the relationship between the current course of the aircraft and the final target, tactical deception is achieved, reducing the accuracy of the enemy's tactical response.

[0087] like Figure 3 The feint attack shown uses a combination of circular and straight flight paths, as illustrated. Figure 4As shown, the double feint attack adds a turning circle to the single feint attack, deceiving the target twice. In the feint attack mode, the information of the two circles can be obtained by using equation (2). Then, the tangent point between the feint target and the initial maneuvering circle is calculated. The tangent equation and the position of the tangent point are solved to form the straight line segment and the arc segment track. The double feint attack requires the above calculation to complete the switching of the feint target. Both feint attack modes change the speed direction of the aircraft through the terminal maneuvering circle to point towards the attack target. The center coordinates (x, y, y) of the terminal maneuvering circle can be obtained by solving the equation (4). E y E ).

[0088]

[0089] Where y = a1x + b1 is the expression for the feint target and the tangent of the initial circle, and y = a2x + b2 is the expression for the line pointing to the target, (x j y j Let y be the intersection of the two lines, y = ax + b be the analytical expression for the angle bisector of the two lines, and r be the radius of the end circle.

[0090] (3) The multi-circle feint attack mode adopts the following... Figure 5 The method of connecting pure circular arc trajectories shown can be used to obtain the maneuvering circle of the initial point and target position through equation (2), and the center (x) of the circumscribed circle can be calculated using equation (5). o y o ).

[0091]

[0092] in, The point of tangency on the circle (x i y i ) and center (x) r y r The vector formed by (x) o y o Let R be the coordinates of the center of the circumcircle, and R be the radius of the circumcircle. Figure 5 The maneuver shown here involves multiple changes in speed and direction, which, combined with collaborative planning, can effectively increase the difficulty of interception.

[0093] Step 3, Select a penetration strategy

[0094] Two penetration strategies were designed: a simultaneous attack strategy and a sequential attack strategy.

[0095] Simultaneous attack strategies such as Figure 6As shown in the left figure, simultaneous attacks require multiple aircraft to arrive at the same time and penetrate the defenses from different directions. Simultaneous attack strategies, by attacking from multiple directions, make it easier to break through the target's defense system. For example... Figure 6 As shown in the right figure, sequential attacks require multiple aircraft to launch consecutive attacks in the same direction with time intervals. This attack method is difficult for defense systems to intercept, increasing the success rate of penetration. While attack strategies require mission negotiation, sequential attacks only require the sequencing and adjustment of flight paths.

[0096] (1) If a simultaneous attack strategy is adopted, task negotiation is required to negotiate the attack direction of each aircraft on the target, and then determine the optimal attack direction of each aircraft.

[0097] Perform trajectory pre-planning and form different mission combinations. Calculate the range of an individual aircraft choosing different attack directions under a set trajectory pattern, forming multiple combination methods, in which the same aircraft selects different attack directions in each combination. Establish a mission allocation matrix D. k :

[0098]

[0099] Where n represents the number of aircraft, m represents the selectable attack direction, and D k The matrix contains information about the attack direction chosen by the aircraft in the k-th combination, d ij This indicates whether the i-th aircraft chooses the j-th attack direction; if d is selected... ij =1, do not select d ij =0.

[0100] For each combination, task negotiation is performed to establish the objective function:

[0101]

[0102]

[0103] L j J1 represents the initial range of each aircraft, J2 represents the minimum maximum range in each combination, and J2 represents the minimum range adjustment within the combination when attacking simultaneously. The combination with the minimum range adjustment and the minimum maximum range is selected as the task allocation method.

[0104] Find the value L that maximizes the range in the selected optimal combination. max It is used to adjust the flight range of an aircraft.

[0105] L max =max{L1, L2, ..., L n} (9)

[0106] (2) When adopting the sequential attack strategy, the routes of different route planning methods are sorted based on the three route planning methods, as shown in Equation (10). This ensures that the adjustment amount of each route is minimized while meeting the sequential arrival requirements, and L is the set of all routes.

[0107] L = {L1, L2, ..., L} n}, (L1>L2>...>L n (10)

[0108] Step 4: Adjust the flight route according to the coordination requirements.

[0109] According to the mission requirements, the arrival time requirement is converted into a flight range constraint, and the flight range is adjusted accordingly. The flight path consists of circles and straight lines. The straight line segment is calculated using Equation (14), and the circular arc segment is calculated using Equation (15). There are three ways to adjust the flight range depending on the different flight path planning methods.

[0110]

[0111] l r =R i θ i (15)

[0112] Where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the line, respectively, and R i θ i Let l be the radius and radian of arc i, respectively. s Let l be the length of the line. r This is the length of the arc.

[0113] (1) In the basic mode, the original flight path consists of two circular arcs and one straight line, such as Figure 7 As shown, the range is increased by adding a circular arc trajectory. Meanwhile, the attack is calculated using equation (11), and the sequential attack is calculated using equation (16). L B Original range in base mode, θ ex To increase the curvature of the arc segment, in the formula c = v·Δt, the distance the aircraft travels at speed v within a specified attack time interval is represented. ex θ ex Let L be the radian corresponding to the radius of the increased arc, and L be the maximum range in the optimal combination. max

[0114] R ex θ ex =L max -L B (11)

[0115] R ex θex =L max -L B -c (16)

[0116] (2) In feint attack mode, the attack direction must be directed towards the feint target; therefore, a three-segment arc method is used, such as... Figure 8 As shown, without changing the velocity direction after extending the path, the distance on the original straight track is increased by three circular arcs. The actual increase in length is the arc length minus the straight length. The arcs traveled consist of two small circular arcs and one large circular arc. The total increase in length can be divided equally into the increase in length of each small circular arc. The increase in length for each arc segment is shown in equation (17), where L f The original range in the feint attack mode is given by θ, where θ is the central angle corresponding to the arc segment, R is the radius of the arc, and L is the maximum range value in the optimal combination. max ,

[0117]

[0118] The arc is uniquely determined by the angle parameter θ, so the problem becomes solving equation (17). However, this equation has no explicit analytical solution and can only be solved numerically. Therefore, Newton's iteration method is used to solve it, according to the standard formula of Newton's method. The iterative formula is constructed as shown in equation (18), and the specific process is as follows:

[0119] As shown in Table 1:

[0120]

[0121] Table 1. Pseudocode for Newton's Iteration Method

[0122]

[0123] After solving for θ, the coordinates of the centers of the three circular arcs are calculated using equations (19)-(21). This represents the unit vector pointing from the start point to the end point of the line segment. (x) Ls y Ls (x) represents the coordinates of the starting point of the straight line segment. si y si (i = 1, 2, 3) are the coordinates of the center of the three circular arcs, and R is the radius of the three circular arcs.

[0124]

[0125]

[0126]

[0127] (3) In multi-circle mode, the range calculation method shown in equation (13) is adopted, which is the sum of the ranges of multiple circular arcs. The range can be adjusted by adjusting the curvature of the arcs. Equation (22) is for simultaneous attacks, while equation (23) is for sequential attacks. R i , Δθ i Here, c = v·Δt represents the distance the aircraft travels at speed v within a specified attack time interval, and L represents the radius of the arc and the central angle adjusted for each arc segment, respectively. R The range in multi-circle mode.

[0128]

[0129]

[0130]

[0131] Step 5, Replanning the Flight Path

[0132] When it is not possible to adjust the flight path, Figure 1 The process involves trajectory replanning. In feint attack mode, the straight-line range has a length limit, and the aircraft's maneuverability also constrains the radius of the arc. As shown in Table 2, taking a turning radius of 150km as an example, there is an upper limit to the range adjustment using a three-segment arc method. If the range adjustment exceeds the upper limit of the range adjustment for the double feint attack strategy, it switches to a single feint attack to renegotiate the mission and replan the trajectory. If a single feint attack also fails to meet the requirements, the basic mode is used to renegotiate the mission and replan the trajectory to ensure that a trajectory that meets the attack requirements is planned.

[0133] Table 2 Maximum Range Adjustment Values

[0134] Turning radius 150km

[0135]

[0136] In multi-circle mode, to satisfy the velocity direction constraints of the starting point and the target point, the angle of each arc also has upper and lower bounds {θ}. min θ max If the flight path adjustment requirements cannot be met, the basic mode will be used to renegotiate the mission and replan the flight path.

[0137] The following simulation example verifies the cooperative trajectory planning scheme. The target location is (100km, -50km), four defense facilities are set up, the maneuver circle radius is 100km, and three aircraft are used to complete the cooperative mission. The trajectory simulation below was performed on an i5-7300 device, and the calculation time is based on this device.

[0138] Simulation example analysis:

[0139] Simultaneous attack strategy:

[0140] like Figure 9 As shown, the initial position is (-700km, 700km), the initial velocity direction is -30°, and the simultaneous attack mission is completed using three trajectory planning methods: basic mode, feint mode, and multi-circle mode. The range of each mode is 1162km, which meets the requirement of simultaneous arrival. The calculation time is 0.015s.

[0141] The initial position and initial velocity direction were changed to (-500km, 500km) and -10°, respectively. The simulation results are as follows. Figure 10 As shown, with Figure 9 Compared to the previous results, switching from a double feint attack to a single feint attack, and exchanging the attack directions of the basic mode and the multi-circle mode through task negotiation, took 0.017 seconds, verifying the feasibility of the task negotiation algorithm.

[0142] With the initial position set to (-250km, 250km), the simulation results are as follows: Figure 11 As shown, due to the limitation of the maneuvering circle radius, there is no solution for the multi-circle trajectory. Switching to the basic mode verifies the role of the trajectory replanning part in the algorithm. Sequential attack strategy:

[0143] The simulation examples of sequential attack strategies all select an attack direction of -60°, such as... Figure 12 As shown, the range difference is set to 12km, the range of the basic mode is 700.46km, the range of the single feint attack is 712.66km, and the range of the multi-circle mode is 724.66km, which meets the requirements of the sequential attack mission and the calculation time is 0.032s.

[0144] like Figure 13 As shown, changing the initial position to (-300km, 300km) results in a range difference of 24km. At this point, the multi-circle mode has no solution. The basic mode range is 534.01km, the single feint attack range is 582.01km, and the other basic mode range is 557.66km. The calculation time is 0.024s, which meets the requirements of sequential attack.

[0145] Figure 14 The initial position was changed, and the range adjustment in the feint attack mode could not meet the requirements, so the basic mode was used instead. The range of the basic mode was 480.32km, the range of another basic mode was 505.81km, and the range of the multi-circle mode was 529.29km. This verified the role of the trajectory replanning part in the algorithm. Table 3 compares the main cases of the two attack schemes.

[0146] Table 3 Comparison of Cooperative Attack Schemes

[0147]

Claims

1. A method for multi-form cooperative penetration trajectory planning and range adjustment based on geometric curves, characterized in that, The method steps are as follows: S1: Acquire aircraft performance parameters, trajectory constraints, and target situation information. The state information of the aircraft at the starting point and the target point. and These are the coordinates of the starting point and the target point, respectively. and These represent the velocity directions of the aircraft at the starting point and the target point, respectively. For the location information of defense facilities, The coordinates of the defensive facilities; 　　　（1） S2: Set the required trajectory planning format for each individual aircraft; S3: Select a coordinated penetration strategy; S4: Based on mission requirements, convert arrival time requirements into flight range constraints and adjust the flight range accordingly; S5: If the route adjustment in step S4 cannot be executed, return to step S2 to replan the route; The trajectory planning methods in step S2 include the basic mode, the feint mode, and the multi-circle mode; S21: The basic mode achieves maneuvering and turning trajectory planning through circular arc trajectory, and controls the speed direction through two circles. The trajectory form is circular arc-straight line-circular arc. S22: The feint attack mode is divided into single feint attack and double feint attack. It adopts a combination of circular arc and straight line trajectory. By hiding the relationship between the current course of the aircraft and the final target, it achieves tactical deception and reduces the accuracy of the enemy's tactical reaction. S23: The multi-circle mode uses the connection of pure circular arc trajectories to form the overall track; Based on mission requirements, the arrival time requirement is converted into a flight range constraint, and the flight range is adjusted accordingly: S41: In the basic mode, the original flight path consists of two circular arcs and one straight line. The flight path is adjusted by adding a circular arc, as shown in equation (11). Original range in base mode To increase the curvature of the arc segment, This is the maximum range among all aircraft. 　　　（11） S42: In feint attack mode, it is necessary to ensure that the attack direction is pointing towards the feint target. Therefore, a three-segment circular arc is used to adjust the range without changing the speed direction after the extended trajectory, as shown in equation (12). The original flight path in feint attack mode. These are the radius of the circle and the central angle of the corresponding arc trajectory, respectively. The lengths of the three arcs The length of the original straight line segment. This represents the maximum range among all aircraft. 　　　（12） S43: The flight distance in multi-circle mode is the sum of the lengths of multiple circular arcs, and the flight distance calculation method is as shown in equation (13): 　　　（13） The flight range is adjusted by modifying the curvature of each arc segment. The original flight path in feint attack mode. These are the radius of the circle and the central angle of the corresponding arc trajectory, respectively.

2. The method for multi-form cooperative penetration trajectory planning and range adjustment based on geometric curves according to claim 1, characterized in that, The steps of the basic mode flight planning method described in step S21 are as follows: S211: Calculate the coordinates of the center of the two maneuvering circles based on the aircraft's status information at the starting point and target point; （2） in, These are the coordinates of the centers of the two maneuvering circles on either side of the initial position. These are the coordinates of the centers of the maneuvering circles on either side of the target point. Indicates the initial directional maneuver. Indicates the direction of the terminal attack. and These are the radii of the initial maneuver circle and the final maneuver circle, respectively. S212: Calculate the tangent equation information connecting the initial and final maneuvering circles; 　　　（3） in, Represents the straight-line distance between the centers of the two circles. and Let represent the angles between the line connecting the point of tangency and the center of the circle and the line connecting the centers of the two circles, respectively. This represents the angle between the line connecting the centers of the circles and the x-axis. and The radii of the initial and final maneuver circles are used to solve for the tangent equations and the positions of the tangent points, thus forming straight line segments and circular arc segments of the flight path.

3. The method for multi-form cooperative penetration trajectory planning and range adjustment based on geometric curves according to claim 1, characterized in that, The steps for flight planning in the single feint attack mode in step S22 are as follows: S221: Calculate the coordinates of the center of the two maneuvering circles based on the aircraft's state information at the starting point and target point; S222: Calculate the tangent point between the feint target and the initial maneuver circle, and solve the tangent equation and the position of the tangent point to form the straight line segment and circular arc segment track; Coordinates of the center of the end-effector's maneuvering circle The solution formula is: 　　　（4） in, The expression for the feint target and the tangent of the initial maneuver circle. The expression for the line pointing towards the attack target. for and The intersection of two straight lines, for and The analytical expression for the angle bisector of two lines. Let be the radius of the end-effector circle.

4. The method for multi-form cooperative penetration trajectory planning and range adjustment based on geometric curves according to claim 3, characterized in that: In step S22, the double feint attack mode is to repeat steps S221 and S222 once to complete the switching of the feint attack target.

5. The method for multi-form cooperative penetration trajectory planning and range adjustment based on geometric curves according to claim 1, characterized in that, The steps for multi-circle mode range planning in step S23 are as follows: S231: Calculate the coordinates of the center of the two maneuvering circles based on the aircraft's state information at the starting point and the target point; S232: Calculate the center of the circumcircle ; 　　　（5） in, Point of tangency on the circle and the center The vector formed, Let these be the coordinates of the center of the desired circumcircle. Let be the radius of the circumcircle.

6. The method for multi-form cooperative penetration trajectory planning and range adjustment based on geometric curves according to claim 1, characterized in that, The collaborative penetration strategy in step S3 includes a simultaneous attack strategy where multiple aircraft arrive at the same time and attack from multiple directions, and a sequential attack strategy where multiple aircraft carry out continuous attacks in the same direction with time intervals. S31: The simultaneous attack strategy requires mission negotiation to negotiate the attack direction of each aircraft towards the target, thereby determining the optimal attack direction for each aircraft. The system performs pre-planning of flight paths and forms different mission combinations. It calculates the range of individual aircraft under different attack directions within a given flight path configuration, resulting in multiple combination methods. In each combination, the same aircraft selects different attack directions, and a mission allocation matrix is ​​established. : 　　　（6） Where n represents the number of aircraft, and m represents the selectable attack directions. The matrix contains information about the attack direction chosen by the aircraft in the k-th combination. This indicates whether the i-th aircraft chooses the j-th attack direction. Do not choose ; For each combination, task negotiation is performed to establish the objective function: 　　　（7） 　　　（8） This represents the initial range of each aircraft. This represents the minimum maximum range in each combination. This represents the combination with the smallest range adjustment when attacking simultaneously. The combination with the smallest range adjustment and the smallest maximum range is selected as the task allocation method. Select the value with the largest range in the optimal combination. Used for adjusting the aircraft's range; 　　　（9） S32: When employing a sequential attack strategy, reorder the routes under different trajectory planning forms to ensure that the adjustment amount for each route is minimized while meeting the sequential arrival requirements. 　　　（10） It is the set consisting of all voyages.

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