A multi-missile two-dimensional cooperative guidance method based on Bezier curve

Abstract

The application provides a multi-missile two-dimensional cooperative guidance method based on a Bezier curve, and is characterized in that the method comprises the following steps: determining a Bezier initial attack trajectory of each missile in a missile group, determining a Bezier curve tracking point of each missile in the missile group, calculating a lateral acceleration of each missile in the missile group, calculating a remaining flight distance of each missile in the missile group, calculating a time of arrival of each missile in the missile group, adjusting the Bezier curve of each missile according to the predicted time of arrival of surrounding missiles, and checking whether the missiles hit the target or not. The application is based on the Bezier curve, the time of arrival is calculated by using a difference method, and the application can better cope with the situation that there is resistance in the flight process. The method has the advantages of small calculation amount and easiness in realization on a missile-borne computer.

Description

Technical Field

[0001] This invention belongs to the field of guidance technology, and specifically relates to a two-dimensional cooperative guidance method for multiple missiles based on Bézier curves. Background Technology

[0002] Unlike traditional guidance technologies that only consider whether a single missile hits its target, swarm guidance involves mutual communication and coordination during flight, exhibiting kinematic laws with specific tactical and strategic significance. Furthermore, with the continuous development of interception technologies, employing multi-missile coordinated penetration can significantly improve the probability of penetration. Simultaneously, for key targets such as airports and ports, specific attack angles must be employed based on the actual situation to maximize the missile's strike effectiveness. This presents a challenge for swarm guidance with constraints on attack angle and attack time.

[0003] Specifically, the transition control methods for vertical / short takeoff and landing (V / STOL) aircraft mainly include geometric methods, offset proportional guidance methods, and sliding mode control methods. Existing geometric methods can typically construct fixed-length flight trajectories using curve tools such as circular arcs and Bézier curves as needed, but they are generally unable to adjust the predetermined trajectory in real time during flight, potentially leading to significant deviations. The basic idea of ​​offset proportional guidance is to add additional parameters responsible for angle and time control to proportional guidance control. To control the attack time, this type of method often needs to assume uniform missile motion and derive the remaining attack time to achieve coordinated attack timing. However, actual ballistic trajectories face velocity changes during flight, leading to increased errors in coordinated time control. Sliding mode control methods also struggle to handle velocity changes and are prone to oscillations near the sliding surface. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a cooperative algorithm that is robust, computationally inexpensive, and allows for control over the attack angle and attack time.

[0005] First, for any missile i at position E1 i (x1 i ,y1 i Point E2, where the target is located. i (x2 i ,y2 i Point, find P c i (x c i ,y c i ) makes E1 i E2 i and P c i Points form a Bézier curve:

[0006]

[0007] P c i (x c i ,y c i A point can generally be chosen as the intersection of the following two lines:

[0008]

[0009] Where θ1 i Let θ2 be the initial track angle. i Let B be the desired angle of attack. Let B be the Bézier curve corresponding to equation (1). i (τ), then the binary search method can be used to retrieve [τ] within a certain range. i (t)-δ,τ i [(t)+δ], the closest point τ on the curve to the missile's current position. i , where τ i (t) is equal to τ at the previous moment. i δ is generally less than 0.1. Therefore, the Bézier curve B... i (τ i The corresponding tangent is the straight line that the missile needs to track, and the lateral acceleration can be calculated as follows:

[0010]

[0011] Where q1 and q2 are parameters, d i For missiles to B i (τ i The distance between the tangents at the point. Let the rate of change of this distance be denoted as... If the angle of inclination is the tangent, then the calculation method is as follows: Next, the Bezier curve trajectories of each missile need to be adjusted according to the actual situation to achieve coordinated attack timing. Specifically, the remaining flight time needs to be estimated first by estimating the remaining flight distance, and then the remaining flight time is obtained based on the difference in the actual speeds of the missiles. For B i (τ i At point ) the remaining flight distance should be along the curve τ i Integrating ≤τ≤1 yields the following:

[0012]

[0013] Integrating this expression yields:

[0014]

[0015] Where N(u) and J can be calculated as:

[0016]

[0017] D i =(J i ·K i ) / |J i | 2 (7)

[0018] J i =E1 i -2P c i +E2 i (8)

[0019] U i =|K i | 2 / |J i | 2 -(J i ·K i ) / |J i | 2 (9)

[0020] K i =P c i -E1 i (10)

[0021] Based on this, for the missile velocity profile, without any maneuvers, the time required to travel different distances at different flight speeds was recorded, forming a difference table. In actual calculations, the time is calculated based on the current speed and... Interpolation is performed to obtain The missile's estimated arrival time is

[0022] Given the estimated arrival time Based on this, each missile adjusts its Bezier curve according to the estimated arrival times of surrounding missiles. For any missile i and missile j, let s ij =1 indicates that missile i and missile j can exchange information, s ij =0 indicates that missile i and missile j cannot exchange information, and therefore each missile The direction of the adjustment is:

[0023]

[0024] Where k i >0 represents the proportionality coefficient. The theoretical basis for the convergence of this algorithm lies in When θ2 remains constant, the length of the Bézier curve monotonically increases with θ1. Furthermore, generally speaking, shortening the length of the Bézier curve can shorten the missile's arrival time. However, if k... i If the value is too large, the missile will lose a lot of kinetic energy during maneuvering when the trajectory changes drastically, resulting in a significantly longer arrival time. In this case, the algorithm will not be able to converge.

[0025] The advantages of this invention are:

[0026] (1) This method does not require the assumption that the missile is moving at a constant speed to estimate the arrival time. It can make good use of the known missile velocity profile to obtain a high-precision estimated arrival time.

[0027] (2) The coordinated attack time error is small, the attack angle control accuracy is high, and the initial track angle convergence speed is fast;

[0028] (3) This method can use binary search extensively to save computation time, and the overall computation amount is small, making it suitable for real-time computation by onboard computers. Attached Figure Description

[0029] Figure 1 The flowchart of the guidance law calculation of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] The specific steps in this embodiment are as follows: Figure 1 As shown. A typical missile dynamics model is as follows:

[0032]

[0033]

[0034] Where D i The resistance m represents the drag experienced by the missile. i C represents the mass of the missile. D (V i Let ρ represent parasitic drag, K represent the induced drag coefficient, ρ represent air density, and S represent the missile's cross-sectional area. For typical parameter values, the induced drag coefficient K = 0.001, and the cross-sectional area S = 0.1m. 2 The mass is 150 kg, and the lateral acceleration is limited to 100 m / s². 2 k i=0.0001, q1=4, q2=4.24. Taking four missiles as an example, missile 1 can communicate with missile 2, missile 2 can communicate with missile 1 and missile 3, missile 3 can communicate with missile 2 and missile 4, and missile 3 can communicate with missile 4. At the initial moment, all missiles are located on the x-axis with horizontal coordinates of -10km, -9km, -10km, and -9.43km, respectively. Their initial velocities are 350m / s, 340m / s, 330m / s, and 360m / s, respectively. Their initial trajectory angles are 90 degrees, 90 degrees, 36.87 degrees, and 32.01 degrees, respectively. Their expected attack angles are -30 degrees, -60 degrees, -83.13 degrees, and -117.99 degrees, respectively. All four missiles are used to attack the target at the (0,0) point.

[0035] During the execution of the cooperative algorithm, the computation steps at each time step are as follows:

[0036] (1) Select the corresponding Bezier curve tracking point for each missile in the missile group;

[0037] (2) Calculate the lateral acceleration for each missile in the missile group;

[0038] (3) Estimate the remaining flight distance for each missile in the missile swarm;

[0039] (4) Estimate the arrival time of each missile in the missile swarm;

[0040] (5) Each missile adjusts its Bezier curve according to the expected arrival time of surrounding missiles;

[0041] (6) Check whether the missile hit the target.

[0042] Simulation results show that the maximum time error at the moment of impact is 0.135 seconds and the maximum error of the attack angle is 0.813 degrees, achieving high-precision collaborative control.

[0043] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method of multi-missile two-dimensional cooperative guidance based on Bezier curve, characterized in that Includes the following steps: S1: Determine the initial Bessel trajectory of each missile in the missile swarm, specifically: Let the track angle of the i-th missile be θi i , the initial track angle be θ1 i , the desired attack angle be θ2 i , the lateral acceleration be a i , the initial position be E1 i (x1 i , y1 i ), the striking target position be E2 i (x2 i , y2 i ), and the intersection of the straight lines y=tanθ1 i (x-x1 i )+y1 i and y=tanθ2 i (x-x2 i )+y2 i be the control point P c i (x c i , y c i ), then E1 i (x1 i , y1 i ), P c i (x c i , y c i ), and E2 i (x2 i , y2 i ) form the initial Bezier curve B i (τ) = (1-τ) 2 E1 i + 2τ(1-τ)P c i + τ 2 E2 i , 0≤τ≤1, wherein τ is the parameter value of the curve, and E1 i P c i correspond to the inclination of the straight lines S2: Select the tracking point of the Bezier curve corresponding to each missile in the missile group, specifically: Select the point of the Bezier curve in S1 closest to the missile as the tracking point, and denote the corresponding parameter value as τ i ; S3: Calculate the lateral acceleration of each missile in the missile swarm, specifically: where q1 and q2 are parameters, d i is the distance from the missile to B i (τ i ) the point of tangency, is the rate of change of this distance, and let the angle of the tangent be then S4: Calculate the remaining flight distance of each missile in the missile swarm, specifically: wherein D i = (J i · K i ) / |J i | 2 , J i = E1 i - 2P c i + E2 i , U i = |K i | 2 / |J i | 2 - (J i · K i ) / |J i | 2 , K i = P c i - E1 i ; S5: Calculate the arrival time of each missile in the missile swarm, specifically: in The time already flown, The time of the upcoming flight; S6: Adjust the Bezier curves of each missile according to the estimated arrival time of surrounding missiles, specifically: For any missile i and missile j, let s ij =1 indicates that missile i and missile j can exchange information, s ij =0 indicates that missile i and missile j cannot exchange information, and therefore each missile The direction of adjustment is in k i >0 represents the proportionality coefficient; S7: Check whether the missile hit the target, specifically: If the target is hit, the algorithm terminates. If the target is not hit, return to step S2.

2. The two-dimensional cooperative guidance method for multiple missiles based on Bézier curves according to claim 1, characterized in that, In step S5 This is calculated based on velocity profile interpolation, specifically: Without any maneuvers, record the time required to fly different distances at different flight speeds, creating a difference table. In actual calculations, this table is used to compare the current speed with... Interpolation is performed to obtain

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