A Four-Stage Two-Dimensional Guidance Method Based on Bessel Curves

Abstract

The present invention proposes a four-stage two-dimensional guidance method based on Bezier curves, which is characterized by steps including determining whether the desired impact angle satisfies the constraint conditions in the line-of-sight coordinate system, adjusting the desired impact angle in the line-of-sight coordinate system, determining whether the length of the Bezier curve matches the remaining flight distance, adjusting the track angle in the line-of-sight coordinate system, determining whether the Bezier trajectory in the fixed line-of-sight coordinate system is tracked completely, generating a lateral acceleration for tracking the Bezier trajectory in the line-of-sight coordinate system, and using the proportional navigation control method to attack the target. Based on the monotonicity law of the two-stage trajectory length, the present invention designs a four-stage guidance control method based on Bezier curves, achieving high-precision control of the attack time and attack angle under variable speed conditions of the aircraft. This method has a wide range of applications and changes the situation that the previous Bezier curve-related guidance laws are not applicable to the cases of too small launch angles and desired impact angles.

Description

Technical Field

[0001] The present invention belongs to the field of guidance technology, and particularly relates to a four-stage two-dimensional guidance method based on Bessel curves. Background Art

[0002] The Impact Time and Angle Control Guidance (ITACG) law, which can control the attack angle and time, enables the aircraft to strike the target at different angles at the same time, and has high practical value. Especially for sea assault, the ITACG guidance law can achieve simultaneous overflight, reducing the interception effect of the opponent's terminal air defense system and increasing the penetration probability. Currently, the ITACG guidance law rarely considers variable speed situations, and the ITACG guidance law based on Bessel curves can better adapt to variable speed situations. However, the current ITACG guidance law based on Bessel curves has large usage limitations and cannot be used for situations where the initial launch angle is too small or the desired impact angle is too small.

[0003] Specifically, other ITACG guidance laws mainly include variable guidance parameter method, sliding mode control method, centralized decision-making method during flight, decentralized decision-making method during flight, etc. These control methods generally have difficulty in adapting to variable speed situations. Summary of the Invention

[0004] To solve the problems existing in the prior art, the present invention provides a two-dimensional cooperative guidance law with good robustness, small computational complexity, and wide application range. The present invention first generates a two-stage guidance trajectory based on Bessel curves, as As shown in Figure 2 shown. The first stage of this trajectory is a Bessel curve and the second stage is a straight line segment where point E3 is the midpoint of the line segment . The two-stage trajectory can be expressed as with a corresponding length of . This trajectory has the characteristic that its length monotonically changes with the magnitude of θ0, theoretically ensuring the correctness of using the bisection method to find a two-stage trajectory with a specific length and using PI to adjust θ0 to further adjust the trajectory length.

[0005] In the first stage of the present invention, the missile needs to adjust the value of the desired impact angle θ in the line-of-sight coordinate system f,LOS . When θ f,LOS is too small, the curvature of the Bessel curve is too large, making it difficult to form an effective strike. To solve this problem, θ f,LOS needs to be adjusted to a reasonable range θ s ≤|θ f,LOS |≤θ b . When 0≤θ f,LOS <θ s or -π<θ f,LOS <-θ bWhen the expected speed should be in the y - direction of the line - of - sight coordinate system, the acceleration in the line - of - sight coordinate system is:

[0006] a LOS = k p,1 ×(θ LOS - π / 2)+ k i,1 ×∫(θ LOS - π / 2)dt

[0007] When - θ s <θ f,LOS <0 or θ b <θ f,LOS <π, the expected speed should be in the - y - direction of the line - of - sight coordinate system, and the acceleration in the line - of - sight coordinate system is:

[0008] a LOS = k p,1 ×(θ LOS + π / 2)+ k i,1 ×∫(θ LOS + π / 2)dt

[0009] When θ f,LOS satisfies θ s ≤|θ f,LOS |≤θ b , it enters the second stage. The goal of the second stage is to adjust the track angle so that the length of the two - segment trajectory formed by the speed direction and the impact direction is equal to the expected flight length. This stage goal is equivalent to where L est represents the flight distance of the missile within the expected time. Then the bisection method can be used here to find Then the expected acceleration in the line - of - sight coordinate system at this time is:

[0010]

[0011] When is close enough in magnitude to L est , it enters the third stage. The goal of this stage is to track and adjust the trajectory generated in the second stage. Select the point B LOS (τ0) on the two - segment trajectory in the line - of - sight coordinate system that is closest to the missile. Let the tangential distance from the missile to this point be d, then the expected acceleration is:

[0012]

[0013] where q1 and q2 are parameters, θ d is the expected direction. During the flight, the trajectory length can be adjusted by correcting . The specific calculation method is:

[0014]

[0015] Where L real The specific calculation method is as follows:

[0016] L real = |J|(N(1 + D)-N(τ0 + D))+||E3E2||

[0017] Where N(u) is:

[0018]

[0019] J, K, U, D can be calculated as follows:

[0020] J = E1 - 2P c + E2

[0021] K = P c - E1

[0022] U = |K| 2 / |J| 2 -(J·K) / |J| 2

[0023] D = (J·K) / |J| 2

[0024] When the missile enters the straight-line segment of the two-stage trajectory or the remaining time is insufficient, it enters the fourth stage.

[0025] The fourth stage is the proportional navigation method, and the calculation method is:

[0026] a = Nω×v

[0027] Where N is the proportional navigation parameter, ω is the line-of-sight angular rate, and v is the missile flight speed.

[0028] The advantages of this invention are as follows:

[0029] (1) In the first stage, it only needs to judge how to increase the impact angle in the line-of-sight coordinate system; in the second and third stages, the bisection method is used, and the computational complexity is logarithmic; the fourth stage is the proportional navigation method. The algorithm calculation amount of each stage is small, which can meet the requirements of real-time calculation;

[0030] (2) The PI control algorithm is designed to adjust the size of the line-of-sight coordinate system in real time and has good robustness to the resistance that may be encountered during the flight of the aircraft, and can achieve high-precision strike time control;

[0031] (3) This guidance law is applicable to the cases where the initial launch angle and the desired impact angle are small, has a wide application range, and effectively expands the range of strikes based on Bessel curves. Description of the Drawings

[0032] Figure 1 Flow chart for calculating the guidance law of the present invention;

[0033] Based on Figure 2 Two-stage guidance trajectory based on Bessel curve. Specific implementation manner

[0034] To make the objectives, technical solutions and advantages of the present application clearer, the technical solutions of the present application will be clearly and completely described below in conjunction with specific embodiments of the present application and the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts fall within the protection scope of the present application.

[0035] The specific steps of this embodiment are as Figure 1 shown. A four-stage two-dimensional guidance method based on Bessel curve includes: a flight trajectory generator, a dynamic trajectory adjuster, and a trajectory tracker. Taking a missile hitting a fixed target as an example, the launch point is E1 = (0,0), the hitting target position is E2 = (10000,0), the initial launch angle is θ0 = -60°, the expected hitting angle is θ f = 0°, and the expected hitting time t D = 60s. Since the initial expected hitting angle is too small, in the first stage, the missile will fly along the negative direction of the Y-axis until the expected hitting angle in the line-of-sight coordinate system meets the condition. After entering the second stage, the missile will quickly adjust the track angle to form a Bessel curve with a suitable length. After entering the third stage, the missile will track the trajectory formed in the previous stage and fly towards the hitting target. In the fourth stage, the proportional guidance method is used to achieve the final hit. For different missiles, the parameters of the first to fourth stages need to be designed. When tracking the trajectory, the trajectory tracker can be selected to track the tangent of the point closest to the missile. Let d be the distance from the missile to the tangent, and θ d be the angle between the tangent and the X-axis. Then the course acceleration can be shown as follows:

[0036]

[0037] where q1 and q2 are parameters, and the typical values of q1 and q2 are 2 and 3.74.

[0038] Although the specific implementation manner of the present invention is described above in conjunction with the drawings, it is not a limitation on the protection scope of the invention. Those skilled in the art should understand that based on the technical solutions of the present invention, various modifications or deformations that can be made by those skilled in the art without creative efforts still fall within the protection scope of the present invention.

Claims

1. A four-stage two-dimensional guidance method based on Bessel curves, characterized in that Including the following steps: S1: Determine whether the expected impact angle θ f satisfies the constraint conditions in the line-of-sight coordinate system. This step and step S2 are the first stage of the guidance law, specifically: Record the initial position as E1(x1, y1), the target position to be struck as E2(x2, y2), and θ f The value in the line-of-sight coordinate system is θ f,LOS , if the constraint condition θ s ≤|θ f,LOS |≤θ b is satisfied, then go to S3; otherwise, execute S2, where is a parameter set before the algorithm runs; S2: Adjust the expected impact angle θ in the line-of-sight coordinate system f,LOS , specifically as follows: If 0 ≤ θ f,LOS < θ s or -Π < θ f,LOS < -θ b , then the tangential acceleration a LOS is as follows: a LOS = k p,1 ×(θ LOS - π / 2) + k i,1 × ∫(θ LOS - π / 2)dt If -θ s <θ f,LOS <0 or θ b <θ f,LOS <π, then the tangential acceleration a in the line-of-sight coordinate system LOS is as follows: a LOS = k p,1 ×(θ LOS + π / 2) + k i,1 × ∫(θ LOS + π / 2) dt where θ LOS represents the value of the track angle in the line-of-sight coordinate system, k p,1 and k i,1 are the proportional and integral parameters respectively, and the acceleration a LOS After execution, return to step S1 for execution; S3: Determine whether the length of the two-stage trajectory matches the remaining flight distance. This step and step S4 are the second stage of the guidance law, specifically: The two-stage trajectory refers to a strike trajectory with a Bezier curve in the first half and a straight line segment in the second half. If the length of the Bezier curve matches the remaining flight distance, a Bezier curve trajectory is formed and step S5 is executed; otherwise, step S4 is executed; S4: Adjust the track angle in the line-of-sight coordinate system, specifically: Calculating the remaining flight distance L in the line-of-sight coordinate system by the bisection method est The corresponding two-segment trajectory track angle The calculation method is for the specified P c The point coordinates are: y c = y1 + tan(θ f,LOs )(x c - x1) For the remaining trajectory length where is the length of curve E1P c the length of E3E2, is the length of curve E1P c the length of E3, let J = E1 - 2P c + E2, K = P c - E1, where the calculation method of where t0 = 0, D = (J × K) / |J| 2 , the calculation method of N(u) is as follows: The calculation method of U is as follows: U = |K| 2 / |J| 2 -(J × K) / |J| 2 The tangential acceleration in the line-of-sight coordinate system is: where k p,2 and k i,2 are the proportional and integral parameters respectively, and the acceleration a LOs After execution, return to step S3; S5: Determine whether the Bezier trajectory in the fixed line-of-sight coordinate system is tracked completely. Here, the fixed line-of-sight coordinate system refers to the line-of-sight coordinate system LOS when exiting step S3 0 , and this step and step S6 are the third stage of the guidance law, specifically: Record the position of the missile when exiting step S3 as Judge whether E2 The composed Bezier trajectory B Los has been tracked completely. If the Bezier curve tracking is completed, go to step S7; otherwise, go to step S6. S6: Generate a lateral acceleration to track the Bezier trajectory in the line-of-sight coordinate system, specifically: Denote the point on the missile distance tracking trajectory that is closest to the target as B LOS (t0), then the tangential acceleration in the line-of-sight coordinate system at this step is: where q1 and q2 are parameters, and d is the distance from the missile to the tangent line of point B LOS (t0). Since the missile speed is variable, the ballistic trajectory should be changed in real time. For L real , then the change amount of is: where k p and k i are the proportional and integral parameters; S7: Use the proportional navigation control method to attack the target, specifically: The tangential acceleration in this stage is: a = Nω × v where N is the proportional navigation gain, ω is the line-of-sight angle rate of change, and v is the missile velocity vector.

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