Angle constraint geometric guidance method for maneuvering target

Abstract

The invention relates to an angle constraint geometric guidance method for a maneuvering target, and the method comprises the steps: converting a problem of tracking the maneuvering target at a constant speed into a problem of tracking a static target at a variable speed according to a conversion relation between the motion parameters of an aircraft and a target; a second-order Bezier curve is adopted in the relative motion coordinate system to generate a relative motion track of the aircraft and the target, a track tracking algorithm is used for obtaining a relative guidance instruction, the guidance instruction of the aircraft is solved through the relation among the acceleration of the aircraft, the acceleration of the target and the relative acceleration, and angle constraint guidance for the maneuvering target is achieved.

Description

Technical Field

[0001] The invention belongs to the field of guidance and control of aerospace vehicles and relates to an angle-constrained geometric guidance method for a maneuvering target. Background Art

[0002] The design focus of classical guidance laws such as proportional guidance is the miss distance between the aircraft and the target. In recent years, the multidimensionalization of tactical and technical indicators has made zero miss distance no longer the only guidance constraint. In some special scenarios, the aircraft is expected to approach the target from a specified direction, and an attack angle constraint should be imposed. For example, in order to improve the penetration effect of the aircraft or the damage effectiveness of the warhead, it is necessary to approach the target at a specific angle. At this time, the control of the attack angle becomes particularly important. In order to meet the requirements of the guidance system, the guidance law that considers both the miss distance and the attack angle constraint has received widespread attention from academia and industry.

[0003] There are some classic methods and theories for the design of guidance laws that meet both miss distance and attack angle constraints, such as optimal control theory, sliding mode control theory, and proportional guidance-based methods. However, these guidance methods are proposed for stationary targets. If the target is a maneuvering target of different types, it is easy to have a large miss distance or even lose the target, and it is even more difficult to meet the attack angle constraint at the end of the guidance. Therefore, it is necessary to design an angle constraint guidance method for maneuvering targets. Summary of the invention

[0004] Technical issues to be solved

[0005] In order to avoid the deficiencies of the prior art, the present invention proposes an angle-constrained geometric guidance method for a maneuvering target.

[0006] Technical Solution

[0007] An angle-constrained geometric guidance method for a maneuvering target, characterized by the following steps:

[0008] In the plane, according to the geometric motion relationship of the aircraft tracking the maneuvering target and the motion parameters of the aircraft and the target, the motion equations of the aircraft and the target in the original coordinate system are established, including the first-order derivative of the relative distance between the aircraft and the target. The first derivative of the line of sight angle between the aircraft and the target The first derivative of the aircraft's flight path angle and the first derivative of the target's track angle

[0009] The original coordinate system takes the initial position of the aircraft as its origin;

[0010] According to the geometric relationship of relative motion, the motion equations of the aircraft and the target in the relative motion coordinate system are established, including the first-order derivative of the relative distance between the aircraft and the target. The first derivative of the line of sight angle between the aircraft and the target The first derivative of the relative track angle between the aircraft and the target and the lead angle η of the relative motion between the aircraft and the target;

[0011] The relative motion coordinate system regards the target as a relatively static point, that is, the position of the target in the relative motion coordinate system is fixed, and the position of the aircraft in the relative motion coordinate system is determined by the relative position of the aircraft and the target in the x-axis and y-axis directions;

[0012] In the relative motion coordinate system, according to the motion equation in the relative motion coordinate system, the second-order Bezier curve is used to generate the relative motion trajectory between the aircraft and the target, so that the relative motion trajectory meets the miss distance and attack angle constraints;

[0013] The miss distance and attack angle constraints are:

[0014] R(t f )=0

[0015] θ R (t f )=θ f

[0016] Among them, t f represents the terminal time, θ f represents the desired terminal relative track angle;

[0017] Taking the relative motion trajectory as the reference trajectory, the reference trajectory is divided into several reference trajectory points. The PLOS tracking algorithm is used to obtain the relative guidance instructions. According to the geometric relationship of the relative motion, the guidance instructions of the aircraft are calculated to realize the angle constrained geometric guidance for the maneuvering target.

[0018] The motion equations of the aircraft and the target in the original coordinate system are:

[0019]

[0020] Among them, V M represents the speed of the aircraft, a M Indicates the acceleration of the aircraft perpendicular to the velocity, V T represents the target's moving speed, a T represents the acceleration of the target perpendicular to the moving speed, θ M represents the flight path angle of the aircraft, θ T represents the target’s track angle, R represents the relative distance between the aircraft and the target, q represents the line of sight angle between the aircraft and the target, Represents the first-order derivative of the relative distance between the aircraft and the target, Represents the first-order derivative of the line-of-sight angle between the aircraft and the target, represents the first-order derivative of the aircraft's track angle, Represents the first derivative of the target's track angle.

[0021] The geometric relationship of the relative motion is:

[0022]

[0023] Where K represents the ratio of the target speed to the aircraft speed, that is, K = V T / V M , V R represents the relative speed between the aircraft and the target, θ R represents the relative track angle between the aircraft and the target, a R represents the relative acceleration perpendicular to the relative motion velocity, θ M represents the flight path angle of the aircraft, θ T Indicates the target's track angle.

[0024] The motion equation in the relative motion coordinate system is:

[0025]

[0026] in, Represents the first-order derivative of the relative distance between the aircraft and the target, Represents the first-order derivative of the line-of-sight angle between the aircraft and the target, represents the first-order derivative of the relative track angle between the aircraft and the target, and represents η the lead angle of the relative motion between the aircraft and the target.

[0027] The process of using the second-order Bezier curve to generate the relative motion trajectory between the aircraft and the target is as follows:

[0028] A second-order Bezier curve consists of two endpoints and a control point Q(x Q ,y Q )Sure:

[0029]

[0030] Where (x, y) represents the position of a point on the Bezier curve. represents the location of endpoint E1, represents the position of the endpoint E2, (x Q ,y Q ) represents the position of the control point Q, and τ is a curve parameter in the interval [0,1];

[0031] The relative initial position O(0,0) is regarded as the endpoint E1 and the relative target position T R (x T -x M ,y T -y M ) is regarded as the endpoint E2, the initial relative track angle is θ0, and the expected attack angle is θ f , then the control points that satisfy the constraints are:

[0032]

[0033] y Q =x Q tanθ0

[0034] Among them, (x M ,y M ) represents the initial position of the aircraft in the original coordinate system, (x T ,y T ) represents the initial position of the target in the original coordinate system.

[0035] The aircraft moves along the relative motion trajectory from endpoint E1 to endpoint E2, and endpoint E2 is the relative target position, that is, the aircraft eventually flies to the target position and can meet the miss amount constraint; and the control point Q is solved based on the two endpoint positions, the initial angle and the desired attack angle, so the flight trajectory generated based on the control point can meet the miss amount and angle constraints.

[0036] The process of obtaining relative guidance instructions using the PLOS tracking algorithm is:

[0037] Initialization: The current position of the aircraft in the relative motion coordinate system is recorded as I = (x I ,y I ), the current relative track angle is denoted as θ, and the nearest reference track point in front of the aircraft is denoted as W i =(x i ,y i ), the nearest reference trajectory point behind the aircraft is denoted as W i+1 =(x i+1 ,y i+1 ), set the initial values ​​of proportional gains k1 and k2;

[0038] Calculate the relative track angle expected at the current moment

[0039] Calculate the current moment trajectory tracking error

[0040] Calculate the relative guidance command a R =(k1(θ d -θ)+k2d)·VR .

[0041] According to the geometric relationship of relative motion, the guidance instructions of the aircraft are calculated as:

[0042]

[0043] An electronic device, characterized in that it includes a processor and a memory, wherein the processor is used to implement the steps of the angle-constrained geometric guidance method for a maneuvering target as described in the data migration when executing a computer program stored in the memory.

[0044] A readable storage medium, characterized in that a computer program is stored on the readable storage medium, and when the computer program is executed by a processor, the steps of the angle-constrained geometric guidance method for a maneuvering target such as data migration are implemented.

[0045] A computer program product, characterized by comprising computer executable instructions, which are used to implement the angle-constrained geometric guidance method for a maneuvering target using data migration when the instructions are executed.

[0046] Beneficial Effects

[0047] The present invention proposes an angle-constrained geometric guidance method for a maneuvering target. First, according to the conversion relationship between the motion parameters of the aircraft and the target, the problem of tracking the maneuvering target at a constant speed is converted into the problem of tracking a stationary target at a variable speed. Then, a second-order Bezier curve is used in a relative motion coordinate system to generate the relative motion trajectory of the aircraft and the target, and a trajectory tracking algorithm is used to obtain relative guidance instructions. Through the relationship between the aircraft acceleration, the target acceleration and the relative acceleration, the guidance instructions of the aircraft are solved, thereby realizing angle-constrained guidance for the maneuvering target. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0049] Figure 1 A flowchart of an angle-constrained geometric guidance method for a maneuvering target according to the present invention;

[0050] Figure 2 A schematic diagram of the geometric motion relationship of the aircraft of the present invention tracking a maneuvering target;

[0051] Figure 3A schematic diagram of the geometric motion relationship of the aircraft of the present invention tracking a maneuvering target in a relative motion coordinate system;

[0052] Figure 4 It is a schematic diagram of the relative motion trajectory based on the second-order Bezier curve of the present invention;

[0053] Figure 5 A schematic diagram of a guidance simulation result of an embodiment of the present invention is shown below:

[0054] in, Figure 5 (a) is the relative motion trajectory between the aircraft and the target and the actual interception trajectory. Figure 5 (b) is the curve of the relative distance between the aircraft and the target changing with time. Figure 5 (c) is the curve of the relative track angle between the aircraft and the target changing with time. Figure 5 (d) is a graph showing the change of the relative acceleration command and the actual acceleration command between the aircraft and the target over time. DETAILED DESCRIPTION

[0055] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0056] See also Figure 1 The present invention provides an angle-constrained geometric guidance method for a maneuvering target, comprising the following steps:

[0057] Step 1: In the plane, the geometric motion relationship diagram of the aircraft tracking the maneuvering target is as follows Figure 2 As shown, according to the motion parameters of the aircraft and the target, the motion equations of the aircraft and the target in the original coordinate system are established;

[0058] The motion equation in the original coordinate system is:

[0059]

[0060] Among them, V M represents the speed of the aircraft, a M Indicates the acceleration of the aircraft perpendicular to the velocity, V T represents the target's moving speed, a T represents the acceleration of the target perpendicular to the moving speed, θ M represents the flight path angle of the aircraft, θ T represents the target’s track angle, R represents the relative distance between the aircraft and the target, q represents the line of sight angle between the aircraft and the target, Represents the first-order derivative of the relative distance between the aircraft and the target, Represents the first-order derivative of the line-of-sight angle between the aircraft and the target, represents the first-order derivative of the aircraft's track angle, Represents the first derivative of the target's track angle.

[0061] Step 2: In order to reduce the number of physical quantities in the coordinate system, the physical quantities of relative motion can be converted from the original coordinate system to Figure 3 In the relative motion coordinate system shown in FIG. According to the geometric relationship of relative motion, the motion equations of the aircraft and the target in the relative motion coordinate system are established;

[0062] The geometric relationship of relative motion can be expressed as:

[0063]

[0064] Where K represents the ratio of the target speed to the aircraft speed, that is, K = V T / V M , V R represents the relative speed between the aircraft and the target, θ R represents the relative track angle between the aircraft and the target, a R represents the relative acceleration perpendicular to the relative motion velocity, θ M represents the flight path angle of the aircraft, θ T Indicates the target's track angle.

[0065] The motion equation in the relative motion coordinate system is:

[0066]

[0067] in, Represents the first-order derivative of the relative distance between the aircraft and the target, Represents the first-order derivative of the line-of-sight angle between the aircraft and the target, represents the first-order derivative of the relative track angle between the aircraft and the target, and represents η the lead angle of the relative motion between the aircraft and the target.

[0068] Step 3: In the relative motion coordinate system, use the second-order Bezier curve to generate the relative motion trajectory between the aircraft and the target, such as Figure 4 As shown, it satisfies the miss distance and attack angle constraints;

[0069] The miss distance and attack angle constraints can be mathematically defined as:

[0070]

[0071] Among them, t f represents the terminal time, θ f Indicates the desired terminal relative track angle.

[0072] A second-order Bezier curve consists of two endpoints and a control point Q(x Q ,yQ ) is determined, the expression is:

[0073]

[0074] Where (x, y) represents the position of a point on the Bezier curve. represents the location of endpoint E1, represents the position of the endpoint E2, (x Q ,y Q ) represents the position of the control point Q, and τ is a curve parameter in the interval [0,1].

[0075] The relative initial position O(0,0) is regarded as the endpoint E1 and the relative target position T R (x T -x M ,y T -y M ) is regarded as the endpoint E2, and the initial relative track angle is θ0, then the control point that satisfies the constraint can be calculated as:

[0076]

[0077] y Q =x Q tanθ0

[0078] Among them, (x M ,y M ) represents the initial position of the aircraft in the original coordinate system, (x T ,y T ) represents the initial position of the target in the original coordinate system.

[0079] The aircraft moves along the relative motion trajectory from endpoint E1 to endpoint E2, and endpoint E2 is the relative target position, that is, the aircraft eventually flies to the target position and can meet the miss amount constraint; and the control point Q is solved based on the two endpoint positions, the initial angle and the desired attack angle, so the flight trajectory generated based on the control point can meet the miss amount and angle constraints.

[0080] Step 4: Record the relative motion trajectory generated in step 3 as the reference trajectory, divide the reference trajectory into 6292 reference trajectory points, use the PLOS tracking algorithm to obtain the relative guidance instructions, and calculate the guidance instructions of the aircraft based on the geometric relationship of the relative motion.

[0081] The PLOS tracking algorithm steps are as follows:

[0082] 1. Initialization: The current position of the aircraft in the relative motion coordinate system is recorded as I = (x I ,y I), the current relative track angle is denoted as θ, and the nearest reference track point in front of the aircraft is denoted as W i =(x i ,y i ), the nearest reference trajectory point behind the aircraft is denoted as W i+1 =(x i+1 ,y i+1 ), set the initial values ​​of proportional gains k1 and k2;

[0083] 2. Calculate the relative track angle expected at the current moment

[0084] 3. Calculate the current moment trajectory tracking error

[0085] 4. Calculate the relative guidance instruction a R =(k1(θ d -θ)+k2d)·V R .

[0086] Further, according to the relative motion geometric relationship in formula (2), the guidance instruction of the aircraft can be calculated as:

[0087]

[0088] In order to verify the effectiveness and superiority of the angle-constrained geometric guidance method for maneuvering targets proposed in the present invention, simulation verification is performed using a simulation verification method.

[0089] Set the initial motion parameters of the aircraft and target:

[0090] Aircraft speed: 2000m / s 2 , target movement speed: 340m / s 2 , Target initial track angle: -10°, Aircraft initial track angle: 20°, Expected terminal relative track angle: -45°, Aircraft initial position: (0,0)m, Target initial position: (10000,0)m, Target maneuvering acceleration: a T =9gsin(πt / 2). The proportional gains of the PLOS algorithm are set to k1=1000 and k2=0.5.

[0091] The simulation results are as follows Figure 5 As shown in the figure, the aircraft accurately hits the maneuvering target, and the relative track angle at the terminal moment is -44.9867°, which can meet the attack angle constraint.

[0092] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An angle-constrained geometric guidance method for a maneuvering target, characterized in that Here are the steps: In the plane, according to the geometric motion relationship of the aircraft tracking the maneuvering target and the motion parameters of the aircraft and the target, the motion equations of the aircraft and the target in the original coordinate system are established, including the first-order derivative of the relative distance between the aircraft and the target. The first derivative of the line of sight angle between the aircraft and the target The first derivative of the aircraft's track angle and the first derivative of the target's track angle The original coordinate system takes the initial position of the aircraft as its origin; According to the geometric relationship of relative motion, the motion equations of the aircraft and the target in the relative motion coordinate system are established, including the first-order derivative of the relative distance between the aircraft and the target. The first derivative of the line of sight angle between the aircraft and the target The first derivative of the relative track angle between the aircraft and the target and the lead angle η of the relative motion between the aircraft and the target; The relative motion coordinate system regards the target as a relatively static point, that is, the position of the target in the relative motion coordinate system is fixed, and the position of the aircraft in the relative motion coordinate system is determined by the relative position of the aircraft and the target in the x-axis and y-axis directions; In the relative motion coordinate system, according to the motion equation in the relative motion coordinate system, the second-order Bezier curve is used to generate the relative motion trajectory between the aircraft and the target, so that the relative motion trajectory meets the miss distance and attack angle constraints; The miss distance and attack angle constraints are: R(t f )=0 i R (t f )=θ f Among them, t f represents the terminal time, θ f represents the desired terminal relative track angle; Taking the relative motion trajectory as the reference trajectory, the reference trajectory is divided into several reference trajectory points. The PLOS tracking algorithm is used to obtain the relative guidance instructions. According to the geometric relationship of the relative motion, the guidance instructions of the aircraft are calculated to realize the angle constrained geometric guidance for the maneuvering target.

2. The angle-constrained geometric guidance method for a maneuvering target according to claim 1, characterized in that: The motion equations of the aircraft and the target in the original coordinate system are: Among them, V M represents the speed of the aircraft, a M Indicates the acceleration of the aircraft perpendicular to the velocity, V T represents the target's moving speed, a T represents the acceleration of the target perpendicular to the moving speed, θ M represents the flight path angle of the aircraft, θ T represents the target’s track angle, R represents the relative distance between the aircraft and the target, q represents the line of sight angle between the aircraft and the target, Represents the first-order derivative of the relative distance between the aircraft and the target, Represents the first-order derivative of the line-of-sight angle between the aircraft and the target, represents the first-order derivative of the aircraft's track angle, Represents the first derivative of the target's track angle.

3. The angle-constrained geometric guidance method for a maneuvering target according to claim 1, characterized in that: The geometric relationship of the relative motion is: Where K represents the ratio of the target speed to the aircraft speed, that is, K = V T / V M , V R represents the relative speed between the aircraft and the target, θ R represents the relative track angle between the aircraft and the target, a R represents the relative acceleration perpendicular to the relative motion velocity, θ M represents the flight path angle of the aircraft, θ T Indicates the target's track angle.

4. The angle-constrained geometric guidance method for a maneuvering target according to claim 1, characterized in that: The motion equation in the relative motion coordinate system is: in, Represents the first-order derivative of the relative distance between the aircraft and the target, Represents the first-order derivative of the line-of-sight angle between the aircraft and the target, represents the first-order derivative of the relative track angle between the aircraft and the target, and represents η the lead angle of the relative motion between the aircraft and the target.

5. The angle-constrained geometric guidance method for a maneuvering target according to claim 1, characterized in that: The process of using the second-order Bezier curve to generate the relative motion trajectory between the aircraft and the target is as follows: A second-order Bezier curve consists of two endpoints and a control point Q(x Q ,y Q )Sure: Where (x, y) represents the position of a point on the Bezier curve. represents the location of endpoint E1, represents the position of the endpoint E2, (x Q ,y Q ) represents the position of the control point Q, and τ is a curve parameter in the interval [0,1]; The relative initial position O(0,0) is regarded as the endpoint E1 and the relative target position T R (x T -x M ,y T -y M ) is regarded as the endpoint E2, the initial relative track angle is θ0, and the expected attack angle is θ f , then the control points that satisfy the constraints are: and Q =x Q ·tanθ0 Among them, (x M ,y M ) represents the initial position of the aircraft in the original coordinate system, (x T ,y T ) represents the initial position of the target in the original coordinate system.

6. The angle-constrained geometric guidance method for a maneuvering target according to claim 5, characterized in that: The aircraft moves along the relative motion trajectory from endpoint E1 to endpoint E2, and endpoint E2 is the relative target position, that is, the aircraft eventually flies to the target position and can meet the miss amount constraint; and the control point Q is solved based on the two endpoint positions, the initial angle and the desired attack angle, so the flight trajectory generated based on the control point can meet the miss amount and angle constraints.

7. The angle-constrained geometric guidance method for a maneuvering target according to claim 1, characterized in that: The process of obtaining relative guidance instructions using the PLOS tracking algorithm is: Initialization: The current position of the aircraft in the relative motion coordinate system is recorded as I = (x I ,y I ), the current relative track angle is denoted as θ, and the nearest reference track point in front of the aircraft is denoted as W i =(x i ,y i ), the nearest reference trajectory point behind the aircraft is denoted as W i+1 =(x i+1 ,y i+1 ), set the initial values ​​of proportional gains k1 and k2; Calculate the relative track angle expected at the current moment Calculate the current moment trajectory tracking error Calculate the relative guidance command a R =(k1(θ d -θ)+k2d)·V R . According to the geometric relationship of relative motion, the guidance instructions of the aircraft are calculated as:

8. An electronic device, characterized in that: It comprises a processor and a memory, wherein the processor is used to implement the steps of the angle-constrained geometric guidance method for a maneuvering target using data migration as claimed in any one of claims 1 to 7 when executing a computer program stored in the memory.

9. A readable storage medium, characterized in that: The readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the angle-constrained geometric guidance method for a maneuvering target using data migration as described in any one of claims 1 to 7.

10. A computer program product, characterized in that The invention comprises computer executable instructions, which are used to implement the angle-constrained geometric guidance method for a maneuvering target by using data migration as claimed in any one of claims 1 to 7 when being executed.

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