Three-dimensional guidance method with time and angle constraints under speed limit condition of aircraft

Abstract

The application discloses a three-dimensional guidance method under time and angle constraints of aircraft speed limit conditions and belongs to the field of aircraft precise guidance. The method comprises the following steps: a vector model is established in a three-dimensional space; an attack angle prediction of space proportional guidance is realized by using a quaternion theory and a space vector guidance model; a corresponding performance index is selected to convert an error control problem into an optimal problem for solution; and an attack angle control is realized by adjusting an error between a predicted final aircraft speed direction and an expected attack angle direction. Under the attack angle constraint guidance law, a trajectory shape and length are irrelevant to aircraft speed variation. An attack time constraint problem is converted into a residual trajectory length control problem, and the residual trajectory length control is realized by axial acceleration control under the aircraft speed limit. The attack angle and time constraint guidance under the aircraft speed limit are realized by combining the attack angle constraint guidance law and the axial thrust control guidance law.

Description

Technical Field

[0001] This invention belongs to the field of precision guidance for aircraft, and relates to a guidance method that, considering the speed limitations of the aircraft in three-dimensional space, enables the aircraft to reach a designated position at a desired attack angle and within a desired attack time. Background Technology

[0002] Aircraft guidance technology is a crucial component of aerospace technology. A typical guidance problem is how to automatically guide an aircraft from an initial state in space to a desired state. With the evolving battlefield situation, the demands of guidance missions are becoming increasingly diverse and complex. Modern weapon guidance problems require consideration not only of miss distance but also various constraints. To improve penetration against armored or deeply buried hard targets, it is necessary to hit the target's weak points at a specified attack angle. Attack angle control guidance technology can significantly enhance weapon combat effectiveness without increasing the cost of the combat platform, making it of significant practical importance. Attack timing control technology aimed at achieving saturation attacks has attracted widespread attention in recent years. Saturation attacks can be achieved by specifying a common attack time for multiple aircraft at the initial moment and then controlling the attack time after launch. Guidance problems with attack time constraints have been extensively studied in recent years, and attack time coordination for saturation attacks is currently a common form of cooperative guidance. However, attack angle constraints and attack time constraints are two different types of spatiotemporal constraints, and their strong coupling further increases the difficulty of solving this problem.

[0003] Planar attack angle constraint guidance laws can solve the single-channel attack angle constraint guidance problem, and this method can achieve good guidance results when the initial flight direction deviation of other channels is not large. However, in practical problems, there are cases where the initial flight direction deviates significantly from the plane containing the attack angle constraint. If a multi-channel attack angle constraint method is used, the spatial kinematic coupling problem of the three-dimensional guidance problem will be ignored, leading to a decrease in guidance performance. To solve the attack angle constraint problem in three-dimensional space, a nonlinear attack angle constraint guidance law needs to be proposed.

[0004] With the development of low-cost unmanned aerial vehicles (UAVs) and modern weaponry, low-cost loitering gliders have become a typical combat platform, and gliding glider formations can achieve coordinated reconnaissance and strike capabilities. However, loitering gliders have a limited thrust range, resulting in an upper speed limit. On the other hand, they also need to maintain a certain lower speed limit to ensure maneuverability. Therefore, a guidance law that adapts to actual combat requirements and takes into account the speed limitations of the aircraft is needed. Summary of the Invention

[0005] This invention discloses a three-dimensional guidance method that considers the speed limit of the aircraft to achieve attack angle constraints and time constraints. The guidance of the powered aircraft is decoupled into independent flight direction control with normal acceleration as input to achieve attack angle constraints, and tangential flight speed control with engine thrust as input to achieve hitting the target at the expected attack time.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] This invention discloses a three-dimensional guidance method for aircraft under speed-constrained conditions with time and angle constraints. A vector model is established in three-dimensional space, and quaternion theory and a spatial vector guidance model are used to solve the attack angle prediction problem in spatial proportional guidance. Appropriate performance indicators are selected to transform the error control problem into an optimization problem for solution. Attack angle control is achieved by adjusting the error between the predicted final aircraft velocity direction and the desired attack angle direction. Under the attack angle constraint guidance law, the trajectory shape and length are independent of changes in aircraft velocity. Considering the influence of aerodynamics, gravity, and engine thrust on aircraft velocity, the attack time constraint problem is transformed into a residual trajectory length control problem. Under the aircraft speed constraint condition, the residual trajectory length is controlled by controlling axial acceleration, enabling the aircraft to hit the target at a preset desired time. By combining the attack angle constraint guidance law and the axial thrust control guidance law, guidance with attack angle and time constraints under aircraft speed constraints is achieved.

[0008] This invention discloses a three-dimensional guidance method for aircraft under speed-constrained conditions with time and angle constraints, comprising the following steps:

[0009] Step 1: Establish a three-dimensional guidance problem vector model for the guidance scenario, and use quaternion theory and spatial vector guidance model to predict the attack angle of three-dimensional spatial proportional guidance.

[0010] R represents the spatial relative position vector, which is

[0011] R = P t -P m (1)

[0012] Among them, P t and P m V represents the position vectors of the target and the aircraft, respectively. m and A m This represents the aircraft's flight speed and acceleration vectors. and These are the normal and tangential acceleration vectors, respectively. Let the velocity vector and the rotational angular velocity vector be Ω. m The line-of-sight angle rotation angular velocity vector is

[0013]

[0014]

[0015] When the velocity is constant, i.e. The three-dimensional proportional guidance command is

[0016]

[0017] The vector of flight speed and rotational angular velocity is

[0018]

[0019] The proportional guidance command is located within the target-missile motion plane. Therefore, under proportional guidance conditions, the guidance process will be completed within the target-missile motion plane, which is the plane containing the aircraft's center of mass, velocity, and the target's center of mass. f It is the terminal velocity vector under proportional guidance, predicted using the kinematic characteristics of proportional guidance. Define V. m The angle between R and R is σ.

[0020]

[0021] In the line-of-sight coordinate system, the angular velocity of the line-of-sight rotation is expressed as:

[0022]

[0023] Where ζ represents the line of sight and V f The angle between them. k L It is along Z L The unit vector of direction is represented as

[0024]

[0025] Furthermore, the flight speed and rotational angular velocity are expressed as:

[0026]

[0027] According to (5),

[0028]

[0029] Determining the current time as the initial time, with the leading angle of the proportional guide terminal set to 0, the integral yields... Combining the definition of σ, we get from V m To V f rotation vector

[0030]

[0031] Where φ is the magnitude of the rotation angle, expressed as...

[0032]

[0033] According to quaternion theory

[0034]

[0035]

[0036] in,

[0037]

[0038] The attack angle error is the predicted final vehicle velocity direction V. f In the direction V of its expectation c The angle between them is expressed as

[0039]

[0040] By establishing a three-dimensional spatial guidance vector model, and combining (13)-(15), the final velocity direction of the aircraft is predicted, and the attack angle error is defined based on this prediction.

[0041] Step 2: Using an offset proportional guidance feedback structure, the offset term is orthogonally decomposed, and the corresponding performance index is selected to transform the error control problem into an optimal problem for solution. By adjusting the error between the predicted final aircraft velocity direction and the desired attack angle direction, the attack angle control is achieved.

[0042] The three-dimensional attack angle constraint guidance command is divided into two parts. in, To ensure missile interception of targets, a proportional guidance law is employed. b The bias term is based on the prediction-correction concept and adjusts the predicted final vehicle velocity direction V. f In the direction V of its expectation c The error between them is used to satisfy the attack angle constraint. Definition

[0043] V = ||V m ||,r=‖R‖ (17)

[0044]

[0045] These variables are unit vectors. Taking the derivative of (16) gives...

[0046]

[0047] in,

[0048]

[0049]

[0050] In the and R e In the plane formed, perpendicular to V m The vector is defined as

[0051]

[0052] The bias term is along k y and k L Orthogonal decomposition of directions yields

[0053] A b =A bL +A by (twenty three)

[0054] Substituting (23) into (19) yields

[0055]

[0056] Among them, A by and A bL Representing A respectively bL and A by Size, k yf Perpendicular to k L and

[0057]

[0058] In the case of k L and k yf The projection of the plane and k yf The included angle is defined as and

[0059]

[0060] Substituting (26) into (24) gives

[0061]

[0062] Write (27) in the following form

[0063]

[0064] in,

[0065]

[0066]

[0067] Select performance metrics

[0068]

[0069] Where M ≥ 1. The resulting optimality problem is as follows:

[0070]

[0071] Solving for the given information

[0072]

[0073] Attack angle constraint guidance command is

[0074]

[0075] The attack angle constraint guidance command ensures that the attack angle error converges, and the offset proportional guidance enables the aircraft to hit the target in three-dimensional space while controlling the attack angle.

[0076] Step 3: Considering that the aircraft speed is affected by aerodynamics, gravity and engine thrust, the attack time constraint problem is transformed into a residual trajectory length control problem. Under the condition of aircraft speed limit, the residual trajectory length is controlled by controlling the axial acceleration, so that the aircraft hits the target in the preset expected time.

[0077] Traditional guidance law design often assumes a constant aircraft velocity, but in real-world guidance problems, variations in flight velocity are common. During actual flight, aircraft velocity is affected by aerodynamics, gravity, and engine thrust. Considering guidance dynamics in the vertical plane, the variation of flight velocity V satisfies...

[0078]

[0079] Where P is the thrust, D is the drag, G is the gravity, and m is the mass of the aircraft. Lift and drag are expressed as...

[0080]

[0081] Among them, C L C is the lift coefficient. D Where S is the drag coefficient, Q is the dynamic pressure, and S is the dynamic pressure. ref The reference area is used. The dynamic pressure is expressed as...

[0082]

[0083] Where ρ is the atmospheric density. The drag coefficient is expressed as...

[0084]

[0085] Among them, C D0K is the zero lift-to-drag ratio coefficient.

[0086] Combining the relative motion relationship between the aircraft and the target,

[0087]

[0088]

[0089]

[0090] Trajectory length is defined as

[0091] s=∫Vdt (41)

[0092] Combining the relative motion equations (38)-(40), we get

[0093]

[0094]

[0095]

[0096] Because the missile's flight trajectory passes through

[0097] R = R e r (45)

[0098] Therefore, it is determined that the dynamic equations for the changes in the flight trajectory of the aircraft, combined with (42)-(44), do not include flight speed, meaning that changes in the magnitude of flight speed will not affect the shape of the flight trajectory. Thus, the attack time constraint problem is transformed into a residual trajectory length control problem, which is achieved by controlling the axial acceleration. On the other hand, considering the actual dynamic characteristics of the aircraft, the magnitude of flight speed is limited.

[0099] V min ≤V≤V max (46)

[0100] The trajectory length s is obtained by integrating the trajectory based on the initial conditions. f Since the trajectory shape is velocity-independent, the effect of velocity changes does not need to be considered during trajectory length calculation. The length of the flown trajectory is obtained by integrating the velocity.

[0101]

[0102] Therefore, the remaining trajectory length s is obtained. tg =s f -s. The tangential acceleration command is...

[0103]

[0104] Where, ε t =t d -t represents the attack time error, t d This represents the expected attack time. f(x) is...

[0105]

[0106] Furthermore, v1 = -(V min +V max ) / 2, v2=(V max -V min ) / 2. c s =f -1 ((v1+V d ) / v2), where V d ∈(V min V max () is the reference speed, k a >0,k b >0. The final guidance law form is

[0107]

[0108] This guidance law enables the aircraft to hit the target at the desired angle and time by characterizing the speed limit of the aircraft.

[0109] Beneficial effects:

[0110] (1) This invention discloses a three-dimensional guidance method that considers attack angle constraints and time constraints. It uses a three-dimensional spatial vector model to describe the guidance problem, considering the spatial kinematic coupling of the three-dimensional guidance problem, thus avoiding the complex nonlinear kinematic relationships in the Euler angle description case. Furthermore, it combines quaternion theory to achieve attack angle prediction for three-dimensional proportional guidance, and controls the attack angle error based on offset proportional guidance, avoiding the problem of decreased guidance performance caused by the neglect of spatial kinematic coupling in three-dimensional guidance by the channel-specific attack angle constraint guidance method.

[0111] (2) The present invention discloses a three-dimensional guidance method that considers attack angle constraints and time constraints. Under the action of this guidance method, the shape of the aircraft trajectory is not affected by the change in the speed of the aircraft. When applied to variable speed aircraft, it ensures the control performance of attack time and attack angle.

[0112] (3) The present invention discloses a three-dimensional guidance method that considers attack angle constraints and time constraints. The aircraft hits the target at a pre-set desired time. The attack time of the aircraft is adjustable. In practical applications, the desired attack time can be adjusted according to different guidance scenarios and mission requirements, which is flexible.

[0113] (4) Some aircraft have limited thrust range, so their flight speed has an upper limit. On the other hand, aircraft need to maintain a certain lower speed limit to ensure maneuverability. The three-dimensional guidance method disclosed in this invention, which considers attack angle constraints and time constraints, is more practical and closer to actual scenarios. Attached Figure Description

[0114] Appendix Figure 1 This is a vector model diagram of the three-dimensional guidance problem in a specific embodiment of the present invention;

[0115] Appendix Figure 2 This is a guidance trajectory diagram;

[0116] Appendix Figure 3 A diagram showing the magnitude of guided flight speed;

[0117] Appendix Figure 4 The graph shows the attack angle error and attack time error.

[0118] Appendix Figure 5 This is a diagram showing the remaining trajectory length and the distance between the projectile and the target.

[0119] Appendix Figure 6 This is a curve diagram of the leading angle;

[0120] Appendix Figure 7 This is a graph of acceleration components;

[0121] Appendix Figure 8 This is a graph of velocity components;

[0122] Appendix Figure 9 This is a force curve diagram.

[0123] Figure 10 This is a flowchart of a three-dimensional guidance method for aircraft under speed and angle constraints according to the present invention. Detailed Implementation

[0124] The following technical solutions and accompanying drawings illustrate the implementation of this invention, making its technical content clearer and easier to understand. The present application will be further described in detail below with reference to the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only for explaining the relevant invention and not for limiting the invention.

[0125] Example:

[0126] Consider a scenario in three-dimensional space where a missile with coordinates (8000, 0, 8000)m strikes a stationary target with coordinates (0, 0, 8000)m. The initial velocity vector of the missile is V. m =(cosθ) l cosψ l cosθ l sinψ lsinθ l ), where θ l =0°,ψ l =18°0. The expected attack time is set to 20 seconds, and the expected attack angle θ is... d =-10°,ψ d = -150°, V c =(cosθ) d cosψ d cosθ d sinψ d sinθ d The guidance parameters are N=4, k a =0.5,k b =0.1.

[0127] like Figure 10 As shown in the figure, this embodiment discloses a three-dimensional guidance method with time and angle constraints under aircraft speed limitations. First, a vector model is established in three-dimensional space. The attack angle of spatial proportional guidance is predicted using quaternion theory. Then, based on bias-corrected Billy guidance and optimal control theory, the attack angle error is controlled by normal control commands. Next, a simplified aircraft aerodynamics and engine model is used to control the remaining trajectory length by tangential acceleration, thereby controlling the attack time, while not exceeding the aircraft speed limit. By combining the proposed normal attack angle constraint guidance law and tangential thrust control guidance law, guidance with attack angle and time constraints under aircraft speed limitations is achieved. The specific implementation of the invention will be described below with reference to the accompanying drawings and embodiments.

[0128] Step 1: First, determine the initial conditions for the aircraft and target, such as their positions, initial velocity magnitude, and direction. After determining the initial conditions, establish a three-dimensional vector model of the guidance scenario. For example... Figure 1 As shown. The guidance command is decomposed into the following: Figure 2 The normal and tangential acceleration vectors shown are... Based on (13)-(15) the terminal velocity vector V under proportional guidance conditions f Make predictions.

[0129] Step 2: Employ an offset proportional guided feedback structure. For bias term A b Orthogonal decomposition, decomposed into A b =A bL k L +A by k y According to equations (8) and (22), k is obtained. L and k y Then calculate A according to (32).bL and A by This yields the normal acceleration command to achieve the attack angle constraint.

[0130] Step 3: Solve for the tangential acceleration command considering flight speed limitations. The projectile dynamics coefficients are taken as m = 9.5632 kg, S... ref =0.004077m 2 C D0 =1.1359, K=0.05, ρ=1.2kg / m 3 The change in missile velocity is calculated according to equations (34)-(37). For a specific guidance scenario, the remaining trajectory length depends on the initial guidance state and the guidance law parameters constrained by the attack angle. The trajectory length s under the initial conditions is... f This can be obtained by integrating the trajectory, with the missile's velocity set to a constant value of 500 m / s during integration. The vehicle's flight speed is limited to [400, 600] m / s, V d =500m / s, a is calculated according to (48) T Receive tangential acceleration command

[0131]

[0132] The above steps yield guidance commands in three-dimensional space that simultaneously consider time constraints, attack angle constraints, and flight speed limitations. From Figure 2 The guidance trajectory in Figure 3 shows that the aircraft hit a stationary target in space. The aircraft's velocity curve in Figure 3 shows that the aircraft's speed remained within the specified limits during flight. Combined with... Figure 4 Attack time error curve and Figure 5 The missile-target distance curve and residual trajectory length curve show that the missile hit the target at the expected time and angle of attack. According to... Figure 6 The lead angle curve shows that the aircraft's lead angle converges to zero within the expected time. From... Figure 7 The acceleration curves show that both the axial and normal accelerations converge to zero at the end of the trajectory. Figure 8 It can also be seen from the components of the aircraft velocity vector that the aircraft velocity vector also converges to the desired attack angle vector. Figure 9 This describes the forces acting on the aircraft. The above analysis shows that, under the guidance law, the aircraft successfully achieved the desired attack angle and time to strike the target despite its limited flight speed.

[0133] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A three-dimensional guidance method for aircraft under speed-constrained conditions with time and angle constraints, characterized in that: Includes the following steps, Step 1: Establish a three-dimensional guidance problem vector model for the guidance scenario, and use quaternion theory and spatial vector guidance model to predict the attack angle of three-dimensional proportional guidance. The implementation method for step one is as follows: R represents the spatial relative position vector, which is R=P t -P m (1) Among them, P t and P m V represents the position vectors of the target and the aircraft, respectively. m and A m This represents the aircraft's velocity and acceleration vectors. and These are the normal and tangential acceleration vectors, respectively. Let the velocity vector and the rotational angular velocity vector be Ω. m The line-of-sight rotational angular velocity vector is Ω. R When the velocity is constant, i.e. The three-dimensional proportional guidance command is The vector of flight speed and rotational angular velocity is The proportional guidance command lies within the target-missile motion plane; therefore, under proportional guidance conditions, the guidance process will be completed within this plane, which is the plane containing the aircraft's center of mass, velocity, and the target's center of mass. f It is the terminal velocity vector under proportional guidance, predicted using the kinematic characteristics of proportional guidance; V is defined. m The angle between R and R is σ. In the line-of-sight coordinate system, the angular velocity of the line-of-sight rotation is expressed as: Where ζ represents the line of sight and V f The angle between them; k L It is along Z L The unit vector of direction is represented as Furthermore, the flight speed and rotational angular velocity are expressed as: According to (5), Determining the current time as the initial time, with the leading angle of the proportional guide terminal set to 0, the integral yields... Combining the definition of σ, we get from V m To V f rotation vector Where φ is the magnitude of the rotation angle, expressed as: According to quaternion theory in, The attack angle error is the predicted final vehicle velocity direction V. f In the direction V of its expectation c The angle between them is expressed as By establishing a three-dimensional spatial guidance vector model, and combining (13)-(15), the final velocity direction of the aircraft is predicted, and the attack angle error is defined based on this prediction. Step 2: Using an offset proportional guidance feedback structure, the offset term is orthogonally decomposed, and the corresponding performance index is selected to transform the error control problem into an optimal problem for solution. By adjusting the error between the predicted final aircraft velocity direction and the desired attack angle direction, the attack angle control is achieved. Step 3: Considering that the aircraft speed is affected by aerodynamics, gravity and engine thrust, the attack time constraint problem is transformed into a residual trajectory length control problem. Under the condition of aircraft speed limit, the residual trajectory length is controlled by controlling the axial acceleration, so that the aircraft hits the target in the preset expected time.

2. The three-dimensional guidance method for aircraft under speed-constrained conditions as described in claim 1, characterized in that: The second step is implemented as follows: The three-dimensional attack angle constraint guidance command is divided into two parts. in, To ensure missile interception of targets, a proportional guidance law is employed; A b The bias term is based on the prediction-correction concept and adjusts the predicted final vehicle velocity direction V. f In the direction V of its expectation c The error between them is used to satisfy the attack angle constraint; definition V=||V m ||,r=‖R‖ (17) The variable is a unit vector; taking the derivative of (16) gives... in, In the and R e In the plane formed, perpendicular to V m The vector is defined as The bias term is along k y and k L Orthogonal decomposition of directions yields A b =A bL +A by (23) Substituting (23) into (19) yields Among them, A by and A bL Representing A respectively bL and A by Size, k yf Perpendicular to k L and In the case of k L and k yf The projection of the plane and k yf The included angle is defined as and Substituting (26) into (24) gives Write (27) in the following form in, Select performance metrics Where M≥1; rearranged, we obtain the following optimal problem. Solving for the given information Attack angle constraint guidance command is The attack angle constraint guidance command ensures that the attack angle error converges, and the offset proportional guidance enables the aircraft to hit the target in three-dimensional space while controlling the attack angle.

3. The three-dimensional guidance method for aircraft under speed-constrained conditions as described in claim 1, characterized in that: The method for implementing step three is as follows: In actual flight, the speed of an aircraft is affected by aerodynamics, gravity, and engine thrust. Considering the guidance dynamics in the vertical plane, the change in flight speed V satisfies Where P is the thrust, D is the drag, G is the gravity, and m is the mass of the aircraft; lift and drag are expressed as... Among them, C L C is the lift coefficient. D Where S is the drag coefficient, Q is the dynamic pressure, and S is the dynamic pressure. ref The reference area is shown; the dynamic pressure is expressed as... Where ρ is the atmospheric density; the drag coefficient is expressed as... Among them, C D0 K is the zero lift-to-drag ratio coefficient; Combining the relative motion relationship between the aircraft and the target, Trajectory length is defined as s=∫Vdt (41) Combining the relative motion equations (38)-(40), we get Because the missile's flight trajectory passes through R=R e r (45) Therefore, it is determined that the dynamic equations for the changes in the flight trajectory of the aircraft, combined with (42)-(44), do not include flight speed, meaning that changes in the magnitude of flight speed will not affect the shape of the flight trajectory; thus, the attack time constraint problem is transformed into a residual trajectory length control problem, and the residual trajectory length is controlled by controlling the axial acceleration; on the other hand, considering the actual dynamic characteristics of the aircraft, the magnitude of flight speed is limited. In min ≤V≤V max (46) The trajectory length s is obtained by integrating the trajectory based on the initial conditions. f Since the trajectory shape is velocity-independent, the effect of velocity changes does not need to be considered in the trajectory length calculation; the length of the already flown trajectory is obtained by integrating the velocity. Therefore, the remaining trajectory length s is obtained. tg =s f -s; the tangential acceleration command is... Where, ε t =t d -t represents the attack time error, t d Represents the expected attack time; f(x) is Furthermore, v1 = -(V min +V max ) / 2, v2=(V max -V min ) / 2; c s =f -1 ((v1+V d ) / v2), where V d ∈(V min V max () is the reference speed, k a >0,k b >0; the final guidance law form is This guidance law enables the aircraft to hit the target at the desired angle and time by characterizing the speed limit of the aircraft.

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