Static prediction based maximum overload constraint analytical guidance method

Abstract

The application discloses a maximum overload constraint analytical guidance method based on static prediction and belongs to the general technical field of guidance control.The application is realized in the following manner: a line-of-sight coordinate system is defined in a longitudinal plane, a target relative motion model of a spacecraft is established on the basis of the line-of-sight coordinate system, an initial connecting line is taken as a reference, a prediction result of overload change from the moment when the spacecraft is launched, i.e., the beginning of the terminal guidance stage, to the moment of hitting is obtained based on optimal control theory and combined with a multi-constraint optimal terminal guidance expression; based on the prediction result of overload change, the prediction result of overload change in the whole process is analyzed, and whether the overload exceeds a constraint limit is judged; after the overload exceeds the constraint limit, the position of a guidance turning point of the spacecraft is changed, whether the overload exceeds the constraint limit is judged again, and the process is repeated until the prediction result of the overload satisfies the constraint condition; and a multi-constraint terminal guidance law considering a landing angle constraint is substituted to realize the maximum overload constraint analytical guidance based on static prediction, so that the spacecraft can satisfy the requirement of overload in the flight process and hit the target with an expected landing angle.

Description

TECHNICAL FIELD

[0001] The application relates to a maximum overload constraint analytical general guidance method based on static prediction and belongs to the technical field of general guidance control. BACKGROUND

[0002] Currently, using a fixed-wing unmanned aerial vehicle to accurately rendezvous with a target is also an important requirement in the development of unmanned aerial vehicle guidance control.

[0003] When multiple constraint guidance is required for a ground target, in order to ensure high hitting accuracy and landing angle control accuracy, a conventional large landing angle guidance law (shaped guidance law) is used, and the aircraft maneuvering capability is required to be high. The maneuvering capability of the current commonly used fixed-wing unmanned aerial vehicle is limited, and cannot meet the requirement of the guidance law, thereby causing the guidance effect to be greatly affected and leading to task failure. SUMMARY

[0004] In order to avoid the problem of guidance task failure caused by overload out-of-limit in the aircraft guidance process, the purpose of the application is to provide a maximum overload constraint analytical guidance method based on static prediction. The dimensionless prediction is static, the prediction result of the overload in the terminal guidance section is obtained, and then the position of the aircraft guidance turning point is adjusted according to the overload prediction, so that the overload of the aircraft in the flight process meets the requirement, and the target is hit with the expected landing angle.

[0005] The purpose of the application is achieved through the following technical scheme.

[0006] The maximum overload constraint analytical guidance method based on static prediction disclosed by the application defines a line-of-sight coordinate system in the longitudinal plane, establishes an aircraft target relative motion model on the basis, takes the initial connecting line as a reference, combines a multi-constraint optimal terminal guidance expression based on the optimal control theory, predicts the overload change result from the aircraft launch, that is, the start of the terminal guidance section, to the hitting instant, analyzes the overall overload change prediction situation based on the overload change prediction result, judges whether the overload exceeds the constraint limit, changes the position of the aircraft guidance turning point after the overload out-of-limit, judges again whether the overload is out-of-limit until the overload prediction result meets the constraint condition, and realizes the maximum overload constraint analytical guidance based on static prediction by substituting the multi-constraint terminal optimal guidance law considering the landing angle constraint.

[0007] The maximum overload constraint analytical guidance method based on static prediction disclosed by the application comprises the following steps:

[0008] Step 1: establishing a target relative motion model;

[0009] Firstly, a line-of-sight coordinate system Ox q y q z q is defined, the origin O is located at the mass center of the aircraft, and the Oxq Axis pointing to the target connecting line direction; Oy q Axis located in the vertical plane passing through the origin, perpendicular to Ox q Axis perpendicular to; Oz q Axis perpendicular to Ox q y q Plane, the positive direction is determined according to the right-hand coordinate system;

[0010] Establish the target relative motion relationship expression in the longitudinal plane, that is, the target relative motion model:

[0011]

[0012] φ = θ - q

[0013] Where, r is the target connecting line distance, V T is the target speed, V M is the aircraft speed, q is the initial target connecting line and the current connecting line angle, referred to as the line of sight angle, θ is the speed inclination angle, φ is the aircraft speed direction and the current aircraft target connecting line direction angle, referred to as the field of view angle, φ T is the aircraft speed direction and the current aircraft target connecting line direction angle, a yc is the aircraft normal overload.

[0014] Step 2: In the coordinate system established in step 1, based on optimal control theory, combined with the multi-constraint optimal terminal guidance expression, an overload static prediction model is established.

[0015] Predict the maximum value of the overload The maximum value of the overload static prediction result is represented as a yc-lim The upper limit of the aircraft overload during the entire flight process is represented.

[0016] The multi-constraint terminal optimal guidance law considering the impact angle constraint is as follows:

[0017]

[0018] Where, V r is the relative speed of the aircraft and the target, V r = V M for a stationary target, V M is the aircraft speed; is the rate of change of the line of sight angle, q F is the impact angle in the inertial coordinate system;

[0019] The flight time t of the aircraft is normalized and dimensionless:

[0020]

[0021] wherein the total flight time is estimated

[0022] The guidance command with time-varying form is obtained by combining the multi-constrained terminal optimal guidance law expression:

[0023]

[0024] wherein ε0 is the initial velocity deviation angle of the aircraft, and the expression is ε0=θ0-q0; θ0 and q0 are the initial velocity inclination angle and the line-of-sight angle; q Fc is the impact angle of the aircraft in the line-of-sight coordinate system defined in step 1, and the expression is q Fc =q F -q0.

[0025] According to the relative position relationship between the aircraft and the target, there is a relationship as follows:

[0026]

[0027] wherein the intermediate variable ΔH-H M -H T , H M , H T are the initial heights of the aircraft and the target; ΔX=X M -X T , X M , X T are the initial horizontal positions of the aircraft and the target; the expression (4) is substituted into the expression (3) to obtain the transformed result of the guidance command prediction expression

[0028]

[0029] Based on the relative position relationship between the aircraft and the target, the line-of-sight angle at the initial time is expressed as:

[0030]

[0031] The result obtained from the expression (6) is substituted into the expression (5) to obtain the static prediction model of the overload based on the current relative position relationship between the aircraft and the target and the impact angle as follows:

[0032]

[0033] Step 3: Based on the static prediction model of the overload in step 2 and the initial position of the aircraft at this time, the maximum predicted overload is calculated The absolute value of the maximum predicted overload is compared with the maximum overload constraint a yc-lim When the judgment result is that the prediction is out of range, i.e., the maximum predicted overload is greater than the overload constraint, step 4 is executed; otherwise, step 5 is executed;

[0034] From equation (7), when the aircraft and target position are given, the change of the static overload prediction model is only related to the dimensionless time variable For the sake of being a linear function of the argument, the maximum value occurs at the end; therefore, there is

[0035]

[0036] The absolute value of the maximum change of the overload prediction obtained from equation (9) is compared with the given overload constraint a yc-lim When the absolute value of is greater than the given overload constraint a yc-lim , the overload is out of bounds, and the guidance turning point of the aircraft is adjusted in step 4; otherwise, the initial horizontal position of the aircraft at this time is recorded as the feasible horizontal position of the aircraft, and step 5 is entered to calculate the guidance command, thereby realizing the guidance process.

[0037] Step 4: Based on the calculated in step 3 and the given overload constraint a yc-lim , the target position is adjusted, and step 3 is executed again.

[0038] When the overload prediction is out of bounds, i.e. , the guidance turning point horizontal position is adjusted according to the maximum value of the overload prediction and the overload constraint; the initial horizontal position of the aircraft guidance turning point at the τth step is denoted by X M (τ), τ is an integer, and τ≥0; the horizontal distance between the aircraft and the target at the τth guidance turning point is denoted by ΔX(τ); the initial horizontal position of the aircraft at the next guidance turning point is denoted by X M (τ+1); the horizontal distance at the next guidance turning point is denoted by ΔX(τ+1). Based on ΔX(τ), an extended term is added to obtain the expression of ΔX(τ+1) as follows

[0039]

[0040] where η is an additional parameter that controls the adjustment amplitude; based on the guidance turning point horizontal distance update result ΔX(τ+1) obtained from equation (9), the initial horizontal position X M (τ+1) of the next aircraft is calculated in reverse; the expression is as follows

[0041]

[0042] Based on the next aircraft initial horizontal position X M (τ+1) obtained from equation (10), step 3 is executed again to determine whether the overload is out of bounds, and a decision is made based on the result of step 5.

[0043] Step 5: the horizontal position of the aircraft in step 3 and the required parameters of the guidance command calculated in the remaining steps 3 are substituted into the multi-constraint terminal optimal guidance law expression in step 2 considering the impact angle constraint to obtain the guidance command, and the whole guidance process is completed.

[0044]

[0045] The line-of-sight angle q and the line-of-sight angle change rate in formula (11) are obtained by the gyroscope of the aircraft; the relative speed V r , the impact angle q F is substituted into formula (11) to obtain the guidance command, and the precise guidance considering the maximum overload constraint based on the static prediction method is realized according to the guidance command.

[0046] Advantages:

[0047] 1. The maximum overload constraint analytical guidance method based on static prediction disclosed in the application, the overload static prediction model is a key, on the basis of a given overload constraint, whether the overload is out of range is judged according to the overload static prediction model, when the overload is out of range, the horizontal position of the aircraft guidance turning point is adjusted based on the predicted maximum value and the overload constraint, and finally the overload constraint condition is met.

[0048] 2. The maximum overload constraint analytical guidance method based on static prediction disclosed in the application, a series of initial guidance parameters are given, and the parameters are processed to obtain an overload static prediction expression, the horizontal position of the aircraft guidance turning point is adjusted according to the proportional relationship between the maximum value of the expression and the overload constraint, and after adjustment, it is judged again until the overload is no longer out of range, and then the overload constraint in the whole guidance process is met.

[0049] 3. The application is based on the optimal control principle, and proposes a maximum overload constraint analytical general guidance method based on static prediction. First, based on the optimal guidance law expression considering the impact angle constraint, under the condition of a given expected impact angle, a method for real-time prediction of the whole flight overload of the aircraft is proposed, and the estimated value of the change of the aircraft overload can be obtained; then, based on the estimated result, the aircraft guidance turning point is adaptively adjusted, so that the demand of the guidance task on the aircraft maneuvering overload is significantly reduced under the condition of ensuring the hit and impact angle control accuracy. DETAILED DESCRIPTION

[0050] Figure 1 is a schematic diagram of a target relative motion model of an aircraft;

[0051] Figure 2 is a schematic diagram of a guidance turning point adjustment process;

[0052] Figure 3 is a schematic diagram of an aircraft overload curve before a modified guidance turning point;

[0053] Figure 4 is a schematic diagram of an aircraft overload curve after a modified guidance turning point;

[0054] Figure 5 is a schematic diagram of an aircraft trajectory curve;

[0055] Figure 6 is a flow chart of the maximum overload constraint analytical guidance method based on static prediction disclosed in the present application. DETAILED DESCRIPTION

[0056] For better illustrating the purposes and advantages of the present application, the following further illustrates the content of the present application in combination with the drawings and examples.

[0057] Example 1

[0058] In this example, the task requirement is that an unmanned aerial vehicle starts from a height of 1 km above the ground at a speed of 100 m / s, interacts with a static target on the ground at a horizontal distance of 3 km from itself, performs a guidance task, the initial speed direction is horizontal, and the angle with the horizontal plane when the task is finally completed is 70°, and the absolute value of the whole course overload does not exceed 2 g.

[0059] As shown in Figure 6 , the maximum overload constraint analytical guidance method based on static prediction disclosed in this example is specifically implemented as follows:

[0060] Step 1: Establish a target relative motion model;

[0061] First, define the line-of-sight coordinate system Ox q y q z q ; the origin O is located at the center of mass of the aircraft; the Ox q axis points to the target connecting line direction; the Oy q axis is located in the vertical plane passing through the origin and is perpendicular to the Ox q axis; the Oz q axis is perpendicular to the Ox q y q plane, and the positive direction is determined according to the right-hand coordinate system;

[0062] Establish the target relative motion relationship expression in the longitudinal plane, i.e. the target relative motion model:

[0063]

[0064]

[0065] wherein r is the target connecting line distance, VT V is the target velocity M V is the aircraft velocity, q is the angle between the initial target line and the current target line, which is called the line-of-sight angle, θ is the velocity inclination angle, φ is the angle between the aircraft velocity direction and the current target line direction, which is called the field-of-view angle, φ T φ is the angle between the aircraft velocity direction and the current target line direction yc a is the aircraft normal overload

[0066] Step 2: In the coordinate system established in step 1, based on optimal control theory, a static overload prediction model is established by combining the multi-constrained optimal terminal guidance expression;

[0067] In this step, the task requirements are integrated to obtain the following guidance parameters: aircraft velocity V M = 100 m / s, initial aircraft height H M = 1000 m, target initial height H T = 0 m, initial horizontal position of the aircraft X M = 0 m, target initial horizontal position X T = 3000 m, initial time trajectory inclination angle θ0= 0°, impact angle q F = -70°, maximum overload constraint a yc-lim = 2g.

[0068] The maximum predicted overload is which represents the maximum value of the static overload prediction result; the maximum overload constraint a yc-lim represents the upper limit of the aircraft overload during the entire flight;

[0069] The multi-constrained terminal optimal guidance law considering the impact angle constraint is as follows:

[0070]

[0071] wherein V r is the relative velocity between the aircraft and the target, and for a stationary target, V r = V M , V M is the aircraft velocity; is the rate of change of the line-of-sight angle, q F is the impact angle in the inertial coordinate system;

[0072] The flight time t of the aircraft is normalized and dimensionless processed:

[0073]

[0074] wherein the estimated total flight time

[0075] Combining the multi-constraint terminal optimal guidance law expression, the guidance command variation with time is obtained:

[0076]

[0077] wherein, ε0is the initial velocity deviation angle of the aircraft, the expression is ε0= θ0- q0; θ0, q0are the initial velocity inclination angle and the line-of-sight angle; q Fc is the impact angle of the aircraft in the line-of-sight coordinate system defined in step 1, the expression is q Fc ≤q F -q0.

[0078] According to the relative position relationship between the aircraft and the target, there is a relationship as follows:

[0079]

[0080] wherein, the intermediate variable ΔH = H M -H T , H M , H T are the initial heights of the aircraft and the target; ΔX = X M -X T , X M , X T are the initial horizontal positions of the aircraft and the target; substituting equation (4) into equation (3), the prediction expression of the guidance command is obtained

[0081]

[0082] Based on the relative position relationship between the aircraft and the target, the initial line-of-sight angle is expressed as:

[0083]

[0084] Substituting the result obtained from equation (6) into equation (5), the static prediction model of the overload based on the current relative position relationship between the aircraft and the target and the impact angle is obtained as follows:

[0085]

[0086] Step 3: Based on the static prediction model of the overload in step 2 and the initial position of the aircraft at this time, the maximum predicted overload is calculated The absolute value of the maximum predicted overload is compared with the maximum overload constraint a yc-lim When the judgment result is that the prediction is out of range, that is, the maximum predicted overload is greater than the overload constraint, step 4 is executed; otherwise, step 5 is executed;

[0087] As can be seen from equation (7), when the positions of the aircraft and the target are given, the variation of the static prediction model of the overload is only related to the dimensionless time variable Related to, for the purpose of Since the expression is a linear function of the independent variable, its maximum value occurs at the end; therefore, we have...

[0088]

[0089] The maximum value of the overload prediction change obtained from equation (9) The absolute value of the given overload constraint a yc-lim When comparing, The absolute value is greater than the given overload constraint a yc-lim If the overload exceeds the limit, proceed to step 4 to adjust the guidance turning point of the aircraft; otherwise, record the initial horizontal position of the aircraft as the feasible horizontal position of the aircraft, proceed to step 5 to calculate the guidance command, and then realize the guidance process.

[0090] Step 4: Based on the calculations in Step 3 And given overload constraint a yc-lim Adjust the target position, and then repeat step 3;

[0091] When an overload prediction exceeds the limit, i.e. At that time, the horizontal position of the guidance inflection point is adjusted according to the predicted maximum overload and the overload constraint; the initial horizontal position of the spacecraft's guidance inflection point in the τth step is represented by X. M (τ) represents the horizontal distance between the vehicle and the target at the τ-th guidance inflection point, where τ is an integer and τ≥0; ΔX(τ) represents the initial horizontal position of the vehicle at the next guidance inflection point. M (τ+1) represents the horizontal distance of the next guidance turning point, denoted by ΔX(τ+1). In this embodiment, the additional parameter controlling the adjustment amplitude is η = 0.1. Adding an extension term to ΔX(τ), the expression for ΔX(τ+1) is obtained as follows:

[0092]

[0093] Where η is an additional parameter for controlling the adjustment amplitude; based on the horizontal distance update result ΔX(τ+1) of the guidance turning point obtained by equation (9), the initial horizontal position X of the aircraft in the next step is calculated in reverse. M (τ+1); the expression is as follows:

[0094]

[0095] Based on equation (10), the initial horizontal position X of the aircraft is obtained for the next step. M (τ+1), repeat step 3 to determine if an overload has occurred, and make a decision based on the result of step 5.

[0096] Step 5: Substitute the horizontal position of the aircraft obtained in step 3 and the other parameters calculated in step 3 into formula (1) in step 2 to obtain the guidance command, and complete the whole process of guidance.

[0097]

[0098] The line-of-sight angle q and the line-of-sight angle change rate in formula (11) can be obtained by the gyroscope of the aircraft. Therefore, the relative velocity V r , the binding angle q F is substituted into formula (11) to obtain the guidance command, and finally the precise guidance considering the maximum overload constraint based on the static prediction method is realized.

[0099] The line-of-sight angle q and the line-of-sight angle change rate in formula (11) can be obtained by the gyroscope of the aircraft. Therefore, the relative velocity V r , the binding angle q F is substituted into formula (11) to obtain the guidance command, and finally the precise guidance considering the maximum overload constraint based on the static prediction method is realized. Figure 3 The overload schematic curve before the guidance turning point is modified is given, and the overload out-of-bounds situation occurs. Figure 4 The overload schematic curve after the guidance turning point is modified is given, and the overload meets the maximum constraint condition. Figure 5 The flight trajectory of the aircraft after the guidance turning point is modified is given.

[0100] The above specific description further details the purpose, technical solutions and beneficial effects of the application. It should be understood that the above description is only a specific embodiment of the application and is not used to limit the protection scope of the application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application should be included in the protection scope of the application.

Claims

1. A maximum overload constraint analytical guidance method based on static prediction, characterized in that: Comprising the following steps, Step 1: establishing a target relative motion model; First define the line-of-sight coordinate system Ox q y q z q ; the origin O is located at the center of mass of the aircraft; Ox q axis points in the direction of the target connecting line; Oy q axis is located in the vertical plane passing through the origin, perpendicular to Ox q axis; Oz q axis is perpendicular to the Ox q y q plane, the positive direction is determined according to the right-hand coordinate system; A target relative motion relationship expression in a longitudinal plane is established, i.e., a target relative motion model: φ = θ - q where r is the target range, V T is the target velocity, V M is the vehicle velocity, q is the angle between the initial target range and the current range, referred to as the line-of-sight angle, θ is the velocity inclination angle, and φ is the angle between the vehicle velocity direction and the current vehicle target range direction, referred to as the field-of-view angle, φ T is the angle between the vehicle velocity direction and the current vehicle target range direction, a yc is the vehicle normal acceleration; Step 2: based on the optimal control theory, a static overload prediction model is established in the coordinate system established in step 1, in combination with a multi-constraint optimal terminal guidance expression; The implementation method of step 2 is, Predicted maximum overload Maximum value of the static prediction of the overload; maximum overload constraint a yc-lim Upper limit of the aircraft overload during the entire flight; The multi-constraint terminal optimal guidance law expression considering the impact angle constraint is as follows: where V r is the relative velocity of the vehicle to the target, V r = V M for a stationary target, and V M is the vehicle velocity; is the rate of change of the line-of-sight angle, q F is the impact angle in the inertial frame; The flight time t of the aircraft is normalized and dimensionless processed: wherein the total flight time is estimated In combination with the multi-constraint terminal optimal guidance law expression, the time-varying form of the guidance command is obtained: wherein ε0 is the aircraft initial time velocity deviation angle, expressed as ε0 = θ0 - q0; θ0, q0 are the initial time velocity inclination angle and line-of-sight angle; q Fc is the aircraft impact angle in the line-of-sight coordinate system defined in step 1, expressed as q Fc = q F - q0; According to the relative position relationship between the aircraft and the target, there is a relationship as follows: where the intermediate variable ΔH = H M -H T , H M , H T is the initial height of the aircraft, target; ΔX = X M -X T , X M , X T is the initial horizontal position of the aircraft, target; substituting equation (4) into equation (3) gives the guidance command prediction expression transformation result Based on the relative position relationship between the aircraft and the target, the initial line-of-sight angle is expressed as: The result obtained from equation (6) is substituted into equation (5), i.e., an overload static prediction model based on the current relative position relationship between the aircraft and the target and the impact angle is obtained as follows: Step 3: Calculate the predicted maximum overload based on the overload static prediction model of Step 2 and the initial position of the aircraft at this time Step 4: Compare the absolute value of the predicted maximum overload with the maximum overload constraint a yc-lim Step 5: If the result of the comparison is that the predicted maximum overload is less than the maximum overload constraint a, then the flight control system is allowed to continue to operate normally. Step 4: Base on the calculation in Step 3 and given overload constraint a yc-lim Adjust the target position and perform Step 3 again; Step 5: the feasible horizontal position of the aircraft obtained in step 3 and the parameters required by the guidance command obtained in the remaining steps 3 are substituted into the multi-constraint terminal optimal guidance law expression considering the impact angle constraint in step 2, to obtain the guidance command, and the whole guidance process is completed.

2. The static prediction based maximum overload constraint analytical guidance method of claim 1, wherein: The implementation method of step 3 is, According to equation (7), when the aircraft, target position is given, the change of the overload static prediction model is only related to the dimensionless time variable Regarding, to be a linear function of the argument, so the maximum occurs at the end; therefore there is The absolute value of the overload prediction change maximum value obtained from formula (9) is compared with the given overload constraint a yc-lim When the absolute value of the overload prediction change maximum value obtained from formula (9) is greater than the given overload constraint a yc-lim , the overload is out of range, and step 4 is entered to adjust the turning point of the aircraft guidance; otherwise, the initial horizontal position of the aircraft at this time is recorded as the feasible horizontal position of the aircraft, and step 5 is entered to calculate the guidance command, thereby realizing the guidance process.

3. The maximum overload constraint analytical guidance method based on static prediction as described in claim 2, characterized in that: The implementation method of step 4 is, When an overload prediction exceeds the limit, i.e. At that time, the horizontal position of the guidance inflection point is adjusted according to the predicted maximum overload and the overload constraint; the initial horizontal position of the spacecraft's guidance inflection point in the τth step is represented by X. M (τ) represents the horizontal distance between the vehicle and the target at the τ-th guidance inflection point, where τ is an integer and τ≥0; ΔX(τ) represents the initial horizontal position of the vehicle at the next guidance inflection point. M (τ+1) represents the horizontal distance of the next guidance turning point; ΔX(τ+1) represents the horizontal distance of the next guidance turning point; by adding an extension term to ΔX(τ), the expression for ΔX(τ+1) is as follows: where η is an additional parameter to control the adjustment amplitude; based on the horizontal distance update result ΔX(τ+1) of the guidance turning point obtained by formula (9), the initial horizontal position X(τ+1) of the next step of the aircraft is reversely calculated; the expression is as follows M X(τ+1) = X(τ) + ΔX(τ+1) Based on equation (10) the next initial horizontal position X of the aircraft is obtained M (τ+1), step 3 is re-executed, it is judged whether the overload is out of range, and a decision is made according to the result of step 5.

4. The maximum overload constraint analytical guidance method based on static prediction as described in claim 3, characterized in that: In step 5, The guidance command is as shown in equation (11) The line-of-sight angle q and the line-of-sight angle change rate in formula (11) are obtained by the gyroscope of the aircraft itself; the relative velocity V r , the binding drop angle q F is substituted into formula (11) to obtain the guidance instruction, and the precise guidance considering the maximum overload constraint based on the static prediction method is realized according to the guidance instruction.

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