Maximum field angle constraint analytical guidance method based on model prediction
By establishing a field-of-view change prediction model on a fixed-wing unmanned aerial vehicle (UAV), and combining optimal control theory and multi-constraint optimal guidance expressions, the guidance command coefficients are calculated. This solves the problem of mission failure caused by excessive field of view during the guidance process of fixed-wing UAVs, and achieves precise control of the field of view and accurate target hit.
Patent Information
- Application Number
- CN202511000005.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-21
- Publication Date
- 2025-12-19
AI Technical Summary
When fixed-wing unmanned aerial vehicles (UAVs) perform multi-constraint guidance on ground targets, insufficient maneuverability leads to an excessively large field of view, affecting the guidance effect and potentially causing mission failure.
The analytical guidance method based on maximum field of view constraint, which is based on model prediction, establishes a relative motion model of the aircraft target by defining a line-of-sight coordinate system in the longitudinal plane, and combines optimal control theory and multi-constraint optimal terminal guidance expression to establish a field of view change prediction model. By differentiation and simultaneous solution, the prediction results of the field of view change are obtained, and the coefficients required for guidance commands are calculated to achieve accurate guidance under maximum field of view constraint.
Under the condition of satisfying the maximum field of view constraint, the aircraft can achieve precise guidance, ensuring that the field of view is always less than the specified maximum value, thereby improving the hit accuracy and landing angle control accuracy of the guidance mission.
Smart Images
Figure CN121165799A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to a kind of analytical guidance method based on aircraft field of view angle prediction model, belong to the field of guidance control technique. BACKGROUND
[0002] Current use fixed wing unmanned aerial vehicle to carry out accurate rendezvous to target also becomes important demand in the development of unmanned aerial vehicle guidance control field.
[0003] When needing to carry out multi-constraint guidance to ground target, to ensure that high enough hit accuracy, and drop angle control accuracy, using existing large drop angle guidance law (shaped guidance law), there is high demand to aircraft maneuverability.For current commonly used fixed wing unmanned aerial vehicle, maneuverability is limited, cannot meet the demand of guidance law, in turn lead to guidance effect is greatly influenced, lead to mission failure. SUMMARY
[0004] In order to avoid the problem that maximum field of view angle is too large in aircraft guidance process and leads to mission failure, the purpose of the present application is to provide a kind of maximum field of view angle constraint analytical guidance method based on model prediction, the prediction result of field of view angle in terminal guidance section is obtained by field of view angle prediction, the guidance parameter is adjusted according to overload prediction result, so that aircraft overload meets the requirement in flight process, and target is hit with expected drop angle.
[0005] The purpose of the present application is realized by the following technical scheme.
[0006] The maximum field of view angle constraint analytical guidance method based on model prediction disclosed in the present application defines sight line coordinate system in longitudinal plane, establishes aircraft target relative motion model based on this, establishes field of view angle change prediction model based on optimal control theory, combined with multi-constraint optimal terminal guidance expression, with initial target connecting line as reference, obtains the prediction result of field of view angle change according to field of view angle change prediction model;The required coefficient of guidance instruction is calculated by inputting guidance parameter, and the prediction result of field of view angle is obtained.Based on the nature of quadratic function of prediction model, the prediction model is differentiated, and the maximum field of view angle corresponding critical guidance coefficient is obtained by simultaneously solving field of view angle change model, the critical guidance coefficient is substituted into guidance law, and accurate guidance based on model analysis under the consideration of maximum field of view angle constraint condition is realized.
[0007] The maximum field of view angle constraint analytical guidance method based on model prediction disclosed in the present application includes the following steps:
[0008] Step 1: define sight line coordinate system in longitudinal plane, and establish aircraft target relative motion model.
[0009] Define sight line 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 to the target connecting line direction; Oy q axis is located in the vertical plane through the origin, perpendicular to Ox q axis is vertical; Oz q axis is perpendicular to Ox q y q plane, the positive direction is determined according to the right-hand coordinate system.
[0010] On the basis of the line-of-sight coordinate system, the attack angle is always a small quantity in the process of aircraft guidance, the relative motion relationship in the longitudinal plane is established, that is, the target relative motion model is constructed as follows:
[0011]
[0012] φ = θ - q
[0013] Wherein, r is the distance of the target connecting line of the aircraft, V T is the target speed, V M is the speed of the aircraft, q is the angle between the initial target connecting line of the aircraft and the current target connecting line, which is called the line-of-sight angle, θ is the speed inclination angle, φ T is the angle between the target speed direction and the current target connecting line direction of the aircraft, φ is the angle between the aircraft speed direction and the current target connecting line direction of the aircraft, φ is the field of view angle.
[0014] Step 2: Based on the optimal control theory, combined with the multi-constrained optimal terminal guidance expression, the field of view angle change prediction model is established.
[0015] In the process of aircraft executing guidance task, the maximum field of view angle and the final impact angle of the aircraft in the flight process need to be considered. Under the condition of given impact angle q Fc , the maximum field of view angle is solved analytically, so that the field of view angle of the aircraft is not greater than the allowable value during the whole guidance task. The given impact angle is only used to control the curvature of the trajectory, and does not need to be finally satisfied, that is, the actual impact angle of the aircraft when hitting the target is less than the given impact angle value q Fc .
[0016] The multi-constrained terminal optimal guidance law expression considering the impact angle and the field of view angle constraints is as follows:
[0017]
[0018] Wherein, V r is the relative speed, r is the distance of the target connecting line of the aircraft, q is the current field of view angle value, q Fcs2 is a landing angle weight value for controlling the trajectory of the aircraft, when s2 is 0, the guidance law (1) degenerates into a proportional navigation guidance law, when s2 tends to infinity, the guidance law (1) approaches a shaping guidance law go is the remaining flight time.
[0019] The flight time of the aircraft is normalized and dimensionless:
[0020]
[0021] Combined with the expression of the multi-constrained terminal optimal guidance law, the time-varying form of the guidance command is obtained:
[0022]
[0023] wherein ε0 is the size of the field of view angle q of the aircraft at the moment of launch, i.e. ε0 = θ0-q0
[0024] The longitudinal displacement of the aircraft is regarded as a state variable, and the definition of the state variable of the aircraft is obtained:
[0025]
[0026] Substitute the guidance command into equation (4), and after normalizing the actual time into dimensionless time, the expression with as the variable is as follows:
[0027]
[0028] Through the small attack angle condition and the geometric condition, the field of view angle change prediction model of the aircraft is obtained:
[0029]
[0030] wherein q F is the landing angle of the aircraft in the line-of-sight coordinate system, the expression is (q F =q Fc -q0), q Fc is the landing angle in the inertial system, and q0 is the initial target line-of-sight angle of the aircraft. Taking the field of view angle change prediction model in equation (6) as the starting point, the field of view angle prediction will be solved analytically in subsequent step 3, the maximum field of view angle analytical expression is obtained by derivation and simultaneous equations (8) and the maximum field of view angle constraint φ maxc , and the corresponding maximum field of view angle critical coefficient s2 is obtained, the maximum field of view angle is limited, so as to satisfy that the maximum field of view angle is less than the given constraint value in the whole flight time.
[0031] Step 3: Given initial guidance parameters: the horizontal component V XM, vertical component of the aircraft speed V YM , aircraft height h M , horizontal position of the aircraft x M , horizontal component of the target speed V XT , vertical component of the target speed V YT , target height h T , target horizontal position x T , maximum allowed field of view angle φ maxc , initial speed inclination angle θ0, given landing angle q Fc , and on this basis, the parameters required for the guidance command are obtained according to the relative relationship between the aircraft and the target.
[0032] The maximum allowed field of view angle φ maxc is defined maxc , which is the maximum value of the field of view angle allowed during the flight of the aircraft, i.e. during the actual flight of the aircraft, the field of view angle should be less than this value at all times. The maximum allowed field of view angle φ maxc is given in advance.
[0033] According to the initial guidance parameters input in step 3, a series of parameters related to the line of sight between the aircraft and the target are obtained:
[0034] V xml = V XM - V XT
[0035] V yml = V YM - V YT
[0036] x ml = x M - x T
[0037] y ml = y M - y T
[0038]
[0039] q F = q Fc - q0 (7)
[0040] wherein V xml is the horizontal component of the relative speed between the aircraft and the target, V yml is the vertical component of the relative speed between the aircraft and the target, x ml is the horizontal relative position between the aircraft and the target, y ml is the vertical relative position (i.e. the height difference) between the aircraft and the target, V rr is the aircraft target relative distance, t is the time F is the remaining flight time estimate, q0 is the initial aircraft target line-of-sight angle, ε0 is the initial field-of-view angle, q F is the line-of-sight coordinate system aircraft impact angle constraint.
[0041] Step 4: According to the guidance parameters given in step 3 and the required parameters of the guidance command, a field-of-view angle analytical analysis model is constructed.
[0042] According to the guidance parameters given in step 3 and the required parameters of the guidance command, a field-of-view angle analytical analysis model is constructed as follows:
[0043]
[0044] The field-of-view angle prediction model shown in equation (8) is regarded as a quadratic curve with respect to the normalized time , where s2, t F , ε0, q F are all constants. At the same time, since ε0, q F are all given in advance, the s2 parameter directly affects the prediction of the change of the field-of-view angle throughout the flight of the aircraft. By substituting different s2 parameters, the overload command during the flight of the aircraft is different, and the trajectory result is also different, so the field-of-view angle change is also different.
[0045] Using the field-of-view angle prediction expression (8), according to the guidance parameters and the required parameters of the guidance command pre-set in step 3, the prediction expression of the field-of-view angle with respect to the dimensionless time is obtained, which is strongly related to the s2 parameter. In subsequent step 5, the s2 parameter will be calculated to find the s2 parameter corresponding to the maximum field-of-view angle, thereby satisfying the maximum field-of-view angle constraint condition.
[0046] Step 5, by analyzing the field-of-view angle prediction model, the field-of-view angle prediction model is differentiated with respect to the dimensionless time , and the dimensionless time at which the derivative is zero is found. Substituting the field-of-view angle prediction model, the maximum value expression of the field-of-view angle prediction is obtained. The maximum value expression of the field-of-view angle prediction is combined with the maximum field-of-view angle φ maxc given in step 3, and the parameter s2 corresponding to the maximum field-of-view angle among all s2 parameters is solved.
[0047] Based on the analysis of the field-of-view angle prediction model in step 4, the field-of-view angle change prediction model is in the form of an open-down quadratic function. The field-of-view angle prediction model is analytically solved by differentiation and simultaneous equations (8) and the maximum field-of-view angle constraint φ maxc , and the s2 parameter corresponding to the maximum field-of-view angle is obtained.
[0048] Consider the extreme point position of formula (8), that is, the maximum field of view angle appears when the first derivative of formula (8) is zero, that is:
[0049]
[0050] where is the dimensionless time when the maximum field of view angle appears.
[0051] Derive formula (7) with respect to time The result is as follows:
[0052]
[0053] Solve the equation :
[0054]
[0055] Substitute formula (10) into formula (7), that is, the maximum field of view angle result expression is as follows:
[0056]
[0057] Based on the above formula (11), combined with the guidance parameters obtained in step 3 and the required parameters of the guidance command, the maximum value of the field of view angle during the flight of the aircraft from the current to the hit of the aircraft is obtained.
[0058] Combined with the preset maximum field of view angle φ maxc in step 3, and based on the flight-related parameters of the aircraft under the current state, the expected landing angle q Fc , the maximum field of view angle critical parameter s 2maxφ is obtained, and the expression is as follows:
[0059]
[0060] When the guidance parameter s2 takes s 2maxφ , the maximum field of view angle of the aircraft during flight is equal to the maximum field of view angle φ maxc preset in step 3, which does not meet the maximum field of view angle constraint. Therefore, s 2maxφ is the critical value of s2 that meets the maximum field of view angle constraint. Only when s2 is less than s 2maxφ , that is, it can guarantee that the field of view angle during the actual flight is less than the maximum field of view angle allowed value φ maxc , the maximum field of view angle constraint is met, and the guidance command is obtained, which limits the maximum field of view angle of the aircraft while hitting the target.
[0061] Step 6: Based on the critical value s 2maxφBy substituting in the appropriate guidance parameter s2, the longitudinal guidance command is obtained. The aircraft then implements precise guidance based on model analysis, taking into account the maximum field of view constraint, according to the longitudinal guidance command.
[0062] In step 5, the critical parameter s corresponding to the maximum field of view is calculated. 2maxφ Substituting s2 into the equation, s2 is less than s 2maxφ A value greater than zero satisfies the maximum field of view constraint, therefore, substituting:
[0063]
[0064] At this point, equation (1) transforms into
[0065]
[0066] Based on the results obtained in step 5 above Upon receiving guidance commands, the aircraft implements precise guidance based on model analysis, taking into account the maximum field of view constraint.
[0067] Beneficial effects:
[0068] 1. The maximum field of view constrained analytical guidance method based on model prediction disclosed in this invention defines a line-of-sight coordinate system in the longitudinal plane, establishes a relative motion model of the aircraft and the target based on this system, takes the initial aircraft-target connection line as the reference, establishes a field of view change prediction model based on optimal control theory and combined with multi-constraint optimal final guidance expression, and obtains the prediction result of the field of view change; by inputting guidance parameters and calculating the coefficients required for guidance commands, the predicted result of the field of view is obtained; based on the characteristics of the quadratic curve of the prediction model, differentiation is performed, and simultaneous solutions are obtained to obtain the critical guidance coefficient corresponding to the maximum field of view, which is then substituted into the guidance law to achieve accurate guidance based on model analysis under the constraint of the maximum field of view.
[0069] 2. The maximum field-of-view constrained analytical guidance method based on model prediction disclosed in this invention is based on optimal control theory and combined with multi-constraint optimal terminal guidance expressions to establish a field-of-view change prediction model. Given initial guidance parameters, and based on this, the parameters required for guidance commands are obtained according to the relative relationship between the aircraft and the target, thus constructing a field-of-view analytical analysis model. Through analytical analysis of the field-of-view prediction model, its relationship with dimensionless time is determined. Find the dimensionless time at which the derivative is zero by taking the derivative. Substituting into the field of view prediction model, we obtain the expression for the maximum value of the predicted field of view. This expression is then compared with the maximum field of view φ given in step 3. maxcSimultaneously, the parameter s2 corresponding to the maximum field angle is obtained from all s2 parameters, and the longitudinal guidance instruction is obtained by substituting the appropriate guidance parameter s2, so that the aircraft realizes the precise guidance based on the model analysis considering the maximum field angle constraint according to the longitudinal guidance instruction, so that the aircraft satisfies the maximum field angle constraint condition in flight, and the field angle of the seeker is constant and less than the specified maximum value.
[0070] 3、The model prediction based maximum field angle constraint analytical guidance method disclosed in the application is based on the optimal control principle, and an optimal guidance law expression considering the impact angle constraint and the field angle constraint is obtained. Under the condition of a given expected impact angle, the field angle of the aircraft changing throughout the flight is predicted, the change of the field angle of the aircraft throughout the process from the moment of launching the aircraft to the end of the flight of the aircraft is estimated, and the estimation is referred to as a field angle prediction model of the aircraft. The field angle prediction model of the aircraft is analyzed and solved, and the guidance coefficient directly related to the maximum field angle is obtained. BRIEF DESCRIPTION OF DRAWINGS
[0071] Figure 1 is a schematic diagram of a target relative motion model of the aircraft;
[0072] Figure 2 is a change curve of the overload of the aircraft;
[0073] Figure 3 is a change curve of the field angle of the aircraft;
[0074] Figure 4 is a trajectory curve of the aircraft;
[0075] Figure 5 is a flow chart of the model prediction based maximum field angle constraint analytical guidance method of the application. DETAILED DESCRIPTION
[0076] In order to better illustrate the purposes and advantages of the application, the content of the application is further illustrated below in combination with the drawings and examples.
[0077] Example 1
[0078] The model prediction based maximum field angle constraint analytical guidance method disclosed in this embodiment has the following specific implementation steps:
[0079] Step 1: Establishing a target relative motion model of the aircraft.
[0080] Defining a line-of-sight coordinate system Ox q y q z q As shown in Figure 1 , the origin O is located at the center of mass of the aircraft; the Ox q axis points to the direction of the connecting line of the aircraft and the target; and the Oy qThe axis is in the vertical plane through the origin, and Ox q The axis is vertical; Oz q The axis is perpendicular to Ox q y q The plane, the positive direction is determined according to the right-hand coordinate system.
[0081] On the basis of the line-of-sight coordinate system, the attack angle is always a small quantity in the process of aircraft guidance, the relative motion relationship of the aircraft target in the longitudinal plane is established, that is, the aircraft target relative motion model is constructed as follows:
[0082]
[0083] φ = θ - q
[0084] Wherein, r is the distance of the aircraft target connecting line, V T is the target speed, V M is the aircraft speed, q is the angle between the initial aircraft target connecting line and the current aircraft target connecting line, which is called the line-of-sight angle in the following, θ is the speed inclination angle, φ T is the angle between the target speed direction and the current aircraft target connecting line direction, φ is the angle between the aircraft speed direction and the current aircraft target connecting line direction, and φ is the field of view angle.
[0085] Step 2: Based on the optimal control theory, the field of view angle change prediction model is established combined with the multi-constraint optimal terminal guidance expression.
[0086] In the process of aircraft flight attacking the target, the maximum field of view angle and the final landing angle of the aircraft in the flight process need to be considered. Under the condition of a given landing angle q Fc , the maximum field of view angle is solved analytically, so that the field of view angle of the aircraft is not greater than the allowable value in the whole flight process. The given landing angle is only used to control the curvature of the aircraft trajectory, and does not need to be finally satisfied, that is, the actual landing angle of the aircraft when hitting the target is less than the given landing angle value q Fc .
[0087] The multi-constraint terminal optimal guidance law expression considering the landing angle and the field of view angle constraint is as follows:
[0088]
[0089] Wherein, V r is the relative speed of the aircraft target, r is the distance of the aircraft target connecting line, q is the current field of view angle value, q Fc is the pre-given landing angle value, s2 is the landing angle weight value, which is used to control the trajectory of the aircraft, when s2 is 0, the guidance law (1) is reduced to proportional guidance law, when s2 tends to infinity, the guidance law (1) is infinitely close to the shaping guidance law; t go is the remaining flight time.
[0090] For the convenience of subsequent derivation, the flight time of the aircraft is normalized and dimensionless:
[0091]
[0092] Combined with the expression of the multi-constrained terminal optimal guidance law, the time-varying form of the guidance command is obtained:
[0093]
[0094] where ε0 is the size of the field of view angle q of the aircraft at the moment of launch, i.e. ε0 = θ0 - q0
[0095] The longitudinal displacement of the aircraft is regarded as the state variable, and the definition of the state variable of the aircraft is obtained:
[0096]
[0097] Substitute the guidance command into equation (4), and after normalizing the actual time into dimensionless time, the expression with as the variable is as follows:
[0098]
[0099] Through the small attack angle condition and the geometric condition, the field of view angle change prediction model of the aircraft is obtained:
[0100]
[0101] where q F is the falling angle of the aircraft in the target line-of-sight coordinate system of the aircraft, the expression is (q F = q Fc - q0), q Fc is the falling angle in the inertial system, and q0 is the initial target line-of-sight angle of the aircraft. Taking the field of view angle change prediction model in equation (6) as the starting point, the field of view angle prediction will be solved analytically in subsequent step 3. By derivation and simultaneous equations, the analytical expression of the maximum field of view angle is obtained, and then the corresponding maximum field of view angle critical coefficient s2 is obtained. The maximum field of view angle is limited, so as to meet the requirement that the maximum field of view angle is less than the given constraint value within the entire flight time.
[0102] Step 3: Given the initial guidance parameters: the horizontal component of the aircraft speed V XM , the vertical component of the aircraft speed V YM , the height of the aircraft h M , the horizontal position of the aircraft x M , the horizontal component of the target speed V XT , the vertical component of the target speed V YT , and the target height hT , target horizontal position x T , maximum allowed field of view angle φ maxc , initial speed inclination angle θ0, given landing angle q Fc , and on this basis, the parameters required for the guidance instruction are obtained according to the target relative relationship of the aircraft.
[0103] The maximum allowed field of view angle φ maxc is defined. maxc The maximum allowed field of view angle φ maxc is the maximum value of the allowed field of view angle during the flight of the aircraft, that is, during the actual flight of the aircraft, the field of view angle should be less than this value at all times. In the present application, the maximum allowed field of view angle φ
[0104] In this step, the following parameters are given: horizontal component of aircraft speed V XM = 140 m / s, vertical component of aircraft speed V YM = 0 m / s, aircraft height h M = 1 km, horizontal position of aircraft x M = 0, horizontal component of target speed V XT = 0 m / s, vertical component of target speed V YT = 0 m / s, target height h T = 0, target horizontal position X T = 3 km, maximum allowed field of view angle φ maxc = 27°, initial speed inclination angle θ0 = 0°, given landing angle q Fc = -75°
[0105] According to the initial guidance parameters input in step 3, a series of parameters related to the line of sight between the aircraft and the target are obtained through further processing:
[0106] V xml = V XM -V XT
[0107] V yml = V YM -V YT
[0108] x ml = x M -x T
[0109] y ml = y M -y T
[0110]
[0111] q F= q Fc - q0 (7)
[0112] where V xml is the horizontal component of the aircraft target relative velocity, V yml is the vertical component of the aircraft target relative velocity, x ml is the horizontal position of the aircraft target relative to the aircraft, y ml is the vertical position of the aircraft target relative to the aircraft (i.e. the height difference), V r is the aircraft target relative velocity, r is the aircraft target relative distance, t F is the remaining flight time estimate, q0 is the initial aircraft target line-of-sight angle, ε0 is the initial field-of-view angle, q F is the aircraft impact angle constraint in the line-of-sight coordinate system.
[0113] In this step, the relevant parameter calculation results are as follows: the horizontal component of the aircraft target relative velocity V XMl = 140 m / s, the vertical component of the aircraft target relative velocity V yml = 0, the horizontal position of the aircraft target relative to the aircraft x ml = -3 km, the vertical position of the aircraft target relative to the aircraft (i.e. the height difference) y ml = 1 km, the aircraft target relative velocity V r = 140 m / s, the aircraft target relative distance r = 3.16 km, the remaining flight time estimate t F = 22.2 s, the initial aircraft target line-of-sight angle q0 = -18.4°, the initial field-of-view angle ε0 = 18.4°, and the aircraft impact angle constraint in the line-of-sight coordinate system q F = -56.6°.
[0114] Step 4: According to the guidance parameters given in Step 3 and the required parameters of the guidance command, a field-of-view angle analytical analysis model is constructed.
[0115] According to the guidance parameters given in Step 3 and the required parameters of the guidance command, a field-of-view angle analytical analysis model is constructed as follows:
[0116]
[0117] The field-of-view angle prediction model shown in equation (8) is regarded as a quadratic curve with respect to the normalized time s2, t F , ε0, q F are all constants. At the same time, since ε0 and q F are given in advance, the s2 parameter directly affects the prediction of the change of the field-of-view angle of the aircraft throughout the flight. By substituting different s2 parameters, the overload command during the flight of the aircraft is different, and the trajectory result is also different, so the change of the field-of-view angle is also different.
[0118] Using the field of view angle prediction expression (8), according to the guidance parameters preset in step 3 and the required parameters of the guidance command, the prediction expression of the field of view angle with respect to the dimensionless time is obtained, which is
[0119]
[0120] The parameters are strongly related. In the subsequent step 5, the s2 parameter will be calculated, and the s2 parameter corresponding to the maximum field of view angle will be found, thereby satisfying the maximum field of view angle constraint condition.
[0121] Step 5, by analyzing the field of view angle prediction model, the field of view angle prediction model is derived with respect to the dimensionless time , and the dimensionless time at which the derivative is zero is found. Substituting the field of view angle prediction model, the maximum value expression of the field of view angle prediction is obtained. The maximum value expression of the field of view angle prediction is combined with the allowed maximum field of view angle φ maxc given in step 3, and all s2 parameters corresponding to the maximum field of view angle s2 are solved.
[0122] Based on the analysis of the field of view angle prediction model in step 4, the field of view angle change prediction model is a downward-opening quadratic function. The field of view angle prediction model is analytically solved by derivation and equation combination, and the s2 parameter corresponding to the maximum field of view angle is obtained.
[0123] The extreme point position of equation (8) is considered, that is, the maximum field of view angle appears when the first-order derivative of equation (8) is zero, that is:
[0124]
[0125] where is the dimensionless time at which the maximum field of view angle appears.
[0126] The derivative of equation (7) with respect to time is taken, and the result is as follows:
[0127]
[0128] Solving equation yields:
[0129]
[0130] Substituting equation (10) into equation (7), the maximum field of view angle result expression is as follows:
[0131]
[0132] Based on the above formula (11), combined with the guidance parameters obtained in step 3 and the required parameters of the guidance command, the maximum value of the field of view angle during the flight of the aircraft from the current to the hit of the aircraft is obtained.
[0133] Combined with the preset maximum field of view angle φ maxc , based on the flight-related parameters of the aircraft in the current state, the desired landing angle q Fc , the maximum field of view angle critical parameter s 2maxφ is obtained. The expression is as follows:
[0134]
[0135] When the guidance parameter s2 takes s 2maxφ , the maximum field of view angle of the aircraft during flight is equal to the maximum field of view angle φ maxc preset in step 3, which does not satisfy the maximum field of view angle constraint. Therefore, s 2maxφ is the critical value of s2 that satisfies the maximum field of view angle constraint. Only when s2 is less than s 2maxφ , that is, the field of view angle during the actual flight process is guaranteed to be less than the maximum field of view angle allowable value φ maxc , the maximum field of view angle constraint is satisfied, and the guidance command is obtained, which limits the maximum field of view angle of the aircraft while hitting the target.
[0136] Step 6: Based on the critical value s 2maxφ of the guidance parameter calculated in step 5, the longitudinal guidance command is obtained by substituting the appropriate guidance parameter s2, and the aircraft realizes accurate guidance based on model analysis considering the maximum field of view angle constraint according to the longitudinal guidance command.
[0137] In step 5, the critical parameter s 2maxφ corresponding to the maximum field of view angle is calculated, and s2 is substituted into s 2maxφ , which is greater than zero, that is, the maximum field of view angle constraint is satisfied, and therefore:
[0138]
[0139] At this time, formula (1) is transformed into
[0140]
[0141] According to the above steps, the guidance command is obtained, and the aircraft realizes accurate guidance based on model analysis considering the maximum field of view angle constraint according to the guidance command. As Figure 2 shown, after substituting , the aircraft's full-range overload curve is shown in the figure.
[0142] The full-range field of view angle curve of the aircraft is shown in Figure 3As shown in the figure, it can be seen that the whole flight field of view angle of the aircraft is less than the allowed maximum field of view angle.
[0143] The whole flight trajectory curve of the aircraft is as shown in the figure Figure 4 As shown in the figure, in combination with Figure 3 , Figure 4 It can be seen that the present application can make the whole flight field of view angle of the aircraft less than the allowed maximum value while achieving accurate attack on the target.
[0144] The above detailed description makes further detailed description of the purpose, technical scheme and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims
1. A maximum field-of-view constrained analytical guidance method based on model prediction, characterized in that: A line-of-sight coordinate system is defined in the longitudinal plane. Based on this, a relative motion model of the aircraft and the target is established. Taking the initial target line as the reference, a field-of-view change prediction model is established based on optimal control theory and combined with the multi-constraint optimal terminal guidance expression. The prediction results of the field-of-sight change are obtained from the field-of-sight change prediction model. By inputting guidance parameters and calculating the coefficients required for guidance commands, the field-of-sight prediction results are obtained. Based on the property of the quadratic function of the prediction model, the model is differentiated, and the field-of-sight change model is solved simultaneously to obtain the critical guidance coefficient corresponding to the maximum field-of-sight. The critical guidance coefficient is substituted into the guidance law to achieve accurate guidance based on model analysis under the constraint of the maximum field-of-sight.
2. The maximum field-of-view constrained analytical guidance method based on model prediction as described in claim 1, characterized in that: Includes the following steps, Step 1: Define a line-of-sight coordinate system in the longitudinal plane and establish a model of the relative motion between the projectile and the target; Step 2: Based on optimal control theory and combined with the multi-constraint optimal terminal guidance expression, establish a field of view angle change prediction model; Step 3: Given initial guidance parameters: missile velocity horizontal component V XM The vertical component of the missile velocity V YM Missile altitude h M Missile horizontal position x M Target velocity horizontal component V XT Vertical component of target velocity V YT Target height h T Target horizontal position x T Maximum permissible field of view φ maxc Initial trajectory inclination angle θ0, given landing angle q Fc Based on this, the parameters required for the guidance command are determined according to the relative relationship between the missile and the target. Step 4: Based on the guidance parameters and parameters required for guidance commands given in Step 3, construct an analytical analysis model for the field of view. Step 5: By performing analytical analysis on the field of view prediction model, the field of view prediction model is applied to dimensionless time. Find the dimensionless time at which the derivative is zero by taking the derivative. Substituting into the field of view prediction model, we obtain the expression for the maximum value of the predicted field of view. We then compare this expression with the maximum allowable field of view φ given in step 3. maxc By combining the equations, we can find the parameter s2 that corresponds to the maximum field of view among all s2 parameters; Step 6: Based on the critical value s of the guidance parameters calculated in Step 5 2maxφ By substituting in the appropriate guidance parameter s2, the longitudinal guidance command is obtained. The missile then achieves precise guidance based on model analysis, taking into account the maximum field of view constraint, according to the longitudinal guidance command.
3. The maximum field-of-view constrained analytical guidance method based on model prediction as described in claim 2, characterized in that: Step 1 is implemented as follows: Define the line-of-sight coordinate system Ox q y q z q The origin O is located at the missile's center of mass; Ox q The axis points in the direction of the line connecting the projectile and the target; Oy q The axis lies in a vertical plane passing through the origin, and is perpendicular to Ox. q Axis perpendicular; Oz q The axis is perpendicular to Ox q y q The positive direction of the plane is determined according to the right-hand coordinate system. Based on the line-of-sight coordinate system, the relative motion relationship between the projectile and the target in the longitudinal plane is established, i.e., the relative motion model between the projectile and the target is constructed as follows: φ=θ-q Where r is the distance between the bullet and the target, and V T For the target velocity, V M Let q be the missile velocity, θ be the angle between the initial missile-target line and the current missile-target line (hereinafter referred to as the line-of-sight angle), θ be the trajectory inclination angle, and φ be the missile velocity. T φ is the angle between the target's velocity direction and the direction of the line connecting the target and the missile, and φ is the angle between the missile's velocity direction and the direction of the line connecting the target and the missile. φ is the field of view angle.
4. The maximum field-of-view constrained analytical guidance method based on model prediction as described in claim 3, characterized in that: Step 2 is implemented as follows: During the missile's flight and target engagement, it is necessary to consider the missile's maximum field of view and final angle of impact; given an angle of impact q... Fc Under these conditions, the maximum field of view is analytically solved to ensure that the missile's field of view does not exceed the allowable value throughout its flight. The pre-given angle of impact is only used to control the trajectory curvature and does not need to be ultimately satisfied; that is, the actual angle of impact when the missile finally hits the target is less than the given angle of impact value q. Fc ; The expression for the multi-constraint terminal optimal guidance law considering the landing angle and field of view constraints is shown below: Among them, V r Let r be the relative velocity between the projectile and the target, r be the distance between the projectile and the target, and q be the current field of view angle. Fc To predetermine the angle of impact, s2 is the angle of impact weight value used to control the missile trajectory. When s2 is 0, the guidance law described in equation (1) reverts to the proportional guidance law. When s2 approaches infinity, the guidance law described in equation (1) approaches the trajectory shaping guidance law infinitely. go Remaining flight time; The missile flight time was normalized to be dimensionless. Combining the multi-constraint terminal optimal guidance law expression, the form of guidance command variation over time is obtained: Where ε0 is the magnitude of the field of view angle q at the instant of missile launch, i.e., ε0 = θ0 - q0 Treating the missile's longitudinal displacement as a state variable, we obtain the definition of the missile state variable: Substituting the guidance command into equation (4), and simultaneously normalizing the actual time by converting it to dimensionless time, we obtain the following: The expression for the variable is as follows: Based on the small angle of attack and geometric conditions, a missile field of view change prediction model is obtained: Where, q F Let q be the missile's angle of impact in the target line-of-sight coordinate system. F =q Fc -q0, q Fc Let q0 be the initial projectile-eye line-of-sight angle, and let q0 be the inertial frame of reference. Starting from the field-of-sight angle change prediction model in equation (6), the field-of-sight angle prediction will be analytically solved in subsequent step 3. This will be achieved by differentiating and solving equations (8) and the maximum field-of-sight angle constraint φ. maxc The analytical expression for the maximum field of view is obtained, and then the corresponding critical coefficient s2 for the maximum field of view is obtained. The maximum field of view is restricted so that the maximum field of view is less than the given constraint value throughout the entire flight time.
5. The maximum field-of-view constrained analytical guidance method based on model prediction as described in claim 4, characterized in that: Step 3 is implemented as follows: The guidance parameters include the horizontal component of the missile velocity V. XM The vertical component of the missile velocity V YM Missile altitude h M Missile horizontal position x M Target velocity horizontal component V XT Vertical component of target velocity V YT Target height h T Target horizontal position x T Maximum permissible field of view φ maxc Initial trajectory inclination angle θ0, given landing angle q Fc Define the maximum permissible field of view φ maxc Maximum permissible field of view φ maxc This refers to the maximum permissible field of view angle during missile flight; in other words, the field of view angle should always be less than this value during actual missile flight. The maximum permissible field of view angle φ is given in advance. maxc ; Based on the initial guidance parameters input in step 3, the following series of parameters related to the missile's line of sight are obtained: V xml =V XM -V XT V yml =V YM -V YT x ml =x M -x T and ml / and M -and T what F =q Fc -q0 (7) Among them, V xml V represents the horizontal component of the relative velocity between the projectile and the target. yml Let x be the vertical component of the relative velocity between the projectile and the target. ml y represents the relative horizontal position of the target. ml V represents the vertical position of the projectile and its target. r Let r be the relative velocity between the projectile and the target, and t be the relative distance between the projectile and the target. F Here, q0 is the estimated remaining flight time, ε0 is the initial missile-target line-of-sight angle, and q is the initial field-of-view angle. F This is a constraint on the missile's impact angle in the line-of-sight coordinate system.
6. The maximum field-of-view constrained analytical guidance method based on model prediction as described in claim 5, characterized in that: Step 4 is implemented as follows: Based on the guidance parameters given in step 3 and the parameters required for the guidance command, the analytical analysis model of the field of view is constructed as follows: The field-of-view prediction model shown in equation (8) can be considered as a normalized time... The quadratic curve, where s2 and t F ε0, q F Both are constants; at the same time, since ε0 and q F All parameters are predetermined, therefore the s2 parameter directly affects the predicted change in the field of view angle throughout the missile's flight; different s2 parameters result in different changes in the field of view angle. Using the field-of-view prediction expression (8), based on the guidance parameters preset in step 3 and the parameters required for the guidance command, the field-of-view angle with respect to dimensionless time is obtained. The predictive expression, which Since the s2 parameter is strongly correlated, the s2 parameter will be calculated in subsequent step 5 to find the s2 parameter corresponding to the maximum field of view, thereby satisfying the maximum field of view constraint condition.
7. The maximum field-of-view constrained analytical guidance method based on model prediction as described in claim 6, characterized in that: Step 5 is implemented as follows: Based on the analysis of the field of view prediction model in step 4, the field of view change prediction model is a quadratic function with the opening downwards. The field of view prediction model is solved analytically by differentiation, solving the simultaneous equations (8), and applying the maximum field of view constraint φ. maxc The s2 parameter corresponding to the maximum field of view is obtained in this way; Consider the location of the extreme point of equation (8), that is, the moment when the first derivative of equation (8) is zero, i.e.: in: The dimensionless moment when the maximum field of view occurs; Regarding equation (7) with respect to time Taking the derivative, the result is as follows: Solve the equation have to: Substituting equation (10) into equation (7), we obtain the expression for the maximum field of view as follows: Based on the above formula (11), combined with the guidance parameters obtained in step 3 and the parameters required for the guidance command, the maximum value of the field of view angle during the missile flight process from the current point until the missile hits the target is obtained. Combined with the maximum field of view φ preset in step 3 maxc Simultaneously, based on the missile's flight parameters under the current conditions and the desired angle of impact q... Fc That is, the critical parameter s for the maximum field of view is obtained. 2maxφ The expression is as follows: When the guidance parameter s2 is taken as s 2maxφ When the size is small, the maximum field of view during the missile's flight is equal to the maximum field of view φ preset in step 3. maxc The maximum field of view constraint is not satisfied; therefore, s 2maxφ To satisfy the critical value of s2 for the maximum field of view constraint, it is only necessary to satisfy s2 < s 2maxφ This means that the field of view angle can be guaranteed to be less than the maximum allowable field of view angle φ throughout the actual flight process. maxc At this point, the maximum field of view constraint is satisfied, and guidance commands are obtained, thus limiting the missile's maximum field of view while hitting the target.
8. The maximum field-of-view constrained analytical guidance method based on model prediction as described in claim 7, characterized in that: Step 6 is implemented as follows: In step 5, the critical parameter s corresponding to the maximum field of view is calculated. 2maxφ Substituting s2 into the equation, s2 is less than s 2maxφ A value greater than zero satisfies the maximum field of view constraint, therefore, substituting: At this point, equation (1) transforms into Based on the results obtained in step 5 above Upon receiving guidance commands, the missile performs precise guidance based on model analysis, taking into account the maximum field-of-view constraint.