CN104965519B - A kind of terminal guidance method with angle of fall constraint based on Bezier - Google Patents

Abstract

The invention discloses a Bezier curve-based terminal guidance method with fall angle constraint, relates to a Bezier curve-based terminal guidance method with fall angle constraint for aircraft guidance, and belongs to the technical field of aircraft guidance. The present invention includes the following steps: step 1, establishing the dynamics kinematics equation of the aircraft particle; step 2, planning the kinematics trajectory based on the Bezier curve _; The angle μ _m guidance command, and real-time feedback on the current status of the aircraft, realizes online trajectory re-planning based on the Bessel model, and calculates the acceleration command at the next moment until the whole process of guidance is completed. The invention can adapt to the requirement of precise strike under the constraints of a wide range of fall angles, and can ensure that the aircraft can finally complete the strike mission even when the control amount is saturated, and has certain robustness to external interference and environmental uncertainty.

Description

A Terminal Guidance Method with Fall Angle Constraint Based on Bezier Curve

technical field

The invention relates to a guidance method with drop angle constraints, in particular to a Bezier curve-based guidance method with drop angle constraints for aircraft guidance, and belongs to the technical field of aircraft guidance.

Background technique

As the final link of the high-speed reentry vehicle's ground strike, high-precision terminal guidance technology is related to the success or failure of the entire flight mission. In actual strike missions, in order to obtain the best damage effect, the terminal angle constraint is often of great significance. In recent years, planning ideas have also been used in guidance law design. The requirements of the terminal position and angle can be met by geometrically planning the flight trajectory, and the analytic control command can be directly obtained by planning the control quantity, and then the corresponding flight trajectory can be obtained by integrating. Using planning techniques can greatly simplify the design process of guidance laws. In addition, other variables can also be introduced into performance indicators to be constrained, which is more in line with the requirements of multi-constraint guidance. Aircraft planning strategies play an important role in improving combat performance and survivability.

Path planning, as an extremely important category of planning strategies, has received extensive attention from relevant scholars. Path planning can plan a satisfactory flight path for the aircraft and improve the flight quality while meeting the different mission requirements of the aircraft, thereby effectively increasing the success rate of the aircraft's ground strike. As a kind of NURBS curve, the Bezier curve has strong geometric flexibility and contains less modeling variables. For the aircraft, because the geometric nature of the flight trajectory is a smooth curve, the Bezier curve can almost Characterizes all smooth curves, so Bezier curves have a better fit when characterizing ballistics.

The following first introduces the basic concept of the Bezier curve. A Bezier curve is a curve defined by a set of control points in space, and the shape change only depends on the number and position of the control points. N+1 control points can define an N-order Bezier curve, and its expression is as follows:

In the formula: P _i (0≤i≤n) is called the i-th control point coordinate of the Bezier curve, connecting P _i in sequence can get the characteristic polygon of the Bezier curve, and the Bezier curve consists of the characteristic polygon Only sure. B _i,n (τ) is the n-degree Bernstein basis function, and its expression is as follows:

Bezier curves have the following properties:

Property 1: The start point and end point of the Bezier curve coincide with the start point and end point of the corresponding feature polygon.

Property 2: The direction of the tangent line at the start point and end point of the Bezier curve is consistent with the direction of the first side and the last side of the feature polygon.

Property 3: The points on the Bezier curve all fall in the convex hull formed by its control points _Pi .

From the above introduction, it can be seen that the Bezier curve has greater geometric flexibility, simple structure, less design parameters, can represent complex trajectory shapes, and meets the fall angle constraint of -180deg to 0deg. The Bezier curve is widely used in the trajectory planning of the gliding and cruising segments of the aircraft. The subduction segment has a complex and changeable flight environment due to drastic changes in aerodynamic parameters. Guidance laws are often required to be high, and it is proposed that it can adapt to the demand for precise strikes under the constraints of a wide range of fall angles, and can ensure that the aircraft can finally complete the strike mission even when the control amount is saturated, and it has great influence on external disturbances and environmental uncertainties. A certain robust terminal guidance method is very necessary.

Contents of the invention

The technical problem to be solved by the present invention is to provide a terminal guidance method with fall angle constraints based on Bezier curves, which can meet the demand for precise strikes under the constraints of a wide range of fall angles, and can also ensure that the control amount is saturated. The aircraft finally completes the strike mission and is robust to external disturbances and environmental uncertainties. The said wide-range fall angle constraint means that the fall angle ranges from -180° to 0°.

The purpose of the present invention is to realize by following technical scheme:

The invention discloses a Bezier curve-based terminal guidance method with a fall angle constraint, comprising the following steps:

Step 1, ignoring the rotation of the earth, and establishing the kinetic equation of the particle dynamics of the aircraft:

Among them: x _m , y _m , z _m are the position coordinates of the aircraft in the inertial system; V _m , γ _m , and χ _m are the velocity, ballistic inclination, and ballistic deflection respectively; g is the gravitational acceleration; μ _m is the roll angle; L _m , D _m are lift force and drag force respectively, where, S _ref is the reference area of the aircraft; ρ is the density of the atmosphere; C _Lm , C _Dm are the lift coefficient and the drag coefficient respectively, and the lift coefficient C _Lm and the drag coefficient C _Dm are functions of the angle of attack α _m and the Mach number Ma.

Step 2, kinematic trajectory planning based on Bezier curves.

The current position information and velocity direction and the terminal position and angle constraints determine the trajectory of the aircraft, respectively constructing Bezier curve trajectories for the longitudinal plane, and the trajectories need to be Bezier curves of third order or higher. A third-order Bezier curve is preferred to construct the Bezier trajectory.

If the given control point coordinates are (x _A ,y _A ,z _A ), (px _A ,py _A ,pz _A ), (px _B ,py _B ,pz _B ), (x _B ,y _B ,z _B ), the third-order Bezier curve equation of the aircraft coordinates can be obtained:

Here, for convenience, the starting point (x _A , y _A , z _A ) and (x _B , y _B , z _B ) of the control polygon are recorded as endpoints, (px _A ,py _A ,pz _A ) and (px _B ,py _B , pz _B ) are still recorded as control points.

x _m ＝a _x τ ³ +b _x τ ² +c _x τ+d _x (9)

y _m ＝a _y τ ³ +b _y τ ² +c _y τ+d _y (10)

z _m =a _z τ ³ +b _z τ ² +c _z τ+d _z (11)

Where: τ∈[0,1] is an intermediate variable, and the polynomial coefficients in formulas (9)-(11) can be determined by the following formulas (12)-(14):

Step 3, based on the trajectory of the aircraft given in step 2, the guidance commands for angle of attack α _m and roll angle μ _m are calculated.

Step 3.1 uses inverse dynamics to solve the guidance commands for angle of attack α _m and roll angle μ _m .

After the trajectory of the aircraft is determined by the Bezier curve, the guidance command is solved using the inverse dynamics theory, and its normal acceleration a _y and longitudinal acceleration a _z are defined as: has the following expression:

Among them, 'represents the derivation of y, and γ′ _m and χ′ _m have the following expressions:

Combined with the above inverse dynamics analysis, it can be seen that the acceleration command of the aircraft is not only related to the current flight state of the aircraft, but also to the shape of the flight trajectory (the first and second derivatives of the range x _m and the horizontal range z _m with respect to the height y _m ) Therefore, the above-mentioned guidance problem is essentially transformed into a trajectory planning problem.

After obtaining the aircraft acceleration a _y and a _z commands, the aircraft roll angle μ _m can be determined by the following formula (18):

From the formula (18) and the aircraft acceleration definition, the aircraft lift L _m and the lift coefficient C _Lm can be deduced, and then the aircraft attack angle α _m command can be deduced inversely.

Step 3.2: Provide real-time feedback on the current status of the aircraft, repeat steps 2 and 3.1 repeatedly to realize online trajectory re-planning based on the Bessel model, and calculate the acceleration command at the next moment until the whole process of guidance is completed. In the case of saturation of the control amount, it is ensured that the aircraft achieves precise strikes under the constraints of the landing angle, and it is robust to external disturbances and environmental uncertainties.

In view of the drastic changes in the environment of the aircraft's dive section and the fact that the control volume is prone to saturation, at this time, the aircraft will deviate from the pre-planned flight trajectory, and it is difficult to guarantee the strike accuracy simply by tracking a fixed trajectory. Introduce the current flight state of the aircraft into the closed-loop feedback, and through real-time feedback, take the current state as the initial condition, repeat steps 2 and 3.1 to realize online trajectory re-planning based on the Bessel model, calculate the acceleration command at the next moment, and bring it into the aircraft The dynamic kinematics model obtains a new flight state, and this process is repeated. When the aircraft passes trajectory re-planning due to external disturbances and control volume saturation, the guidance law can gradually correct the deviation, and finally complete the whole process of guidance.

Beneficial effect

1. The present invention uses Bezier curves for trajectory planning, which greatly simplifies the amount of calculation and has strong engineering operability. The Bezier curve has greater geometric flexibility, simple structure, less design parameters, can represent complex trajectory shapes, can cover a wide range of fall angle requirements from -180° to 0°, and achieve full fall angle strike requirements on targets .

2. The present invention has strong robustness to external disturbances and uncertainties, and can effectively deal with the control amount saturation phenomenon in the guidance process.

Description of drawings

Figure 1(a) shows the Bezier parameter design method where the end angle is constrained to be an acute angle;

Figure 1(b) shows the Bezier parameter design method where the end angle is constrained to be an obtuse angle;

Figure 1(c) is the Bessel parameter design method with the end angle constrained to be a right angle;

Fig. 2 is a kind of flow chart of the terminal guidance method based on Bezier curve of the present invention with drop angle constraint;

Fig. 3 is the trajectory curve of two Bezier curve splicing;

Fig. 4 is a schematic diagram of parameter selection in the Bezier curve splicing strategy;

Figure 5(a) is the flight trajectory curve under different fall angle constraints for the two-dimensional situation;

Figure 5(b) is the change curve of ballistic inclination under different fall angle constraints for the two-dimensional situation;

Figure 5(c) is the speed change curve under different fall angle constraints for the two-dimensional situation;

Figure 5(d) is the change curve of the angle of attack under different fall angle constraints for the two-dimensional case;

Figure 6(a) is the flight trajectory curves under different initial angles for the two-dimensional situation;

Fig. 6(b) is the change curve of ballistic inclination under different initial angles for the two-dimensional situation;

Figure 6(c) is the change curve of angle of attack under different initial angles for the two-dimensional situation;

Figure 7(a) is the flight trajectory curve under the constraint of large drop angle (-160°～-180°) for the two-dimensional situation;

Figure 7(b) is the ballistic inclination angle change curve under the constraint of large drop angle (-160°～-180°) for the two-dimensional situation;

Figure 7(c) is the change curve of the angle of attack under the constraint of a large fall angle (-160°～-180°) for the two-dimensional case;

Fig. 8(a) is the flight trajectory curve under different fall angle constraints in three-dimensional space;

Figure 8(b) is the change curve of ballistic inclination under different fall angle constraints in three-dimensional space;

Figure 8(c) is the variation curve of ballistic deflection angle under different fall angle constraints in three-dimensional space;

Figure 8(d) is the variation curve of angle of attack under different fall angle constraints in three-dimensional space;

Fig. 8(e) is the change curve of roll angle under different fall angle constraints in three-dimensional space;

Fig. 9 (a) is the flight trajectory curve under different initial conditions in three-dimensional space;

Figure 9(b) is the variation curve of ballistic inclination angle under different initial conditions in three-dimensional space;

Figure 9(c) is the ballistic deflection angle variation curve under different initial conditions in three-dimensional space;

Figure 9(d) is the variation curve of angle of attack under different initial conditions in three-dimensional space;

Fig. 9(e) is the variation curve of roll angle under different initial conditions in three-dimensional space.

Detailed ways

In order to better illustrate the purpose and advantages of the present invention, the technical solution will be further described in detail below in conjunction with the accompanying drawings and examples.

Embodiment 1: This embodiment provides a guidance example in which the fall angle in the longitudinal plane is constrained within the range of -150° to 0° for two-dimensional space.

Step 1, ignoring the rotation of the earth, establish the dynamic kinematic equations of the aircraft particles in two-dimensional space as shown in formulas (19)-(22).

Step 2, kinematic trajectory planning based on Bezier curves.

The current position information and velocity direction and the terminal position and angle constraints determine the trajectory of the aircraft, respectively constructing Bezier curve trajectories for the longitudinal plane, and the trajectories need to be Bezier curves of third order or higher. A third-order Bezier curve is preferred to construct the Bezier trajectory.

If the coordinates of the given control points are (x _A ,y _A ), (px _A ,py _A ), (px _B ,py _B ), (x _B ,y _B ), for convenience, the starting point of the control polygon ( x _A ,y _A ) and (x _B ,y _B ) are recorded as endpoints, and (px _A ,py _A ) and (px _B ,py _B ) are still recorded as control points.

The specific forms of aircraft range x _m and altitude y _m are shown in formulas (9)-(10), and polynomial parameters are determined by formulas (12)-(13).

In the construction process of Bezier curve, in order to simplify the selection of parameters, a new variable Bezier parameter is defined. The selection method of the Bezier curve and parameters in the xoy plane is given below.

1) -90°<γ _f <0°

0≤k ₁ ≤k ₂ ≤1 (24)

When realizing the task of tracking strikes, if the ballistic inclination is expected to be small, as shown in Figure 1(a), the abscissas of the control points are all located on the closed interval [x _A , x _B ], and the inequality in the formula ensures the smoothness of the curve and accessibility.

2) -150°<γ _f <-90°

As the strike mission changes, for the head-on strike mission, a larger collision angle constraint must be achieved at the moment of collision. At this time, the parameter design method given in equations (23)-(24) is no longer applicable, and the following parameters are used The selection method is shown in Figure (1)b:

Among them: (px _i , py _i ) is the intersection point coordinates of the tangent line at the starting point of the Bezier curve and the tangent line at the end point of the curve.

When the Bessel parameters are determined, the corresponding control point coordinates can be obtained:

When the expected fall angle is -90°, when the above method is continued to construct the Bessel parameters, the coordinates of the control points obtained by formula (26) - formula (28) will appear singular, and through deformation, the figure 1(b ) is transformed into Figure 1(c), and the corresponding control point coordinates can be obtained as follows:

It should be noted here that the Bessel parameter construction method given by formula (25) is also applicable to some cases of -90°<γ _f <0°, but when the expected ballistic inclination γ _f and line-of-sight angle λ satisfy the condition |γ _f | <|λ|, the tangent lines at the endpoints of the Bezier curves cannot intersect, and formula (25) will not apply.

Step 3, based on the trajectory of the aircraft given in step 2, the guidance command for the angle of attack α _m is solved.

Step 3.1 uses inverse dynamics to solve the angle of attack α _m guidance command.

Since the flight altitude of the aircraft during the dive is generally monotonously decreasing, according to experience, using altitude instead of t _go as an independent variable to build a model can simplify the analysis, which is more in line with engineering practice and reduces the error introduced by t _go estimation. Express the aircraft particle dynamics and kinematics equations as equations with the height y _m as the independent variable:

In the formula: ' represents the derivation of y _m , a _y represents the longitudinal acceleration, and they have the following expressions:

From formula (33), the acceleration expression can be reversed as follows:

That is, the acceleration command can be expressed by the instant position, velocity, angle, and _γ′m . Using the inverse dynamics theory, the expression of _γ′m can be obtained by continuing to derive the formula (31):

γ′ _m ＝-sin ² γ _m x″ (36)

Combining equations (35)-(36), the aircraft guidance command is closely related to the aircraft trajectory, so the above-mentioned guidance problem is transformed into a trajectory planning problem, combined with formula (18), the aircraft acceleration command a _y can be obtained, and then the aircraft acceleration command a y can be obtained by reverse deduction. angle of attack α _m . ' in the formulas (31)-(33) all represent the derivation of the height y _m , and the Bessel expressions are all expressed as the function of the intermediate variable τ, and the changes are sorted out by using the derivation rule of the composite function:

Step 3.2: Provide real-time feedback on the current status of the aircraft, repeat steps 2 and 3.1 repeatedly to realize online trajectory re-planning based on the Bessel model, and calculate the acceleration command at the next moment until the whole process of guidance is completed. In the case of saturation of the control amount, it is ensured that the aircraft achieves precise strikes under the constraints of the landing angle, and it is robust to external disturbances and environmental uncertainties.

In view of the drastic changes in the environment of the aircraft's dive section and the fact that the control volume is prone to saturation, at this time, the aircraft will deviate from the pre-planned flight trajectory, and it is difficult to guarantee the strike accuracy simply by tracking a fixed trajectory. Introduce the current flight state of the aircraft into the closed-loop feedback, and through real-time feedback, take the current state as the initial condition, repeat steps 2 and 3.1 to realize online trajectory re-planning based on the Bessel model, calculate the acceleration command at the next moment, and bring it into the aircraft The dynamic kinematics model obtains a new flight state, and this process is repeated. When the aircraft passes trajectory re-planning due to external disturbances and control volume saturation, the guidance law can gradually correct the deviation, and finally complete the whole process of guidance.

This embodiment gives a guidance example in which the fall angle in the longitudinal plane is constrained within the range of -150° to 0°. Firstly, the simulation situation of the expected fall angles of 0°, -30°, -90° and -150° for hitting the stationary target point is given, and the initial value of the ballistic inclination angle is -3°. Figure 5 shows the simulation results. It can be seen from the given aircraft trajectory and ballistic inclination angle change curve that a terminal guidance method based on a Bezier curve in this embodiment with a fall angle constraint can meet a wide range of requirements. Accurate strike on the target is achieved under the constraints of the falling angle. At the same time, at the time of strike, the aircraft has a higher speed, which improves the damage effect. From the change curve of the angle of attack given in Figure 5(d), it can be seen that when the flight trajectory has a large turning tendency, the command angle of attack α _m fluctuates significantly, which also leads to a large attenuation of the aircraft speed.

Figure 6 shows the guidance effect with a large initial deviation. The initial ballistic inclination angles are selected as 25°, 10°, -10° and -25° respectively. The desired ballistic inclination is set to -60°. It can be seen from the simulation results that even if there is a large initial deviation, the aircraft can achieve high precision under the constraint of the drop angle under the guidance of a terminal guidance method based on the Bezier curve in this embodiment. guidance. It can be seen from the change curve of the angle of attack that the control amount is saturated at the beginning of the flight stage. The terminal guidance method based on the Bezier curve with the drop angle constraint in this embodiment can still ensure the trend of the aircraft towards the target, and finally successfully Complete strike missions.

Embodiment 2: For two-dimensional space, this embodiment gives a guidance example in which the fall angle in the longitudinal plane is constrained within the range of -180°～-150°, so as to verify a kind of guidance in this embodiment under a large fall angle. Effectiveness of Bezier curve-based terminal guidance method with drop angle constraints.

Step 1 is the same as in Example 1.

Step 2, kinematic trajectory planning based on Bezier curves.

The specific forms of aircraft range x _m and altitude y _m are shown in formulas (9)-(10), and polynomial parameters are determined by formulas (12)-(13).

When the aircraft needs to hit the target head-on at a large angle (-150°～-180°), using the guidance strategy given in the previous section will cause a large amount of misses. From the geometrical properties of the third-order Bezier curve, it can be seen that in the early stage of the flight trajectory for a long distance, the change of the inclination angle of the ballistic trajectory is small, and a large maneuvering turn does not occur until it approaches the target, at which time the second-order derivative of the curve appears larger The fluctuation changes, that is, the overload demand increases, and the control amount is prone to saturation. Once saturation occurs, within a short distance, even if trajectory re-planning is used, it cannot guarantee that the aircraft can accurately hit the target at the desired angle.

The flexibility of curve planning can be greatly improved by splicing two segments of third-order Bezier curves. However, as the number of curves increases, the amount of calculation for parameter adjustment also increases accordingly. When using two segments of Bezier curves for trajectory planning and design, the number of parameters that need to be adjusted increases to seven, including the Bezier curve of the first segment. The Serre parameters k ₁₁ , k ₁₂ , the end point (x _mid , y _mid ) of the first curve, the slope K _mid and the Bessel parameters k ₂₁ , k ₂₂ of the second curve. Figure 3 shows the trajectory curve in the case of splicing two Bezier curves.

In order to ensure the smooth connection of two Bezier curves, it is required that the first-order derivative or even the second-order derivative of the curve be continuous, and the curve satisfies the continuous condition of the first-order derivative at the middle point (x _mid , y _mid ), namely At this time, the first segment and the second segment of the Bezier curve have the same tangent direction at the middle point.

The method for determining the middle point (x _mid , y _mid ) is given below.

When using the strategy of splicing two Bezier curves, the coordinates of the middle point (x _mid , y _mid ) and the slope K _mid of the curve need to be determined as debugging parameters. Generally speaking, the selection of the middle point must meet two conditions: Condition 1 is to minimize the length of the first segment of the trajectory, and condition 2 is to make the entire control amount as small as possible. There is no unique optimal solution for the middle selection, so in the selection process, the principle is to simplify parameter adjustment.

Aiming at the strike task under the constraint of large drop angle, a construction method for the middle point (x _mid , y _mid ) and slope K _mid of the Bezier curve is given below:

① First determine the coordinates of the middle point (x _mid , y _mid ). The selection method is shown in Figure 4. For the convenience of selection, the middle point and the target point are located on the same vertical line, and the selection range of the abscissa is within 40% to 60% of the total flying height.

② Determine the slope K _mid of the curve at the middle point. The corresponding cut angle is selected within the range of 25% to 30% of the expected drop angle.

Combining engineering practice experience, here select y _mid =y ₀ -50%Δy K _mid =γ ₀ -tan(30%Δγ).

In the formula: Δy=y ₀ -y _B , Δγ=γ ₀ -γ _f .

When the angle constraint at the end of the Bezier curve is satisfied in the interval (-90°, 0°], the Bezier parameter construction method is shown in formula (23) and formula (28).

When the angle constraint at the end of the Bezier curve is satisfied in the interval [-180°, -90°), the Bezier parameter construction method is shown in formulas (25)-(28).

Step 3 is the same as in Example 1.

Numerical simulation is carried out on the strike situation in the two-dimensional plane, and the initial ballistic inclination angle is selected as -3°. The simulation results are shown in Figure 7. The red marked point in Figure 7(a) represents the splicing point of two Bezier curves. It can be seen that due to the geometric properties of the Bezier curve, the splicing point is a necessary point for the route. It can be seen from the simulation results that the guidance strategy can realize the guidance of the aircraft under the constraint of a large fall angle, and achieve high accuracy, and the error of the ballistic inclination angle is not more than 0.8°, which is within the allowable range of error. At the end of the flight, the overload command did not appear to saturate.

It is noted that applying a Bezier curve-based terminal guidance method with fall angle constraints in this embodiment, the trajectory at the connection point only satisfies the continuous condition, but does not satisfy the smooth condition, that is, the second-order continuous condition. Since the control variable expression The form includes the second-order derivative x″, z″ of the trajectory curve of the aircraft. At this time, the acceleration command will jump at the connection, but generally the jump range is small. By adding the second-order lag link, better smoothness can be obtained. Affects the tracking effect of the control system.

Example 3:

This embodiment provides a guidance example in a three-dimensional space, and verifies the guidance effect in a three-dimensional space of a terminal guidance method based on a Bezier curve with a fall angle constraint in this embodiment.

Step 1, ignoring the rotation of the earth, establish the dynamic kinematics equations of the aircraft particles as shown in formulas (3)-(8).

Step 2, kinematic trajectory planning based on Bezier curves.

The invention adopts the Bezier curve to plan the trajectory of the aircraft in order to realize the position and angle constraints on the end of the aircraft. A third-order Bezier curve is preferred to construct the Bezier trajectory. If the given control point coordinates are (x _A ,y _A ,z _A ), (px _A ,py _A ,pz _A ), (px _B ,py _B ,pz _B ), (x _B ,y _B ,z _B ), where for the convenience of representation, the control polygon starting points (x _A , y _A , z _A ) and (x _B , y _B , z _B ) are recorded as endpoints, (px _A , py _A , pz _A ) and (px _B ,py _B ,pz _B ) are still recorded as control points.

The specific forms of aircraft range x _m , altitude y _m , and traverse z _m are shown in formulas (9)-(11), and polynomial parameters are determined by formulas (12)-(14).

In the process of constructing the Bezier curve, in order to simplify the selection of parameters, the method for selecting Bezier parameters is shown in Embodiment 1.

When the Bessel parameters are determined, the corresponding control point coordinates can be obtained:

Step 3, based on the trajectory of the aircraft given in step 2, the guidance commands for angle of attack α _m and roll angle μ _m are calculated.

Step 3.1 uses inverse dynamics to solve the guidance commands for angle of attack α _m and roll angle μ _m .

Since the flight altitude of the aircraft during the dive is generally monotonously decreasing, according to experience, using altitude instead of t _go as an independent variable to build a model can simplify the analysis, which is more in line with engineering practice and reduces the error introduced by t _go estimation. Express the aircraft particle dynamics and kinematics equations as equations with the height y _m as the independent variable:

In the formula: ' represents the derivation of y _m , a _y , a _z represent the acceleration in the longitudinal direction and the normal direction, and they have the following expressions:

From the formulas (45)-(47), the acceleration expression can be reversed as follows:

That is to say, the acceleration command can be expressed by the real-time position, velocity, angle and γ′ _m , χ′ _m . Using the inverse dynamics theory, we can obtain γ′ _m , χ′ _m by continuing to derive the formula (42)-(43). expression:

Combined with formula (50), formula (18) can be reversed to obtain the command of aircraft attack angle α _m and roll angle μ _m .

' in formulas (42)-(46) all represent the derivation of the height y _m , and the Bessel expressions are all expressed as the function of the intermediate variable τ, and the changes are sorted out by using the derivation rule of the compound function:

Step 3.2: Provide real-time feedback on the current status of the aircraft, repeat steps 2 and 3.1 repeatedly to realize online trajectory re-planning based on the Bessel model, and calculate the acceleration command at the next moment until the whole process of guidance is completed. In the case of saturation of the control amount, it is ensured that the aircraft achieves precise strikes under the constraints of the landing angle, and it is robust to external disturbances and environmental uncertainties.

First, under the given initial conditions, the guidance results under different expected fall angle constraints are given; then, under the same terminal constraints, the Bezier curve-based steering angle of this embodiment is verified by simulation. Guidance performance of constrained terminal guidance method with large initial deviation.

Figure 8(a)-Figure 8(e) shows the simulation results under different fall angle constraints in three-dimensional space, and Figure 8(a)-Figure 8(e) respectively shows the flight trajectory curve and ballistic inclination angle γ _m Change curve, ballistic deflection angle χ _m change curve, attack angle α _m change curve, roll angle μ _m change curve.

Figure 8(a)-Figure 8(e) shows the simulation results under different initial angle constraints in three-dimensional space, and Figure 9(a)-Figure 9(e) respectively shows the flight trajectory curve and ballistic inclination angle γ _m Change curve, ballistic deflection angle χ _m change curve, attack angle α _m change curve, roll angle μ _m change curve.

It can be seen from the simulation results of Fig. 8(a)-Fig. 8(e) and Fig. 9(a)-Fig. The terminal guidance method of the Searle curve with fall angle constraints still has good guidance performance in the case of strikes in three-dimensional space, and at the same time can achieve strike tasks under the constraints of a large range of fall angles while ensuring a small amount of miss. The absolute value of the ballistic inclination angle and ballistic deflection angle error at any moment does not exceed 0.8°, which is within the allowable range of error. The angle of attack and roll angle commands are smooth and easy to track for the rudder control system.

To sum up, the present invention discloses a Bezier curve-based terminal guidance method with drop angle constraints, which can realize the fixed target zone on the ground in two-dimensional plane and three-dimensional space under the condition of complicated environment and saturated control amount. The precise strike under the constraint of drop angle has high engineering application value.

The scope of protection of the present invention is not only limited to the three embodiments provided by the present invention, the embodiments are used to explain the present invention, and all changes or modifications under the same principle and conceptual conditions as the present invention are within the scope of protection disclosed by the present invention .

Claims (6)

1. A terminal guidance method based on a Bezier curve with a drop angle constraint, characterized in that: comprise the steps, Step 1, ignoring the rotation of the earth, establishing the kinematics equation of the particle dynamics of the aircraft, Among them, x _m , y _m , z _m are the position coordinates of the aircraft in the inertial system; V _m , γ _m , and χ _m are the velocity, ballistic inclination, and ballistic deflection respectively; g is the gravitational acceleration; μ _m is the roll angle; L _m , D _m are lift force and drag force respectively, where, S _ref is the reference area of the aircraft; ρ is the density of the atmosphere; C _Lm , C _Dm are the lift coefficient and the drag coefficient respectively, and the lift coefficient C _Lm and the drag coefficient C _Dm are functions about the angle of attack α _m and the Mach number Ma; Step 2, kinematic trajectory planning based on the Bezier curve; Determine the trajectory of the aircraft through the current position information and speed direction and the terminal position and angle constraints, and construct a Bezier curve trajectory. The Bezier curve trajectory needs to be a Bezier curve above the third order; If the given control point coordinates are (x _A ,y _A ,z _A ), (px _A ,py _A ,pz _A ), (px _B ,py _B ,pz _B ), (x _B ,y _B ,z _B ), the third-order Bezier curve equation of the aircraft coordinates can be obtained: For the convenience of representation, the starting points (x _A , y _A , z _A ) and (x _B , y _B , z _B ) of the control polygon are recorded as the endpoints, (px _A ,py _A ,pz _A ) and (px _B ,py _B , pz _B ) is still recorded as the control point; x _m ＝a _x τ ³ +b _x τ ² +c _x τ+d _x (7) y _m ＝a _y τ ³ +b _y τ ² +c _y τ+d _y (8) z _m =a _z τ ³ +b _z τ ² +c _z τ+d _z (9) Among them: τ∈[0,1] is an intermediate variable, and the polynomial coefficients in formulas (7)-(9) are determined by the following formulas (10)-(12): Step 3, based on the trajectory of the aircraft given in step 2, solve the guidance command of the angle of attack α _m and the roll angle μ _m , and give real-time feedback on the current status of the aircraft, realize online re-planning of the trajectory based on the Bessel model, and calculate the next moment Acceleration command until the full guidance is completed. 2. A terminal guidance method based on a Bezier curve with a drop angle constraint as claimed in claim 1, characterized in that: step 3 implementation method comprises steps 3.1, 3.2, Step 3.1 Use inverse dynamics to solve the guidance commands for angle of attack α _m and roll angle μ _m ; After the trajectory of the aircraft is determined by the Bezier curve, the guidance command is solved using the inverse dynamics theory, and its normal acceleration a _y and longitudinal acceleration a _z are defined as: has the following expression: Among them, ' represents the derivation of y _m , and γ′ _m , χ′ _m have the following expressions: Combined with the above-mentioned inverse dynamics analysis, the aircraft acceleration command is not only related to the current flight state of the aircraft, but also related to the shape of the flight trajectory, that is, related to the first and second derivatives of the range x _m and the horizontal range z _m with respect to the height y _m , so the above guidance problem is essentially transformed into a trajectory planning problem; After obtaining the aircraft acceleration a _y and a _z commands, the aircraft roll angle μ _m is determined by the following formula (16): From the formula (16) and the aircraft acceleration definition, the aircraft lift L _m and the lift coefficient C _Lm can be deduced, and then the aircraft attack angle α _m command can be deduced inversely; Step 3.2: Provide real-time feedback on the current status of the aircraft, repeat step 2 and step 3.1 repeatedly to realize online trajectory re-planning based on the Bessel model, and calculate the acceleration command at the next moment until the whole process of guidance is completed. In the case of saturation of the control amount To ensure that the aircraft achieves precise strikes under the constraints of the landing angle, and has certain robustness to external disturbances and environmental uncertainties. 3. A terminal guidance method based on Bezier curves with drop angle constraints as claimed in claim 1 or 2, characterized in that: said Bezier curves have the following characteristics, Property 1: The start point and end point of the Bezier curve coincide with the start point and end point of the corresponding feature polygon; Property 2: The direction of the tangent at the start and end of the Bezier curve is consistent with the direction of the first and last sides of the feature polygon; Property 3: The points on the Bezier curve all fall in the convex hull formed by its control points _Pi . 4. A terminal guidance method based on a Bezier curve with a drop angle constraint as claimed in claim 3, characterized in that: in order to adapt to the guidance requirements in the range of -180°～-150°, it is necessary to use a Bessel curve The terminal guidance method with drop angle constraint of Erle curve splicing includes the following steps: Step 1 is the same as step 1 in claim 1; Step 2, kinematic trajectory planning based on the Bezier curve; The specific forms of aircraft range x _m and height y _m are shown in formulas (7)-(8), and the polynomial parameters are determined by formulas (10)-(11); Splicing two segments of third-order Bezier curves can improve the flexibility of curve planning; however, as the number of curves increases, the amount of calculation for parameter adjustment also increases accordingly. When two segments of spliced Bezier curves are used for trajectory planning, The number of parameters to be adjusted is increased to 7, including the Bessel parameters k ₁₁ , k ₁₂ of the first curve, the end point (x _mid , y _mid ) of the first curve, the slope K _mid and the Bessel parameters of the second curve. Searle parameters k ₂₁ , k ₂₂ ; In order to ensure the smooth connection of two Bezier curves, it is required that the first-order derivative or even the second-order derivative of the curve be continuous, and the curve satisfies the continuous condition of the first-order derivative at the middle point (x _mid , y _mid ), namely At this time, the first segment and the second segment of the Bezier curve are in the same tangent direction at the middle point; Give the determination method of the middle point (x _mid , y _mid ); the coordinates of the middle point (x _mid , y _mid ) and the slope K _mid of the curve need to be determined as debugging parameters, and the selection of the middle point must meet two conditions: Condition 1 In order to minimize the length of the first segment of the trajectory, condition 2 is to make the whole control amount as small as possible; Step 3 is the same as step 3 in claim 1. 5. a kind of terminal guidance method based on the band fall angle constraint of Bezier curve as claimed in claim 4, is characterized in that: Aiming at the striking task under the constraint of large falling angle, a construction method of the middle point (x _mid , y _mid ) and slope K _mid of the Bezier curve is given, ① First determine the coordinates of the middle point (x _mid , y _mid ); for the convenience of selection, let the middle point and the target point be on the same vertical line, and the abscissa selection range is within 40% to 60% of the total flight altitude; ②Determine the slope K _mid of the curve at the middle point; select the corresponding cut angle within the range of 25% to 30% of the expected drop angle; Combined with engineering practice experience, select y _mid = y ₀ -50%Δy, y ₀ is the initial flying height of the aircraft, K _mid =γ ₀ -tan(30%Δγ); Where: Δy=y ₀ -y _B , Δγ=γ ₀ -γ _f ; When the angle constraint at the end of the Bezier curve is satisfied in the interval (-90°,0°], the Bezier parameter construction method is shown in formula (17) and formula (22); When the angle constraint at the end of the Bezier curve is satisfied in the interval [-180°, -90°), the Bezier parameter construction method is shown in formulas (19)-(22); 0≤k ₁ ≤k ₂ ≤1 (18) 6. A kind of terminal guidance method based on Bezier curves with drop angle constraints as claimed in claim 1, characterized in that: the Bezier curve described in step 2 is a third-order Bezier curve construction Bezier curved track.