CN113687660B - An aerodynamically assisted force prediction-correction guidance method considering rotation angle constraints - Google Patents

Abstract

The invention discloses a pneumatically assisted force prediction-correction guidance method that takes into account rotation angle constraints, and belongs to the field of aerospace technology. The implementation method of the present invention is as follows: on the premise of given maneuvering target of aerodynamic assist borrowing, establish a flight dynamics model; establish the beginning and end constraints of the state quantity during the aerodynamic assist borrowing process through the orbit root number relationship before and after the aerodynamic assist borrowing; based on the aviation The trajectory angle feedback is used to design the guidance law for the descent stage, the guidance law for the constant altitude cruise stage is designed based on the altitude change rate of 0, and the constant guidance law for the ascent stage is designed based on the terminal constraint requirements, so that the aircraft can rise and fly out of the atmosphere according to the terminal constraints; by giving three The time connection equation of each stage is limited by the time connection equation. The rotation angle of the constant-height cruise arc segment is given through finite difference correction. Combined with the constraint equation of the target rotation angle, the control angle profile of the entire process of aerodynamic assist borrowing is given to achieve Closed-loop prediction-correction precise guidance of aerodynamically assisted force borrowing under the force rotation angle constraint.

Description

An aerodynamically assisted force prediction-correction guidance method considering rotation angle constraints

Technical field

The present invention relates to an aerodynamic assisted borrowing force prediction-correction guidance method that considers rotation angle constraints, and in particular to an aerodynamic coordinated force borrowing guidance method suitable for interplanetary transfer processes, and belongs to the field of aerospace technology.

Background technique

Planetary borrowing is an important way for spacecraft to achieve low-energy interstellar transfer, and aerodynamic assist (AGA) can achieve a larger orbital parameter coverage area than pure gravitational borrowing, that is, a wider borrowing angle. and velocity vector change range, thus becoming one of the potential interstellar orbit transfer maneuver strategies with lower energy consumption. In the early stages of research, aerodynamically assisted borrowing maneuvers are usually carried out under the assumption of arc-shaped atmospheric flight trajectories. This assumption obviously deviates from the basic dynamics of the actual atmospheric flight process. Therefore, the initial research only includes aerodynamically assisted borrowing maneuvers. Simple assessment of performance. However, in order to apply aerodynamic assistance to actual interstellar transfer missions, it is necessary to develop high-precision guidance algorithms to ensure the reliability and constraint requirements of the mission execution process. For this reason, since the beginning of this century, guidance methods for aerodynamically assisted maneuvering have begun to appear. However, due to model simplification and relaxed constraints, large deviations in parameters such as guidance angles have occurred. Therefore, highly reliable and high-precision closed-loop guidance algorithms are still the core difficulty in research on pneumatic assist force borrowing issues. To this end, the aerodynamically assisted borrowing prediction-correction guidance method that considers rotation angle constraints proposed in this patent can not only achieve the rotation angle requirements of the constrained target, but also provide a borrowing maneuver process that is suitable for different planets, and can be generally used in the general solar system. Interstellar transfer leverages mobile mission requirements.

Among the advanced technologies developed for spacecraft aerodynamically assisted force-assisted guidance methods [1] (see: Lyons DT, Sklyanskiy E, Casoliva J, et al. Parametric Optimization and Guidance for an Aerogravity Assisted Atmospheric Sample Return from Mars and Venus[ C].AIAA/AAS Astrodynamics Specialist Conference and Exhibit, Honolulu, Hawaii, August 18-21, 2008.) gives an open-loop guidance strategy using the angle of attack as the control variable. Although the guidance prediction link is optimized, However, this open-loop algorithm does not have bias feedback, and the research did not analyze the reliability and accuracy in the presence of random errors, so it is difficult to determine the reliability of use in actual tasks.

Prior technology [2] (See: Casoliva J, Lyons D T, Wolf AA, et al. Robust Guidance via a Predictor-Corrector Algorithm with Drag Tracking for Aero-GravityAssist Maneuvers [C]. AIAA Guidance, Navigation, and Control Conference and Ex-hibit, Reston, VA, August 18-21, 2008.) developed a type of aerodynamically assisted force-assisted guidance algorithm for resistance tracking. This algorithm uses the inclination angle as the modulation variable and realizes segmented resistance tracking through feedback linearization. However, digital simulation shows that due to the introduction of roll control, this algorithm has a large orbital surface deviation, making it difficult to ensure the accuracy of orbital maneuvering constraints in actual mission use.

Contents of the invention

The technical problem to be solved by the aerodynamic-assisted prediction-correction guidance method considering rotation angle constraints disclosed by the present invention is: by designing the guidance law in stages for the aerodynamic-assisted flight process, and realizing the guidance law under the rotation angle constraint through the staged guidance law Pneumatically assisted closed-loop prediction-correction precision guidance. The invention has the following advantages: (1) strong robustness and high repeatability; (2) high flexibility and suitable for a variety of planetary borrowing environments; (3) no strict restrictions and constraints on spacecraft system parameters; ( 4) The target rotation constraint has a wide range of application.

The purpose of the present invention is achieved through the following technical solutions:

The invention discloses an aerodynamically assisted borrowing force prediction-correction guidance method that considers rotation angle constraints. Under the premise of given aerodynamically assisted borrowing force maneuvering targets, an aerodynamically assisted borrowing force flight dynamics model is established. Through the relationship between the orbital elements before and after the force borrowing, the beginning and end constraints of the state quantities during the pneumatic auxiliary force borrowing process are established. By dividing the aerodynamically assisted atmospheric flight process into a descent section, a constant altitude cruise turning section and an ascent section, the guidance law for the descent section is designed based on track angle feedback, and the guidance law for the constant altitude cruise section is designed based on the altitude change rate of 0, and based on Terminal constraints require the design of a constant guidance law during the ascent stage so that the aircraft rises and flies out of the atmosphere according to the terminal constraints. By giving the time connection equations of the three stages, and under the constraints of the time connection equations, the rotation angle of the constant-height cruise arc segment is given through finite difference correction, and combined with the constraint equation of the target rotation angle, the whole process of aerodynamic assist borrowing is given. Control the angle profile to achieve closed-loop prediction-correction precise guidance of aerodynamic assisted borrowing under the borrowing angle constraint.

The invention discloses a pneumatically assisted force prediction-correction guidance method that considers rotation angle constraints, including the following steps:

Step 1: Establish aerodynamic-assisted flight dynamics model.

For the atmospheric flight process with aerodynamic assistance, since the aircraft is affected by aerodynamic forces, the flight trajectory will no longer coincide with the hyperbolic orbit, so a separate dynamic model of the atmospheric flight process needs to be established. Considering that the change of the orbital plane during the borrowing process is actually achieved by correcting the orientation of the entering planet, the aerodynamic borrowing process does not consider out-of-plane maneuvers. In addition, due to the high speed of the aircraft and the short atmospheric flight time, the influence of planetary rotation is directly ignored. In summary, the dynamic model of the aerodynamically assisted atmospheric flight process can be obtained as

Among them, r, V, γ, and δ represent the position, speed, track angle, and instantaneous flight angle of the aircraft respectively. m represents the mass of the aircraft, and S represents the reference area of the aircraft. μ represents the planet's gravitational constant. In addition, the aircraft dynamic pressure q=1/2ρV ² , where ρ is the density of the planet's atmosphere and is a function of the position vector diameter r. In addition, the control variable is the lift coefficient C _L . The lift and drag coefficient of the aircraft satisfies the approximate relationship of the parabolic drag polar line, that is

Among them, C _D0 is the zero-lift drag coefficient, and K is the induced drag factor. The specific value is determined by the aerodynamic shape of the aircraft and the atmospheric environment of the planet.

Step 2: Establish the initial state quantity expression and rotation angle constraint equation during the pneumatic auxiliary force borrowing process.

Step 2.1: Establish the initial state quantity expression during the pneumatic auxiliary force borrowing process;

When the aircraft When a hyperbolic superspeed flies into the vicinity of a planet, the angular momentum of flying into a hyperbolic orbit is

where a ₀ and e ₀ are the semi-major axis and eccentricity of the fly-in orbit respectively. When the aircraft flies to the edge of the atmosphere, its position vector diameter is equal to the position vector diameter of the atmosphere edge, that is

r ₀ ＝R+h _atm (4)

Among them, R is the radius of the planet, and h _atm is equal to the height of the edge of the atmosphere. According to the orbital energy equation, the speed of the aircraft when it reaches the edge of the atmosphere is

In addition, the track angle at the initial moment of atmospheric flight (because the planet's rotation is not considered, it is equal to the flight path angle) is solved by the velocity component, that is

Among them, V _0,⊥ =H ₀ /r ₀ is the velocity component perpendicular to the radial direction when the aircraft flies to the edge of the atmosphere. In addition, considering that the role of the rotation angle δ here is to record the rotation angle of the atmospheric flight process, the initial rotation angle δ ₀ =0° is taken. So far, the expressions of the initial states r ₀ , V ₀ , γ ₀ , and δ ₀ of the aerodynamically assisted atmospheric flight process have been given.

Step 2.2: Establish the rotation angle constraint equation of aerodynamic auxiliary force.

According to the triangular relationship of the aerodynamically assisted maneuvering process, the rotation angle δ ₁ when flying to the edge of the atmosphere can be written directly as

δ ₁ =180°-β ₀ -[(360°-υ ₀ )+(90°-|γ ₀ |) (7)

Among them, β ₀ = arccos (1/e ₀ ) is the angle between the asymptote and the arc line of flying into the hyperbolic orbit, υ ₀ is the true periapsis angle at the edge of the atmosphere when flying into the hyperbolic orbit, where the true The periapsis angle is υ∈ [0°, 360°], and there is no true periapsis angle in the hyperbolic orbit in the interval [υ _∞ ,360°-υ _∞ ]. The true periapsis angle is calculated directly from the initial angular momentum H ₀ , the eccentricity e ₀ , and the radial and tangential velocity components.

When the aircraft completes atmospheric flight and reaches the atmospheric exit position, its position vector diameter is r _f = r ₀ , the speed at the atmospheric exit is V _f , the track angle is γ _f , and the rotation angle value is δ _f . In addition, the orbital root number after exiting the atmosphere can be given according to the angular momentum H _f =r _f V _f cosγ _f . From the orbital equation, the rotation angle at the atmosphere exit is

δ _a =δ _f (8)

In addition, the hyperbolic speed of an aircraft after it leaves the atmosphere is only related to the number of hyperbolic orbits it flies out of. According to the trigonometric relationship of the aerodynamically assisted maneuvering process, the rotation angle δ ₂ of the aircraft from the atmospheric exit to infinity is directly written as

δ ₂ =180°-β _f -[υ _f +(90°-|γ _f |)] (9)

Among them, β _f is the angle between the asymptote of the hyperbolic orbit and the arch line, and υ _f is the true periapsis angle at the atmospheric exit moment of the hyperbolic orbit.

Therefore, during the guidance process, the constraint equation of the target rotation angle is

E(ζ)＝δ ₁ +δ _a (ζ)+δ ₂ (ζ)-δ _T =0 (10)

Among them, ζ is the turning angle of the constant-height cruise section, which is also set as the guidance parameter characterizing the cruise arc. δ _a (ζ)=δ _f -δ ₀ , δ _T is the total target rotation angle. δ ₂ is affected by the state of the atmospheric outlet, and the state of the outlet atmosphere is directly affected by ζ. Therefore, δ ₂ is also affected by ζ.

That is to say, the initial state expression of the atmospheric flight process in the aerodynamically assisted borrowing force is obtained as shown in (4) (5) (6), and the borrowing force rotation angle constraint equation is as shown in formula (10).

Step 3: Divide the aerodynamically assisted atmospheric flight process into three flight stages: the descent section, the constant altitude cruise turning section and the ascent section. The guidance law for the descent section is designed based on the track angle feedback, and the guidance law for the descent section enables the aircraft to accurately reach the entry conditions of the constant altitude cruise section; the guidance law for the constant altitude cruise section is designed based on the altitude change rate of 0, and the guidance law for the constant altitude cruise section enables the aircraft to The aircraft achieves constant altitude flight; a constant guidance law in the ascent segment is designed based on the terminal constraint requirements, so that the aircraft rises and flies out of the atmosphere according to the terminal constraints.

During the atmospheric flight, the aircraft goes through three flight stages, namely the descent section ab, the contour cruise turning section bc and the ascent section cd. During aerodynamically assisted atmospheric flight, the aircraft enters the atmosphere in a certain initial state, and adjusts the lift coefficient C _L (ie, the control variable) in the atmosphere to achieve the target borrowing angle.

Taking into account the differences in each stage, the guidance law will be designed according to the three stages. During the atmospheric descent stage ab, the quasi-equilibrium cruise (QEC) lift coefficient needs to be On the basis of adding track angle deviation feedback and considering the lift coefficient boundary saturation C _L ≤ C _L,max , at this time, by drawing on the boundary saturation characteristics of the tangent function, the following open-loop guidance law is designed:

Among them, the quasi-balanced cruise lift coefficient That is the lift coefficient when the track angle change rate dγ/dt is 0. In addition, in equation (11), the purpose of the quasi-equilibrium track angle γ ^QEC is to maintain the aircraft in the constant-altitude cruise stage as much as possible. Here, based on the height proportional coefficient, the value of γ ^QEC is given

Among them, λ is the height adjustment coefficient, which is given based on actual task analysis. The cruise altitude corresponding to γ ^QEC is the pericenter height h _p of flying into the hyperbolic orbit.

Quasi-balanced cruise bc (QEC) lift coefficient That is the open-loop guidance law of the cruise segment.

In addition, G is a proportional coefficient, which is mainly used to adjust the magnitude between the feedback term and the quasi-balanced cruise lift coefficient. Considering that the magnitude difference is mainly caused by the atmospheric density between different altitudes, it is taken as

G＝ρ(λh)/ρ(h) (13)

The function of coefficient α is to adjust the rate at which the tangent function approaches its extreme value.

During the ascent section cd, since the aircraft only needs to fly out of the planetary atmosphere normally, the open-loop guidance law of the ascent section needs to be set to a constant value within a guidance cycle of the ascent section based on specific terminal constraints. Make the aircraft ascend and fly out of the atmosphere according to the terminal constraints.

Step 4: Distinguish the three flight stages by giving the time connection equations of the three stages. Under the constraints of the time connection equation, the rotation angle of the equal-height cruise arc segment is given through finite difference correction. Combined with the constraint equation of the target rotation angle, it is given Control angle profile of the entire process of pneumatic auxiliary force borrowing. By controlling the flight process of the angular profile guidance aircraft, the aerodynamically assisted borrowed flight process with precise rotation angle constraints is realized, that is, the closed-loop prediction-correction precise guidance of the aerodynamically assisted borrowed force under the rotation angle constraint is realized through the staged guidance law.

The process of borrowing force guidance includes prediction and correction links. Since the prediction link involves atmospheric flight trajectory recursion, it is necessary to provide the termination conditions for each stage of flight, that is, the termination conditions of the prediction link. The three flight phases are distinguished by giving time connecting equations for the three phases. The end time of the descent section is the start time of the constant altitude cruise section, which is

The aircraft enters the constant altitude cruising flight segment. The turning angle of the constant-height cruise section is ζ, which is set as the guidance parameter characterizing the cruise arc. When the constant angle of the constant-altitude cruising section is, the end time of the constant-altitude cruising section is

When t>t _c , the aircraft begins to rise until it flies out of the atmosphere to complete the aerodynamic assistance process.

Under the constraints of the time connection equation, the rotation angle of the constant-height cruise arc segment is given through finite difference correction. Combined with the constraint equation (10) of the target rotation angle, the control angle profile of the entire process of aerodynamic assist borrowing is corrected. In the correction link, it is necessary to correct the turning angle of the constant altitude cruise segment to ζ through multiple iterations to satisfy the turning angle constraint equation (10). Therefore, during the guidance process, in each guidance link, the equation that satisfies the constraint (10) is solved. High cruise angle ζ, and equation (10) can be directly equivalent to a function of ζ. Since this formula belongs to a single-variable implicit function, the Newton–Raphson method is directly used to iteratively solve it here, that is, at the k+1th iteration, the value of ζ is

in, By finite difference approximation. Through formula (16), the guidance parameter value that satisfies the rotation angle constraint (10) under the allowed accuracy is obtained in the finite-step iteration, which is:

ζ ^* ={ζ ^(k+1) ||E(ζ ^(k+1) )|≤ε<|E(ζ ^(k) )|} (17)

The initial state x ₀ = [r ₀ , V ₀ , γ ₀ , δ ₀ ] ^T of the aerodynamically assisted maneuver is given in step 2, combined with the segmented open-loop guidance law of step 3, and the rotation angle parameter ( 17), under the constraints of the time connection equations (14) and (15), the control angle profile of the aerodynamic assist borrowing force is given. According to the control angle profile, the aerodynamic assist borrowing force of the aircraft from the initial state until it flies out of the atmosphere is obtained. The whole trajectory of the force is realized to realize the aerodynamically assisted borrowing flight process with precise rotation angle constraints, that is, the closed-loop prediction-correction precise guidance of the aerodynamically assisted borrowing force under the rotation angle constraint is realized through the staged guidance law.

Beneficial effects:

1. The present invention discloses a pneumatic auxiliary force prediction-correction guidance method that considers rotation angle constraints, and establishes the initial state quantity expression and rotation angle constraint equation in the pneumatic auxiliary force borrowing process. The aerodynamically assisted atmospheric flight process is divided into three flight stages: the descent stage, the constant altitude cruise turning stage and the ascent stage. The descent stage guidance law is designed based on track angle feedback. The descent stage guidance law enables the aircraft to accurately reach the contour cruise stage. The entry condition of the section; the guidance law for the constant altitude cruise section is designed based on the altitude change rate of 0, so that the aircraft can achieve constant altitude flight through the guidance law for the constant altitude cruise section; the constant guidance law for the ascent section is designed based on the terminal constraint requirements, so that the aircraft can fly according to the terminal constraints. Rise and fly out of the atmosphere. Since the three stages cover the existing basic flight process of aerodynamic assistance, they are universal.

2. The present invention discloses an aerodynamically assisted prediction-correction guidance method that considers rotation angle constraints. In the three-stage open-loop guidance law design process, the control angle of the constant-height cruise section is fed back through the track angle deviation and The tangent function expression of the lift coefficient boundary saturation is analytically given, so the prediction link of the guidance is highly efficient and has obvious advantages.

3. The present invention discloses an aerodynamically assisted force prediction-correction guidance method that considers rotation angle constraints, and distinguishes three flight stages by giving time connection equations for the three stages, because the time connection equation only depends on the initial characteristics of each stage. parameters, so the division of the flight process is not affected by the specific task form and is highly robust.

4. The present invention discloses an aerodynamically assisted borrowing force prediction-correction guidance method that considers rotation angle constraints. Since the target rotation angle constraint equation does not strictly limit or constrain the target rotation angle range of the borrowing maneuver, the initial state and aircraft parameters are arbitrarily given. , so it has a wide range of application for force-borrowing maneuvers.

Description of the drawings

Figure 1 is a schematic diagram of the pneumatic assisted force-borrowing maneuver in step 3 of the present invention;

Figure 2 is a flow chart of a pneumatically assisted force prediction-correction guidance method considering rotation angle constraints of the present invention;

Figure 3 is the aerodynamically assisted atmospheric flight trajectory under different total rotation angle constraints in this embodiment;

Figure 4 is the control variable (lift coefficient) profile under different total rotation angle constraints in this embodiment;

Detailed ways

In order to better illustrate the purpose and advantages of the present invention, the present invention will be explained in detail below by conducting a simulation analysis on a pneumatically assisted guidance problem.

Example 1:

As shown in Figure 2, this embodiment discloses a pneumatically assisted force-borrowing prediction-correction guidance method that considers rotation angle constraints, including the following steps:

Step 1: Establish aerodynamic-assisted flight dynamics model.

For the atmospheric flight process with aerodynamic assistance, since the aircraft is affected by aerodynamic forces, the flight trajectory will no longer coincide with the hyperbolic orbit, so a separate dynamic model of the atmospheric flight process needs to be established. Considering that the change of the orbital plane during the borrowing process is actually achieved by correcting the orientation of the entering planet, the aerodynamic borrowing process does not consider out-of-plane maneuvers. In addition, due to the high speed of the aircraft and the short atmospheric flight time, the influence of planetary rotation is directly ignored. In summary, the dynamic model of the aerodynamically assisted atmospheric flight process can be obtained as

Among them, r, V, γ, and δ represent the position, speed, track angle, and instantaneous flight angle of the aircraft respectively. m represents the mass of the aircraft, and S represents the reference area of the aircraft. μ represents the planet's gravitational constant. In addition, the aircraft dynamic pressure q=1/2ρV ² , where ρ is the density of the planet's atmosphere and is a function of the position vector diameter r. In addition, the control variable is the lift coefficient C _L . The lift and drag coefficient of the aircraft satisfies the approximate relationship of the parabolic drag polar line, that is

Among them, C _D0 is the zero-lift drag coefficient, and K is the induced drag factor. The specific value is determined by the aerodynamic shape of the aircraft and the atmospheric environment of the planet.

Step 2: Establish the initial state quantity expression and rotation angle constraint equation during the pneumatic auxiliary force borrowing process.

Step 2.1: Establish the initial state quantity expression during the pneumatic auxiliary force borrowing process;

When the aircraft When a hyperbolic superspeed flies into the vicinity of a planet, the angular momentum of flying into a hyperbolic orbit is

where a ₀ and e ₀ are the semi-major axis and eccentricity of the fly-in orbit respectively. When the aircraft flies to the edge of the atmosphere, its position vector diameter is equal to the position vector diameter of the atmosphere edge, that is

r ₀ ＝R+h _atm (4)

Among them, R is the radius of the planet, and h _atm is equal to the height of the edge of the atmosphere. According to the orbital energy equation, the speed of the aircraft when it reaches the edge of the atmosphere is

In addition, the track angle at the initial moment of atmospheric flight (because the planet's rotation is not considered, it is equal to the flight path angle) is solved by the velocity component, that is

Among them, V _0,⊥ =H ₀ /r ₀ is the velocity component perpendicular to the radial direction when the aircraft flies to the edge of the atmosphere. In addition, considering that the role of the rotation angle δ here is to record the rotation angle of the atmospheric flight process, the initial rotation angle δ ₀ =0° is taken. So far, the expressions of the initial states r ₀ , V ₀ , γ ₀ , and δ ₀ of the aerodynamically assisted atmospheric flight process have been given.

Step 2.2: Establish the rotation angle constraint equation of aerodynamic auxiliary force.

In order to intuitively reflect the geometric relationship of the rotation angle during the pneumatically assisted borrowing maneuver, Figure 1 shows a schematic diagram of the pneumatically assisted borrowing force.

According to the triangular relationship of the aerodynamically assisted maneuvering process, the rotation angle δ ₁ when flying to the edge of the atmosphere can be written directly as

δ ₁ =180°-β ₀ -[(360°-υ ₀ )+(90°-|γ ₀ |)] (7)

Among them, β ₀ = arccos (1/e ₀ ) is the angle between the asymptote and the arc line of flying into the hyperbolic orbit, υ ₀ is the true periapsis angle at the edge of the atmosphere when flying into the hyperbolic orbit, where the true The periapsis angle is υ∈ [0°, 360°], and there is no true periapsis angle in the hyperbolic orbit in the interval [υ _∞ ,360°-υ _∞ ]. The true periapsis angle is calculated directly from the initial angular momentum H ₀ , the eccentricity e ₀ , and the radial and tangential velocity components.

When the aircraft completes atmospheric flight and reaches the atmospheric exit position, its position vector diameter is r _f = r ₀ , the speed at the atmospheric exit is V _f , the track angle is γ _f , and the rotation angle value is δ _f . In addition, the orbital root number after exiting the atmosphere can be given according to the angular momentum H _f =r _f V _f cosγ _f . From the orbital equation, the rotation angle at the atmosphere exit is

δ _a =δ _f (8)

In addition, the hyperbolic speed of an aircraft after it leaves the atmosphere is only related to the number of hyperbolic orbits it flies out of. According to the trigonometric relationship of the aerodynamically assisted maneuvering process, the rotation angle δ ₂ of the aircraft from the atmospheric exit to infinity is directly written as

δ ₂ =180°-β _f -[υ _f +(90°-|γ _f |)] (9)

Among them, β _f is the angle between the asymptote of the hyperbolic orbit and the arch line, and υ _f is the true periapsis angle at the atmospheric exit moment of the hyperbolic orbit.

Therefore, during the guidance process, the constraint equation of the target rotation angle is

E(ζ)＝δ ₁ +δ _a (ζ)+δ ₂ (ζ)-δ _T =0 (10)

Among them, ζ is the turning angle of the constant-height cruise section, which is also set as the guidance parameter characterizing the cruise arc. δ _a (ζ)=δ _f -δ ₀ , δ _T is the total target rotation angle. δ ₂ is affected by the state of the atmospheric outlet, and the state of the outlet atmosphere is directly affected by ζ. Therefore, δ ₂ is also affected by ζ.

That is to say, the initial state expression of the atmospheric flight process in the aerodynamically assisted borrowing force is obtained as shown in (4) (5) (6), and the borrowing force rotation angle constraint equation is as shown in formula (10).

Step 3: Divide the aerodynamically assisted atmospheric flight process into three flight stages: the descent section, the constant altitude cruise turning section and the ascent section. The guidance law for the descent section is designed based on the track angle feedback, and the guidance law for the descent section enables the aircraft to accurately reach the entry conditions of the constant altitude cruise section; the guidance law for the constant altitude cruise section is designed based on the altitude change rate of 0, and the guidance law for the constant altitude cruise section enables the aircraft to The aircraft achieves constant altitude flight; a constant guidance law in the ascent segment is designed based on the terminal constraint requirements, so that the aircraft rises and flies out of the atmosphere according to the terminal constraints.

During the atmospheric flight, the aircraft goes through three flight stages, namely the descent section ab, the contour cruise turning section bc and the ascent section cd. During aerodynamically assisted atmospheric flight, the aircraft enters the atmosphere in a certain initial state, and adjusts the lift coefficient C _L (ie, the control variable) in the atmosphere to achieve the target borrowing angle.

Taking into account the differences in each stage, the guidance law will be designed according to the three stages. During the atmospheric descent stage ab, the quasi-equilibrium cruise (QEC) lift coefficient needs to be On the basis of adding track angle deviation feedback and considering the lift coefficient boundary saturation |C _L |≤C _L,max , at this time, by drawing on the boundary saturation characteristics of the tangent function, the following open-loop guidance law is designed:

Among them, the quasi-balanced cruise lift coefficient That is the lift coefficient when the track angle change rate dγ/dt is 0. In addition, in equation (11), the purpose of the quasi-equilibrium track angle γ ^QEC is to maintain the aircraft in the constant-altitude cruise stage as much as possible. Here, based on the height proportional coefficient, the value of γ ^QEC is given

Among them, λ is the height adjustment coefficient, which is given based on actual task analysis. The cruise altitude corresponding to γ ^QEC is the pericenter height h _p of flying into the hyperbolic orbit.

Quasi-balanced cruise bc (QEC) lift coefficient That is the open-loop guidance law of the cruise segment.

In addition, G is a proportional coefficient, which is mainly used to adjust the magnitude between the feedback term and the quasi-balanced cruise lift coefficient. Considering that the magnitude difference is mainly caused by the atmospheric density between different altitudes, it is taken as

G＝ρ(λh)/ρ(h) (13)

The function of coefficient α is to adjust the rate at which the tangent function approaches its extreme value.

During the ascent section cd, since the aircraft only needs to fly out of the planetary atmosphere normally, the open-loop guidance law of the ascent section needs to be set to a constant value within a guidance cycle of the ascent section based on specific terminal constraints. Make the aircraft ascend and fly out of the atmosphere according to the terminal constraints.

Step 4: Distinguish the three flight stages by giving the time connection equations of the three stages. Under the constraints of the time connection equation, the rotation angle of the equal-height cruise arc segment is given through finite difference correction. Combined with the constraint equation of the target rotation angle, it is given Control angle profile of the entire process of pneumatic auxiliary force borrowing. By controlling the flight process of the angular profile guidance aircraft, the aerodynamically assisted borrowed flight process with precise rotation angle constraints is realized, that is, the closed-loop prediction-correction precise guidance of the aerodynamically assisted borrowed force under the rotation angle constraint is realized through the staged guidance law.

The process of borrowing force guidance includes prediction and correction links. Since the prediction link involves atmospheric flight trajectory recursion, it is necessary to provide the termination conditions for each stage of flight, that is, the termination conditions of the prediction link. The three flight phases are distinguished by giving time connecting equations for the three phases. The end time of the descent section is the start time of the constant altitude cruise section, which is

The aircraft enters the constant altitude cruising flight segment. The turning angle of the constant-height cruise section is ζ, which is set as the guidance parameter characterizing the cruise arc. When the constant angle of the constant-altitude cruising section is, the end time of the constant-altitude cruising section is

When t>t _c , the aircraft begins to rise until it flies out of the atmosphere to complete the aerodynamic assistance process.

Under the constraints of the time connection equation, the rotation angle of the constant-height cruise arc segment is given through finite difference correction. Combined with the constraint equation (10) of the target rotation angle, the control angle profile of the entire process of aerodynamic assist borrowing is corrected. In the correction link, it is necessary to correct the turning angle of the constant altitude cruise segment to ζ through multiple iterations to satisfy the turning angle constraint equation (10). Therefore, during the guidance process, in each guidance link, the equation that satisfies the constraint (10) is solved. High cruise angle ζ, and equation (10) can be directly equivalent to a function of ζ. Since this formula belongs to a single-variable implicit function, the Newton–Raphson method is directly used to iteratively solve it here, that is, at the k+1th iteration, the value of ζ is

in, By finite difference approximation. Through formula (16), the guidance parameter value that satisfies the rotation angle constraint (10) under the allowed accuracy is obtained in the finite-step iteration, which is:

ζ ^* ={ζ ^(k+1) ||E(ζ ^(k+1) )|≤ε<|E(ζ ^(k) )|} (17)

The initial state x ₀ = [r ₀ , V ₀ , γ ₀ , δ ₀ ] ^T of the aerodynamically assisted maneuver is given in step 2, combined with the segmented open-loop guidance law of step 3, and the rotation angle parameter ( 17), under the constraints of the time connection equations (14) and (15), the control angle profile of the aerodynamic assist borrowing force is given. According to the control angle profile, the aerodynamic assist borrowing force of the aircraft from the initial state until it flies out of the atmosphere is obtained. The whole trajectory of the force is realized to realize the aerodynamically assisted borrowing flight process with precise rotation angle constraints, that is, the closed-loop prediction-correction precise guidance of the aerodynamically assisted borrowing force under the rotation angle constraint is realized through the staged guidance law.

In order to verify the feasibility of the method, take the aerodynamic auxiliary force of Venus as an example, take the radius of Venus R = 6052km, and the gravitational constant of Venus μ = 324900km ³ /s ² . In addition, take the atmospheric height of Venus h _atm =140km. Take the one that flies into the hyperbola orbit According to the atmospheric characteristics of Venus, the pericenter height h _p = 100km is selected to fly into the hyperbolic orbit. Among the guidance parameters, take the height adjustment coefficient λ = 0.8. In addition, the rate coefficient α that adjusts the tangent function to the extreme value is set to 2.

The initial parameters of the aerodynamic-assisted force-assisted guidance can be given through equations (4) to (6), and then through steps three and four, the aerodynamic-assisted force-assisted maneuvering guidance trajectory and control angle profile that satisfy the rotation angle constraints can be obtained. In order to verify the adaptability and stability advantages of the method under different constraint conditions, the simulation analysis of aerodynamic assist force prediction-correction guidance under different rotation angle constraints is given below.

Here, δ _t o _tal is taken to be 80°, 90°, 100° and 110° respectively. By gradually increasing the total rotation angle, the characteristic changes of the pneumatic assist borrowing process are analyzed. Table 1 shows the changing rules of key parameters such as rotation angle and hyperbolic overspeed V _∞ + after exiting the atmosphere under different δ _t o _tal , where t _atm represents the total atmospheric flight time. Figure 2 shows the corresponding atmospheric flight trajectory.

Table 1 Characteristic parameters of pneumatic auxiliary force under different total rotation angle constraints

δ _total ,deg δ _a ,deg δ ₂ ,deg V _∞ ⁺ ,km/s ζ ^* ,deg t _atm ,s 80 53.1319 15.852 11.2011 37.531 354.4 90 62.0302 16.961 10.6942 46.342 419.2 100 70.8514 18.135 10.2028 55.070 485.0 110 79.6136 19.377 9.7255 63.726 551.9

It can be clearly seen from the results in Table 1 that as the total rotation angle increases, the rotation angle δ _a of the atmospheric flight section and the rotation angle ζ* of the constant-altitude cruise section increase rapidly, which accordingly results in a significant extension of the total atmospheric flight time t _atm . Combined with The atmospheric flight trajectory in Figure 2 shows that if you want to increase the turning angle during the aerodynamically assisted borrowing process, you only need to increase the turning arc length of the atmospheric flight. From the side, it embodies the aerodynamically assisted borrowing guidance algorithm of the present invention during the large turn borrowing process. advantages in.

In order to verify the robustness and accuracy of the guidance algorithm proposed in this patent, the precision dispersion of the target rotation angle is analyzed by applying a random deviation in each guidance cycle. Among them, all deviations are converted into the calculation of lift and drag acceleration, the deviations are taken to meet the standard normal distribution, and the 3σ value is taken to be 25% of the nominal value. Figure 3 shows the accuracy distribution of the total borrowing angle when the target rotation angle δ _total is set to 80°. As can be seen from the figure, the standard deviation of the _total distribution of the total rotation angle δ is 0.07. The rotation angles are all near the target rotation angle 80°. The maximum deviation is about ±0.1° and the maximum deviation occurs very rarely. The above conclusion can also verify the accuracy and reliability of this patented guidance algorithm.

The above-mentioned specific description further explains the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above-mentioned are only specific embodiments of the invention and are used to explain the invention and are not used for The protection scope of the present invention is limited. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims (4)

1. A pneumatically assisted predictive-corrective guidance method considering rotational constraints, characterized by comprising the following steps: Step 1: Establish an aerodynamic model for assisted flight; Step 2: Establish the initial state quantity expressions and target rotation angle constraint equations during the aerodynamic assisted leverage process; Step 3: Divide the aerodynamic-assisted atmospheric flight process into three phases: descent, constant-altitude cruise, and ascent. Design a descent guidance law based on track angle feedback to ensure the aircraft accurately reaches the entry conditions for the constant-altitude cruise phase. Design a constant-altitude cruise guidance law based on a zero altitude change rate to enable the aircraft to achieve constant-altitude flight. Design a constant-value ascent guidance law based on terminal constraint requirements to enable the aircraft to ascend and exit the atmosphere according to the terminal constraints. Step 4: By providing the time connection equations for the three stages, the three flight stages are distinguished. Under the constraints of the time connection equations, the turning angle of the constant altitude cruise stage is given through finite difference correction. Combined with the target turning angle constraint equation, the control angle profile of the entire aerodynamic assisted leverage process is given. By guiding the flight process of the aircraft through the control angle profile, the aerodynamic assisted leverage flight process with precise turning angle constraints is realized. That is, the closed-loop prediction-correction precision guidance of aerodynamic assisted leverage under the turning angle constraint is realized through the staged guidance law. The method for implementing step three is as follows: During atmospheric flight, the aircraft goes through three phases: descent phase... Altitude cruise section and rising segment During aerodynamic-assisted atmospheric flight, the aircraft enters the atmosphere with a defined initial state and adjusts the lift coefficient _CL , i.e., the control variable, to achieve the target lever-assisted turning angle. Considering the differences in each stage, guidance laws are designed according to the three stages; in the descent stage... The quasi-balanced cruise lift coefficient needs to be Based on this, track angle deviation feedback is added, and considering the lift coefficient boundary saturation | _CL |≤CL _,max , the following open-loop guidance law is designed by referencing the boundary saturation characteristics of the tangent function: Where γ represents the flight path angle of the aircraft, and the quasi-equilibrium cruise lift coefficient is... This is the lift coefficient when the rate of change of track angle dγ/dt is 0; furthermore, in equation (11), the purpose of the quasi-equilibrium track angle ^γQEC is to maintain the aircraft in the constant altitude cruise phase. Here, based on the altitude ratio coefficient, the value of ^γQEC is given. Wherein, λ is the altitude adjustment coefficient, given according to the actual mission analysis; the cruise altitude corresponding to ^γQEC is taken as the altitude h_{_p} of the pericenter point when flying into the hyperbolic orbit; Quasi-balanced cruise lift coefficient This is the open-loop guidance law for the cruise phase at constant altitude; Furthermore, G is a proportionality coefficient, primarily used to adjust the magnitude of the difference between the feedback term and the quasi-balanced cruise lift coefficient. Considering that the magnitude difference is mainly caused by atmospheric density at different altitudes, it is taken as... G＝ρ(λh)/ρ(h) (13) The coefficient α is used to adjust the rate at which the tangent function approaches its extreme value; In the ascending phase Since the spacecraft only needs to fly out of the planetary atmosphere normally, the open-loop guidance law during the ascent phase needs to be set to a constant value within one guidance cycle of the ascent phase, based on the specific terminal constraints. This allows the aircraft to ascend and fly out of the atmosphere according to the terminal constraints. 2. The aerodynamic-assisted prediction-correction guidance method considering rotational constraints as described in claim 1, characterized in that: the implementation method of step one is as follows: For the atmospheric flight process in aerodynamic-assisted glide, the flight trajectory will no longer coincide with the hyperbolic orbit due to the aerodynamic forces acting on the spacecraft. Therefore, a separate dynamic model of the atmospheric flight process needs to be established. Considering that the change in the orbital plane during the glide process is actually achieved by correcting the orientation of the approach to the planet, out-of-plane maneuvers are not considered in the aerodynamic glide process. Furthermore, due to the high speed of the spacecraft and the short atmospheric flight time, the influence of planetary rotation is directly ignored. In summary, the dynamic model of the aerodynamic-assisted glide atmospheric flight process is as follows: Where r, V, and δ represent the spacecraft's position, velocity, and instantaneous flight angle, respectively; m represents the spacecraft's mass; S represents the spacecraft's reference area; μ represents the planetary gravitational constant; furthermore, the spacecraft's dynamic pressure q = 1/ ^2ρV² , where ρ is the planetary atmospheric density and a function of the position vector r; additionally, the control variable is the lift coefficient _CL ; the spacecraft's lift-drag coefficients satisfy an approximate parabolic drag polarity relationship, i.e. Wherein, C _D0 is the zero-lift drag coefficient, and K is the induced drag factor, the specific values of which are determined by the aerodynamic shape of the spacecraft and the atmospheric environment of the planet it is leveraging. 3. The aerodynamic-assisted prediction-correction guidance method considering rotational constraints as described in claim 2, characterized in that: the implementation method of step two is as follows: Step 2.1: Establish the initial state quantity expression for the pneumatic-assisted leverage process; When the aircraft When the hyperbolic object speeds into the vicinity of the planet, its angular momentum upon entering the hyperbolic orbit is... Where a _₀ and e _₀ are the semi-major axis and eccentricity of the flight path, respectively; when the spacecraft reaches the edge of the atmosphere, its position vector is equal to the position vector at the edge of the atmosphere, i.e. r ₀ ＝R+h _atm (4) Where R is the planetary radius, and h _atm is equal to the atmospheric edge height; according to the orbital energy equation, the velocity of the spacecraft at the moment of reaching the atmospheric edge is... Furthermore, the initial trajectory angle of atmospheric flight is solved using the velocity components, i.e. Where V _{_0,⊥} = H _₀ / r _₀ is the velocity component perpendicular to the radial direction when the aircraft reaches the edge of the atmosphere; in addition, considering that the role of the rotation angle δ here is to record the rotation angle of the atmospheric flight process, the initial rotation angle δ _₀ = 0° is taken; at this point, the expressions for the initial state r _₀, V _₀ , γ ₀, and δ_₀ of the aerodynamic-assisted atmospheric flight process have been given; Step 2.2: Establish the target rotation angle constraint equation for aerodynamic assistance; Based on the triangular relationship in the aerodynamic-assisted maneuvering process, the turning angle _δ1 at the moment of reaching the atmospheric edge can be directly written as: δ ₁ =180°-β ₀ -[(360°-υ ₀ )+(90°-|γ ₀ |)] (7) Where _β0 = arccos(1/ _e0 ) is the angle between the asymptote and the camber of the hyperbolic orbit, and _υ0 is the true anomaly angle at the atmospheric edge when the hyperbolic orbit enters the orbit. Here, the true anomaly angle is υ∈[0°,360°]. The hyperbolic orbit does not have a true anomaly angle in the interval [ _υ∞ ,360° _-υ∞ ]. The true anomaly angle is calculated directly from the initial angular momentum, eccentricity, and radial and tangential velocity components. When the spacecraft completes atmospheric flight and reaches the atmospheric exit position, its position vector magnitude is r_{_f} = r_₀. Let the velocity at the atmospheric exit be V_{_f} , the track angle be γ_{_f}, and the turning angle be δ_{_f}. Furthermore, the orbital elements after exiting the atmosphere can be given by the angular momentum H _{_f} = r _{_f}V _{_f}cosγ_{_f}. The turning angle at the atmospheric exit is obtained from the orbital equations. _δa = _δf (8) Furthermore, the hyperbolic speedup of the aircraft after exiting the atmosphere is only related to the elements of the hyperbolic trajectory; based on the triangular relationship of the aerodynamic-assisted maneuver, the turning angle _δ2 of the aircraft from the atmospheric exit to infinity can be directly written as... δ ₂ =180°-β _f -[υ _f +(90°-|γ _f |)] (9) Where _βf is the angle between the asymptote and the arch after exiting the hyperbolic orbit, and _υf is the true anomaly angle at the atmospheric exit moment after exiting the hyperbolic orbit. Therefore, during the guidance process, the target rotation angle constraint equation is: E(ζ)＝δ ₁ +δ _a (ζ)+δ ₂ (ζ)-δ _T =0 (10) Where ζ is the turning angle of the cruise segment at constant altitude, and is also set as the guidance parameter characterizing the cruise arc; _δa (ζ)＝ _δf - _δ0 , _δT is the total turning angle of the target; _δ2 is affected by the state of the exit atmosphere, and the state of the exit atmosphere is directly affected by ζ, therefore, _δ2 is also affected by ζ. The initial state expressions for the atmospheric flight process in aerodynamic assistance are shown in (4)(5)(6), and the target rotation angle constraint equation is shown in formula (10). 4. The aerodynamic-assisted prediction-correction guidance method considering rotational constraints as described in claim 3, characterized in that: the implementation method of step four is as follows: The guided flight process includes prediction and correction phases. The prediction phase involves atmospheric flight trajectory recursion, thus requiring the termination conditions for each flight stage; these are the termination conditions for the prediction phase itself. The three flight stages are distinguished by providing time connection equations. The termination time of the descent phase coincides with the start time of the iso-altitude cruise phase. The aircraft enters the altitude-contact cruise phase; the turning angle of the altitude-contact cruise phase is ζ, which is set as the guidance parameter characterizing the cruise arc; when the turning angle of the altitude-contact cruise phase is constant, the end time of the altitude-contact cruise phase is... When t> _tc , the aircraft begins to rise until it flies out of the atmosphere and completes the aerodynamic assisted leverage process; Under the constraint of the time connection equation, the turning angle of the cruise segment at constant altitude is given by finite difference correction. Combined with the target turning angle constraint equation (10), the control angle profile of the entire process of aerodynamic assistance is given by correction. In the correction process, the turning angle ζ of the cruise segment at constant altitude needs to be corrected by multiple iterations so that the turning angle constraint equation (10) is satisfied. Therefore, in the guidance process, in each guidance stage, the turning angle ζ of the cruise segment at constant altitude that satisfies the constraint (10) is solved. Equation (10) can be directly equivalent to a function of ζ. Since this equation is a single-variable implicit function, the Newton-Raphson method is directly used to solve iteratively. That is, in the (k+1)th iteration, the value of ζ is in, By using finite difference approximation; and by iterating through a finite number of steps using equation (16), the guidance parameter values that satisfy the rotation constraint (10) under the allowable accuracy are obtained, which are... By giving the initial state _x0 = [ _r0 , _V0 , _γ0 , _δ0 ] ^T for aerodynamic assisted maneuvering in step two, and combining the piecewise open-loop guidance law in step three, the guidance parameters (17) given by iterative guidance are used to give the control angle profile of aerodynamic assisted maneuvering under the constraints of time connection equations (14) and (15). Based on the control angle profile, the aerodynamic assisted maneuvering trajectory of the aircraft from the initial state to atmospheric flight until it flies out of the atmosphere is obtained, realizing the aerodynamic assisted maneuvering process with precise turning angle constraint. That is, the closed-loop prediction-correction precise guidance of aerodynamic assisted maneuvering under the turning angle constraint is realized through the phased guidance law.