Burnup optimal pneumatic auxiliary orbit descending efficient prediction-correction guidance method

Abstract

The invention discloses an efficient prediction-correction guidance method for burn-up optimal pneumatic-assisted orbit descending, which belongs to the field of aerospace, and comprises the following steps: establishing a spacecraft pneumatic-assisted orbit descending flight dynamics model and a pulse maneuvering model required by a spacecraft entering a target orbit after the spacecraft exits the atmosphere; and decoupling and extracting a simplified longitudinal in-plane motion equation from the kinetic model, performing variable substitution, converting an independent variable into a variable in an energy form, obtaining a mapping relation between a heeling angle control quantity and flight states such as a flight path angle, planning a flight path angle profile based on the trajectory characteristics of the burnup optimal pneumatic auxiliary orbit descent, and finally obtaining a flight path angle profile. And deriving an analytical expression of a guidance instruction, designing a three-stage guidance scheme, and realizing efficient prediction-correction guidance. By the adoption of the method, efficient prediction-correction guidance can be carried out under the pneumatically-assisted orbit descending task scenes with remarkably different conditions, the flexibility and adaptability of the method are embodied, and effective technical guarantee can be provided for maneuvering orbit transfer tasks of spacecrafts.

Description

Technical Field

[0001] The invention relates to the field of aerospace technology, and in particular to a fuel-optimized aerodynamically assisted orbit lowering high-efficiency prediction-correction guidance method. Background Art

[0002] When a spacecraft passes through a planetary atmosphere and uses aerodynamic forces to reduce its orbital altitude, it needs to be supported by an accurate, efficient and reliable guidance method to cope with the highly dynamic atmospheric environment and ensure safe entry into the target orbit with low fuel consumption. In the existing aerodynamic-assisted orbit reduction prediction-correction guidance method, the prior art proves that the aerodynamic-assisted orbit reduction with optimal fuel consumption theoretically has a bang-bang control structure, and proposes a numerical prediction-correction guidance method based on a step-type control profile. This method has the characteristics of optimal fuel consumption, but relies on a numerically integrated dynamic equation group to predict the terminal state of the trajectory, which has a large amount of calculation and is currently difficult to achieve online application. The prior art proposes an analytical prediction-correction method that refers to the characteristics of aerodynamic capture trajectory with optimal fuel consumption, and derives the analytical expression of the atmospheric exit velocity by parameterizing aerodynamic parameters and track angle-altitude profiles. This method has the characteristics of approximately optimal fuel consumption and higher computational efficiency, but its derivation is based on a dynamic model with altitude as the independent variable, and can only be applied to the prediction-correction guidance in the stage of monotonic altitude change in the scenario of full aerodynamic deceleration. It is not universal, and its adaptability to different mission scenarios needs to be improved. Summary of the invention

[0003] The purpose of the present invention is to provide a fuel-optimized aerodynamically assisted orbit lowering efficient prediction-correction guidance method to solve the problems existing in the background technology.

[0004] To achieve the above object, the present invention provides a fuel-optimized aerodynamic-assisted orbit lowering high-efficiency prediction-correction guidance method, comprising the following steps:

[0005] S1. Establishing a dynamic model of the atmospheric flight phase of the spacecraft aerodynamically assisted orbit reduction taking into account the influence of celestial body rotation and J2 perturbation. The atmospheric flight dynamic model of the spacecraft aerodynamically assisted orbit reduction is a three-degree-of-freedom dynamic equation. The motion equation in the longitudinal plane is extracted by decoupling the three-degree-of-freedom dynamic equation.

[0006] S2. Establish the impulse maneuver model required for the spacecraft to enter the target orbit after leaving the atmosphere;

[0007] S3, perform variable substitution, convert the independent variable from time to a variable in energy form, and obtain the mapping relationship between the roll angle control amount and the track angle and other states;

[0008] S4. Plan the track angle profile based on the trajectory characteristics of the aerodynamic-assisted orbit descent with optimal fuel consumption, and then derive the analytical expression of the guidance command;

[0009] S5. Design an efficient prediction-correction guidance scheme based on the trajectory characteristics of the fuel-optimal aerodynamic-assisted orbit descent and the analytical expression of the guidance instructions.

[0010] Preferably, the content of S1 is as follows:

[0011] The dimensionless three-degree-of-freedom dynamic equation of the spacecraft during the aerodynamic-assisted orbit reduction flight is:

[0012]

[0013] Among them, r represents the radial vector from the center of the celestial body to the center of mass of the spacecraft; θ represents the longitude; φ represents the latitude; V represents the velocity of the spacecraft relative to the celestial body; γ represents the track angle of the velocity vector relative to the celestial body; ψ represents the heading angle; σ represents the roll angle, which is used as a control variable in the flight process; ω represents the angular velocity of the celestial body's rotation;

[0014]

[0015] Where L and D represent the aerodynamic lift acceleration and aerodynamic drag acceleration respectively; ρ is the dimensional atmospheric density; S is the dimensional spacecraft reference area; C L , C D are lift coefficient and drag coefficient respectively; m is the dimensional spacecraft mass; R 0 is the equatorial radius of the celestial body;

[0016]

[0017] Among them, g r and g φ are the radial and latitudinal components of the dimensionless gravitational acceleration, respectively; J 2 Characterizes the dynamic flattening of the celestial body; ω is the angular velocity of the celestial body's rotation. In order to facilitate the subsequent derivation, the longitudinal motion parameters of the spacecraft: height h (corresponding to the radius vector r), velocity V and track angle γ are extracted from the three-degree-of-freedom dynamic equation (1) to form a simplified longitudinal decoupled motion model:

[0018]

[0019]

[0020]

[0021] Preferably, the content of S2 is as follows:

[0022] After passing through and flying out of the atmosphere, the spacecraft needs one or two pulse maneuvers during the exoatmospheric flight phase to establish the desired target orbit. The total velocity increment ΔV required is

[0023]

[0024] Where: r atgt , r ptgt are the apocenter radius and pericenter radius of the target orbit respectively. For a single pulse maneuver, r a0 =r atgt ; r a0 and r p0 are the apocenter and pericenter radii of the orbit after leaving the atmosphere, respectively, and are determined by the following formula:

[0025]

[0026]

[0027] Where: a is the semi-major axis of the trajectory after aerodynamic capture, r EI 、V exit and γ exit are the radial vector, inertial velocity and track angle under atmospheric exit conditions. The kinetic energy and potential energy at the atmospheric exit determine the semi-major axis of the orbit outside the atmosphere:

[0028]

[0029] Preferably, the content of S3 is as follows:

[0030] Introduce a new independent variable:

[0031]

[0032] This variable represents the negative value of orbital energy. Ignoring the influence of celestial body J2 perturbation and rotation, the time derivative is:

[0033]

[0034] That is, e is monotonically increasing in the process of passing through the atmosphere. Then, e is used to replace the time variable and the longitudinal motion equations are transformed into:

[0035]

[0036]

[0037]

[0038] Processing equation (16), the roll angle control value is extracted and obtained

[0039]

[0040] Among them, σ cmd is the roll angle command.

[0041] Preferably, the content of S4 is as follows:

[0042] Theoretically, the fuel-optimized aerodynamically assisted orbit descent has a roll angle control profile with a bang-bang structure. Considering that sinγ≈γ when the track angle is near 0, according to the optimal γ-e profile characteristics in different scenarios, a piecewise expression about e can be designed to parameterize the sinγ term, for example:

[0043]

[0044] Among them, K, N, A 0 , A 1 , B 0 , B 1 , B 2 is the coefficient of the corresponding fitting function, B 1 is the preset coefficient, and the values ​​of the remaining coefficients can be determined by the two-point boundary value information; e swi The bang-bang switching point corresponding to the control section; γ 0 is the current track angle of the spacecraft; γ f is the track angle of the aerodynamically assisted orbit lowering terminal.

[0045] When e>e swi When , we can differentiate (19) with respect to e and apply the chain rule to obtain:

[0046]

[0047] Further sorting gives:

[0048]

[0049] Substituting the above formula into formula (18), we get:

[0050]

[0051] The closed-loop roll angle guidance command is:

[0052]

[0053] Preferably, the content of S5 is as follows:

[0054] In order to simulate the bang-bang control structure of the optimal aerodynamic assisted orbit descent as much as possible, the guidance can be divided into three stages:

[0055] A1. Initial descent open-loop guidance stage: the roll angle command remains constant:

[0056] σ cmd =σ 0 (twenty four)

[0057] Among them, σ 0is a smaller constant value of the roll angle, for example, the minimum roll angle σ min When the track angle γ approaches 0, it enters the predicted switching point stage.

[0058] A2. Predicting the switching point: The guidance parameter is taken as the energy e corresponding to the switching point of the open-closed loop guidance. swi . In the selected swi After that, the spacecraft state at the atmosphere exit (r EI ,V exit ,γ exit ), and further determine the orbital parameters after the atmosphere through equations (9) to (12). swi The radius of the apocenter of the orbit after leaving the atmosphere can be changed a0 To match the apocenter radius r of the target orbit atgt , so the optimal guidance parameter can be determined by the single variable root finding method Sure After that, if the current energy Then σ cmd =σ 0 ;like Then switch to the closed-loop prediction-correction guidance phase.

[0059] A3, closed-loop prediction-correction guidance phase: The fitting function of the spacecraft state is set to pass through the preset point (γ set ,e set ), where γ set is the preset point track angle, e set is the preset point energy. Select γ set As a correctable guidance parameter, based on the current state of the spacecraft (γ 0 ,e 0 ) and preset point information, the coefficients of the fitting function in equation (19) can be calculated by the following formula:

[0060]

[0061]

[0062] After determining the fitting function, the spacecraft state at the atmosphere exit can be efficiently predicted (r EI ,V exit ,γ exit ), and further determine the orbital parameters after the atmosphere through equations (9) to (12). By adjusting γ set The radius of the apocenter of the orbit after leaving the atmosphere can be changed a0 To match the apocenter radius r of the target orbit atgt , so the optimal guidance parameter can be determined by the single variable root finding method The corresponding roll angle command σ is further determined by equation (23): cmd This prediction-correction scheme is repeated during each guidance cycle until the spacecraft exits the atmosphere.

[0063] Therefore, the present invention adopts the above-mentioned fuel consumption optimal aerodynamic assisted orbit lowering efficient prediction-correction guidance method, which has the following beneficial effects:

[0064] (1) Based on energy substitution, the mapping relationship between the roll angle control amount and the track angle and other states is constructed, and the analytical expression of the guidance command is derived, which realizes efficient prediction-correction guidance, has low requirements on the computing power of the equipment, and ensures the real-time performance of the guidance;

[0065] (2) By correcting the roll angle, a track angle profile with optimal fuel consumption is planned, so that the method has the optimal fuel consumption characteristic and can minimize the fuel consumption required for orbit lowering;

[0066] (3) The energy that changes monotonically throughout the atmospheric flight is used as the independent variable for derivation, and guidance can be performed during the descent or ascent phases, with a wide range of applications;

[0067] (4) It can adapt to significant changes in the atmospheric environment, entry state, and target orbit parameters, making it suitable for various aerodynamically assisted orbit reduction mission scenarios.

[0068] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flow chart of a fuel-optimized aerodynamically assisted orbit lowering efficient prediction-correction guidance method according to an embodiment of the present invention;

[0070] Figure 2 The velocity-altitude profile obtained by the guidance of the embodiment of the present invention in the earth aerodynamic assisted orbit reduction scenario;

[0071] Figure 3 The roll angle control profile obtained by the guidance of the embodiment of the present invention in the earth aerodynamic assisted orbit reduction scenario;

[0072] Figure 4 The velocity-altitude profile obtained by the guidance of the embodiment of the present invention in the Mars aerodynamic assisted orbit lowering scenario;

[0073] Figure 5 It is the roll angle control profile obtained by the guidance of the embodiment of the present invention in the Mars aerodynamic assisted orbit lowering scenario. DETAILED DESCRIPTION

[0074] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] See also Figure 1 , a fuel consumption optimal aerodynamic assisted orbit lowering efficient prediction-correction guidance method, comprising the following steps:

[0076] S1. A dynamic model of the atmospheric flight phase of the spacecraft aerodynamically assisted orbit reduction is established, which takes into account the influence of celestial body rotation and J2 perturbation. The atmospheric flight dynamic model of the spacecraft aerodynamically assisted orbit reduction is a three-degree-of-freedom dynamic equation. The motion equation in the longitudinal plane is extracted by decoupling the three-degree-of-freedom dynamic equation.

[0077] The dimensionless three-degree-of-freedom dynamic equation of the spacecraft during the aerodynamic-assisted orbit reduction flight is:

[0078]

[0079] Among them, r represents the radial vector from the center of the celestial body to the center of mass of the spacecraft; θ represents the longitude; φ represents the latitude; V represents the velocity of the spacecraft relative to the celestial body; γ represents the track angle of the velocity vector relative to the celestial body; ψ represents the heading angle; σ represents the roll angle, which is used as a control variable in the flight process;

[0080]

[0081]

[0082] Where L and D represent the aerodynamic lift acceleration and aerodynamic drag acceleration respectively; ρ is the dimensional atmospheric density; S is the dimensional spacecraft reference area; C L , C D are lift coefficient and drag coefficient respectively; m is the dimensional spacecraft mass; R 0 is the equatorial radius of the celestial body;

[0083]

[0084]

[0085] Among them, g r and g φ are the radial and latitudinal components of the dimensionless gravitational acceleration, respectively; J 2Characterizes the dynamic flattening of the celestial body; ω is the angular velocity of the celestial body's rotation. In order to facilitate the subsequent derivation, the longitudinal motion parameters of the spacecraft: height h (corresponding to the radius vector r), velocity V and track angle γ are extracted from the three-degree-of-freedom dynamic equation (1) to form a simplified longitudinal decoupled motion model:

[0086]

[0087]

[0088]

[0089] S2. Establish a pulse maneuver model required for the spacecraft to enter the target orbit after leaving the atmosphere.

[0090] After passing through and flying out of the atmosphere, the spacecraft needs one or two pulse maneuvers during the exoatmospheric flight phase to establish the desired target orbit. The total velocity increment ΔV required is

[0091]

[0092] Where: r atgt , r ptgt are the apocenter radius and pericenter radius of the target orbit respectively. For a single pulse maneuver, r a0 =r atgt ; r a0 and r p0 are the apocenter and pericenter radii of the orbit after leaving the atmosphere, respectively, and are determined by the following formula:

[0093]

[0094]

[0095] Where: a is the semi-major axis of the trajectory after aerodynamic capture, r EI 、V exit and γ exit are the radial vector, inertial velocity and track angle under atmospheric exit conditions. The kinetic energy and potential energy at the atmospheric exit determine the semi-major axis of the orbit outside the atmosphere:

[0096]

[0097] S3. Perform variable substitution to convert the independent variable from time to a variable in energy form, and obtain the mapping relationship between the roll angle control amount and the track angle and other states.

[0098] Introduce a new independent variable:

[0099]

[0100] This variable represents the negative value of orbital energy. Ignoring the influence of celestial body J2 perturbation and rotation, the time derivative is:

[0101]

[0102] That is, e is monotonically increasing in the process of passing through the atmosphere. Then, e is used to replace the time variable and the longitudinal motion equations are transformed into:

[0103]

[0104]

[0105]

[0106] Processing equation (16), the roll angle control value is extracted and obtained

[0107]

[0108] Among them, σ cmd is the roll angle command.

[0109] S4. Plan the track angle profile based on the trajectory characteristics of the fuel-optimal aerodynamic-assisted orbit descent, and then derive the analytical expression of the guidance command.

[0110] Theoretically, the fuel-optimized aerodynamically assisted orbit descent has a roll angle control profile with a bang-bang structure. Considering that sinγ≈γ when the track angle is near 0, according to the optimal γ-e profile characteristics in different scenarios, a piecewise expression about e can be designed to parameterize the sinγ term, for example:

[0111]

[0112] Among them, K, N, A 0 , A 1 , B 0 , B 1 , B 2 is the coefficient of the corresponding fitting function, B 1 is the preset coefficient, and the values ​​of the remaining coefficients can be determined by the two-point boundary value information; e swi The bang-bang switching point corresponding to the control section; γ 0 is the current track angle of the spacecraft; γ f is the track angle of the aerodynamically assisted orbit lowering terminal.

[0113] When e>e swi When , we can differentiate (19) with respect to e and apply the chain rule to obtain:

[0114]

[0115] Further sorting gives:

[0116]

[0117] Substituting the above formula into formula (18), we get:

[0118]

[0119] The closed-loop roll angle guidance command is:

[0120]

[0121] S5. Design an efficient prediction-correction guidance scheme based on the trajectory characteristics of the fuel-optimal aerodynamic-assisted orbit descent and the analytical expression of the guidance instructions.

[0122] In order to simulate the bang-bang control structure of the optimal aerodynamic assisted orbit descent as much as possible, the guidance can be divided into three stages:

[0123] A1. Initial descent open-loop guidance stage: the roll angle command remains constant:

[0124] σ cmd =σ 0 (twenty four)

[0125] Among them, σ 0 is a smaller constant value of the roll angle, for example, the minimum roll angle σ min When the track angle γ approaches 0, it enters the predicted switching point stage.

[0126] A2. Predicting the switching point: The guidance parameter is taken as the energy e corresponding to the switching point of the open-closed loop guidance. swi . In the selected swi After that, the spacecraft state at the atmosphere exit (r EI ,V exit ,γ exit ), and further determine the orbital parameters after the atmosphere through equations (9) to (12). swi The radius of the apocenter of the orbit after leaving the atmosphere can be changed a0 To match the apocenter radius r of the target orbit atgt , so the optimal guidance parameter can be determined by the single variable root finding method Sure After that, if the current energy Then σ cmd =σ 0 ;like Then switch to the closed-loop prediction-correction guidance phase.

[0127] A3, closed-loop prediction-correction guidance phase: The fitting function of the spacecraft state is set to pass through the preset point (γ set ,e set ), where γ set is the preset point track angle, e set is the preset point energy. Select γ set As a correctable guidance parameter, based on the current state of the spacecraft (γ 0 ,e 0 ) and preset point information, the coefficients of the fitting function in equation (19) can be calculated by the following formula:

[0128]

[0129] After determining the fitting function, the spacecraft state at the atmosphere exit can be efficiently predicted (r EI ,V exit ,γ exit ), and further determine the orbital parameters after the atmosphere through equations (9) to (12). By adjusting γ set The radius of the apocenter of the orbit after leaving the atmosphere can be changed a0 To match the apocenter radius r of the target orbit atgt , so the optimal guidance parameter can be determined by the single variable root finding method The corresponding roll angle command σ is further determined by equation (23): cmd This prediction-correction scheme is repeated during each guidance cycle until the spacecraft exits the atmosphere.

[0130] The velocity-altitude profile of the entire atmospheric flight in the Earth aerodynamic assisted orbit reduction scenario is obtained by using the guidance method of this embodiment as follows: Figure 2 As shown in Figure 1. It can be seen that the spacecraft speed mainly decays in the 60-75km altitude range, and the speed decreases to about 7.8km / s when leaving the atmosphere. The roll angle control profile in this scenario is as follows Figure 3 As shown in FIG. 1 , after switching to closed-loop prediction-correction guidance, the roll angle first rolls to about 130 degrees, and then gradually saturates to 180 degrees. Under the guidance of the method of this embodiment, the speed increment required for the spacecraft to insert into the target orbit after leaving the atmosphere is 60.3 m / s, which is close to the theoretical optimal fuel consumption value.

[0131] The velocity-altitude profile of the entire atmospheric flight in the Mars aerodynamic assisted orbit reduction scenario is obtained by using the guidance method of this embodiment as follows: Figure 4 As shown in Figure 1, the spacecraft speed mainly decays in the 35-50km altitude range, and the speed decreases to about 3.9km / s when leaving the atmosphere. The roll angle control profile in this scenario is shown in Figure 1. Figure 5As shown, it can be seen that the profile generally conforms to the optimal bang-bang switching structure. Under the guidance of the method of this embodiment, the speed increment required for the spacecraft to change its orbit is 54.2m / s, which is close to the theoretical optimal fuel consumption value.

[0132] Therefore, the present invention adopts the above-mentioned fuel-optimal aerodynamically assisted orbit reduction efficient prediction-correction guidance method, which can perform efficient prediction-correction guidance in aerodynamically assisted orbit reduction mission scenarios with significantly different conditions, reflecting the flexibility and adaptability of the method, and can provide effective technical support for spacecraft maneuvering orbit change missions.

[0133] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A fuel-optimized aerodynamically assisted orbit lowering high-efficiency prediction-correction guidance method, characterized in that: The following steps are involved: S1. Establish a dynamic model of the atmospheric flight phase of the spacecraft aerodynamically assisted orbit reduction taking into account the influence of celestial body rotation and J2 perturbation. The atmospheric flight dynamic model of the spacecraft aerodynamically assisted orbit reduction is a three-degree-of-freedom dynamic equation. The motion equation in the longitudinal plane is extracted from the three-degree-of-freedom dynamic equation by decoupling. S2. Establish the impulse maneuver model required for the spacecraft to enter the target orbit after leaving the atmosphere; S3, performing variable substitution, converting the independent variable from time to a variable in energy form, and processing to obtain a mapping relationship between the roll angle control amount and the track angle state; S4. Plan the track angle profile based on the trajectory characteristics of the aerodynamic-assisted orbit descent with optimal fuel consumption, and then derive the analytical expression of the guidance command; S5. Design an efficient prediction-correction guidance scheme based on the trajectory characteristics of the fuel-optimal aerodynamic-assisted orbit descent and the analytical expression of the guidance instructions.

2. The method for efficient prediction-correction guidance with optimal fuel consumption and aerodynamically assisted orbit lowering according to claim 1, characterized in that: S1 content is as follows: The dimensionless three-degree-of-freedom dynamic equation of the spacecraft during the aerodynamic-assisted orbit reduction flight is: Among them, r represents the radial vector from the center of the celestial body to the center of mass of the spacecraft; θ represents the longitude; φ represents the latitude; V represents the velocity of the spacecraft relative to the celestial body; γ represents the track angle of the velocity vector relative to the celestial body; ψ represents the heading angle; σ represents the roll angle, which is used as a control variable in the flight process; ω represents the angular velocity of the celestial body's rotation; Where L and D represent the aerodynamic lift acceleration and aerodynamic drag acceleration respectively; ρ is the dimensional atmospheric density; S is the dimensional spacecraft reference area; C L , C D are lift coefficient and drag coefficient respectively; m is the dimensioned mass of the spacecraft; R0 is the equatorial radius of the celestial body; Among them, g r and g φ are the radial and latitudinal components of dimensionless gravitational acceleration, respectively; J2 represents the celestial body dynamics flattening; ω is the celestial body rotation angular velocity; The spacecraft longitudinal motion parameters: height h, velocity V and track angle γ are extracted from the three-degree-of-freedom dynamic equation (1) to form a simplified longitudinal decoupled motion model:

3. The method for efficient prediction-correction guidance with optimal fuel consumption and aerodynamically assisted orbit lowering according to claim 2 is characterized in that: The contents of S2 are as follows: After the spacecraft passes through and flies out of the atmosphere, the spacecraft performs pulse adjustment during the exoatmospheric flight phase to establish the desired target orbit. The required total velocity increment ΔV is: In the formula, r atgt , r ptgt are the apocenter radius and pericenter radius of the target orbit respectively; for a single pulse maneuver, r a0 =r atgt ; r a0 and r p0 are respectively the apocenter and pericenter radii of the orbit after leaving the atmosphere, as shown in equations (10) and (11): Where a is the semi-major axis of the trajectory after aerodynamic capture; r EI 、V exit and γ exit are the radial vector, inertial velocity and track angle under atmospheric exit conditions; The kinetic energy and potential at the atmospheric exit determine the semi-major axis of the orbit outside the atmosphere:

4. The method for efficient prediction-correction guidance with optimal fuel consumption and aerodynamically assisted orbit lowering according to claim 3 is characterized in that: The S3 content is as follows: Introduce a new independent variable: This variable characterizes the negative value of orbital energy; Ignoring the influence of celestial body J2 perturbation and rotation, the derivative of the introduced independent variable with respect to time is obtained: e is monotonically increasing in the process of passing through the atmosphere, so e is used to replace the time variable and the longitudinal motion equations are transformed into: The roll angle control value is extracted by processing equation (16) and obtained as follows: Among them, σ cmd is the roll angle command.

5. The method for efficient prediction-correction guidance with optimal fuel consumption and aerodynamically assisted orbit lowering according to claim 4 is characterized in that: S4 content is as follows: When the track angle is near 0, sinγ≈γ. According to the optimal γ-e profile characteristics in different scenarios, a piecewise expression about e is designed to parameterize the sinγ term, as shown in formula (19): Among them, K, N, A0, A1, B0, B1, B2 are the coefficients of the corresponding fitting function; B1 is the preset coefficient; e swi The bang-bang switching point corresponding to the control profile; γ0 is the current track angle of the spacecraft; γ f is the track angle of the aerodynamically assisted orbit lowering terminal; When e>e swi When , we can differentiate (19) with respect to e and apply the chain rule to obtain: Further sorting gives: Substituting formula (21) into formula (18), we obtain: The closed-loop roll angle guidance command is:

6. The method for efficient prediction-correction guidance with optimal fuel consumption and aerodynamically assisted orbit lowering according to claim 5, characterized in that: S5 is a bang-bang control structure that simulates the optimal aerodynamic assisted orbit descent. The guidance is divided into the following three stages: A1. Initial descent open-loop guidance stage: the roll angle command remains constant: s cmd =σ0 (24) Among them, σ0 is a small constant value of the roll angle. When the track angle γ is close to 0, it enters the prediction switching point stage; A2. Predicting the switching point: The guidance parameter is taken as the energy e corresponding to the switching point of the open-closed loop guidance. swi , in the selected swi Finally, the spacecraft state at the atmosphere exit (r EI ,V exit ,γ exit ), and further determine the orbital parameters after the atmosphere through equations (9) to (12), and adjust e swi Change the orbital apocenter radius r after leaving the atmosphere a0 To match the apocenter radius r of the target orbit atgt , use the single variable root-finding method to determine the optimal guidance parameter Sure After that, if the current energy Then σ cmd =σ0; if Then switch to the closed-loop prediction-correction guidance stage; A3, closed-loop prediction-correction guidance phase: The fitting function of the spacecraft state is set to pass through the preset point (γ set ,e set ), where γ set is the preset point track angle, e set is the preset point energy; select γ set As a correctable guidance parameter, based on the current state of the spacecraft (γ0, e0) and the preset point information, the coefficients of the fitting function in equation (19) are calculated by equations (25) and (26): After determining the fitting function, the spacecraft state at the atmosphere exit can be predicted (r EI ,V exit ,γ exit ), and further determine the orbital parameters after the atmosphere through equations (9) to (12); By adjusting γ set Change the orbital apocenter radius r after leaving the atmosphere a0 To match the apocenter radius r of the target orbit atgt , use the single variable root-finding method to determine the optimal guidance parameter The corresponding roll angle command σ is further determined by equation (23): cmd , which is repeated in each guidance cycle until the spacecraft flies out of the atmosphere.

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