An optimal-burn aerodynamic-assisted de-orbiting efficient predictive-correction guidance method

Abstract

The application discloses a kind of fuel consumption optimal aerodynamic auxiliary deorbiting high-efficiency prediction-correction guidance methods, belong to aerospace field, including establishing spacecraft aerodynamic auxiliary deorbiting flight dynamics model, and the impulse maneuver model required after spacecraft enters atmosphere, into target orbit, decoupling extraction is carried out in dynamics model simplified longitudinal plane motion equation and makes variable substitution, convert independent variable into energy form variable, obtain the mapping relationship of flight state such as roll control variable and flight path angle, and trajectory characteristic is planned based on fuel consumption optimal aerodynamic auxiliary deorbiting flight path angle profile, the analytical expression of guidance instruction is deduced, three-stage guidance scheme is designed, and high-efficiency prediction-correction guidance is realized.The application uses the above method, can carry out high-efficiency prediction-correction guidance in the aerodynamic auxiliary deorbiting task scene that condition is significantly different, reflect the flexibility and adaptability of method, can provide effective technical support for spacecraft maneuvering orbit transfer mission.

Description

Technical Field

[0001] The present 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 traverses a planetary atmosphere and uses aerodynamic forces to lower its orbital altitude, it requires precise, efficient, and reliable guidance methods to cope with the highly dynamic atmospheric environment and ensure safe entry into the target orbit with minimal fuel consumption. Among existing prediction-correction guidance methods for aerodynamically assisted orbit reduction, existing techniques have demonstrated that aerodynamically assisted orbit reduction with optimal fuel consumption theoretically possesses a bang-bang control structure. A numerical prediction-correction guidance method based on a stepped control profile has been proposed. While this method exhibits optimal fuel consumption, it relies on numerical integration of a system of dynamic equations to predict the terminal trajectory state, resulting in a high computational load and currently difficult to implement online. Existing techniques have proposed an analytical prediction-correction method that references the characteristics of aerodynamically captured trajectory with optimal fuel consumption. This method, by parameterizing aerodynamic parameters and the track angle-altitude profile, derives an analytical expression for the atmospheric exit velocity. While this method exhibits near-optimal fuel consumption and improved computational efficiency, its derivation is based on a dynamic model with altitude as the independent variable. This method is applicable only to prediction-correction guidance during the monotonically changing altitude phase under full aerodynamic deceleration. It lacks universal applicability and its adaptability to diverse mission scenarios needs improvement. Summary of the Invention

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

[0004] To achieve the above objectives, the present invention provides a fuel-optimized aerodynamically assisted orbit lowering and efficient prediction-correction guidance method, comprising the following steps:

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

[0006] S2. Build a model for the impulse maneuvers required for the spacecraft to exit the atmosphere and enter the target orbit;

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

[0008] S4. Plan the flight path angle profile based on the trajectory characteristics of the fuel-optimized aerodynamically assisted orbit descent, 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 aerodynamically 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 aerodynamically assisted orbit reduction flight is:

[0012]

[0013] Among them, r represents the radius 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 the control variable of the flight process; ω represents the angular velocity of the celestial body;

[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 the lift coefficient and drag coefficient respectively; m is the dimensionless mass of the spacecraft; R0 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; J2 represents the celestial body's dynamical flattening; and ω is the celestial body's rotational angular velocity. To facilitate subsequent derivation, the spacecraft's longitudinal motion parameters: 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: ratgt , r ptgt are the far and near point radii of the target orbit, respectively, and r a0 = r atgt ; r a0 and r p0 are the far and near point radii of the post-atmospheric orbit, respectively, determined by:

[0025]

[0026]

[0027] where a is the semi-major axis of the post-aerocapture orbit, r EI , V exit and γ exit are the radial, inertial velocity and flight path angle at the exit of the atmosphere. The kinetic and potential energy at the exit of the atmosphere determines the semi-major axis of the post-atmospheric orbit:

[0028]

[0029] Preferably, S3 is as follows:

[0030] A new independent variable is introduced:

[0031]

[0032] This variable represents the negative value of the orbital energy, ignoring the J2 perturbation and the rotation of the celestial body, and its derivative with respect to time is:

[0033]

[0034] If e is monotonically increasing during the crossing of the atmosphere, then the longitudinal motion equations are grouped using e as the independent variable:

[0035]

[0036]

[0037]

[0038] Processing equation (16), the roll control variable is extracted, and the following is obtained:

[0039]

[0040] where σ cmd is the roll angle command.

[0041] Preferably, S4 is as follows:

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

[0043]

[0044] Among them, K, N, A0, A1, B0, B1, B2 are the coefficients of the corresponding fitting function, B1 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 profile; γ0 is the current track angle of the spacecraft; γ f is the track angle at the terminal of aerodynamically assisted orbit lowering.

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

[0046]

[0047] Further sorting out:

[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 fuel-optimized aerodynamically assisted orbit descent as much as possible, the guidance can be divided into three stages:

[0055] A1. Initial descent open-loop guidance phase: The bank angle command remains constant:

[0056] σ cmd =σ0 (24)

[0057] Among them, σ0 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.

[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 selectedswi 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). By adjusting e swi The radius r of the orbital apocenter 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 is still maintained cmd =σ0; if 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 (γ0, e0) and the 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 predicted efficiently (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 r of the orbital apocenter 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 in 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, a mapping relationship between the roll angle control variable and the track angle and other states is constructed, and an analytical expression of the guidance command is derived, which realizes efficient prediction-correction guidance, requires low computing power of the equipment, and ensures the real-time performance of the guidance;

[0065] (2) By correcting the roll angle, a trajectory 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 reduction;

[0066] (3) The derivation is based on the energy that changes monotonically throughout the atmospheric flight as the independent variable. It can provide guidance during both the descent and ascent phases, and has 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 embodiment of the present invention in the Earth aerodynamically assisted orbit reduction scenario;

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

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

[0073] Figure 5 This is the roll angle control profile obtained by the guidance of an 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 claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0075] See also Figure 1 A fuel consumption-optimized aerodynamically assisted orbit lowering efficient prediction-correction guidance method includes the following steps:

[0076] S1. Establish a dynamic model for the atmospheric flight phase of a spacecraft aerodynamically assisted orbit reduction that takes into account the effects of celestial body rotation and J2 perturbation. The atmospheric flight dynamics model for a spacecraft aerodynamically assisted orbit reduction is a three-degree-of-freedom dynamics equation. The longitudinal plane motion equation is extracted by decoupling the three-degree-of-freedom dynamics equation.

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

[0078]

[0079] Among them, r represents the radius 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 the control variable of 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 the lift coefficient and drag coefficient respectively; m is the dimensionless mass of the spacecraft; R0 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; J2 represents the celestial body's dynamical flattening; and ω is the celestial body's rotational angular velocity. To facilitate subsequent derivation, the spacecraft's longitudinal motion parameters: 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 for the spacecraft after it exits the atmosphere and enters the target orbit.

[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 radius vector, inertial velocity, and track angle at 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 energy, 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 increases monotonically during 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 formula (16), extracting the roll angle control amount, we get

[0107]

[0108] where σ cmd is the bank angle command.

[0109] S4, the trajectory characteristic planning of the flight path angle profile based on the fuel-optimal aerodynamic assisted de-orbit, and then deducing the analytical expression of the guidance command.

[0110] The fuel-optimal aerodynamic assisted de-orbit has a bang-bang structure of the bank angle control profile in theory. Considering that sinγ≈γ when the flight path angle is near 0, according to the optimalγ-e profile characteristics under different scenarios, the segmented expression about e can be designed to parameterize the sinγterm, for example:

[0111]

[0112] where K, N, A0, A1, B0, B1, B2 are the coefficients of the corresponding fitting functions, B1 is a preset coefficient, and the values of the remaining coefficients can be determined by two-point boundary information; e swi is the bang-bang switching point of the control profile; γ0 is the current flight path angle of the spacecraft; γ f is the flight path angle of the terminal of the aerodynamic assisted de-orbit.

[0113] When e>e swi , the derivative of formula (19) about e is obtained, and the chain rule is used to obtain:

[0114]

[0115] Further arrangement obtains:

[0116]

[0117] Substituting the above formula into formula (18) obtains:

[0118]

[0119] Then the closed-loop bank angle guidance command is:

[0120]

[0121] S5, according to the trajectory characteristics of the fuel-optimal aerodynamic assisted de-orbit and the analytical expression of the guidance command, an efficient predictive-correction guidance scheme is designed.

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

[0123] A1. Initial descent open-loop guidance phase: The bank angle command remains constant:

[0124] σ cmd =σ0 (24)

[0125] Among them, σ0 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). By adjusting e swi The radius r of the orbital apocenter 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 is still maintained cmd =σ0; if 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 (γ0, e0) and the 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 predicted efficiently (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 r of the orbital apocenter after leaving the atmosphere can be changed a0 To match the apocenter radius r of the target orbitatgt , 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 in 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 using the guidance method of this embodiment as follows: Figure 2 As shown in Figure 2, the spacecraft speed mainly decays in the 60-75km altitude range, and decreases to about 7.8km / s when leaving the atmosphere. The roll angle control profile in this scenario is shown in Figure 2. Figure 3 As shown, after switching to closed-loop prediction-correction guidance, the roll angle first rolls to around 130 degrees before gradually saturating to 180 degrees. Under the guidance method of this embodiment, the velocity increment required for the spacecraft to enter the target orbit after exiting the atmosphere is 60.3 m / s, 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 using the guidance method of this embodiment as follows: Figure 4 As shown in Figure 2, the spacecraft speed mainly decays in the 35-50km altitude range, and decreases to about 3.9km / s when leaving the atmosphere. The roll angle control profile in this scenario is shown in Figure 2. Figure 5 As 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 trajectory is 54.2m / s, which is close to the theoretical optimal fuel consumption value.

[0132] Therefore, the present invention adopts the above-mentioned fuel-optimized 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 solutions of the present invention rather than to limit the same. 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 solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A fuel-optimized aerodynamically assisted orbit lowering and efficient prediction-correction guidance method, characterized by: The following steps are involved: S1. Establish a dynamic model for the atmospheric flight phase of the spacecraft aerodynamically assisted orbit reduction, taking into account the effects of celestial body rotation and J2 perturbation. The atmospheric flight dynamics model for the spacecraft aerodynamically assisted orbit reduction is a three-degree-of-freedom dynamics equation. Decouple the three-degree-of-freedom dynamics equation to extract the longitudinal plane motion equation. S2. Build a model for the impulse maneuvers required for the spacecraft to exit the atmosphere and enter the target orbit; S3. Perform variable substitution to convert the independent variable from time to energy, and obtain the mapping relationship between the roll angle control amount and the track angle state; S4. Plan the flight path angle profile based on the trajectory characteristics of the fuel-optimized aerodynamically assisted orbit descent, 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 aerodynamically assisted orbit descent and the analytical expression of the guidance instructions.

2. The fuel consumption optimized aerodynamic assisted orbit lowering high-efficiency prediction-correction guidance method according to claim 1 is characterized in that: S1 content is as follows: The dimensionless three-degree-of-freedom dynamic equation of the spacecraft during the aerodynamically assisted orbit reduction flight is: (1) in, Characterizes the radius vector from the center of the celestial body to the center of mass of the spacecraft; Represents longitude; Characterize latitude; Characterize the speed of the spacecraft relative to the celestial body; Characterizes the track angle of the velocity vector relative to the celestial body; Characterizes the heading angle; Characterize the bank angle as a control variable during flight; It represents the angular velocity of the celestial body's rotation; (2) (3) in, and Respectively represent the aerodynamic lift acceleration and aerodynamic drag acceleration; is the dimensionless atmospheric density; is the dimensioned spacecraft reference area; , are the lift coefficient and the drag coefficient respectively; is the dimensioned spacecraft mass; is the equatorial radius of the celestial body; (4) (5) in, and are the radial and latitudinal components of the dimensionless gravitational acceleration, respectively; Characterize the astrodynamic oblateness; The longitudinal motion parameter of the spacecraft: height ,speed and track angle Extracted from the three-degree-of-freedom dynamic equation (1), a simplified longitudinal decoupled motion model is constructed: (6) (7) (8)。 3. The fuel consumption optimized aerodynamic assisted orbit lowering high-efficiency prediction-correction guidance method according to claim 2, characterized in that: The content of S2 is as follows: After the spacecraft passes through and flies out of the atmosphere, the spacecraft performs pulse adjustments during the exoatmospheric flight phase to establish the desired target orbit. The total velocity increment required is for: (9) Where, , are the apocenter radius and pericenter radius of the target orbit respectively; For a single pulse maneuver, ; and are the apocenter and pericenter radii of the orbit after leaving the atmosphere, such as Equations (10) and (11): (10) (11) Where, is the semi-major axis of the track after aerodynamic capture; 、 and are the radius 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: (12)。 4. The fuel consumption optimized aerodynamic assisted orbit lowering high-efficiency prediction-correction guidance method according to claim 3 is characterized in that: The S3 content is as follows: Introduce a new independent variable: (13) This variable characterizes the negative value of the 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: (14) In the process of passing through the atmosphere, it is monotonically increasing, so Substituting the time variable, the longitudinal motion equations are transformed into: (15) (16) (17) By processing Equation (16) and extracting the roll angle control value, we can obtain: (18) in, Roll angle guidance command.

5. The fuel consumption optimized aerodynamic assisted orbit lowering high-efficiency prediction-correction guidance method according to claim 4 is characterized in that: S4 content is as follows: When the track angle is near 0, , according to the optimal - Sectional features, design about Parameterize the piecewise expression Item, as shown in formula (19): (19) in, , , , , , , are the coefficients of the corresponding fitting function; is the preset coefficient; is the bang-bang switching point of the corresponding section; is the current track angle of the spacecraft; is the track angle of the aerodynamically assisted orbit lowering terminal; when When Taking the derivative and applying the chain rule we get: (20) Further sorting out: (21) Substituting formula (21) into formula (18) yields: (22) The closed-loop roll angle guidance command is: (23)。 6. The fuel consumption optimized aerodynamic assisted orbit lowering high-efficiency prediction-correction guidance method according to claim 5, characterized in that: S5 simulates the bang-bang control structure of aerodynamic-assisted descent with optimal fuel consumption. The guidance is divided into the following three stages: A1. Initial descent open-loop guidance phase: The bank angle guidance command remains constant: (24) in, is a small constant value of the roll angle, when the track angle When it approaches 0, it enters the predicted switching point stage; A2. Predicting the switching point: The guidance parameter is taken as the energy corresponding to the switching point of the open-closed loop guidance. , in the selected Finally, the spacecraft state at the atmospheric exit is efficiently predicted based on the fitting function (19) and the parameters of the theoretical optimal fuel consumption profile. , and further determine the orbital parameters after the atmosphere through equations (9) to (12), by adjusting Change the orbital apocenter radius after leaving the atmosphere To match the apocenter radius of the target orbit , use the single variable root-finding method to determine the optimal guidance parameter ; Sure After that, if the current energy , then still maintain ;like , then switch to the closed-loop prediction-correction guidance stage; A3. Closed-loop prediction-correction guidance phase: The fitting function of the spacecraft state will pass through the preset point ,in is the preset point track angle, is the preset point energy; select As a correctable guidance parameter, it is based on the current state of the spacecraft and preset point information, calculate the coefficients of the fitting function in formula (19) through formula (25) and formula (26): (25) (26) After determining the fitting function, the spacecraft state at the atmospheric exit can be predicted , and further determine the orbital parameters after the atmosphere through equations (9) to (12); by adjusting Change the orbital apocenter radius after leaving the atmosphere To match the apocenter radius of the target orbit , use the single variable root-finding method to determine the optimal guidance parameter , and further determine the corresponding roll angle guidance command by formula (23) , which is repeated in each guidance cycle until the spacecraft flies out of the atmosphere.

Images