Energy substitution-based efficient generation method for optimal trajectory of pneumatic-assisted rail-descending fuel consumption

Abstract

The invention discloses an energy substitution-based efficient generation method for an optimal trajectory of aerodynamic-assisted orbit drop burn-up, which belongs to the field of aerospace and comprises the following steps of: establishing a spacecraft aerodynamic-assisted orbit drop flight dynamics model, extracting a motion equation in a longitudinal plane, converting an independent variable into a variable in an energy form, and generating the optimal trajectory of the aerodynamic-assisted orbit drop burn-up. Obtaining a height and energy decoupling differential equation, and parameterizing the change of the aerodynamic acceleration; designing a segmented parameterization expression of the track angle with respect to energy, and realizing high-precision fitting of the optimal track angle change; based on the fitting function, deriving an expression of terminal energy in different situations, and further predicting the trajectory speed; and corresponding speeds are calculated at different height points, a burnup optimal reference trajectory is efficiently generated, and it is guaranteed that the spacecraft is transferred to a target orbit with low burnup. According to the energy substitution-based efficient generation method for the optimal burnup trajectory of pneumatic auxiliary rail descending, provided by the invention, efficient generation of the subsequent optimal burnup trajectory can be realized no matter in a height descending section or a height ascending section.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a method for efficiently generating a fuel-optimal trajectory for aerodynamically assisted orbit reduction based on energy exchange. Background Art

[0002] The planetary atmospheric environment is complex, changeable and difficult to predict. When a spacecraft passes through the atmosphere and consumes excess energy with the help of aerodynamic forces to lower its own orbit, it needs to continuously predict and generate subsequent reference trajectories based on the measured state parameters, so as to correct the guidance and control instructions based on the reference trajectory information, realize the adjustment of the spacecraft's flight trajectory, and ensure that it flies out of the atmosphere and transfers to the target orbit with lower fuel consumption. At present, there are two main methods for generating reference trajectories: numerical methods and analytical methods. The numerical method is based on the reference control profile and recursively deduces the subsequent trajectory through the numerical integration of the dynamic equations. It has high accuracy but is very dependent on the accuracy of the model and the computing power of the equipment. It is currently difficult to apply it online on the spacecraft. In contrast, the analytical method predicts and generates the subsequent trajectory by deriving the analytical expression of the trajectory. It has high computational efficiency and has the potential for real-time online application. However, the analytical method is usually less adaptable. When faced with different mission scenarios and parameter uncertainties, the accuracy of trajectory prediction is difficult to guarantee.

[0003] Among the existing methods for efficient trajectory generation of aerodynamically assisted orbit descent, the prior art (see: Cihan IH, Kluever CA. Analytical Earth-Aerocapture Guidance with Near-Optimal Performance [J]. Journal of Guidance, Control, and Dynamics, 2020, 44 (1): 45-56.) proposed an analytical method for reference fuel-optimal aerodynamic capture trajectory characteristics, which solves the explicit expression of the atmospheric exit velocity by parameterizing aerodynamic parameters and track angle-altitude profile. This method can be applied to the generation and prediction of the ascent trajectory in the scenario of full aerodynamic deceleration, but its derivation is based on a dynamic model with altitude as the independent variable, and it assumes that the altitude changes monotonically. Therefore, it cannot be applied to the generation and prediction of the trajectory in the initial descent phase, and is not universal and adaptable to different mission scenarios. Summary of the invention

[0004] The purpose of the present invention is to provide a method for efficiently generating a fuel-optimal trajectory for aerodynamically assisted orbit lowering based on energy exchange, so as to solve the problems mentioned in the background technology.

[0005] To achieve the above object, the present invention provides a method for efficiently generating a fuel-optimal trajectory for aerodynamically assisted orbit lowering based on energy exchange, comprising the following steps:

[0006] S1. Establish a dynamics model of aerodynamically assisted orbit reduction flight for spacecraft that takes into account the effects of celestial body rotation and oblateness. The dynamics model of aerodynamically assisted orbit reduction flight for spacecraft is a three-degree-of-freedom dynamics equation. The motion equation in the longitudinal plane is extracted by decoupling the three-degree-of-freedom dynamics equation.

[0007] S2. Perform variable substitution to convert the independent variable from time to energy form, obtain the differential equation for decoupling height from energy, and use the fitting function with height as the independent variable to parameterize the change of aerodynamic acceleration;

[0008] S3. Based on the trajectory characteristics of the aerodynamically assisted orbit descent with optimal fuel consumption, a piecewise parameterized expression of the track angle with respect to energy is designed to achieve high-precision fitting of the optimal track angle change in different and similar scenarios;

[0009] S4. Based on the fitting functions of the aerodynamic drag acceleration and the track angle in S2 and S3, the expression of the terminal energy is derived in different cases. When the fitting function is determined, the solution process of the terminal state integral expression is not affected by the non-monotonic change of the altitude. The trajectory speed is predicted by solving the subsequent trajectory energy in both the descent and ascent phases of the aerodynamic assisted maneuver.

[0010] S5. Based on the trajectory velocity solution method obtained in S4, the corresponding velocity magnitudes at different altitudes along the trajectory are predicted, and an aerodynamically assisted orbit lowering reference trajectory is quickly generated to assist the spacecraft in maneuvering during flight, so that the spacecraft can enter the target orbit with low fuel consumption while meeting the mission constraints.

[0011] Preferably, the content of S1 is as follows:

[0012] The three-degree-of-freedom dynamic equation of the spacecraft during the aerodynamic-assisted orbit reduction flight is as follows:

[0013]

[0014] Among them, the variables are dimensionless quantities, r represents the radial vector from the center of the celestial body to the center of mass of the spacecraft; θ represents longitude; φ represents 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 angle during the flight process; L and D They represent the dimensionless aerodynamic lift acceleration and aerodynamic drag acceleration, respectively, as shown in equations (2) and (3):

[0015]

[0016]

[0017] Where ρ is the dimensional atmospheric density; S is the dimensional spacecraft reference area; C L , CD are the lift coefficient and drag coefficient respectively; m is the dimensioned mass of the spacecraft; R0 is the equatorial radius of the celestial body; g r and g φ are the radial and latitudinal components of the dimensionless gravitational acceleration, such as equations (4) and (5):

[0018]

[0019] Among them, J2 represents the dynamical flattening of the celestial body; ω is the angular velocity of the celestial body's rotation;

[0020] 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:

[0021]

[0022]

[0023] Preferably, the content of S2 is as follows:

[0024] Introduce a new independent variable:

[0025]

[0026] This variable represents the negative value of orbital energy. Ignoring the effects of celestial body flattening and rotation, the derivative with respect to time is:

[0027]

[0028] 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:

[0029]

[0030] Substituting equation (3) and equation (13) into equation (11), we obtain:

[0031]

[0032] During the whole process of pneumatic assisted track change, Close to 1 but less than 1, and with small changes, so the constant C is used r Substituting (14) And separating the variables gives:

[0033]

[0034] The variable on the left side of formula (15) is related to the height, and the fitting function f D (h) to parameterize ρC D / m:

[0035]

[0036] Among them, f D (h) is a fitting function of any form that can be explicitly integrated.

[0037] Preferably, the content of S3 is as follows:

[0038] The fuel-optimal aerodynamically assisted orbit descent theoretically has a roll angle control profile with a bang-bang structure; 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:

[0039]

[0040] Among them, K, N, A0, A1, B0, B1, B2 are the coefficients of the corresponding fitting function, and their values ​​are determined by the two-point boundary value information; swi The bang-bang switching point corresponding to the control profile; γ0 is the initial track angle of the spacecraft; γ f is the track angle of the aerodynamically assisted orbit lowering terminal;

[0041] Substituting equation (16) and equation (17) into equation (15), we obtain:

[0042]

[0043] Preferably, the content of S4 is as follows:

[0044] During the flight, the spacecraft determines the initial state corresponding to the current moment through the navigation measurement system; Integrate both sides of equation (18) from the initial state (e0, h0, γ0) to the terminal state (e f ,h f ,γ f ), when the integral interval does not cross the switching point e swi When , the integral expressions are:

[0045]

[0046] in, is an explicit integral expression; the equation (19) is analyzed in different cases:

[0047] A1. When e≤e swi When , we can rearrange formula (19) to obtain:

[0048]

[0049] When h f When it is known, formula (20) is about e fA one-variable nonlinear equation;

[0050] A2. When e>e swi When the track angle decreases, e is obtained by formula (19): f The analytical expression of e f It can be solved numerically quickly:

[0051]

[0052] in,

[0053]

[0054] A3. When e>e swi When the track angle increases, the formula (19) can be used to obtain:

[0055]

[0056] When h f When it is known, formula (23) is about e f A nonlinear equation in one variable, e f Can be solved numerically quickly;

[0057] A4. When the integral interval contains the switching point, e swi ∈(e0,e f ), perform piecewise integration:

[0058]

[0059] in,

[0060]

[0061] Refer to the process of A2 and A3 to solve e f ; After getting e f Then, the terminal velocity V is obtained by formula (13): f .

[0062] Preferably, the content of S5 is as follows:

[0063] From equations (20), (21), (23) and (24), we know that during the aerodynamic-assisted orbit descent process, when the current state of the spacecraft and the fitting function are given, the velocity V of each point on the subsequent trajectory is a function of the height h at that point, denoted as V = Z(h). N discrete points are taken on the subsequent trajectory to form a height set:

[0064] S h ={h i |h i ≤h EI ,i=1,2,...,N} (26)

[0065] Among them, h EI is the height corresponding to the atmospheric boundary; for the set S h Each height h in i , both by V i = Z(h i ) calculates the speed at the corresponding height and forms a speed set:

[0066] S V = {V i |V i = Z(h i ),i=1,2,...,N} (27)

[0067] According to the set S h , S V Rapidly generate open-loop reference trajectories for aerodynamically assisted orbit descent.

[0068] Therefore, the present invention adopts the above-mentioned method for efficiently generating the optimal trajectory of aerodynamically assisted orbit reduction based on energy exchange, which has the following beneficial effects:

[0069] (1) Through energy substitution and parameter fitting based on the characteristics of the optimal trajectory for fuel consumption, the expressions of trajectory energy and speed are derived, which enables efficient generation of the optimal trajectory for fuel consumption. This reduces the computing power requirements of the equipment and ensures the real-time performance of online trajectory generation.

[0070] (2) By converting the dynamic independent variable into a variable in the form of energy that increases monotonically throughout the process, it is ensured that the spacecraft can efficiently generate subsequent trajectories during the descent or ascent phase, thus expanding the application range of the method;

[0071] (3) There are no strict requirements on the specific form of the aerodynamic parameter fitting function, and the fitting function can be updated according to the aerodynamic data measured during the flight of the spacecraft to ensure that the real-time changes of the aerodynamic parameters can be reflected, which reduces the dependence on the aerodynamic model and improves the flexibility of the method;

[0072] (4) The characteristics of optimal trajectories with different fuel consumption are taken into account, and the system can adapt to significant changes in the atmospheric environment, entry track angle, and target orbit parameters, making it suitable for various aerodynamically assisted orbit reduction mission scenarios.

[0073] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is a flow chart of a method for efficiently generating a fuel consumption optimal trajectory for aerodynamically assisted orbit lowering based on energy exchange according to an embodiment of the present invention;

[0075] Figure 2Generate a trajectory for this embodiment in the Earth Aerodynamic Assisted Orbit Descent scenario in the embodiment of the present invention (the starting point is located in the descending section);

[0076] Figure 3 Generate a trajectory for the Mars aerodynamic assisted orbit descent scenario in the embodiment of the present invention (the starting point is located in the descent stage);

[0077] Figure 4 The trajectory comparison is generated in the earth aerodynamic assisted orbit descending scenario in the embodiment of the present invention (the starting point is located in the ascending stage);

[0078] Figure 5 This is a trajectory comparison generated for the Mars aerodynamic assisted orbit descent scenario in an embodiment of the present invention (the starting point is located in the ascending stage). DETAILED DESCRIPTION

[0079] 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.

[0080] Consider two scenarios of aerodynamically assisted orbit lowering, and their entry conditions are shown in the following table:

[0081] Table 1 Inertial entry conditions in two scenarios

[0082]

[0083]

[0084] In the Earth scenario, the target orbit is a circular orbit with an altitude of 200×200km; in the Mars scenario, the target orbit is an elliptical orbit with an altitude of 3000×300km. The parameter model of the spacecraft takes the Orion multi-purpose manned spacecraft as an example. Figure 1 The specific implementation steps of the efficient generation method of the optimal trajectory for aerodynamically assisted orbit reduction based on energy substitution are as follows:

[0085] S1. Establish a spacecraft aerodynamic-assisted orbit reduction flight dynamics model that takes into account the effects of celestial body rotation and oblateness. The spacecraft aerodynamic-assisted orbit reduction flight dynamics model is a three-degree-of-freedom dynamics equation, and the motion equation in the longitudinal plane is extracted by decoupling the three-degree-of-freedom dynamics equation.

[0086] The three-degree-of-freedom dynamic equation of the spacecraft during the aerodynamic-assisted orbit reduction flight is:

[0087]

[0088] Among them, the variables are all dimensionless quantities, r represents the radius vector from the center of the celestial body to the center of mass of the spacecraft; θ represents longitude; φ represents 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 angle during the flight process; L and D represent the dimensionless aerodynamic lift acceleration and aerodynamic drag acceleration, respectively.

[0089]

[0090] Where ρ is the dimensional atmospheric density, S is the dimensional spacecraft reference area, and C L , C D are the lift coefficient and drag coefficient respectively, m is the dimensioned mass of the spacecraft, R0 is the equatorial radius of the celestial body; g r and g φ are the radial and latitudinal components of the dimensionless gravitational acceleration,

[0091]

[0092] Among them, J2 represents 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, namely the 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:

[0093]

[0094] S2. Perform variable substitution to convert the independent variable from time to energy form, obtain the differential equation that decouples altitude from energy, and use the fitting function with altitude as the independent variable to parameterize the change of aerodynamic acceleration.

[0095] Introduce a new independent variable:

[0096]

[0097] This variable represents the negative value of orbital energy. Ignoring the effects of celestial body flattening and rotation, the derivative with respect to time is:

[0098]

[0099] 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:

[0100]

[0101] Substituting equation (3) and equation (13) into equation (11), we obtain:

[0102]

[0103] Considering the whole process of pneumatic assisted track change, It is close to 1 (but less than 1) and has a small change, so the constant C can be used r Substituting And separating the variables gives:

[0104]

[0105] The variables on the left side of the above equation are mainly related to the height, and the fitting function f D (h) to parameterize ρC D / m:

[0106]

[0107] Among them, f D (h) is an arbitrary form of fitting function that can be explicitly integrated. In this embodiment, a sixth-order polynomial function can be used:

[0108] S3. Based on the trajectory characteristics of the aerodynamically assisted orbit descent with optimal fuel consumption, a piecewise parameterized expression of the track angle with respect to energy is designed to achieve high-precision fitting of the optimal track angle changes in different scenarios.

[0109] The fuel-optimized aerodynamically assisted orbit reduction has a bang-bang structured roll angle control profile in theory. In this embodiment, the track angle shows a decreasing trend after the switching point in the Earth scenario, while the track angle shows an increasing trend after the switching point in the Mars scenario. 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 is designed to parameterize the sinγ term:

[0110]

[0111] Among them, K, N, A0, A1, B0, B1, B2 are the coefficients of the corresponding fitting function, and their values ​​can be determined by the boundary value information of the two points; swi The bang-bang switching point corresponding to the control profile; γ0 is the initial track angle of the spacecraft; γ f is the track angle of the aerodynamically assisted orbit lowering terminal.

[0112] Substituting equation (16) and equation (17) into equation (15), we obtain:

[0113]

[0114] S4. Based on the fitting functions of aerodynamic drag acceleration and track angle in S2 and S3, the expression of terminal energy is derived for each case to predict the trajectory speed.

[0115] During the flight, the spacecraft can determine the initial state corresponding to the current moment through the navigation measurement system. Integrate both sides of the above equation from the initial state (e0, h0, γ0) to the terminal state (e f ,h f ,γ f ), when the integral interval does not cross the switching point e swi When , the integral expressions are:

[0116]

[0117] in, is an explicit integral expression. Analyze the above equation in different cases.

[0118] A1. When e≤e swi When , we can rearrange the above formula to get:

[0119]

[0120] When h f When it is known, the above formula is about e f A nonlinear equation in one variable, e f It can be solved numerically quickly.

[0121] A2. When e>e swi When the track angle decreases, e can be obtained from formula (19): f The analytical expression of is:

[0122]

[0123] in,

[0124]

[0125] A3. When e>e swi When the track angle increases, we can get

[0126]

[0127] When h f When it is known, the above formula is about e f A nonlinear equation in one variable, e f It can be solved numerically quickly.

[0128] A4. When the integral interval contains the switching point, that is, e swi ∈(e0,e f ), a piecewise integration is required:

[0129]

[0130] in,

[0131]

[0132] Therefore, we can refer to the process of A2 and A3 to solve e f .

[0133] Get e f Then, the terminal velocity V can be obtained by formula (13): f It can be seen that when the fitting function is determined, the solution process of the above integral is not affected by the non-monotonic change of altitude, so the subsequent trajectory velocity can be efficiently solved regardless of the descent or ascent phase of the aerodynamic-assisted maneuver.

[0134] S5. Based on the efficient solution method for trajectory velocity obtained in S4, the corresponding velocity magnitude is predicted at different altitude points along the trajectory, and the aerodynamically assisted orbit lowering reference trajectory is quickly generated to assist the spacecraft in maneuvering during flight. Under the premise of meeting the mission constraints, it is ensured that the spacecraft accurately enters the target orbit with less fuel consumption.

[0135] During the aerodynamically assisted orbit descent process, given the current state of the spacecraft and the fitting function, the velocity V of each point on the subsequent trajectory will be a function of the height h at that point, denoted as V = Z(h). Take N discrete points on the subsequent trajectory to form a height set:

[0136] S h ={h i |h i ≤h EI ,i=1,2,...,N} (26)

[0137] Among them, h EI is the height corresponding to the atmospheric boundary. h Each height h in i , can be obtained by V i = Z(h i ) calculates the speed at the corresponding height and forms a speed set:

[0138] S V = {V i |V i = Z(h i ),i=1,2,...,N} (27)

[0139] According to the set S h , S V That is, the open-loop reference trajectory of aerodynamic-assisted orbit descent is quickly generated. This reference trajectory can be used in the guidance and control link to assist the spacecraft in maneuvering and ensure that the spacecraft accurately enters the target orbit with less fuel consumption while meeting the mission constraints.

[0140] In this embodiment, the initial state of the spacecraft is first set in the altitude descent phase, and the subsequent trajectory is efficiently generated. It is compared with the theoretical optimal trajectory of fuel consumption obtained by numerically integrating the dynamic equations (1) based on the bang-bang control structure. The results under different scenarios are as follows: Figure 2 and Figure 3 It can be seen that in both scenarios, the generated trajectory of this embodiment can be closely close to the theoretical optimal trajectory, indicating that the trajectory quickly generated by this embodiment starting from the descending stage can maintain a small error with the theoretical optimal trajectory.

[0141] Furthermore, the initial state of the spacecraft was set in the altitude ascent phase, and the subsequent trajectory was quickly generated and compared with the theoretical optimal trajectory and the ascent phase trajectory generated by the existing technical methods, such as Figure 4 and Figure 5 As shown. It can be seen that in both scenarios, compared with the existing technical methods, the trajectory generated by this embodiment is obviously closer to the theoretical optimal trajectory, indicating that this embodiment can efficiently generate a trajectory close to the theoretical optimal fuel consumption in mission scenarios with significantly different conditions, reflecting the flexibility and adaptability of the method, and can lay a solid foundation for the generation of subsequent spacecraft guidance and control instructions.

[0142] Therefore, the present invention adopts the above-mentioned method for efficiently generating the optimal trajectory for aerodynamically assisted orbit reduction based on energy substitution, and constructs and derives the correlation expressions of the track angle, altitude and speed in the process of aerodynamically assisted orbit reduction through variable substitution and optimal profile approximation. This can achieve efficient generation of the subsequent optimal trajectory for fuel consumption regardless of the altitude descent or ascent phase of the spacecraft.

[0143] 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 method for efficiently generating an optimal trajectory for aerodynamically assisted orbit reduction based on energy substitution, characterized in that: S1. Establish a dynamics model of aerodynamically assisted orbit reduction flight for spacecraft that takes into account the effects of celestial body rotation and oblateness. The dynamics model of aerodynamically assisted orbit reduction flight for spacecraft is a three-degree-of-freedom dynamics equation. The motion equation in the longitudinal plane is extracted by decoupling the three-degree-of-freedom dynamics equation. S2. Perform variable substitution to convert the independent variable from time to energy form, obtain the differential equation for decoupling height from energy, and use the fitting function with height as the independent variable to parameterize the change of aerodynamic acceleration; S3. Based on the trajectory characteristics of the aerodynamically assisted orbit descent with optimal fuel consumption, a piecewise parameterized expression of the track angle with respect to energy is designed to achieve high-precision fitting of the optimal track angle change in different and similar scenarios; S4. Based on the fitting functions of the aerodynamic drag acceleration and the track angle in S2 and S3, the expression of the terminal energy is derived in different cases. When the fitting function is determined, the solution process of the terminal state integral expression is not affected by the non-monotonic change of the altitude. The trajectory speed is predicted by solving the subsequent trajectory energy in both the descent and ascent phases of the aerodynamic assisted maneuver. S5. Based on the trajectory velocity solution method obtained in S4, the corresponding velocity magnitudes at different altitudes along the trajectory are predicted, and an aerodynamically assisted orbit lowering reference trajectory is quickly generated to assist the spacecraft in maneuvering during flight, so that the spacecraft can enter the target orbit with low fuel consumption while meeting the mission constraints.

2. The method for efficiently generating the optimal trajectory for aerodynamically assisted orbit reduction based on energy exchange according to claim 1 is characterized in that: S1 content is as follows: The three-degree-of-freedom dynamic equation of the spacecraft during the aerodynamic-assisted orbit reduction flight is as follows: Among them, all variables are dimensionless quantities, r represents the radius vector from the center of the celestial body to the center of mass of the spacecraft; θ represents longitude; φ represents latitude; V represents the velocity of the spacecraft relative to the celestial body; ω is the angular velocity of 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 angle during the flight process; L and D represent the dimensionless aerodynamic lift acceleration and aerodynamic drag acceleration, respectively, as shown in equations (2) and (3): Where 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 dimensioned mass of the spacecraft; R0 is the equatorial radius of the celestial body; g r and g φ are the radial and latitudinal components of the dimensionless gravitational acceleration, such as equations (4) and (5): Among them, J2 represents the astrodynamic oblateness; 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 efficiently generating the optimal trajectory for aerodynamically assisted orbit reduction based on energy exchange according to claim 2 is characterized in that: The content of S2 is as follows: Introduce a new independent variable: This variable represents the negative value of orbital energy. Ignoring the effects of celestial body flattening and rotation, the derivative with respect to time is: 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: Substituting equation (3) and equation (13) into equation (11), we obtain: During the whole process of pneumatic assisted track change, Close to 1 but less than 1, and with small changes, so use the constant C r Substituting (14) And separating the variables gives: The variable on the left side of formula (15) is related to the height, and the fitting function f D (h) to parameterize ρC D / m: Among them, f D (h) is a fitting function of any form that can be explicitly integrated.

4. The method for efficiently generating the optimal trajectory for aerodynamically assisted orbit reduction based on energy exchange according to claim 3 is characterized in that: The S3 content is as follows: The fuel-optimal aerodynamically assisted orbit descent theoretically has a roll angle control profile with a bang-bang structure; 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: Among them, K, N, A0, A1, B0, B1, B2 are the coefficients of the corresponding fitting function, and their values ​​are determined by the two-point boundary value information; swi The bang-bang switching point corresponding to the control profile; γ0 is the initial track angle of the spacecraft; γ f is the track angle of the aerodynamically assisted orbit lowering terminal; Substituting equation (16) and equation (17) into equation (15), we obtain:

5. The method for efficiently generating the optimal trajectory for aerodynamically assisted orbit reduction based on energy exchange according to claim 4 is characterized in that: S4 content is as follows: During the flight, the spacecraft determines the initial state corresponding to the current moment through the navigation measurement system; Integrate both sides of equation (18) from the initial state (e0, h0, γ0) to the terminal state (e f ,h f ,γ f ), when the integral interval does not cross the switching point e swi When , the integral expressions are: in, is an explicit integral expression; the equation (19) is analyzed in different cases: A1. When e≤e swi When , we can rearrange formula (19) to obtain: When h f When it is known, formula (20) is about e f A nonlinear equation in one variable, e f Rapid numerical solution; A2. When e>e swi When the track angle decreases, e is obtained by formula (19): f The analytical expression of is: in, A3. When e>e swi When the track angle increases, the formula (19) can be used to obtain: When h f When it is known, formula (23) is about e f A nonlinear equation in one variable, e f Rapid numerical solution; A4. When the integral interval contains the switching point, e swi ∈(e0,e f ), perform piecewise integration: in, Refer to the process of A2 and A3 to solve e f ; After getting e f Then, the terminal velocity V is obtained by formula (13): f .

6. The method for efficiently generating the optimal trajectory for aerodynamically assisted orbit reduction based on energy exchange according to claim 5 is characterized in that: S5 content is as follows: From equations (20), (21), (23) and (24), we know that during the aerodynamic-assisted orbit descent process, when the current state of the spacecraft and the fitting function are given, the velocity V of each point on the subsequent trajectory is a function of the height h at that point, denoted as V = Z(h). N discrete points are taken on the subsequent trajectory to form a height set: S h ={h i |h i ≤h EI ,i=1,2,...,N} (26) Among them, h EI is the height corresponding to the atmospheric boundary; for the set S h Each height h in i , both by V i = Z(h i ) calculates the speed at the corresponding height and forms a speed set: S V ={V i |V i =Z(h i ),i=1,2,...,N} (27) According to the set S h , S V Rapidly generate open-loop reference trajectories for aerodynamically assisted orbit descent.

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