An analytical aerodynamic capture open-loop trajectory prediction method for multi-task scenarios

Abstract

The present invention discloses an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios, which belongs to the field of aerospace technology. The implementation method of the present invention is: extracting the motion equation in the longitudinal plane with altitude as the independent variable from the aerodynamic capture flight dynamics model of the spacecraft. Fitting the aerodynamic parameters according to the aerodynamic data measured in the descent phase of the spacecraft. Fitting the optimal profile characteristics when the track angle increases or decreases by means of a piecewise inverse proportional function. Deriving the analytical expression of the velocity with respect to altitude based on the motion equation in the longitudinal plane, constructing the velocity analytical expressions for the drag term and the gravity term in the velocity differential equation respectively, and adding the gravity effect as a correction term to the velocity analytical expression of the drag term, thereby obtaining a complete analytical form of the ascent trajectory velocity. Based on the complete analytical expression of the ascent trajectory velocity, an aerodynamic capture open-loop prediction trajectory is generated to ensure that the spacecraft accurately enters the target orbit with minimal fuel consumption.

Description

Technical Field

[0001] The present invention relates to an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios, and in particular to an analytical trajectory prediction method suitable for spacecraft performing aerodynamic capture maneuvers on Earth and Mars, belonging to the field of aerospace technology. Background Art

[0002] An aerocapture maneuver involves a spacecraft transitioning from a hyperbolic orbit to an elliptical orbit through a single atmospheric transit. Compared to traditional orbital maneuvers using thrusters alone, aerocapture leverages the target planet's atmosphere to reduce the spacecraft's velocity, saving significant fuel and enabling the spacecraft to carry a larger payload. However, this translates to higher peak heat flux. Furthermore, the aerocapture process is subject to numerous parameter uncertainties and perturbations, making the flight process more dangerous. Therefore, it is necessary to predict the subsequent trajectory based on the spacecraft's current state and measured parameters to assist in maneuvering, accurately entering the target orbit, and meeting mission constraints. Currently, trajectory prediction primarily involves numerical and analytical methods. Numerical prediction derives the subsequent trajectory by numerically integrating the spacecraft's dynamic equations. While this method can guarantee accurate predictions provided the model is accurate, it places high demands on the computing power of the device, making it difficult to implement in real-time online applications. Analytical prediction, on the other hand, derives an analytical form of the trajectory to deduce the subsequent trajectory. This method offers high computational efficiency and potential for real-time online applications, but it is generally less adaptable and poses challenges in ensuring accurate predictions under varying mission scenarios and perturbations.

[0003] Among the analytical trajectory prediction methods developed for aerodynamic capture, the prior art [1] (see: Cerimele C, Gamble JA simplified guidance algorithm for lifting aeroassist orbital transfer vehicles [C] / / 23rd Aerospace Sciences Meeting. 1985: 348.) proposed a simple analytical trajectory prediction method for Earth aerodynamic capture. Based on the reference altitude change rate required to reach the target apogee altitude, an analytical expression for the velocity on the trajectory was derived, and the control of the exit phase was implemented. However, this method requires the assumption that the reference altitude change rate is a constant, which not only produces a large error, but also fails to consider the optimality of the trajectory.

[0004] Prior art [2] (see: Cihan IH, Kluever CA. Analytical Earth-Aerocapture Guidance with Near-Optimal Performance [J]. Journal of Guidance, Control, and Dynamics, 2020: 1-12.) proposed an analytical prediction method based on the fuel-optimal aerodynamic capture trajectory profile, which uses an analytical function of atmospheric density and track angle to predict the atmospheric exit velocity, and tracks the target apogee altitude by interpolating the exit track angle. This method can be used to predict aerodynamic capture trajectories with a small track angle in the Earth scenario, but for other scenarios, such as large track angles, its prediction accuracy cannot be guaranteed, or even fails completely, and therefore lacks versatility and adaptability to multi-task modes. Summary of the Invention

[0005] The main purpose of the present invention is to provide an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-mission scenarios. By constructing and deriving analytical expressions for the track angle and velocity in the aerodynamic capture trajectory, a fast and high-precision analytical prediction of the spacecraft aerodynamic capture trajectory is achieved. The present invention is applicable to a variety of mission scenarios, including different planetary atmospheric environments and different entry track angles. The present invention has the following advantages: (1) fast trajectory prediction speed, strong real-time performance, and online application capability; (2) high flexibility and applicability to a variety of mission scenarios; (3) wide applicability to planetary atmospheric environments; and (4) no strict restrictions or constraints on the track angle of the spacecraft entering and exiting the atmosphere.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] The present invention discloses an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-mission scenarios. It establishes a spacecraft aerodynamic capture flight dynamics model that takes into account the influence of J2 perturbation and celestial body rotation, and decouples and extracts a simplified longitudinal plane motion equation with altitude as the independent variable from the spacecraft aerodynamic capture flight dynamics model. Based on the aerodynamic data measured during the descent phase of the spacecraft, a high-order polynomial is used to fit the aerodynamic parameters to characterize the comprehensive changes in the actual atmospheric environment and the aerodynamic performance of the spacecraft, facilitating the derivation of subsequent velocity analytical expressions. According to the initial state of the spacecraft and the atmospheric exit conditions, based on the trajectory profile characteristics with optimal fuel consumption, a fitting function expression of the track angle with respect to altitude is given. The optimal profile characteristics when the track angle increases or decreases are fitted using a piecewise inverse proportional function, and high-precision fitting of the track angle with respect to altitude changes can be achieved in different track angle change scenarios. Based on the aerodynamic parameter fitting function and the track angle fitting function, an analytical expression for velocity with respect to altitude is derived from the equation of motion in the longitudinal plane. Analytical velocity expressions are constructed for the drag and gravity terms in the velocity differential equation, and the gravitational effect is added as a correction term to the analytical velocity expression for the drag term. This results in a complete analytical form for the ascent trajectory velocity, improving the efficiency of trajectory velocity prediction. Based on this complete analytical expression for the ascent trajectory velocity, the corresponding velocity magnitudes are predicted at different altitudes, generating an open-loop prediction trajectory for aerodynamic capture. This predicted trajectory assists the spacecraft in maneuvering during the aerodynamic capture process, ensuring that the spacecraft accurately enters the target orbit with minimal fuel consumption while meeting mission constraints.

[0008] The present invention discloses an analytical aerodynamic capture open-loop trajectory prediction method applicable to multi-task scenarios, comprising the following steps:

[0009] Step 1: Establish a spacecraft aerodynamic capture flight dynamics model that takes into account the effects of J2 perturbation and celestial body rotation. The spacecraft aerodynamic capture flight dynamics model is a three-degree-of-freedom dynamics equation, and the motion equation in the longitudinal plane is decoupled and extracted from the three-degree-of-freedom dynamics equation.

[0010] The three-degree-of-freedom dynamic equation of the spacecraft during aerodynamic capture flight is:

[0011]

[0012] Where r is the radial distance from the center of the Earth to the center of mass of the spacecraft; θ is the longitude; φ is the latitude; V is the velocity of the spacecraft relative to the celestial body; γ is the track angle of the velocity vector relative to the celestial body, that is, the ballistic inclination angle; ψ is the heading angle, that is, the ballistic deviation angle, which is positive when it turns clockwise from due north to the projection of the relative velocity vector of the celestial body on the local horizontal plane; σ is the roll angle, which is the control angle of the spacecraft aerodynamic capture process; L and D are the aerodynamic lift acceleration and aerodynamic drag acceleration, respectively.

[0013]

[0014]

[0015] Where ρ is the atmospheric density, S is the aircraft reference area; g r and g φ are the radial and latitudinal components of gravitational acceleration,

[0016]

[0017]

[0018] Where μ is the gravitational parameter of the celestial body, R0 is the equatorial radius of the celestial body, J2 is the celestial body's dynamical flattening, and ω is the celestial body's rotational angular velocity. When the spacecraft is performing aerodynamic capture, the initial state is usually given in real time based on the navigation measurement system. Therefore, the initial state constraint is x0 = [r0, θ0, φ0, V0, γ0, ψ0] T In order to facilitate the subsequent derivation of the trajectory analytical solution, it is necessary to separate the longitudinal motion parameters of the spacecraft, namely the altitude, velocity and track angle, to form a simplified longitudinal decoupled motion model. Since the radial distance r is the sum of the radius R0 and the altitude h of the celestial body, the change in the radius of the celestial body during the aerodynamic capture maneuver is negligible, and the time rate of change of the radial velocity and altitude can be equated. In the absence of the celestial body's oblateness and rotation terms, the motion equation in the longitudinal plane can be extracted from the three-degree-of-freedom dynamic equation (1):

[0019]

[0020]

[0021]

[0022] Changing the independent variable from time to height h, we get

[0023]

[0024]

[0025] Step 2: Based on the aerodynamic data measured during the spacecraft's descent, a high-order polynomial is used to fit the aerodynamic parameters, facilitating the subsequent derivation of analytical expressions for velocity. Because the aerodynamic parameters are derived from real-time aerodynamic data, the corresponding fitted polynomial can represent the combined changes in the actual atmospheric environment and the spacecraft's aerodynamic performance.

[0026] During the descent phase of the aerodynamic capture, the spacecraft continuously measures the lift acceleration L and drag acceleration D at the corresponding altitude. According to the previous definition, each aerodynamic acceleration involves the product of the atmospheric density ρ and the corresponding aerodynamic coefficient divided by the mass. A sixth-order or higher polynomial parameterized by altitude is selected to parameterize ρC. L / m and ρC D / m:

[0027]

[0028]

[0029] where a n , b n is a constant coefficient and n is the degree of the corresponding term.

[0030] Step 3: According to the initial state of the spacecraft and the atmospheric exit conditions, based on the trajectory profile characteristics with optimal fuel consumption, a fitting function expression of the track angle with respect to altitude is given. The optimal profile characteristics when the track angle increases or decreases are fitted through a piecewise inverse proportional function. High-precision fitting of the track angle with respect to altitude changes can be achieved in different track angle change scenarios.

[0031] When the performance indicator is the minimum fuel consumption required for track insertion after aerodynamic capture, a control profile with a bang-bang structure and the corresponding optimal trajectory are obtained according to optimal control theory. According to the characteristics of the optimal trajectory profile in different mission scenarios, a piecewise inverse proportional function with respect to altitude is used to fit the sinγ term related to the track angle:

[0032]

[0033] Among them, A0 and A1 are constant coefficients, γ0 is the initial track angle of the spacecraft, and γ f is the track angle at the aerodynamic capture terminal.

[0034] The initial altitude of the spacecraft is set to h0, and the aerodynamic capture terminal is selected at the boundary of the atmosphere, corresponding to the altitude h EI , we can use the given initial conditions (h0,γ0) and terminal conditions (h EI ,γ f ), determine the coefficients A0, A1 by solving the following system of equations:

[0035]

[0036]

[0037] Step 4: Based on the aerodynamic parameter fitting function in step 2 and the track angle fitting function in step 3, the analytical expression of velocity with respect to altitude is derived according to the simplified longitudinal plane motion equation in step 1. Analytical velocity expressions are constructed for the drag term and gravity term in the velocity differential equation respectively, and the gravity effect is added as a correction term to the analytical velocity expression of the drag term, thereby obtaining a complete analytical form of the trajectory velocity in the ascent phase, thereby improving the prediction efficiency of the trajectory velocity.

[0038] Step 4.1 Consider the influence of atmospheric drag and derive an analytical expression for the velocity.

[0039] In formula (9), the factors that cause velocity changes mainly include atmospheric drag and gravity, among which the influence of atmospheric drag is dominant. Therefore, starting from determining the velocity change caused only by drag, the differential equation excluding the contribution of gravity is extracted from formula (9):

[0040]

[0041] Substituting the fitting function (12) about aerodynamic drag and the fitting function (13) about track angle into (16), we can obtain

[0042]

[0043] Separating the variables in formula (17), we get

[0044]

[0045] The constant B = -S / (2A0). Integrating both sides of Equation (18) from the initial condition (h0, V0) to the prediction point condition (h, V) yields

[0046]

[0047] Solving the above equation (19), we can get the velocity of the ascending section considering only the effect of resistance:

[0048]

[0049] Step 4.2 Consider the influence of gravity and derive the analytical expression of the gravitational correction term of the velocity.

[0050] Since the change of the celestial body radius during the aerodynamic capture maneuver is negligible, dh = dr, the gravitational term is extracted from the velocity differential equation (9):

[0051]

[0052] Separating the variables and integrating the above equation from the initial condition (h0, V0) to the prediction point condition (h, V) yields

[0053]

[0054] Where r and r0 are the radius vectors corresponding to the heights h and h0 respectively. The gravitational correction term for velocity is defined as

[0055] ΔV grav =V grav -V0 (23)

[0056] Step 4.3: Consider the effects of atmospheric drag and gravity to obtain a complete analytical expression for velocity.

[0057] Add the gravity correction term (23) to the velocity expression (20) of the ascending stage considering only the effect of resistance:

[0058] V=V drag +ΔV grav (twenty four)

[0059] That is to say, the complete analytical expression of the velocity of the ascending trajectory is obtained.

[0060] Step 5: Based on the complete analytical expression of the ascent trajectory velocity obtained in step 4, the corresponding velocity magnitudes are predicted at different altitudes to generate an open-loop prediction trajectory for aerodynamic capture. The predicted trajectory is used to assist the spacecraft in maneuvering during the aerodynamic capture process, ensuring that the spacecraft accurately enters the target orbit with minimal fuel consumption while meeting the mission constraints.

[0061] From equations (20), (22) and (24), we know that in the current state x0 and the atmospheric outlet condition (h EI ,γ f ) is given, the velocity V of each point on the subsequent trajectory will be a function of the height h at that point, denoted as V = F(h). In the height interval [h0,h EI ] Take N discrete points on it to form a height set:

[0062] A h ={h i |h0 <h i ≤h EI ,i=1,2,...,N} (25)

[0063] For set A h Each height h in i , can be obtained by V i =F(h i ) calculates the speed at the corresponding height and forms a speed set:

[0064] A V ={V i |V i =F(h i),i=1,2,...,N} (26)

[0065] According to the set A h , A V This generates an open-loop predicted trajectory for aerodynamic capture. This predicted trajectory assists the spacecraft in maneuvering during aerodynamic capture, ensuring accurate entry into the target orbit with minimal fuel consumption while meeting mission constraints.

[0066] Beneficial effects:

[0067] 1. The present invention discloses an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios. The method decouples the dynamic model to extract a simplified longitudinal dynamic equation, and fits the aerodynamic parameters and the optimal track angle profile therein. The atmospheric drag and gravity effects in the velocity differential equation are considered respectively. By combining the integral correction of the drag term and the integral correction of the gravity term, an analytical expression for the aerodynamic capture ascent speed is obtained, thereby achieving efficient open-loop prediction of the trajectory, improving the real-time performance of the estimation and prediction under conditions with limited computing resources, and enabling online application.

[0068] 2. The present invention discloses an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-mission scenarios. Based on the trajectory profile characteristics with optimal fuel consumption, a fitting function expression of the track angle with respect to altitude is given. Since the profile of the track angle with respect to altitude is fitted by a piecewise inverse proportional function, the optimal profile characteristics when the track angle increases or decreases are considered, namely, γ f ≤γ0 and γ f >γ0, so the method can achieve high-precision fitting of the track angle with respect to altitude changes in different track angle change scenarios, has no strict restrictions and constraints on the track angle of the spacecraft entering and leaving the atmosphere, and has strong universality.

[0069] 3. The present invention discloses an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-mission scenarios. Based on the aerodynamic data measured during the descent phase of the spacecraft, a sixth-order or higher polynomial is used to fit the aerodynamic parameters. Since high-order polynomials are highly adaptable and sufficient to fit the comprehensive and real-time changes in atmospheric density, lift / drag coefficients, and spacecraft mass, this method is applicable to the atmospheric environments of multiple planets and a variety of aircraft models, and has good robustness.

[0070] 4. The present invention discloses an analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios. On the basis of achieving the above-mentioned beneficial effects, it can assist the guidance and control system of the spacecraft in generating control instructions according to the predicted trajectory, guide the spacecraft to maneuver during the aerodynamic capture process, and ensure that the spacecraft accurately enters the target orbit with minimal fuel consumption while meeting the mission constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1is a schematic diagram of aerodynamic capture of a spacecraft in the present invention;

[0072] Figure 2 It is a flow chart of an analytical aerodynamic capture open-loop trajectory prediction method applicable to multi-task scenarios of the present invention;

[0073] Figure 3 It is the optimal track angle-altitude profile of the ascent phase under two aerodynamic capture scenarios on Earth and Mars;

[0074] Figure 4 3. It is a schematic diagram comparing the prediction of the ascending trajectory of the method according to the embodiment of the present invention and the method according to the prior art in the scenario of earth aerodynamic capture;

[0075] Figure 5 3 is a schematic diagram comparing the ascent trajectory prediction of the embodiment method of the present invention and the prior art method in the Mars aerodynamic capture scenario. DETAILED DESCRIPTION

[0076] In order to better illustrate the purpose and advantages of the present invention, the present invention is explained in detail below by performing a simulation analysis on the trajectory prediction problem of the aerodynamic capture ascent phase of a spacecraft.

[0077] Example 1:

[0078] like Figure 2 As shown, this embodiment discloses an analytical aerodynamic capture open-loop trajectory prediction method applicable to multi-task scenarios, and the specific implementation steps are as follows:

[0079] Step 1: Establish a spacecraft aerodynamic capture flight dynamics model that takes into account the effects of J2 perturbation and celestial body rotation. The spacecraft aerodynamic capture flight dynamics model is a three-degree-of-freedom dynamics equation, and the motion equation in the longitudinal plane is decoupled and extracted from the three-degree-of-freedom dynamics equation.

[0080] The three-degree-of-freedom dynamic equation of the spacecraft during aerodynamic capture flight is:

[0081]

[0082] Where r is the radial distance from the center of the Earth to the center of mass of the spacecraft; θ is the longitude; φ is the latitude; V is the velocity of the spacecraft relative to the celestial body; γ is the track angle of the velocity vector relative to the celestial body, that is, the ballistic inclination angle; ψ is the heading angle, that is, the ballistic deviation angle, which is positive when it turns clockwise from due north to the projection of the relative velocity vector of the celestial body on the local horizontal plane; σ is the roll angle, which is the control angle of the spacecraft aerodynamic capture process; L and D are the aerodynamic lift acceleration and aerodynamic drag acceleration, respectively.

[0083]

[0084]

[0085] Where ρ is the atmospheric density, S is the aircraft reference area; g r and g φ are the radial and latitudinal components of gravitational acceleration,

[0086]

[0087]

[0088] Where μ is the gravitational parameter of the celestial body, R0 is the equatorial radius of the celestial body, J2 is the celestial body's dynamical flattening, and ω is the celestial body's rotational angular velocity. When the spacecraft is performing aerodynamic capture, the initial state is usually given in real time based on the navigation measurement system. Therefore, the initial state constraint is x0 = [r0, θ0, φ0, V0, γ0, ψ0] T In order to facilitate the subsequent derivation of the trajectory analytical solution, it is necessary to separate the longitudinal motion parameters of the spacecraft, namely the altitude, velocity and track angle, to form a simplified longitudinal decoupled motion model. Since the radial distance r is the sum of the radius R0 and the altitude h of the celestial body, the change in the radius of the celestial body during the aerodynamic capture maneuver is negligible, and the time rate of change of the radial velocity and altitude can be equated. In the absence of the celestial body's flattening and rotation terms, the motion equation in the longitudinal plane can be extracted from the three-degree-of-freedom dynamic equation (27):

[0089]

[0090]

[0091]

[0092] Changing the independent variable from time to height h, we get

[0093]

[0094]

[0095] Step 2: Based on the aerodynamic data measured during the descent phase of the spacecraft, high-order polynomials are used to fit the aerodynamic parameters to facilitate the subsequent derivation of the velocity analytical expression. Since the aerodynamic parameters are obtained based on the real-time measured aerodynamic data, the corresponding fitting polynomials can represent the comprehensive changes in the actual atmospheric environment and the spacecraft's aerodynamic performance.

[0096] During the descent phase of the aerodynamic capture, the spacecraft continuously measures the lift acceleration L and drag acceleration D at the corresponding altitude. According to the previous definition, each aerodynamic acceleration involves the product of the atmospheric density ρ and the corresponding aerodynamic coefficient divided by the mass. A sixth-order or higher polynomial parameterized by altitude is selected to parameterize ρC. L / m and ρC D / m:

[0097]

[0098]

[0099] where a n , b n is a constant coefficient and n is the degree of the corresponding term.

[0100] Step 3: According to the initial state of the spacecraft and the atmospheric exit conditions, based on the trajectory profile characteristics with optimal fuel consumption, a fitting function expression of the track angle with respect to altitude is given. The optimal profile characteristics when the track angle increases or decreases are fitted through a piecewise inverse proportional function. High-precision fitting of the track angle with respect to altitude changes can be achieved in different track angle change scenarios.

[0101] When the performance indicator is the minimum fuel consumption required for track insertion after aerodynamic capture, a control profile with a bang-bang structure and the corresponding optimal trajectory are obtained according to optimal control theory. According to the characteristics of the optimal trajectory profile in different mission scenarios, a piecewise inverse proportional function with respect to altitude is used to fit the sinγ term related to the track angle:

[0102]

[0103] Among them, A0 and A1 are constant coefficients, γ0 is the initial track angle of the spacecraft, and γ f is the track angle at the aerodynamic capture terminal.

[0104] The initial altitude of the spacecraft is set to h0, and the aerodynamic capture terminal is selected at the boundary of the atmosphere, corresponding to the altitude h EI , we can use the given initial conditions (h0,γ0) and terminal conditions (h EI ,γ f ), determine the coefficients A0, A1 by solving the following system of equations:

[0105]

[0106]

[0107] Step 4: Based on the aerodynamic parameter fitting function in step 2 and the track angle fitting function in step 3, the analytical expression of velocity with respect to altitude is derived according to the simplified longitudinal plane motion equation in step 1. Analytical velocity expressions are constructed for the drag term and gravity term in the velocity differential equation respectively, and the gravity effect is added as a correction term to the analytical velocity expression of the drag term, thereby obtaining a complete analytical form of the trajectory velocity in the ascent phase, thereby improving the prediction efficiency of the trajectory velocity.

[0108] Step 4.1 Consider the influence of atmospheric drag and derive an analytical expression for the velocity.

[0109] In equation (35), the factors that cause velocity changes mainly include atmospheric drag and gravity, among which the influence of atmospheric drag is dominant. Therefore, starting from determining the velocity change caused only by drag, the differential equation excluding the contribution of gravity is extracted from equation (35):

[0110]

[0111] Substituting the fitting function (38) about aerodynamic drag and the fitting function (39) about track angle into (42) we can obtain

[0112]

[0113] Separating the variables in equation (43), we get

[0114]

[0115] The constant B = -S / (2A0). Integrating both sides of Equation (44) from the initial condition (h0, V0) to the prediction point condition (h, V) yields

[0116]

[0117] Solving equation (45), we can get the velocity of the ascending section considering only the effect of resistance:

[0118]

[0119] Step 4.2 Consider the influence of gravity and derive the analytical expression of the gravitational correction term of the velocity.

[0120] Since the change of the celestial body radius during the aerodynamic capture maneuver is negligible, dh = dr, the gravitational term is extracted from the velocity differential equation (35):

[0121]

[0122] Separating the variables and integrating the above equation from the initial condition (h0, V0) to the prediction point condition (h, V) yields

[0123]

[0124] Where r and r0 are the radius vectors corresponding to the heights h and h0 respectively. The gravitational correction term for velocity is defined as

[0125] ΔV grav =V grav -V0 (49)

[0126] Step 4.3: Consider the effects of atmospheric drag and gravity to obtain a complete analytical expression for velocity.

[0127] Add the gravity correction term (49) to the velocity expression (46) of the ascending stage considering only the drag effect.

[0128] V=V drag +ΔV grav (50)

[0129] That is to say, the complete analytical expression of the velocity of the ascending trajectory is obtained.

[0130] Step 5: Based on the complete analytical expression of the ascent trajectory velocity obtained in step 4, the corresponding velocity magnitudes are predicted at different altitudes to generate an open-loop prediction trajectory for aerodynamic capture. The predicted trajectory is used to assist the spacecraft in maneuvering during the aerodynamic capture process, ensuring that the spacecraft accurately enters the target orbit with minimal fuel consumption while meeting the mission constraints.

[0131] From equations (46), (48) and (50), we know that in the current state x0 and the atmospheric outlet condition (h EI ,γ f ) is given, the velocity V of each point on the subsequent trajectory will be a function of the height h at that point, denoted as V = F(h). In the height interval [h0,h EI ] Take N discrete points on it to form a height set:

[0132] A h ={h i |h0 <h i ≤h EI ,i=1,2,...,N} (51)

[0133] For set A h Each height h in i , can be obtained by V i =F(h i ) calculates the speed at the corresponding height and forms a speed set:

[0134] A V ={V i |V i =F(h i ),i=1,2,...,N} (52)

[0135] According to the set A h , A V This generates an open-loop predicted trajectory for aerodynamic capture. This predicted trajectory assists the spacecraft in maneuvering during aerodynamic capture, ensuring accurate entry into the target orbit with minimal fuel consumption while meeting mission constraints.

[0136] In order to verify the feasibility and universality of the method, two aerodynamic capture scenarios are considered, and their entry conditions are shown in the following table:

[0137] Table 1 Inertia entry conditions under two scenarios

[0138]

[0139]

[0140] In the Earth scenario, the target orbit is a circular orbit with an altitude of 200km; in the Mars scenario, the target orbit is an elliptical orbit with an apogee altitude of 3000km and a perigee altitude of 300km. The parameter model of the spacecraft takes the Orion Multi-Purpose Crew Vehicle (MPCV) as an example. Based on the above conditions and the bang-bang control structure of the optimal control theory, the reference optimal actual trajectory of the aerodynamic capture can be generated. The optimal track angle-altitude profile of the ascent phase in the two aerodynamic capture scenarios of Earth and Mars is shown as follows: Figure 3 shown.

[0141] In step 1, select Figure 3 The starting point state of the reference trajectory shown is used as the predicted initial state x0, and a simplified longitudinal decoupled motion model with height as the independent variable is established. The aerodynamic parameters ρC obtained by the measurement are calculated using the sixth-order polynomial in step 2. L / m and ρC D / m is fitted. Then, based on the piecewise inverse proportional function in step 3, the change profile of sinγ relative height h is fitted, and the atmospheric exit state (h EI ,γ f ) as the terminal condition, and (h0,γ0) in x0 as the initial condition, determine the coefficients A0 and A1 according to equations (40) and (41). Then in step 4, based on the aerodynamic parameter ρC L / m,ρC D The fitting function of / m and sinγ is used to obtain the velocity V at height h considering only the drag effect. drag , the gravitational correction term △V is obtained from formula (49) grav , and the predicted velocity V is obtained by equation (50). Finally, the trajectory of the ascent segment is discretized in step 5, and the velocity is analytically calculated at each altitude of the trajectory to obtain the complete velocity-altitude open-loop predicted trajectory for both aerodynamic capture scenarios. During the aerodynamic capture process, this method can be used to continuously predict the subsequent flight trajectory of the spacecraft. By determining whether the predicted trajectory meets the mission constraints, the spacecraft's guidance and control system can continuously generate and correct control instructions to guide the spacecraft to maneuver, ensuring that the spacecraft accurately enters the target orbit with minimal fuel consumption while meeting the mission constraints.

[0142] Comparison of the ascending trajectory prediction of the embodiment of the present invention and the prior art method in the earth aerodynamic capture scenario Figure 4 As shown in the figure, it can be seen that the prediction accuracy of the method of the embodiment of the present invention is close to or even slightly better than the prediction accuracy of the existing technology method. The comparison of the ascent trajectory prediction of the method of the embodiment of the present invention and the existing technology method in the Mars aerodynamic capture scenario is as follows: Figure 5 As shown, the existing method completely fails in this scenario, while the method of the present invention still maintains high prediction accuracy. Simulation results in both scenarios demonstrate that the analytical aerodynamic capture trajectory prediction method of the present invention can achieve relatively accurate predictions in mission scenarios with significantly different conditions, demonstrating the method's flexibility and adaptability, and laying a solid foundation for the generation of subsequent spacecraft guidance and control commands.

[0143] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention, which is used to explain the present invention and is not used to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. An analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios, characterized by: The following steps are included: Step 1: Establish a spacecraft aerodynamic capture flight dynamics model that takes into account the effects of J2 perturbation and celestial body rotation. The spacecraft aerodynamic capture flight dynamics model is a three-degree-of-freedom dynamics equation, and the longitudinal plane motion equation is extracted from the three-degree-of-freedom dynamics equation; Step 2: Based on the aerodynamic data measured during the spacecraft's descent, a high-order polynomial is used to fit the aerodynamic parameters to facilitate the subsequent derivation of the velocity analytical expression. Because the aerodynamic parameters are derived from real-time aerodynamic data, the corresponding fitting polynomial can represent the combined changes in the actual atmospheric environment and the spacecraft's aerodynamic performance. Step 3: Based on the initial state of the spacecraft and atmospheric exit conditions, and the trajectory profile characteristics with optimal fuel consumption, a fitting function expression for the track angle with respect to altitude is given. The optimal trajectory profile characteristics for increasing or decreasing track angles are fitted using a piecewise inverse proportional function. This allows for high-precision fitting of track angle variations with respect to altitude under various track angle variation scenarios. Step 4: Based on the aerodynamic parameter fitting function in step 2 and the track angle fitting function in step 3, the analytical expression of velocity with respect to altitude is derived according to the simplified longitudinal plane motion equation in step 1. Analytical velocity expressions are constructed for the drag term and gravity term in the velocity differential equation respectively. The gravity effect is added as a correction term to the analytical velocity expression of the drag term, thereby obtaining a complete analytical form of the trajectory velocity in the ascent phase, thereby improving the efficiency of trajectory velocity prediction. Step 5: Based on the complete analytical expression of the ascent trajectory velocity obtained in step 4, the corresponding velocity magnitudes are predicted at different altitudes to generate an open-loop prediction trajectory for aerodynamic capture. The predicted trajectory is used to assist the spacecraft in maneuvering during the aerodynamic capture process, ensuring that the spacecraft accurately enters the target orbit with minimal fuel consumption while meeting the mission constraints.

2. The analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios according to claim 1, characterized in that: The implementation method of step one is: The three-degree-of-freedom dynamic equation of the spacecraft during aerodynamic capture flight is: Where r is the radial distance from the center of the Earth to the center of mass of the spacecraft; θ is the longitude; φ is the latitude; V is the velocity of the spacecraft relative to the celestial body; γ is the track angle of the velocity vector relative to the celestial body, that is, the ballistic inclination angle; ψ is the heading angle, that is, the ballistic deviation angle, which is positive when it turns clockwise from due north to the projection of the relative velocity vector of the celestial body on the local horizontal plane; σ is the roll angle, which is the control angle of the spacecraft aerodynamic capture process; L and D are the aerodynamic lift acceleration and aerodynamic drag acceleration, respectively. Where ρ is the atmospheric density, S is the aircraft reference area; g r and g φ are the radial and latitudinal components of gravitational acceleration, Where μ is the gravitational parameter of the celestial body, R0 is the equatorial radius of the celestial body, J2 is the dynamical flattening of the celestial body, ω is the angular velocity of the celestial body, and when the spacecraft is performing aerodynamic capture, the initial state is usually given in real time according to the navigation measurement system. Therefore, the initial state constraint is x0 = [r0, θ0, φ0, V0, γ0, ψ0] T In order to facilitate the subsequent derivation of the trajectory analytical solution, it is necessary to separate the spacecraft longitudinal motion parameters, namely the altitude, velocity and track angle, to form a simplified longitudinal decoupled motion model. Since the radial distance r is the sum of the celestial body radius R0 and the altitude h, the change of the celestial body radius during the aerodynamic capture maneuver is negligible, and the time rate of change of the radial velocity and altitude can be equated. In the absence of the celestial body oblateness and rotation terms, the longitudinal plane motion equation can be extracted from the three-degree-of-freedom dynamic equation (1): Changing the independent variable from time to height h, we get:

3. The analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios according to claim 2, characterized in that: The implementation method of step 2 is: During the descent phase of aerodynamic capture, the spacecraft continuously measures the lift acceleration L and drag acceleration D at the corresponding altitude. According to the previous definition, each aerodynamic acceleration involves the product of the atmospheric density ρ and the corresponding aerodynamic coefficient divided by the mass; a sixth-order or higher polynomial parameterized with altitude as the independent variable ρC is selected. L / m and ρC D / m: where a n , b n is a constant coefficient and n is the degree of the corresponding term.

4. The analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios according to claim 3, characterized in that: The implementation method of step three is: When the minimum fuel consumption required for track insertion after aerodynamic capture is used as the performance indicator, a control profile with a bang-bang structure and the corresponding optimal trajectory are obtained according to the optimal control theory. According to the characteristics of the optimal trajectory profile in different mission scenarios, a piecewise inverse proportional function with respect to altitude is used to fit the sinγ term related to the track angle: Among them, A0, A1 are constant coefficients, γ0 is the initial track angle of the spacecraft, γ f is the track angle of the aerodynamic capture terminal; the initial altitude of the spacecraft is set to h0, and the aerodynamic capture terminal is selected at the boundary of the atmosphere, and the corresponding altitude is h EI , we can use the given initial conditions (h0,γ0) and terminal conditions (h EI ,γ f ), determine the coefficients A0, A1 by solving the following system of equations:

5. The analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios according to claim 4, characterized in that: The implementation method of step 4 is: Step 4.1 Consider the influence of atmospheric drag and derive the analytical expression of velocity; In formula (9), the factors that cause velocity changes mainly include atmospheric drag and gravity, among which the influence of atmospheric drag is dominant. Therefore, starting from determining the velocity change caused only by drag, the differential equation excluding the contribution of gravity is extracted from formula (9): Substituting the fitting function (12) about aerodynamic drag and the fitting function (13) about track angle into (16), we can obtain Separating the variables in formula (17), we get Where constant B = -S / (2A0); Integrating both sides of equation (18) from the initial condition (h0, V0) to the prediction point condition (h, V) yields Solving the above equation (19), we can get the velocity of the ascending section considering only the effect of resistance: Step 4.2 Consider the influence of gravity and derive the analytical expression of the gravity correction term of the velocity; Since the change of the celestial body radius during the aerodynamic capture maneuver is negligible, dh = dr, the gravitational term is extracted from the velocity differential equation (9): Separating the variables and integrating the above equation from the initial condition (h0, V0) to the prediction point condition (h, V) yields Among them, r and r0 are the radius vectors corresponding to the heights h and h0 respectively; the gravitational correction term defining the velocity is ΔV grav =V grav -V0 (23) Step 4.3: Consider the effects of atmospheric drag and gravity to obtain a complete analytical expression for velocity. Add the gravity correction term (23) to the velocity expression (20) of the ascending stage considering only the effect of resistance: V=V drag +ΔV grav (24) That is to say, the complete analytical expression of the velocity of the ascending trajectory is obtained.

6. The analytical aerodynamic capture open-loop trajectory prediction method suitable for multi-task scenarios according to claim 5, characterized in that: The implementation method of step five is: From equations (20), (22) and (24), we know that in the current state x0 and the atmospheric outlet condition (h EI ,γ f ) is given, the velocity V of each point on the subsequent trajectory will be a function of the height h at that point, denoted as V = F(h); in the height interval [h0,h EI ] Take N discrete points on it to form a height set: A h ={h i |h0<h i ≤h EI ,i=1,2,...,N} (25) For set A h Each height h in i , can be done by V i =F(h i ) calculates the speed at the corresponding height and forms a speed set: A V ={V i |V i =F(h i ),i=1,2,...,N} (26) According to the set A h , A V That is, an open-loop predicted trajectory for aerodynamic capture is generated; this predicted trajectory can assist the spacecraft in maneuvering during the aerodynamic capture process, ensuring that the spacecraft accurately enters the target orbit with minimal fuel consumption while meeting mission constraints.

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