A method for determining a Mars aerodynamic assisted de-orbit corridor boundary analysis

Abstract

The application discloses a Mars aerodynamic auxiliary deorbit corridor boundary analysis determination method and belongs to the technical field of aerospace. The application realizes the method as follows: on the basis of given initial orbit root or entrance state, dynamics equation of a spacecraft in the atmosphere is established. The lower limit and the upper limit of the aerodynamic auxiliary orbit transfer maneuver are determined by the method of large step length traversal shooting. A single variable nonlinear equation about the entrance boundary flight path angle is obtained by establishing the mapping relationship among the atmospheric entrance, control quantity and exit state. The corridor upper and lower limit values of the given spacecraft structure parameters are accurately solved point by point by using the conjugate gradient method based on the trust region, and the complete aerodynamic corridor about the spacecraft structure parameters is obtained. The application has the following advantages: (1) strong robustness and high repeatability; (2) high precision and convenient adjustment; (3) fast calculation speed and strong convergence; and (4) the spacecraft flight dynamics can be replaced according to actual needs, and the application range is wide.

Description

Technical Field

[0001] This invention relates to a method for determining the boundary of a Mars aerodynamically assisted descent corridor, and more particularly to a method applicable to determining the boundary of a Mars aerodynamically assisted descent corridor without thrust coordination, belonging to the field of aerospace technology. Background Technology

[0002] Aerodynamic-assisted orbital maneuvers are important low-fuel-consumption orbital maneuver strategies in space and planetary exploration missions. These strategies allow spacecraft to have a greater maneuver range and stronger maneuverability within a given fuel consumption. For aerodynamic capture missions, the corresponding atmospheric entry corridor is called the aerodynamic capture corridor. The aerodynamic capture corridor refers to the range within which a spacecraft can safely enter the atmosphere and, after a certain atmospheric flight distance, be captured by a planet into an orbital trajectory at the angle of entry (or re-entry). Figure 1 As shown. For aerodynamic orbit descent missions, the aerodynamic orbit descent corridor is the range of entry angles within which the spacecraft, after entering the atmosphere, can fly through a section of atmospheric flight and then escape the atmosphere to reach a new orbit. Since aerodynamic capture technology and aerodynamic-assisted orbit descent technology are not fundamentally different in terms of their targets, they are collectively referred to as aerodynamic-assisted orbit descent technology. In the Martian scenario, due to the thin Martian atmosphere, low atmospheric density, and low altitude, the control capability of a typical thrustless spacecraft performing aerodynamic-assisted orbit change atmospheric flight is limited by simply controlling the spacecraft's state through tilt angle. Especially for spacecraft with a low lift-to-drag ratio, the trajectory angle of the spacecraft upon atmospheric entry largely determines whether the spacecraft can successfully descend to its new orbit. Currently, there is no direct method for solving the Martian aerodynamic-assisted orbit descent corridor. If the general integral traversal method is used to address this problem, it faces the problems of long computation time and low accuracy. Therefore, the Martian aerodynamic-assisted orbit descent corridor boundary analysis and determination method proposed in this patent can not only quickly calculate the boundary through target practice, but also has high accuracy and a wide range of applications, thus meeting the engineering calculation needs of Martian aerodynamic-assisted maneuver mission design.

[0003] The prior art in the developed method for determining the boundary of the Mars aerodynamic assisted descent corridor [1] (see Lin Xiqiang, Zhang Yulin. A method for determining the reachable range of aerodynamic assisted orbit change in different planes [J]. Journal of National University of Defense Technology, 2000, 22(2):7-10.) derived a calculation formula for the range of inclination changes of a certain spacecraft relative to the initial orbit (assuming the initial orbit inclination is 0) through coordinate transformation, obtained the aerodynamic assisted orbit reachable range at any initial inclination, and at the same time gave the range of change of other orbital elements in the aerodynamic assisted orbit process in different planes. This method is mainly for the case of orbital plane maneuvering in different planes, and the calculation conditions cannot be directly applied to the aerodynamic assisted descent scenario, so it cannot be applied to the general case of aerodynamic assistance.

[0004] Prior art [2] (see: Guelman M. Planar Aeroassisted Attainability Domain[J]. Journal of Guidance, Control, and Dynamics, 1997, 20(3): 422-427.) studied the reachability range of planar aerodynamic assisted trajectory changes, taking the angle of attack as the control variable of aerodynamic assistance. Through derivation, it was concluded that the boundary of the aerodynamic assisted reachability domain depends on the initial angle of attack, thus transforming the problem into a single-variable optimization problem. Finally, the reachability range trajectory boundary in the atmosphere and the terminal reachability domain at the exit position were given. This method is limited to the reachability range of planar aerodynamic assisted trajectory changes and cannot be directly extended to the task design of three-dimensional aerodynamic assisted trajectories faced in actual engineering.

[0005] Neither of the aforementioned prior technologies is directly aimed at solving for aerodynamically assisted descent corridors. In fact, there is very little discussion or technology regarding aerodynamically assisted descent corridors in publicly available information. Therefore, for solving for aerodynamically assisted descent corridors on Mars, the boundary range of the aerodynamic descent corridor can be solved with high precision and quickly through a point-by-point precise target-shooting method, which has significant advantages in engineering applications. Summary of the Invention

[0006] The main objective of this invention is to provide a method for determining the boundary of a Mars aerodynamic descent corridor. By using a point-by-point precise target method, the boundary range of the aerodynamic descent corridor can be quickly determined. It has the following advantages: (1) strong robustness and high repeatability; (2) high accuracy and easy adjustment; (3) fast calculation speed and strong convergence; (4) the flight dynamics of the spacecraft can be changed according to actual needs, and it has a wide range of applications.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] This invention discloses a method for determining the boundary of a Mars aerodynamic-assisted descent corridor. Based on given initial orbital elements or inlet conditions, it establishes the dynamic equations of the spacecraft in the atmosphere. The approximate ranges of the lower and upper bounds of the aerodynamic-assisted trajectory maneuver are determined by a large-step traversal target practice method. By establishing a mapping relationship between atmospheric inlet, control variables, and outlet conditions, a single-variable nonlinear equation regarding the inlet boundary track angle is obtained. The upper and lower bounds of the corridor for given spacecraft structural parameters are precisely solved point-by-point using the trust region-based conjugate gradient method, resulting in a complete aerodynamic corridor for the spacecraft structural parameters.

[0009] This invention discloses a method for determining the boundary of a Mars aerodynamically assisted descent corridor, comprising the following steps:

[0010] Step 1: Establish the atmospheric flight dynamics equations for the aircraft;

[0011] The polar coordinate dynamics of a Mars probe flying through the Martian atmosphere are as follows:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018] in:

[0019]

[0020]

[0021] Where r is the distance between the spacecraft's center of mass and the planet's center; θ is longitude; φ is latitude; V is the speed; and γ is the spacecraft's flight path angle or track angle. The track angle of the spacecraft at the atmospheric inlet is denoted as γ0, called the entry angle; the track angle of the spacecraft at the atmospheric exit is denoted as γ... f ψ is the aircraft's heading angle; S is the aircraft's reference area; C L C D These represent the lift coefficient and drag coefficient, respectively; m is the mass of the aircraft; atmospheric density ρ = ρ0exp(-h / h) s ), where ρ0 is the atmospheric density of the planet's surface, h s ω is the atmospheric density coefficient. e ω is the angular velocity of Mars' rotation; μ is the gravitational constant of the planet.

[0022] Step 2: Given the inlet state and the range of aircraft structural parameters to be calculated; use large-step traversal integration to determine the initial range of the aerodynamic descent corridor boundary;

[0023] In step two, the large step-size traversal integration determines the initial range of the aerodynamic descent corridor boundary. Preferably, the large step-size refers to a step-size range of 1° to 5°.

[0024] The aerodynamically assisted descent corridor is a range of atmospheric entry angles within which a Mars probe can controllably reduce its orbital energy by traversing the Martian atmosphere. The upper and lower boundaries of this range are called the corridor's upper and lower boundaries, or the entry angle's upper and lower boundaries. If the probe's atmospheric entry angle falls outside this corridor, the aerodynamically assisted descent mission will inevitably fail.

[0025] For a given Mars probe, assuming its ballistic coefficient is β and its lift-to-drag ratio is L / D, for a single atmospheric flight process with a given initial state x0, assuming a constant roll angle, the atmospheric exit state x is obtained by numerically integrating the spacecraft's atmospheric flight dynamics equations. f The termination condition for integration is r = r atm , or t = t fmax Where r atm This represents the radius vector at the top of Mars' atmosphere, which is the sum of Mars' radius and atmospheric altitude. fmax The upper bound of the integration time is given and should be sufficiently large in actual calculations. The mapping relationship between the initial state of the aircraft, the aircraft's ballistic coefficient and lift-to-drag ratio, the roll angle, and the atmospheric exit state is denoted as:

[0026] x f =f(x0,σ,β,L / D) (9)

[0027] Where x0=[r0,θ0,φ0,V0,γ0,ψ0] T x f =[r f ,θ f ,φ f V f ,γ f ,ψ f ] T r0, θ0, φ0, V0, γ0, ψ0 represent the position vector magnitude, longitude, latitude, velocity magnitude, track angle, and heading angle at the atmospheric inlet, respectively. f ,θ f ,φ f V f ,γ f ,ψ f These represent the position vector magnitude, longitude, latitude, velocity magnitude, track angle, and heading angle at the atmospheric exit, respectively. Given r0, θ0, φ0, V0, and ψ0, the entry angle γ0 and the exit state variable x are obtained. f The corresponding relationship is used to determine whether the spacecraft is falling into the atmosphere, flying out of the atmosphere and entering an orbit, or flying away from the planet.

[0028] When solving for the initial range of the lower boundary of the corridor under aerodynamically assisted descent conditions, σ = σ min =0, at which point, under the given entry conditions, it is most advantageous for the aircraft to reduce energy loss and thus fly out of the atmosphere;

[0029] The mapping from the inlet state to the exit track angle is established according to equation (9):

[0030] γ f =g γ(t0,x0,σ,β,L / D) (10)

[0031] If the maximum integration time limit t is reached by integrating the atmospheric flight dynamics equations of the aircraft... fmax If the aircraft exits at state γ, it is determined that the aircraft is falling into the atmosphere; f >0 and r = r atm When the aircraft exits the atmosphere, it is determined that it has exited the atmosphere; when the aircraft exits the atmosphere at the critical point, γ f =0 and t f <t fmax .

[0032] When the tilt angle takes a constant value σ = σ max When the angle is 180°, it is most favorable for the spacecraft to consume energy and complete the descent, but it also maximizes the risk of crashing into the atmosphere; according to equation (9), combined with the transformation relationship between orbital state and exit state, we obtain

[0033] e f =g e (t0,x0,σ,β,L / D) (11)

[0034] e f This represents the orbital eccentricity corresponding to the exit state. If the maximum integration time t is reached by integrating the atmospheric flight dynamics equations of the aircraft, then... fmax If the eccentricity e of the exit orbit is [value missing], then it is determined that the spacecraft is falling into the atmosphere; f <1 and t f <t fmax When the exit orbit eccentricity e is reached, it indicates that the spacecraft has successfully decelerated through atmospheric flight and entered an elliptical orbit; f >1 and t f <t fmax When the eccentricity e of the exit orbit is insufficient, it indicates that the spacecraft did not decelerate sufficiently through atmospheric flight, entered a planetary hyperbolic orbit, and flew away from the planet, resulting in a failed descent. f When the angle is 1, the corresponding atmospheric entry angle is the upper limit of the aerodynamic descent corridor;

[0035] According to equations (9) to (11), the entry angles range from 0 to 90°. The entry angles closest to the upper and lower boundaries of the corridor in the integral results corresponding to the traversed nodes are denoted as γ. max0 ,γ min0 That is, the initial selection range of the aerodynamically assisted descent corridor [γ] is obtained. min0 ,γ max0 ].

[0036] Step 3: Use the conjugate gradient method based on the trust region to accurately hit the target and obtain the corridor boundary value, that is, solve the nonlinear equation to obtain the aerodynamic assisted descent corridor boundary under the given ballistic coefficient and lift-to-drag ratio.

[0037] Based on (10), establish the lower boundary γ of the corridor min A univariate nonlinear equation with values ​​of:

[0038] g γ (t0,x0,σ min ,β,L / D)=0 (12)

[0039] At this time, x0 = [r0, θ0, φ0, V0, γ] min ,ψ0] T .

[0040] Based on (11), establish a univariate nonlinear equation regarding the value of the upper bound γ0 of the corridor:

[0041] g e (t0,x0,σ max ,β,L / D)-1=0 (13)

[0042] At this time, x0 = [r0, θ0, φ0, V0, γ] max ,ψ0] T .

[0043] The conjugate gradient method based on the trust region is used to solve the nonlinear equations (12) and (13) to obtain the aerodynamic assisted descent corridor boundary under the given ballistic coefficient and lift-to-drag ratio.

[0044] Step 4: Based on the sequential traversal of the ballistic coefficient and lift-to-drag ratio from Steps 1 to 3, determine the surface relating the ballistic coefficient and lift-to-drag ratio at the boundary of the entry corridor.

[0045] In step two, the initial range of the aerodynamic descent corridor boundary determined by the ergonomic integration of the entry angle is only used in the first calculation of the ballistic coefficient and lift-to-drag ratio ergonomic integration. The initial values ​​for subsequent ergonomic integrations are the corridor boundary values ​​obtained in the previous solution.

[0046] For solving the aerodynamic descent corridor of a spacecraft in a Mars scenario, a point-by-point precise target-hitting method based on the trust region is used to improve the efficiency of determining the boundary range of the aerodynamic descent corridor, resulting in a complete aerodynamic corridor with respect to the spacecraft's structural parameters. The determined corridor provides the entry angle selection range for the Mars probe during the aerodynamic descent mission. Outside this range, the descent mission cannot be completed; within the range, the Mars aerodynamic descent is completed by controlling the tilt angle, improving the efficiency, robustness, and safety of the Mars aerodynamic descent mission.

[0047] Beneficial effects:

[0048] 1. The present invention discloses a method for determining the boundary of a Mars aerodynamic-assisted descent corridor. It replaces the strategy of large-scale small-step traversal in the control parameter domain with a point-by-point precise target-hitting strategy based on the conjugate gradient method of the trust region. It does not require strong nonlinear constraints such as the form of dynamics or atmospheric models, and has a wide range of applications.

[0049] 2. The present invention discloses a method for determining the boundary of a Mars aerodynamic-assisted descent corridor. It accurately delineates the initial target value by traversing under typical parameters, with fast convergence speed, strong robustness, and high repeatability.

[0050] 3. The present invention discloses a method for determining the boundary of a Mars aerodynamically assisted descent corridor. By using the conjugate gradient method based on the trust region to solve the boundary, the accuracy can be flexibly adjusted according to the actual engineering calculation needs.

[0051] 4. The Mars aerodynamic assisted descent corridor boundary analysis method disclosed in this invention has no requirements for the initial orbital parameters of the spacecraft and is applicable to the engineering calculation of most aerodynamic capture and descent scenarios in the Mars scenario. Therefore, it has a wide range of applicability to the initial orbit.

[0052] 5. The method for determining the boundary of the Mars aerodynamic-assisted descent corridor disclosed in this invention has a fast convergence speed and high computational efficiency because the initial value is very close to the actual solution of the equation during calculation.

[0053] 6. The present invention discloses a method for determining the boundary of the Mars aerodynamic assisted descent corridor. Based on the above-mentioned beneficial effects, it can obtain a complete aerodynamic corridor with respect to the structural parameters of the spacecraft. The determined corridor provides the entry angle selection range for the Mars probe to perform aerodynamic assisted descent mission. Outside this range, the descent mission cannot be completed. Within the range, the Mars aerodynamic assisted descent is completed by controlling the tilt angle, thereby improving the efficiency, robustness and safety of Mars aerodynamic descent. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the aerodynamically assisted orbit-descending corridor concept proposed in this invention under the Mars scenario;

[0055] Figure 2 This is a flowchart of a method for determining the boundary of a Mars aerodynamic-assisted descent corridor according to the present invention;

[0056] Figure 3 This is a surface view of the upper boundary of the pneumatically assisted lowering corridor in this embodiment;

[0057] Figure 4 This is a three-dimensional area diagram of the pneumatically assisted descent corridor in this embodiment. Detailed Implementation

[0058] To better illustrate the purpose and advantages of this invention, a simulation analysis of the entry corridor for the aircraft's structural parameters under an aerodynamically assisted landing scenario is conducted below to provide a detailed explanation of the invention.

[0059] Example 1:

[0060] In the design of a certain Mars aerodynamic-assisted orbit descent mission, the range of selectable ballistic coefficients for the Mars probe is β∈[100,800]kg / m. 2 The lift-to-drag ratio ranges from L / D ∈ [0.2, 1.6]. Due to the constraints of the probe payload, the detector's state at the atmospheric inlet is r0 = 3524 km, θ0 = 10°, φ0 = 10°, V0 = 5.9 km / s, and ψ0 = 80°. Figure 1 The image shows the state of a typical Mars probe at the atmospheric inlet during aerodynamic deceleration maneuver using aerodynamic assistance. To achieve successful orbit descent and deceleration, the range of atmospheric entry angles needs to be calculated for mission analysis to verify navigation and orbit correction accuracy. Given ω... e The rotational angular velocity of Mars is 7.0883 × 10⁻⁶. -5 rad / s; μ is the planetary gravitational constant, which is 42828 km. 3 ·s -2 The radius vector at the top of Mars' atmosphere is r. atm =3524km.

[0061] The following analysis of the present invention is used to design and determine the corridor for the aerodynamically assisted orbit descent for this mission.

[0062] This embodiment discloses a method for determining the boundary analysis of a Mars aerodynamically assisted descent corridor. The specific implementation steps are as follows:

[0063] Step 1: Establish the atmospheric flight dynamics equations for the aircraft;

[0064] The polar coordinate dynamics of a Mars probe flying through the Martian atmosphere are as follows:

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071] in:

[0072]

[0073]

[0074] Where r is the distance between the spacecraft's center of mass and the planet's center; θ is longitude; φ is latitude; V is the speed; and γ is the spacecraft's flight path angle or track angle. The track angle of the spacecraft at the atmospheric inlet is denoted as γ0, called the entry angle; the track angle of the spacecraft at the atmospheric exit is denoted as γ... f ψ is the aircraft's heading angle; S is the aircraft's reference area; C L C D These represent the lift coefficient and drag coefficient, respectively; m is the mass of the aircraft; atmospheric density ρ = ρ0exp(-h / h) s ), where ρ0 is the atmospheric density of the planet's surface, h s This is the atmospheric density coefficient.

[0075] Step 2: Given the inlet state and the range of aircraft structural parameters to be calculated; use large-step traversal integration to determine the initial range of the aerodynamic descent corridor boundary;

[0076] For a given Mars probe, assuming its ballistic coefficient is β and its lift-to-drag ratio is L / D, for a single atmospheric flight process with a given initial state x0, assuming a constant roll angle, the atmospheric exit state x is obtained by numerically integrating the spacecraft's atmospheric flight dynamics equations. f The termination condition for integration is r = r atm , or t = t fmax Where r atm This represents the radius vector at the top of Mars' atmosphere, which is the sum of Mars' radius and atmospheric altitude. fmax The upper bound of the integration time is given and should be sufficiently large in actual calculations. The mapping relationship between the initial state of the aircraft, the aircraft's ballistic coefficient and lift-to-drag ratio, the roll angle, and the atmospheric exit state is denoted as:

[0077] x f =f(x0,σ,β,L / D) (22)

[0078] Where x0=[r0,θ0,φ0,V0,γ0,ψ0] T x f =[r f ,θ f ,φ f V f ,γ f ,ψ f ] T r0, θ0, φ0, V0, γ0, ψ0 represent the position vector magnitude, longitude, latitude, velocity magnitude, track angle, and heading angle at the atmospheric inlet, respectively.f ,θ f ,φ f V f ,γ f ,ψ f These represent the position vector magnitude, longitude, latitude, velocity magnitude, track angle, and heading angle at the atmospheric exit, respectively. Given r0, θ0, φ0, V0, and ψ0, the entry angle γ0 and the exit state variable x are obtained. f The corresponding relationship is used to determine whether the spacecraft is falling into the atmosphere, flying out of the atmosphere and entering an orbit, or flying away from the planet.

[0079] When solving for the initial range of the lower boundary of the corridor under aerodynamically assisted descent conditions, σ = σ min At this point, under the given entry conditions, it is most advantageous for the aircraft to reduce energy loss and thus fly out of the atmosphere;

[0080] The mapping from the inlet state to the exit track angle is established according to equation (22):

[0081] γ f =g γ (t0,x0,σ,β,L / D) (23)

[0082] If the maximum integration time limit t is still reached after integrating the atmospheric flight dynamics equations of the aircraft. fmax If the aircraft exits at state γ, it is determined that the aircraft is falling into the atmosphere; f >0 and r = r atm When the aircraft exits the atmosphere, it is determined that it has exited the atmosphere; when the aircraft exits the atmosphere at the critical point, γ f =0 and t f <t fmax .

[0083] When the tilt angle takes a constant value σ = σ max At this time, it is most conducive to the spacecraft consuming energy and completing the descent, but at the same time, it also maximizes the risk of falling into the atmosphere; according to equation (22), combined with the transformation relationship between orbital state and exit state, we obtain

[0084] e f =g e (t0,x0,σ,β,L / D) (24)

[0085] e f This represents the orbital eccentricity corresponding to the exit state. If the maximum integration time t is reached by integrating the atmospheric flight dynamics equations of the aircraft, then... fmax If the eccentricity e of the exit orbit is [value missing], then it is determined that the spacecraft is falling into the atmosphere; f <1 and t f <t fmaxWhen the exit orbit eccentricity e is reached, it indicates that the spacecraft has successfully decelerated through atmospheric flight and entered an elliptical orbit; f >1 and t f <t fmax When the eccentricity e of the exit orbit is insufficient, it indicates that the spacecraft did not decelerate sufficiently through atmospheric flight, entered a planetary hyperbolic orbit, and flew away from the planet, resulting in a failed descent. f When the angle is 1, the corresponding atmospheric entry angle is the upper limit of the aerodynamic descent corridor;

[0086] According to equations (23) and (24), with the lower boundary L / D = 0.2 and β = 100 kg / m selected for the lift-to-drag ratio and ballistic coefficient,... 2 In this case, traversing the entry angle from 0 to 90°, and taking a traversal step size of 3°, the initial values ​​of the upper and lower bounds of the track angle are obtained as γ. min0 = -12°, γ max0 = -9°.

[0087] Step 3: Accurately target and obtain corridor boundary values ​​using the trust region-based conjugate gradient method;

[0088] Based on (10), establish the lower boundary γ of the corridor min A univariate nonlinear equation with values ​​of:

[0089] g γ (t0,x0,σ min ,β,L / D)=0 (25)

[0090] At this time, x0 = [r0, θ0, φ0, V0, γ] min ,ψ0] T .

[0091] Based on (11), establish a univariate nonlinear equation regarding the value of the upper bound γ0 of the corridor:

[0092] g e (t0,x0,σ max ,β,L / D)-1=0 (26)

[0093] At this time, x0 = [r0, θ0, φ0, V0, γ] max ,ψ0] T .

[0094] The conjugate gradient method based on the trust region is used to solve the nonlinear equations (25) and (26) to obtain the aerodynamic assisted descent corridor boundary under the given ballistic coefficient and lift-to-drag ratio; here, the fsolve function in the MATLAB tool is used.

[0095] Step 4: By sequentially iterating through the ballistic coefficients and lift-to-drag ratio in Steps 1 to 3, the relationship surface between the entry corridor boundary and the aircraft's ballistic coefficients and lift-to-drag ratio can be obtained. It should be noted that the iteration of the entry angle in Step 2 only needs to be used in the first calculation of the ballistic coefficients and lift-to-drag ratio; the initial value for subsequent iterations can be the corridor boundary value obtained in the previous solution.

[0096] In step three, the relative error of the solver is set to 10. -6 The traversal step size for the ballistic coefficient is set to 1, and the lift-to-drag ratio traversal step size is set to 0.05. The calculated upper bound surface is as follows: Figure 2 As shown, the region between the upper and lower boundaries is as follows: Figure 3 As shown.

[0097] To further illustrate the significance of verifying this invention, the ballistic coefficient of the aircraft is β = 381 kg / m. 2 When the lift-to-drag ratio L / D = 0.27, several typical entry angle and constant tilt angle values ​​were selected, and the exit state was calculated through integration, as shown in Table 1. Under the ballistic coefficient and lift-to-drag ratio of this aircraft, the aerodynamically assisted landing corridor is [-10.3044°, -12.5100°]. As can be seen from the table, when the atmospheric entry angle is outside the corridor, successful landing is impossible; however, when it is inside the corridor, successful landing can be achieved by taking a certain tilt angle.

[0098] Table 1: Exit Status under Typical Entry Angle and Normal Incline Angle Values

[0099] -15° 0° Plunging into the atmosphere -15° 180° Plunging into the atmosphere -11° 45° Entering an elliptical orbit, descent successful. -11° 90° Entering an elliptical orbit, descent successful. -12° 0° Entering an elliptical orbit, descent successful. -12° 30° Entering an elliptical orbit, descent successful. -8° 0° Flying away from the planet, failed to descend to its final orbit -8° 180° Flying away from the planet, failed to descend to its final orbit

[0100] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is used to explain the present invention. It is not intended 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 within the scope of protection of the present invention.

Claims

1. A method for determining the boundary of a Mars aerodynamically assisted descent corridor, characterized in that: Includes the following steps, Step 1: Establish the atmospheric flight dynamics equations for the aircraft; Step 2: Given the inlet state and the range of aircraft structural parameters to be calculated; use large-step traversal integration to determine the initial range of the aerodynamic descent corridor boundary; Step two is implemented as follows: For a given Mars probe, let its ballistic coefficient be... The rise-to-drag ratio is For a given initial state During an atmospheric flight process, with a constant tilt angle, the atmospheric exit state is obtained by numerically integrating the atmospheric flight dynamics equations of the aircraft. ; The termination condition for integration is ,or ;in This is the magnitude of the radius vector at the top of Mars' atmosphere, which is the sum of the Martian radius and the atmospheric height. Given the upper bound of the integration time; the mapping relationship between the initial state of the aircraft, the aircraft ballistic coefficient and lift-to-drag ratio, the roll angle and the atmospheric exit state is denoted as: in , ; These represent the position vector magnitude, longitude, latitude, velocity magnitude, track angle, and heading angle at the atmospheric inlet, respectively. These represent the position vector magnitude, longitude, latitude, velocity magnitude, track angle, and heading angle at the atmospheric exit, respectively; Given the conditions, obtain the entry angle. Export status quantity The corresponding relationship is used to determine whether the spacecraft is falling into the atmosphere, flying out of the atmosphere and entering an orbit, or flying away from the planet. When solving for the initial range of the lower boundary of the corridor under aerodynamically assisted orbit descent conditions, At this point, under the given entry conditions, it is most advantageous for the aircraft to reduce energy loss and thus fly out of the atmosphere; The mapping from the inlet state to the exit track angle is established according to equation (9): If the maximum integration time limit is still reached after integrating the atmospheric flight dynamics equations of the aircraft. If the aircraft is in a certain state, it is determined that it has fallen into the atmosphere; if the aircraft's exit state is... and When the aircraft exits the atmosphere, it is determined that it has exited the atmosphere; when the aircraft exits the atmosphere at the critical point, and ; Based on equation (9), and combining the transformation relationship between orbital state and exit state, we obtain... This represents the orbital eccentricity corresponding to the exit state; When the exit orbit eccentricity At that time, the corresponding atmospheric entry angle is taken as the upper boundary of the aerodynamic descent corridor; According to equations (9) to (11), the entry angles from 0 to 90° are traversed. The entry angles closest to the upper and lower boundaries of the corridor in the integral results corresponding to the traversed nodes are denoted as follows: This yields the initial selection range of the aerodynamically assisted descent corridor. ; Step 3: Use the conjugate gradient method based on the trust region to accurately hit the target and obtain the corridor boundary value, that is, solve the nonlinear equation to obtain the aerodynamic assisted descent corridor boundary under the given ballistic coefficient and lift-drag ratio. Step 4: Based on the sequential traversal of ballistic coefficients and lift-to-drag ratios from Steps 1 to 3, determine the surface relating the aircraft's ballistic coefficients and lift-to-drag ratio at the boundary of the entry corridor. In step two, the initial range of the aerodynamic descent corridor boundary determined by the ergonomic integration of the entry angle is only used in the first calculation of the ballistic coefficient and lift-to-drag ratio ergonomic integration. The initial values ​​for subsequent ergonomic integrations are the corridor boundary values ​​obtained in the previous solution.

2. The method for determining the boundary of a Mars aerodynamic-assisted descent corridor as described in claim 1, characterized in that: The implementation method for step one is as follows: The polar coordinate dynamics of a Mars probe flying through the Martian atmosphere are as follows: in: in, This is the distance between the spacecraft's center of mass and the planet's center. Longitude; Latitude; The magnitude of the speed; The flight path angle or track angle of an aircraft; the track angle of an aircraft at the atmospheric inlet is denoted as... The angle of entry is called the approach angle; the flight path angle of the aircraft at the atmospheric exit is denoted as . ; The heading angle of the aircraft; For the reference area of ​​the aircraft; , These are the lift coefficient and the drag coefficient, respectively. For aircraft mass; atmospheric density ,in The density of the planet's surface atmosphere. Atmospheric density coefficient; This is the angular velocity of Mars' rotation. is the planetary gravitational constant.

3. The method for determining the boundary of a Mars aerodynamically assisted descent corridor as described in claim 1, characterized in that: The method for implementing step three is as follows: according to Establishment of the lower boundary of the corridor A univariate nonlinear equation with values ​​of: at this time ; according to Establish the upper boundary of the corridor A univariate nonlinear equation with values ​​of: at this time ; The conjugate gradient method based on the trust region is used to solve the nonlinear equations (12) and (13) to obtain the aerodynamic assisted descent corridor boundary under the given ballistic coefficient and lift-to-drag ratio.

4. The method for determining the boundary of a Mars aerodynamically assisted descent corridor as described in claim 1, characterized in that: In step two, the large step length refers to a step length range of 1° to 5°.

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