Landing trajectory initial value design method, device and equipment based on velocity profile parameters

Abstract

The application relates to a method, device and equipment for designing initial values of a moon landing orbit based on a velocity surface parameter. The method comprises the following steps: determining the value range of each variable according to engineering constraints and constants; calculating a first velocity surface parameter equation meeting an apogee height constraint; calculating a second velocity surface parameter equation meeting a perigee height constraint, and solving the equations simultaneously to construct a third velocity surface parameter equation of a general moon orbit; performing traversal assignment on each variable according to the value range of the variable; substituting each assignment into the third velocity surface parameter equation to calculate a tangential velocity; correcting the tangential velocity meeting a tolerance to obtain a corrected tangential velocity; obtaining a corresponding variable initial value set based on the corrected tangential velocity; and then screening the variable initial values in the variable initial value set through engineering constraints to obtain variable initial values meeting the conditions. The application can improve the orbit design precision and reliability.

Description

Technical Field

[0001] This invention relates to the field of spacecraft orbital dynamics and control technology, and in particular to a method, apparatus and equipment for initial value design of lunar landing orbit based on velocity surface parameters. Background Technology

[0002] Lunar orbit design is one of the core issues in manned lunar landing missions, and the quality of its design methodology directly affects the mission's feasibility, safety, and economy. Orbit design involves not only the orbit's geometric characteristics but also complex factors such as multibody dynamics, gravity assistance, energy optimization, and mission constraints. Manned lunar landing missions require orbit design to meet the astronauts' physiological needs (e.g., limited flight time), mission safety (e.g., rapid return capability after emergency orbit abort), and telemetry and tracking support constraints. These constraints make orbit design a highly challenging and complex engineering problem.

[0003] In the early stages of orbit design, it is crucial to quickly and effectively determine the initial orbital values ​​that meet the basic mission requirements. This lays the foundation for subsequent precise numerical optimization and orbit determination. There are many types of Earth-Moon space orbits, including but not limited to Earth-Moon transfer orbits, free return orbits, Earth-Moon return orbits, distant retrograde orbits (DRO), translational point orbits, and low-energy transfer orbits. These orbits play important roles in different phases of manned lunar landing missions.

[0004] Traditional lunar orbit design methods mainly fall into two categories: numerical methods and analytical methods. Numerical methods employ high-precision dynamic models, such as the JPL ephemeris and Legendre polynomials, which can more accurately simulate the actual flight trajectory. However, numerical methods require significant computational resources and are prone to non-convergence due to initial value problems when solving highly sensitive orbits. Analytical methods are typically based on simplified models, such as the two-body assumption, which divides the Earth-Moon orbit into a geocentric segment and a lunar segment, designing the orbit by splicing parameters. However, this method neglects complex factors such as the non-spherical perturbation of the Moon and the gravitational forces of the Earth-Moon-Sun three-body system, resulting in larger model errors and difficulty in adapting to complex constraints. Summary of the Invention

[0005] Therefore, it is necessary to provide a method, apparatus, and equipment for initial value design of lunar orbit based on velocity surface parameters, which can improve design efficiency and enhance the accuracy and reliability of orbit design, in order to address the above-mentioned technical problems.

[0006] A method for initial value design of a lunar orbit based on velocity surface parameters, the method comprising:

[0007] Determine the range of values ​​for each variable based on engineering constraints and constants;

[0008] Calculate the first velocity surface parametric equation that satisfies the perigee height constraint; and calculate the second velocity surface parametric equation that satisfies the lunar perigee height constraint; solve the first and second velocity surface parametric equations simultaneously to construct the third velocity surface parametric equation for a general Earth-Moon orbit;

[0009] Based on the range of the variables, each variable is iterated and assigned a value; each assigned value is substituted into the third velocity surface parameter equation for calculation to obtain the tangential velocity; it is determined whether the tangential velocity meets the tolerance, and the tangential velocity that meets the tolerance is corrected to obtain the corrected tangential velocity;

[0010] Based on the corrected tangential velocity, the corresponding set of initial variable values ​​is obtained; then, the initial variable values ​​in the set of initial variable values ​​are filtered by engineering constraints to obtain the initial variable values ​​that meet the conditions.

[0011] On the other hand, a lunar orbit initial value design device based on velocity surface parameters is also provided, including:

[0012] The value range determination module is used to determine the value range of each variable based on engineering constraints and constants.

[0013] The velocity surface parametric equation construction module is used to calculate the first velocity surface parametric equation that satisfies the perigee height constraint; and to calculate the second velocity surface parametric equation that satisfies the lunar perigee height constraint; and to solve the first velocity surface parametric equation and the second velocity surface parametric equation simultaneously to construct the third velocity surface parametric equation for a general Earth-Moon orbit.

[0014] The modified tangential velocity calculation module is used to iterate and assign values ​​to each variable based on the range of the variable values; substitute each assigned value into the third velocity surface parameter equation to calculate the tangential velocity; determine whether the tangential velocity meets the tolerance, and correct the tangential velocity that meets the tolerance to obtain the corrected tangential velocity;

[0015] The variable initial value determination module is used to obtain the corresponding set of variable initial values ​​based on the corrected tangential velocity; then, the variable initial values ​​in the set of variable initial values ​​are filtered by engineering constraints to obtain variable initial values ​​that meet the conditions.

[0016] On the other hand, a computer device is also provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the above-mentioned lunar orbit initial value design method based on velocity surface parameters.

[0017] Compared with existing technologies, the lunar orbit initial value design method, apparatus, and equipment based on velocity surface parameters provided by this invention have the following advantages:

[0018] 1. By solving the first and second velocity surface parametric equations simultaneously, the key geometric constraints of the Earth-Moon transfer orbit are transformed into parametric equations, forming the third velocity surface parametric equation. This can accurately describe the dynamic characteristics of the orbit in the gravitational fields of the Earth and the Moon, thus improving the accuracy of orbit design.

[0019] 2. Based on the value range, variables are iterated and assigned values, and then substituted into the equation to calculate the tangential velocity. Invalid values ​​can be quickly filtered out through tolerance judgment to ensure that the initial values ​​assigned can meet the accuracy requirements, thereby achieving efficient search and optimization of initial values ​​and improving track design efficiency.

[0020] 3. This invention, through the simultaneous application of multiple surface parameters and tolerance correction, can quickly locate feasible solutions under complex constraints, avoiding trajectory design failures due to initial value deviations and improving robustness in highly constrained scenarios. Furthermore, the range of variable values ​​can be adjusted according to mission requirements to adapt to different lunar landing missions, enhancing the reliability and flexibility of lunar trajectory design. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention, and those skilled in the art can obtain other related drawings based on these drawings without creative effort.

[0022] Figure 1 A flowchart illustrating the initial value design method for lunar orbit based on velocity surface parameters provided in Example 1;

[0023] Figure 2 A schematic diagram of the instantaneous coordinate system and the location of the inlet (outlet) point of the lunar influence sphere provided in Example 1;

[0024] Figure 3 This is a schematic diagram of the instantaneous coordinate system and the lunar orbit coordinate system provided in Example 1;

[0025] Figure 4 A velocity cylindrical coordinate diagram of the exit point of the lunar influence sphere provided in Example 1;

[0026] Figure 5 A schematic diagram of the hyperbola entering the track provided in Example 1;

[0027] Figure 6 This is a schematic diagram of the process for solving the reachability domain of the lunar return orbit reentry point (RP) using the method proposed in this invention, as provided in Example 1.

[0028] Figure 7 The geographic latitude and longitude cloud map of the reachable region of the Earth-Moon return orbit for a given departure time provided in Example 1;

[0029] Figure 8 This is a structural block diagram of the lunar orbit initial value design device based on velocity surface parameters provided in Example 2;

[0030] Figure 9 This is an internal structural diagram of the computer device provided in Example 2.

[0031] The objectives, features, and advantages of this invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0033] It should be noted that in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0034] The technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0035] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0036] Example 1

[0037] This invention proposes a lunar orbit initial value design method based on velocity surface parameters. Employing the assumption of a two-body model, it constructs surfaces using velocity parameters (such as the components of the velocity vector in a specific coordinate system). By analyzing the intersection relationships between these surfaces and mission constraints (such as altitude, inclination, and time), the existence of solutions for specific orbit types can be quickly determined, thus efficiently solving initial values ​​for various orbit types, including Earth-Moon transfer orbits, free return orbits, and Moon-Earth return orbits. This method is particularly suitable for use in the early stages of manned lunar orbit design, providing high-quality initial guesses for subsequent high-precision numerical optimization, greatly improving design efficiency, and offering a more flexible and reliable orbit design tool for manned lunar missions.

[0038] like Figure 1As shown, the lunar orbit initial value design method based on velocity surface parameters provided in this embodiment includes the following steps:

[0039] Step 201: Determine the range of values ​​for each variable based on engineering constraints and constants.

[0040] Determining the range of variable values ​​based on engineering constraints can prevent design parameters from exceeding the actual feasible domain, reduce invalid calculations, and improve the efficiency of subsequent traversals.

[0041] Step 202: Calculate the first velocity surface parameter equation that satisfies the perigee height constraint; and calculate the second velocity surface parameter equation that satisfies the lunar perigee height constraint; solve the first and second velocity surface parameter equations simultaneously to construct the third velocity surface parameter equation for a general Earth-Moon orbit.

[0042] The first velocity surface parametric equation ensures the minimum altitude at which the orbit escapes Earth, while the second velocity surface parametric equation guarantees a safe altitude for lunar capture. By simultaneously solving the first and second velocity surface parametric equations, a third velocity surface equation is formed, providing a theoretical basis for solving the initial values ​​and ensuring that the orbit simultaneously satisfies the physical conditions of "escaping Earth" and "being captured by the Moon."

[0043] Step 203: Based on the range of variable values, assign values ​​to each variable; substitute each assigned value into the third velocity surface parameter equation for calculation to obtain the tangential velocity; determine whether the tangential velocity meets the tolerance, and correct the tangential velocity that meets the tolerance to obtain the corrected tangential velocity.

[0044] The system iterates through the variables according to the preset value range, assigns values, and calculates the tangential velocity by substituting them into the third velocity surface parameter equation, thus completing the automatic search for initial values. At the same time, it filters invalid values ​​through tolerance judgment to ensure that the assigned initial values ​​can meet the accuracy requirements, thereby achieving efficient search and optimization of initial values ​​and improving track design efficiency.

[0045] Step 204: Based on the corrected tangential velocity, obtain the corresponding set of initial variable values; then, filter the initial variable values ​​in the set of initial variable values ​​through engineering constraints to obtain the initial variable values ​​that meet the conditions.

[0046] By using engineering constraints to select executable solutions from the initial set of variable values, cost tasks can be optimized while ensuring engineering feasibility, thus balancing economy and safety.

[0047] Before providing a detailed description of this embodiment, let's define the relevant coordinate system and auxiliary physical quantities:

[0048] (1) Lunar Influence Sphere (LSI): In the two-body model, the influence sphere is the boundary of the dynamic model transformation. Specifically, within the lunar influence sphere, the spacecraft is only subject to the Moon's gravity, while outside it is only subject to the Earth's gravity. The radius of the lunar influence sphere is... express.

[0049] (2) Entry (exit) points (EN, EX): such as Figure 2 As shown, in the two-body model, the entry (exit) point is the point where the hypothetical spacecraft passes through the moon and affects the surface of the sphere. At this point, the dynamic models (lunar two-body model and geocentric two-body model) are interchanged.

[0050] (3) Inertial coordinate system (EJ2000): The geocentric J2000.0 coordinate system is selected for calculation in this invention. Its definition is common knowledge in this field and will not be elaborated here.

[0051] (4) Geocentric fixed coordinate system (ECF): Its definition is common knowledge in this field and will not be elaborated further.

[0052] (5) Instantaneous coordinate system (ILI): At a certain moment, given the position and velocity of the moon in EJ2000, then From the Earth's center to the Moon's center, The direction of the lunar orbital angular momentum. Determined by the right-hand rule. For example... Figure 2 As shown, Represents the geocentric instantaneous coordinate system (EILI). Represents the lunar instantaneous coordinate system (MILI).

[0053] (6) Lunar orbital coordinate system (SLO): passing through the entrance point of the lunar sphere of influence There are countless orbits, one of which can determine the SLO (Solution Log). From the exit point of the lunar influence sphere towards the center of the moon, The direction of the orbital angular momentum is... Determined by the right-hand rule. For the remaining orbital velocities passing through the lunar influence sphere's exit point, the direction can be determined by the flight path angle. and velocity azimuth angle express. Figure 3 A diagram of SLO is provided.

[0054] (7) Velocity cylindrical coordinate system (VCC): such as Figure 4 The diagram shown illustrates the influence of the moon on the velocity at the sphere's entry point within the VCC. The direction of the VCC is... Radial velocity direction, and The direction needs to be determined by identifying the exit point of the lunar influence sphere.

[0055] (8) Latitude and longitude of the entrance (exit) point under MILI and :like Figure 2 As shown, around Axis rotation but From the shaft to the inlet (outlet) point At the projection point in the plane, around Axis rotation back, The axis points to the inlet (outlet) point.

[0056] (9) Latitude and longitude of the entrance (exit) point under EILI and :when and Once confirmed, proceed according to... and Using the same rotation method, you can obtain... and .

[0057] (10) Flight path angle :like Figure 3 and Figure 5 As shown, flight path angle It is the angle between the velocity vector and the local horizontal plane in a hyperbolic orbit.

[0058] In the specific implementation of step 201, the engineering constraints include: near-ground departure altitude. Return to vacuum perigee altitude Near-moon altitude Track inclination Type of elevator rail, landing area, etc.; among which, near-ground departure altitude Return to vacuum perigee altitude Near-moon altitude These are the most important constraints. Constants include the distance from the lunar center to the perigee. Vacuum perigee Earth-center distance Lunar return time The Moon's influence on the sphere's radius Earth's gravitational constant Lunar gravitational constant Variables include the longitude of the entry or exit point, the latitude of the entry or exit point, and the flight path angle. Velocity azimuth angle When calculating the range of values ​​for each variable, this embodiment uses the longitude of the exit point. Latitude of the exit point To illustrate, therefore, , , , Additionally, radial velocity .

[0059] In the specific implementation of step 202, the first velocity surface parameter equation is first constructed, thereby solving for the velocity surface parameters of the entry (exit) point that satisfy the perigee height constraint. It can be understood that the geocentric segment orbit of the Earth-Moon transfer is generally a highly elliptical orbit. By analyzing the far end of the highly elliptical orbit that satisfies the perigee height constraint, the general law of the far end velocity can be obtained, thus obtaining the velocity surface parameter equation of the entry (exit) point, i.e., the first velocity surface parameter equation.

[0060] Specifically, when the distance from the pericenter of the large elliptical orbit Given, as the distance from the centroid becomes... The change in distance at a given location At that time, the radial velocity at that point and tangential velocity It can be calculated using formula (1):

[0061] (1)

[0062] In the formula, This represents the Earth's gravitational constant.

[0063] The distance to the centroid is obtained using formula (1). Taking the derivative, we get the following equation:

[0064] (2)

[0065] For elliptical orbits, and All greater than As the distance from the centroid increases Increase, radial velocity and tangential velocity It is also constantly increasing. For remote locations, it satisfies... ,but Here, "far greater than" means more than 10 times. This shows that for the distance to the pericenter of a large elliptical orbit... When fixed, as the distance from the centroid increases... Changes in radial velocity It is more important than tangential velocity. The changes are much faster. There is also a velocity limit, as shown in formula (3), which corresponds to the distance of the parabolic trajectory at a given position. radial velocity at that point and tangential velocity .

[0066] (3)

[0067] Simultaneously, radial velocity and tangential velocity There exists a minimum value. When When both have a minimum value, the expression is:

[0068] (4)

[0069] For the distant position, there are two possibilities: going out or going back. Therefore, the radial velocity... There are positive and negative values; the radial velocity is given below. and tangential velocity The range of values ​​for is expressed as:

[0070] (5)

[0071] For tangential velocity When the range of values ​​is substituted into specific numerical values, the variation is found to be very small. Therefore, in actual calculations, it can be approximated as a constant.

[0072] like Figure 4 As shown, it is easy to see that under VCC, the moon affects the velocity of the sphere's inlet (outlet) point. (The subscript EN indicates the ingress point, and EX indicates the egress point):

[0073] (6)

[0074] in and These are parameters, and their initial value range during calculation is as follows: The radial velocity range is given by formula (5). In reality, the lunar influence at the sphere's inlet (outlet) point corresponds to the above formula. The value will be truncated. This affects the inside of the ball. Negative values ​​will not be truncated, while positive values ​​will be truncated; if it is on the outer side, positive values ​​will not be truncated, while negative values ​​will be truncated. However, preliminary calculations can be performed using formula (5).

[0075] For ease of subsequent calculations, the velocity surface parametric equations obtained under VCC can be transformed to ILI. Based on the definition of the inlet (outlet) point, from... and It can be obtained and The calculation formula is as follows:

[0076] (7)

[0077] (8)

[0078] In the formula, This indicates the Earth-Moon distance at the moment the spacecraft arrives at the entrance (exit) point.

[0079] Due to VCC shaft edge Direction, the key to the EILI to VCC conversion is both z Simply align the axes; in VCC... The definition is determined by the rotation matrix from EILI to VCC. Therefore, the transformation matrix from IIL to VCC is:

[0080] (9)

[0081] in,

[0082] (10)

[0083] Based on this, the parametric equations of the velocity surface at the entrance (exit) point of the lunar influence sphere in the instantaneous coordinate system (ILI) are obtained, namely the parametric equations of the first velocity surface, and the expression is:

[0084] (11)

[0085] In the formula, This indicates the velocity at the sphere's entry point in the instantaneous coordinate system, representing the influence of the moon. This represents the transition from the velocity cylindrical coordinate system to the instantaneous coordinate system. The velocity at the entry point of the sphere is represented by the lunar influence in the cylindrical velocity coordinate system.

[0086] Then, the second velocity surface parametric equation is constructed to solve for the velocity surface parameters at the entry (exit) points that satisfy the perilune altitude constraint. It can be understood that the orbit after entering the lunar influence sphere is a hyperbolic orbit, so we first take the entry point as an example to study the quantitative relationship between the far-end velocity of the hyperbolic orbit and the perilune altitude. For example... Figure 5 As shown, after entering the lunar sphere of influence, the spacecraft will orbit in a hyperbolic orbit. The lunar center position vector of the entry point is... The velocity relative to the Moon's entry velocity is The entry point flight path angle is The true anterior angle of the entry point is... The dashed lines represent the asymptotes of the hyperbolic orbit, and the vector representing the position of the perigee is... The plane shown by the dashed line is through Any plane. The velocity azimuth angle is relative to the lunar approach velocity. The angle between the projection of the eccentricity vector onto the plane, .pass The traversal can extend the hyperbolic orbit problem to three dimensions.

[0087] Specifically, we only study the two-dimensional in-plane entry problem, where the distance from a given entry point is... We want to know the magnitude of the entry velocity. Flight path angle and the distance to the nearest moon The relationship is represented as:

[0088] (12)

[0089] In the formula, It is the lunar gravitational constant.

[0090] because Therefore, the numerator of formula (12) is greater than 0. Thus, whether formula (12) has a solution depends on the denominator; for the flight path angle, we have... .

[0091] when hour, .

[0092] when hour, There is no solution.

[0093] when hour, Negative values ​​represent exit points, so they are discarded.

[0094] To ensure that the entry track is a hyperbolic track, therefore for velocity at position There is a lower limit. It can be calculated using a parabolic trajectory, with the expression:

[0095] (13)

[0096] Then we have:

[0097] (14)

[0098] Therefore .

[0099] Thus, the lunar center distance at the nearest point is obtained. , magnitude of entry speed and flight path angle The quantitative relationship and the range of values ​​for relevant parameters. Through It can extend quantitative relationships to three-dimensional situations.

[0100] like Figure 3 As shown, under SLO, this represents the entry velocity that satisfies the perigee altitude requirement. Curved surface. It can be obtained that when... hour, There is a solution. The parametric equations are in the following form:

[0101] (15)

[0102] remember:

[0103] (16)

[0104] in, and It is a parameter, and its value range is... , .

[0105] For ease of calculation, the entry velocity needs to be expressed in the ILI coordinate system. Figure 3 As shown, since only the relative position of the spacecraft leaving the moon is known, the relative velocity distribution resembles a slender cone. Therefore, the corresponding orbital plane passes through the line segment. Since it is not possible to obtain SLO precisely from any plane, it is assumed here that the transformation matrix from ILI to SLO satisfies the following:

[0106] (17)

[0107] in, and The definition can be found by referring to Figure 2 First, wrap MILI around Axis rotation Angle, then around Axis rotation After the angle, With SLO Axis coincidence.

[0108] (18)

[0109] Therefore, under ILI, the parametric equation of the second velocity surface is expressed as:

[0110] (19)

[0111] In the formula, Represented in the instantaneous coordinate system ,in, This is the entry velocity relative to the Moon; This represents the transformation matrix from the lunar orbital coordinate system to the instantaneous coordinate system; In the lunar orbit coordinate system The entry point velocity; This represents the transformation matrix from the instantaneous coordinate system to the lunar orbital coordinate system.

[0112] Finally, the first and second velocity surface parameter equations are solved simultaneously to construct the third velocity surface parameter equation, thereby solving for the velocity surface parameters of the general Earth-Moon orbit.

[0113] Specifically, under ILI, the expression for the parametric equation of the third velocity surface is:

[0114] (20)

[0115] In the formula, This indicates the velocity at the sphere's entry point in the instantaneous coordinate system, representing the influence of the moon. This represents the lunar velocity vector in the instantaneous coordinate system.

[0116] In the specific implementation of step 203, the third velocity surface parameter equation is simplified to obtain the simplified velocity surface parameter equation.

[0117] Based on the range of variable values, the flight path angle and velocity azimuth angle are first assigned values ​​through a traversal process, and the flight time within the lunar influence sphere is calculated to obtain the lunar ephemeris.

[0118] Based on the lunar ephemeris, the longitude and latitude of the entry or exit point are traversed and assigned values. The values ​​of the flight path angle and velocity azimuth angle are then substituted into the simplified velocity surface parameter equation for calculation to obtain the tangential velocity.

[0119] Then, it is determined whether the tangential velocity meets the tolerance. If the tangential velocity meets the tolerance, it is corrected to obtain the corrected tangential velocity.

[0120] Specifically, in the parametric equations of the third velocity surface The calculation formula is:

[0121] (twenty one)

[0122] In the formula, The position of the Moon relative to Earth at the moment of entry point can be obtained through the JPL ephemeris. This represents the transformation matrix from the EJ2000 coordinate system to the ILI coordinate system. It can be calculated using formula (22):

[0123] (twenty two)

[0124] In the formula, The lunar orbital elements at the entry point time can also be obtained through the JPL ephemeris.

[0125] Therefore, formula (20) can be transformed into:

[0126] (twenty three)

[0127] Simplify formula (23) by letting:

[0128] (twenty four)

[0129] Based on this, formula (23) is simplified to obtain the simplified velocity surface parametric equation, which is expressed as:

[0130] (25)

[0131] In the formula, , Represents a constant matrix; , , Represents the velocity surface equation in the lunar orbital coordinate system; Indicates the azimuth angle of the velocity; Indicates the flight path angle; Indicates tangential velocity; Indicates radial velocity; The parameters represent the velocity cylindrical coordinate system.

[0132] It can be seen that, given the position and time when the spacecraft reaches the exit point of the lunar influence sphere, in formula (25) and It is a constant matrix (the position of the moon's influence on the sphere's entry point is fixed). Determine the transformation matrix from ILI to SLO. Sure. A matrix is ​​composed of Confirmed, and and This is related, and therefore determined by the location and time of the spacecraft's exit point from the lunar influence sphere. Among these, (related to lunar ephemeris), therefore, the only variable in formula (25) is... , , and The range of parameter values ​​is... , Flight path angle and radial velocity The range of values ​​needs to be calculated by taking into account specific constraints.

[0133] The specific calculation process is as follows: traverse the velocity and azimuth angles by incrementing the values. and flight path angle Calculate the impact on the flight time inside the sphere And calculate the exit point time epoch. This allows us to obtain the lunar ephemeris.

[0134] Based on the lunar ephemeris, the longitude of the exit point is traversed in an incremental manner. Latitude of the exit point And calculate formula (25), substitute the values ​​of flight path angle and velocity azimuth angle into formula (25), and then sum the squares of the left values ​​of the first two rows to eliminate the parameters. ,judge To determine whether the tolerance is met, further examine whether the left-hand value of the third row in formula (25) is within the radial velocity parameter. Within the range. If satisfied, then the corresponding value is assigned. , , and The solution is what needs to be found, and it is stored in the initial value set of variables. Until... , , and If the value of a variable does not fall within the range of possible values, the iteration stops, and the final set of initial variable values ​​is obtained.

[0135] It is worth noting that when calculating tangential velocity... At that time, formula (25) is a fixed value, but in reality, the tangential velocity increases with the distance from the apogee. The value will increase slightly. This leads to a model error in the solution, and now the tangential velocity at the exit point needs to be determined. Make corrections to ensure vacuum perigee altitude Given.

[0136] Distance from the centroid Tangential velocity that meets tolerance After correction, the calculation expression is as follows:

[0137] (26)

[0138] In the formula, This indicates the corrected tangential velocity; This indicates the lunar center position of the entry point in the geocentric instantaneous coordinate system; Represents the Earth's gravitational constant; This indicates the distance from the Earth's center to the vacuum perigee.

[0139] Therefore, the set of initial values ​​for variables includes .

[0140] It is worth noting that the corrected velocity pulse is on the order of 1 m / s, which is acceptable for engineering implementation.

[0141] In the specific implementation of step 204, the track inclination angle in the engineering constraints can be used. Data such as the type of elevator rail and the landing point area are used to filter the set of initial variable values ​​to obtain initial variable values ​​that meet the conditions.

[0142] One embodiment also provides an example of solving the reachability domain of the reentry point of the lunar-Earth return orbit based on initial values ​​of variables that meet certain conditions. The calculation of the reachability domain of the lunar-Earth return orbit uses the exit point (EX), and steps 201 to 204 provide a general formula for the entry point (EN). The calculation of the exit point is the same as that of the entry point, except that the longitude of the entry point is different. The range of values ​​is .

[0143] The orbital elements of the Earth-Moon return orbit segment are calculated using steps 201 to 204. According to the orbital elements of the geocentric segment Flight time with the lunar core Calculate the true anterior angle of the reentry point. The expression is:

[0144] (27)

[0145] Then, through and It can calculate the flight time of the Earth's core segment. The total return time is .

[0146] Then, based on the true anterior angle of the reentry point... Distance from reentry point to Earth Calculate the reentry point position under EJ2000. The expression is:

[0147] (28)

[0148] in,

[0149] (29)

[0150] Assuming the moon's return time is , At the reentry point, we have:

[0151] (30)

[0152] definition The transformation matrix from EJ2000 to ECF is: Then, based on the reentry point's position in EJ2000... Transformation matrix from EJ2000 to ECF at reentry point Calculate the location of the spacecraft's reentry point at the ECF. ,for:

[0153] (31)

[0154] Based on the principles of spherical geometry, and considering the location of the spacecraft's reentry point within the ECF... Solve for the latitude of the reentry point and reentry point longitude The expression is:

[0155] (32)

[0156] (33)

[0157] like Figure 6 The diagram shows a flowchart illustrating the process of solving the reachable region of the lunar return orbit reentry point (RP) using the method proposed in this invention, as provided in this embodiment. The process includes:

[0158] The initial value range is given based on engineering constraints. Here, the vacuum perigee height is assumed. Near-month altitude Lunar return time The time is 01:00:00 on February 18, 2028. Then define a constant. and calculate The range of values ​​for is: , , , , .

[0159] Velocity azimuth angle and flight path angle Calculate the impact on the flight time inside the sphere Calculate the exit point time epoch This allows us to obtain the lunar ephemeris.

[0160] Traverse the exit point locations Then calculate the simplified velocity surface parameter equation using formula (25). Determine the left-hand side value obtained from the equation. Does it meet the tolerance (generally)? (It will be automatically satisfied), and if the tolerance range is met, then it will be satisfied using formula (26). Correction. Simultaneously, store the variables from the calculation process, including... .

[0161] judge If the value is still within the range, return and continue iterating through the exit point positions in an incremental manner. If not, then determine the flight path angle. If the value is still within the range, return and continue iterating in an incremental manner. If not, the main program terminates. The variables stored in the initial value set are filtered according to project constraints to obtain the initial values ​​that meet the conditions.

[0162] Then, the orbital elements are calculated using the initial values ​​of the variables that meet the conditions, and the reentry point position is calculated using formulas (27), (28), and (29). And true near point angle The reentry point time is calculated using formula (30). The transformation matrix from EJ2000 to ECF is obtained. The reentry point at the ECF is calculated using formula (31). Finally, the latitude of the reentry point under ECF is obtained through formulas (32) and (33). and longitude .

[0163] Under the conditions of satisfying engineering constraints, the geographical latitude and longitude range that can be reached when the satellite returns to Earth at 01:00:00 on February 18, 2028 is obtained as follows: Figure 7 The method takes 327.269590 seconds to compute on an Intel i7-13700KF CPU, significantly improving computational efficiency.

[0164] It should be understood that, although this embodiment Figure 1 , Figure 6 The steps are shown sequentially as indicated by the arrows, but they are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are performed; they can be executed in other orders. Figure 1 , Figure 6 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0165] Example 2

[0166] Based on the lunar orbit initial value design method based on velocity surface parameters in Embodiment 1, this embodiment discloses a lunar orbit initial value design device based on velocity surface parameters, such as... Figure 8As shown, the lunar orbit initial value design device based on velocity surface parameters includes: a value range determination module 401, a velocity surface parameter equation construction module 402, a modified tangential velocity calculation module 403, and a variable initial value determination module 404, wherein:

[0167] The value range determination module 401 is used to determine the value range of each variable based on engineering constraints and constants.

[0168] The velocity surface parametric equation construction module 402 is used to calculate the first velocity surface parametric equation that satisfies the perigee height constraint; and to calculate the second velocity surface parametric equation that satisfies the lunar perigee height constraint; and to solve the first and second velocity surface parametric equations simultaneously to construct the third velocity surface parametric equation for a general Earth-Moon orbit.

[0169] The modified tangential velocity calculation module 403 is used to iterate and assign values ​​to each variable based on the variable value range; substitute each assigned value into the third velocity surface parameter equation to calculate the tangential velocity; determine whether the tangential velocity meets the tolerance, and correct the tangential velocity that meets the tolerance to obtain the corrected tangential velocity.

[0170] The variable initial value determination module 404 is used to obtain the corresponding set of variable initial values ​​based on the corrected tangential velocity; then, the variable initial values ​​in the set of variable initial values ​​are filtered by engineering constraints to obtain the variable initial values ​​that meet the conditions.

[0171] In this embodiment, the specific working process and working principle of the value range determination module 401, the velocity surface parameter equation construction module 402, the modified tangential velocity calculation module 403, and the variable initial value determination module 404 are the same as those in Embodiment 1, and therefore will not be described again in this embodiment. Each unit module can be implemented entirely or partially through software, hardware, or a combination thereof. Each unit module can be embedded in or independent of the processor in a computer device in hardware form, or it can be stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to the above unit modules.

[0172] Example 3

[0173] like Figure 9 The diagram illustrates a terminal device disclosed in this embodiment, comprising a transmitter, a receiver, a memory, and a processor. The transmitter transmits instructions and data, the receiver receives instructions and data, the memory stores computer-executed instructions, and the processor executes the computer-executed instructions stored in the memory to implement the method described in Embodiment 1 above.

[0174] It is important to note that the aforementioned memory can be either standalone or integrated with the processor. When the memory is set up independently, the terminal device also includes a bus for connecting the memory and the processor.

[0175] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0176] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0177] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for initial value design of a lunar orbit based on velocity surface parameters, characterized in that, The method includes: Determine the range of values ​​for each variable based on engineering constraints and constants; Calculate the first velocity surface parametric equation that satisfies the perigee height constraint; and calculate the second velocity surface parametric equation that satisfies the lunar perigee height constraint; solve the first and second velocity surface parametric equations simultaneously to construct the third velocity surface parametric equation for a general Earth-Moon orbit; Based on the range of the variables, each variable is iterated and assigned a value; each assigned value is substituted into the third velocity surface parameter equation for calculation to obtain the tangential velocity; it is determined whether the tangential velocity meets the tolerance, and the tangential velocity that meets the tolerance is corrected to obtain the corrected tangential velocity; Based on the corrected tangential velocity, the corresponding set of initial variable values ​​is obtained; then, the initial variable values ​​in the set of initial variable values ​​are filtered by engineering constraints to obtain the initial variable values ​​that meet the conditions. The expression for the parametric equation of the first velocity surface is: ； In the formula, This indicates the velocity at the sphere's entry point in the instantaneous coordinate system, representing the influence of the moon. This represents the transformation matrix from the velocity cylindrical coordinate system to the instantaneous coordinate system; The velocity at the sphere's entry point is represented by the influence of the moon in a cylindrical velocity coordinate system. The expression for the second velocity surface parametric equation is: ； In the formula, Represented in the instantaneous coordinate system ,in, This is the entry velocity relative to the Moon; This represents the transformation matrix from the lunar orbital coordinate system to the instantaneous coordinate system; In the lunar orbit coordinate system The entry point velocity; This represents the transformation matrix from the instantaneous coordinate system to the lunar orbital coordinate system; The third velocity surface parameter equation is expressed as follows: ； In the formula, This indicates the velocity at the sphere's entry point in the instantaneous coordinate system, representing the influence of the moon. Represented in the instantaneous coordinate system ,in, This is the entry velocity relative to the Moon; This represents the lunar velocity vector in the instantaneous coordinate system.

2. The method for initial value design of lunar orbit based on velocity surface parameters according to claim 1, characterized in that, Based on the range of values ​​of the variables, each variable is iterated and assigned a value; Substituting each assigned value into the third velocity surface parameter equation, the tangential velocity is obtained, including: The third velocity surface parametric equation is simplified to obtain the simplified velocity surface parametric equation; Based on the range of the variables, the flight path angle and velocity azimuth angle are first assigned values ​​through a traversal process, and the flight time within the lunar influence sphere is calculated to obtain the lunar ephemeris. Based on the lunar ephemeris, the longitude and latitude of the entry or exit point are assigned values, and the values ​​of the flight path angle and velocity azimuth angle are substituted into the simplified velocity surface parameter equation for calculation to obtain the tangential velocity.

3. The lunar orbit initial value design method based on velocity surface parameters according to claim 2, characterized in that, The simplified expression for the velocity surface parametric equation is as follows: ； In the formula, , Represents a constant matrix; , , Represents the velocity surface equation in the lunar orbital coordinate system; Indicates the azimuth angle of the velocity; Indicates the flight path angle; Indicates tangential velocity; Indicates radial velocity; The parameters represent the velocity cylindrical coordinate system.

4. The method for initial value design of lunar orbit based on velocity surface parameters according to claim 2, characterized in that, The tangential velocity that meets the tolerance is corrected, and the calculation expression is as follows: ； In the formula, This indicates the corrected tangential velocity; This indicates the lunar center position of the entry point in the geocentric instantaneous coordinate system; Represents the Earth's gravitational constant; Indicates the distance from the centroid; This indicates the distance from the Earth's center to the vacuum perigee.

5. The method for initial value design of lunar orbit based on velocity surface parameters according to claim 4, characterized in that, Also includes: Based on the initial values ​​of variables that meet the conditions, solve for the reachable domain of the reentry point of the lunar-Earth return orbit; The calculation of the reachable region of the reentry point on the lunar-Earth return orbit includes: Calculate the orbital elements of the Earth-Moon return orbit segment to the Earth's center. According to the orbital elements of the aforementioned geocentric segment Flight time with the lunar core Calculate the true anterior angle of the reentry point. ; According to the true anterior angle of the reentry point Distance from reentry point to Earth Calculate the reentry point position under EJ2000. ; Based on the reentry point's location under EJ2000 Transformation matrix from EJ2000 to ECF at reentry point Calculate the location of the spacecraft's reentry point at the ECF. ; Based on the principles of spherical geometry, and considering the location of the spacecraft's reentry point within the ECF... Solve for the latitude of the reentry point and reentry point longitude .

6. A device for initial value design of lunar orbit based on velocity surface parameters, characterized in that, The apparatus employing the lunar orbit initial value design method based on velocity surface parameters as described in any one of claims 1 to 5 includes: The value range determination module is used to determine the value range of each variable based on engineering constraints and constants. The velocity surface parametric equation construction module is used to calculate the first velocity surface parametric equation that satisfies the perigee height constraint; and to calculate the second velocity surface parametric equation that satisfies the lunar perigee height constraint; and to solve the first velocity surface parametric equation and the second velocity surface parametric equation simultaneously to construct the third velocity surface parametric equation for a general Earth-Moon orbit. The modified tangential velocity calculation module is used to iterate and assign values ​​to each variable based on the range of the variable values; substitute each assigned value into the third velocity surface parameter equation to calculate the tangential velocity; determine whether the tangential velocity meets the tolerance, and correct the tangential velocity that meets the tolerance to obtain the corrected tangential velocity; The variable initial value determination module is used to obtain the corresponding set of variable initial values ​​based on the corrected tangential velocity; then, the variable initial values ​​in the set of variable initial values ​​are filtered by engineering constraints to obtain variable initial values ​​that meet the conditions.

7. A computer device, comprising a memory and a processor, characterized in that, The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the lunar orbit initial value design method based on velocity surface parameters as described in any one of claims 1 to 5.

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