A method for rapid planning of low earth orbit spacecraft rendezvous window

Abstract

The application discloses a kind of low-orbit spacecraft's meeting window fast planning method, belong to aerospace field.The application implementation method is: after being applied to the rocket of ground launch reaches the edge of atmosphere, rocket carries out a maneuver, and meets target spacecraft in ascending process.Meeting window for spacecraft meeting target task is obtained.Meeting window fast planning is mainly divided into three steps, first, according to the envelope of rocket shutdown point and pulse size, the ascending reachable range is obtained.Second, the height of this ascending device, the range of the target in the fixed system is used to judge the coarse window.Third, after obtaining the coarse window, the rocket is shot to the target direction, and the shutdown point position in the inertial system is obtained.Based on the point, the Lambert method is used to calculate the velocity increment.If the constraint is satisfied, it is determined that the rocket can meet the target, i.e.the low-orbit spacecraft's meeting window fast planning is realized.The application has the advantages of fast planning speed and strong applicability.

Description

Technical Field

[0001] This invention relates to a rapid planning method for rendezvous windows of low-Earth orbit spacecraft, and particularly to a method for rapidly planning rendezvous windows for rendezvous problems of non-cooperative low-Earth orbit spacecraft, belonging to the field of aerospace. Background Technology

[0002] Near-Earth space is the primary domain for many space activities, including satellite launches, space exploration, and the International Space Station. However, it also presents numerous hidden dangers, such as space debris and abandoned satellite fragments. Rendezvous with low-Earth orbit (LEO) spacecraft is an effective means of ensuring the safety of LEO missions. A large number of spacecraft are constantly present in LEO space, and when abandoned or potentially threatening spacecraft are detected, timely rendezvous is necessary. Rendezvous technology for LEO spacecraft is a key technology in this field, and determining the rendezvous window is a prerequisite for successful rendezvous.

[0003] In the research on spacecraft rendezvous window calculation, the prior technology [1] (see [1] Jia Feida, Han Hongwei, Wen Changxuan. Target interception launch window calculation based on ascending trajectory reachable range [J]. Journal of Astronautics, 2022, 43(04): 403-412.) proposes a launch window planning method based on ascending trajectory reachable range analysis for low-orbit target interception missions. Based on the ascending trajectory optimization model, the ascending reachable range of the interceptor is determined. According to the crossing relationship between the target sub-satellite point and the outer envelope of the ascending trajectory reachable range, the launch window is initially screened. Finally, for the screened quasi-launch window, the precise launch window is obtained by accurately determining the positional relationship between the target sub-satellite point and each ascending duration reachable range sub-ring. Since it is necessary to continuously optimize the trajectory and compare the reachable range, it takes a long time and cannot solve the problem of rapid planning of rendezvous windows for non-cooperative spacecraft. At the same time, this technology does not consider conditions such as fuel consumption constraints and illumination constraints, and cannot solve the rendezvous window problem considering multiple constraints.

[0004] The prior art [2] (see Duan J H. Rapid onboard generation of two-dimensional rendezvous windows for autonomous rendezvous mission[J].The Journal of the Astronautical Sciences,2020,67:1320-1343.) is based on the two-dimensional reachability domain of the spacecraft. First, it considers the waiting time constraint to calculate the reachable phase range on the target orbit. Then, based on the interceptor fuel constraint, it further determines the reachable phase range of the target orbit within the interceptor reachability domain. Finally, it obtains the final rendezvous window based on the constraint of the total mission duration. However, this method is only applicable to space-based interception problems and cannot solve the ground-based launch interception problem facing spacecraft targets. Summary of the Invention

[0005] The rendezvous described in this invention refers to the overlap of spacecraft positions, with no constraints on relative velocity. The rendezvous problem for low-Earth orbit (LEO) targets is characterized by the unpredictable nature of the target's actions. Therefore, it is necessary to obtain a rendezvous window that satisfies constraints such as velocity increments and illumination within a short time to achieve rendezvous with the target spacecraft. The technical problem addressed by the rapid rendezvous window planning method for LEO spacecraft disclosed in this invention is: for non-cooperative LEO spacecraft, under conditions such as fuel consumption and illumination constraints, to solve for a rendezvous window that meets the constraints based on the spacecraft's capability boundaries, and then plan the spacecraft's rendezvous trajectory based on the obtained rendezvous window. This invention has the advantages of fast planning speed and strong applicability.

[0006] The objective of this invention is achieved through the following technical solution.

[0007] This invention discloses a rapid rendezvous window planning method for low-Earth orbit (LEO) spacecraft. This method is applied to a ground-launched rocket that, after reaching the atmospheric edge and performing a maneuver, rendezvous with a target spacecraft during its ascent. The method yields a rendezvous window for the spacecraft's target rendezvous mission. The rapid rendezvous window planning mainly consists of three steps: First, the achievable ascent range is calculated based on the rocket's shutdown point envelope and pulse magnitude. Second, a coarse window is determined using the ascent unit's altitude, achievable range, and the target's position in the Earth-fixed frame. Third, after obtaining the coarse window, the rocket's trajectory is rotated to the target direction to obtain the shutdown point position in the inertial frame. Based on this point, the velocity increment is calculated using the Lambert method. If the constraints are satisfied, the rocket and target are determined to be capable of rendezvous, thus achieving rapid rendezvous window planning for LEO spacecraft.

[0008] This invention discloses a rapid rendezvous window planning method for low-Earth orbit spacecraft, comprising the following steps:

[0009] Step 1: Consider the rocket shutting down after exiting the Earth's atmosphere. Apply a pulse at the shutdown point, and then the rocket continues to ascend until it stops at the highest point, thus achieving the prediction of the reachability range.

[0010] The reachable range refers to the set of positions that can be reached during the process from the application of the pulse by the rocket to the arrival of the highest point.

[0011] Ignoring the Earth's rotation, all directions can be achieved by adjusting the rocket's trajectory, and the maximum reachable range in any direction is simplified to the in-plane reachable range. The rocket's state when powered off is defined as x0 = [r0, θ0, v]. r0 ,v t0 ] T Where r0 is the geocentric radius vector when the device is powered off, θ0 is the geocentric angle in the motion plane when the device is powered off, and v r0 v is the radial velocity magnitude. t0 Let be the magnitude of the velocity perpendicular to the geocentric radius vector in the plane of motion, and let Δv be the velocity increment corresponding to the pulse. Assuming the maneuvering direction is α, then the rocket state x1 after the pulse is...

[0012] x1=[r0,θ0,v r ,v t ] T =[r0,θ0,v r0 +Δvcosα,v t0 +Δvsinα] T (1)

[0013] Where v r v is the magnitude of the radial velocity after the maneuver. t It represents the magnitude of the velocity perpendicular to the geocentric radius vector in the plane of motion after the maneuver.

[0014] From this state, the eccentricity e and true anomaly angle f0 of the rocket after the pulse are obtained.

[0015]

[0016]

[0017] Where μ is the gravitational constant of the central celestial body. Let be the velocity after the pulse. Then the position the rocket can reach is p = [r, θ]. T The velocity increment direction α and the instantaneous true anomaly angle f are completely determined, where r is the instantaneous geocentric radius vector and θ is the incenter angle in the instantaneous plane of motion. The reachable range of the rocket is... Represented as

[0018]

[0019] The altitude h can be easily obtained from the rocket's position p. r =rRe And the range s = θ - θ0 + s0 = f - f0 + s0, where R e Where is the Earth's radius, and s0 is the rocket's ascent distance within the atmosphere.

[0020] The reachable range of the rocket is solved using formulas (5)-(14). At the terminal radius r... f Under fixed conditions, its range s is expressed as

[0021]

[0022] Where h is the angular momentum after the maneuver, and r f The terminal geocentric vector is denoted as .

[0023] intermediate function g(r) f ,α)

[0024]

[0025] The pulse direction corresponding to the extreme value of the range then satisfies

[0026]

[0027] In the above formula

[0028]

[0029] By rearranging, squaring, and simplifying equation (7), we obtain the equation...

[0030]

[0031] Where a, b, and d are intermediate variables:

[0032]

[0033] Equation (9) is a high-order trigonometric function equation of α, which is difficult to solve directly. However, when α is determined, it is r f The quadratic equation is thus solved in reverse. Fixing α, we solve for the corresponding r that satisfies (9). f Then in r f At point α, the range reaches its extreme value.

[0034] Since only r needs to be considered f ≠ r0, therefore equation (9) is further simplified to obtain information about r f If the equation is a linear equation, then r f The analytical formula is

[0035]

[0036] Where a j ,b jAs an intermediate variable:

[0037]

[0038] Traversing α∈[0,2π), the corresponding extreme terminal height is calculated using equation (11). During the derivation process, the ascent conditions of the rocket are relaxed, so a judgment condition needs to be added. If the obtained height satisfies equation (13), then it meets the conditions for the rocket's ascent period, and can be substituted into equation (5) to obtain the range corresponding to this height.

[0039]

[0040] Furthermore, since only the reachable range during ascent is considered, the above envelope is incomplete; the case where the range reaches the boundary rather than the extreme value must also be considered. When the range reaches the boundary, the true anomaly angle is 180°. Therefore, the extreme range and altitude corresponding to the velocity increment direction α are:

[0041]

[0042] At this point, the reachable envelope of a single shutdown point has been obtained. By traversing the states of the shutdown points and finding their union, the reachable range of the rocket during its ascent phase can be obtained.

[0043] Step Two: The entire coarse window calculation consists of three steps. Step One, for t... c First, the target's position relative to the launch point is calculated. Then, its position vector is calculated to determine the range. This range is compared with the reachable range obtained in step one. If it is less than the maximum range, the rocket and target are determined to be capable of intersecting. The time interval is iterated to obtain a coarse window 1 that satisfies the intersecting condition. The second step, based on coarse window 1, is to calculate t... c At the target altitude, determine if the range at that altitude is sufficient. If it is, determine that the rocket and target can rendezvous. In the third step, based on coarse window 2, calculate the illumination conditions. If the rendezvous time is within the Earth's shadow area, remove the window to obtain the final coarse window 3.

[0044] Step 3: Based on the obtained coarse window 3, first calculate t within the window. c The target's trajectory relative to the launch point is determined, and the shutdown point envelope is transformed to this trajectory to obtain the shutdown point's state in the inertial frame. Based on this point, the Lambert algorithm is used for calculation. If the minimum velocity increment is less than the allowable velocity increment Δv, it is determined that the rocket and target can intersect, thus achieving precise window acquisition.

[0045] Step 4: For the low-Earth orbit spacecraft at the predetermined altitude, plan the rendezvous trajectory of the spacecraft based on the rendezvous precision window obtained in Step 3, thereby realizing the rendezvous between the rocket and the low-Earth orbit spacecraft.

[0046] Beneficial effects:

[0047] 1. The present invention discloses a rapid planning method for rendezvous windows for low-Earth orbit spacecraft. It predicts the reachability range for each shutdown point and does not limit the number of shutdown points. Therefore, it is applicable to the calculation of rendezvous windows given multiple atmospheric edge states.

[0048] 2. The present invention discloses a rapid rendezvous window planning method for low-Earth orbit spacecraft. It calculates the reachable range of the rocket's ascent phase using an analytical method and makes a judgment based on the geometric relationship between the reachable range and the target. Therefore, the rendezvous window planning speed is fast. The planning speed is faster than that of the previous technology [1].

[0049] 3. The present invention discloses a rapid planning method for rendezvous windows for low-Earth orbit spacecraft. By considering constraints such as illumination and Earth's shadow area on the basis of a coarse window, the method performs fine calculation on the window, thus making it suitable for rendezvous window planning that considers multiple constraints. The rendezvous trajectory of the spacecraft is planned according to the obtained rendezvous window, thereby realizing the rendezvous between the rocket and the low-Earth orbit spacecraft. Attached Figure Description

[0050] Figure 1 This is a flowchart of a rapid rendezvous window planning method for low-Earth orbit spacecraft disclosed in this invention.

[0051] Figure 2 This invention discloses a shutdown point reachability envelope diagram for a rapid rendezvous window planning method for low-Earth orbit spacecraft. Detailed Implementation

[0052] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0053] Example 1:

[0054] After reaching the atmospheric edge, the ground-launched rocket performs a maneuver and then rendezvous with the target spacecraft during its ascent. Obtaining the rendezvous window is the first step in a spacecraft rendezvous mission and a fundamental condition for its successful execution. The calculation of the rendezvous window mainly consists of three steps: First, the achievable ascent range is determined based on the rocket's shutdown point envelope and pulse magnitude; second, a coarse window is determined using the ascent unit's altitude, achievable range, and the target's position in the Earth-fixed frame; third, after obtaining the coarse window, the rocket's trajectory is redirected to the target direction to obtain the shutdown point position in the inertial frame, and the velocity increment is calculated using the Lambert method based on this point. If the constraints are met, rendezvous is considered possible. The atmospheric edge conditions are shown in Table 1.

[0055] Table 1 Atmospheric Edge Conditions

[0056]

[0057]

[0058] Step 1: Considering the rocket shutting down after exiting the Earth's atmosphere, apply a pulse at the shutdown point. The rocket then continues to ascend, stopping at its highest point. This allows for the prediction of the rocket's reachable range. In this invention, the reachable range refers to the set of positions the rocket can reach during the process from the application of the pulse to reaching its highest point.

[0059] Ignoring the Earth's rotation, all directions can be obtained by adjusting the rocket's trajectory, and the maximum reachable range in any direction can be simplified to the in-plane reachable range. For a given shutdown point, the reachable range corresponding to each shutdown point is calculated, and then the outer envelope is predicted. The outer envelope is composed of the shortest range curve for the first shutdown point, the longest range curve for the last shutdown point, and the curve connecting the farthest reachable points for each shutdown point, approximating a fan shape. The longest range is 3400 km, and the maximum altitude is 3379 km. This is converted into an altitude-range table with an altitude interval of 50 km; the results are shown in Table 2.

[0060] Table 2 Altitude Range Table

[0061]

[0062]

[0063] Step Two: The entire coarse window calculation consists of three steps: First, for t... c First, the target's position relative to the launch point is calculated. Then, its position vector is calculated to determine the range. This range is compared with the reachable range obtained in step one. If it is less than the maximum range, the rocket and target are determined to be capable of intersecting. The time interval is iterated to obtain a coarse window 1 that satisfies the intersecting condition. The second step, based on coarse window 1, is to calculate t... c At the target altitude, determine if the range at that altitude is sufficient. If it is, determine that the rocket and target can rendezvous. In the third step, based on coarse window 2, calculate the illumination conditions. If the rendezvous time is within the Earth's shadow area, remove the window to obtain the final coarse window 3.

[0064] For t c At any given time, the target's position relative to the launch point is first calculated, then its position vector is calculated to determine the range. This range is compared with the reachable range obtained in the previous section. If the range is less than the maximum range, the target is considered to be capable of intersecting. The time period is iterated to obtain a coarse window 1 that satisfies the intersecting condition. For target A (six roots, see Table 3), the coarse window 1 for the day starting from 00:00 on April 21, 2021 is shown in Table 4.

[0065] Table 3 Target Six Roots

[0066]

[0067] Table 4 Coarse Window 1

[0068]

[0069] Based on coarse window 1, calculate t c At the target's altitude at any given time, determine if the range at that altitude meets the requirement. If it does, the target is considered to be able to intersect. Iterate through the time frame of coarse window 1 to obtain coarse window 2. Table 5 shows coarse window 2 for target A within one day starting from 00:00 on April 21, 2021.

[0070] Table 5 Coarse Window 2

[0071]

[0072] Based on coarse window 2, the illumination conditions are calculated. If the intersection occurs within the Earth's shadow zone, the window is removed, resulting in the final coarse window 3. Table 6 shows the coarse window 3 for target A within one day starting from 00:00 on April 21, 2021.

[0073] Table 6 Coarse Window 3

[0074]

[0075] Step 3: Based on the obtained coarse window 3, first calculate t within the window. c The target's trajectory relative to the launch point is determined, and the shutdown point envelope is transformed to this trajectory to obtain the shutdown point's state in the inertial frame. Based on this point, the Lambert algorithm is used for calculation. If the minimum velocity increment is less than the allowable velocity increment Δv, it is determined that the rocket and target can intersect, thus achieving precise window acquisition.

[0076] The precise window for Target A within one day starting from 00:00 on April 21, 2021 is shown in Table 7.

[0077] Table 7 Fine Window

[0078]

[0079] Step 4: For a low-Earth orbit spacecraft at an altitude of 1100km, plan the rendezvous trajectory of the spacecraft based on the rendezvous window obtained in Step 3, thereby realizing the rendezvous between the rocket and the low-Earth orbit spacecraft.

[0080] 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 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 rapid rendezvous window planning method for low-Earth orbit spacecraft, characterized in that: Includes the following steps, Step 1: Consider the rocket shutting down after exiting the Earth's atmosphere. Apply a pulse at the shutdown point, and then the rocket continues to ascend until it stops at the highest point, thus achieving the prediction of the reachability range. The reachable range refers to the set of positions that can be reached during the process from the application of the pulse by the rocket to the arrival of the highest point; Ignoring the effects of Earth's rotation, all directions can be achieved by adjusting the rocket's trajectory, and the maximum reachable range in any direction is simplified to the in-plane reachable range; the rocket's state when powered off is defined as... ,in The geocentric radius when the device is powered off. The central angle of the moving plane when the device is powered off. The magnitude of the radial velocity. The magnitude of the velocity in the plane of motion, perpendicular to the geocentric radius vector, is given by the velocity increment corresponding to the pulse. Let the direction of maneuver be Then the rocket state after the pulse for in The magnitude of the radial velocity after the maneuver. It represents the magnitude of the velocity perpendicular to the geocentric radius vector in the plane of motion after the maneuver. The eccentricity of the rocket after the pulse is obtained from this state. And true near point angle in The gravitational constant of the central celestial body, Given the velocity after the pulse, the position the rocket can reach is... From the direction of velocity increment and instantaneous true proximity angle Completely certain, among which For instantaneous geocentric radius, The central angle of the instantaneous motion plane, the reachable range of the rocket. Represented as From the position of the rocket Easily obtainable height and range ,in For the Earth's radius, The range of the rocket ascent within the atmosphere; According to the formula - Solve for the reachability range of the rocket; at the terminal radius... Under fixed conditions, its range Represented as in The angular momentum after the maneuver. The terminal geocentric radius; intermediate function The pulse direction corresponding to the extreme value of the range then satisfies In the above formula The formula By transposing, squaring, and simplifying, we obtain the equation. in As an intermediate variable: Mode for The higher-order trigonometric equations are difficult to solve directly; however, when When determined, it is The quadratic equation is thus solved in reverse; fixed Solve for the corresponding satisfaction of Then in At this point, the speed increment is taken At that time, the voyage reached its extreme value; Since only consideration is needed The situation, therefore, Further simplification yields information about The linear equation is then The analytical formula is in As an intermediate variable: Traversal , using Calculate the corresponding extreme end height; In the derivation process, the ascent conditions of the rocket are relaxed, therefore a judgment condition needs to be added; if the obtained altitude satisfies the equation... If it meets the conditions for the rocket's ascent phase, then it can be substituted into the equation. This gives the range corresponding to this altitude; Furthermore, since only the reachable range during ascent is considered, the resulting reachable range envelope is incomplete. The case where the range reaches its boundary rather than its extreme value must also be considered; when the range reaches its boundary, the true anomaly angle is 180°; therefore, the direction of velocity increment... The corresponding extreme range and altitude are At this point, the reachable range envelope of a single shutdown point has been obtained. By traversing the states of the shutdown points and finding their union, the reachable range of the rocket during its ascent phase can be obtained. Step Two: The entire coarse window calculation is divided into three steps; the first step, for At any given time, first calculate the target's position relative to the launch point, then calculate its position vector to obtain the range. Compare this range with the reachable range obtained in step one. If the range is less than the maximum range, then the rocket and the target are determined to be able to intersect. Iterate through the time period to obtain the first coarse window 1 that satisfies the intersecting conditions. The second step is to calculate based on the first coarse window 1. At the target altitude, determine whether the range at this altitude is sufficient. If it is, determine that the rocket and the target can rendezvous, and obtain the second coarse window 2. In the third step, based on the second coarse window 2, calculate the illumination conditions. If the rendezvous time is within the Earth's shadow area, remove the window and obtain the final third coarse window 3. Step 3: Based on the obtained third coarse window 3, first calculate the value within the window. Given the target's trajectory relative to the launch point, the reachable envelope of a single shutdown point is converted to that trajectory to obtain the state of the shutdown point in the inertial frame. Based on this point, the Lambert algorithm is used for calculation. If the minimum speed increment is less than the allowable speed increment... If so, it is determined that the rocket and the target can rendezvous, thus achieving precise window acquisition; Step 4: For the low-Earth orbit spacecraft at the predetermined altitude, plan the rendezvous trajectory of the spacecraft based on the rendezvous precision window obtained in Step 3, thereby realizing the rendezvous between the rocket and the low-Earth orbit spacecraft.

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