A multi-spacecraft rendezvous orbit interval determination method

Abstract

The application discloses a multi-spacecraft rendezvous orbit interval determination method, and belongs to the technical field of aerospace. The method is as follows: according to the task scale and the carrying capacity of a spacecraft mother ship, the maximum number of sub-spacecraft that can be carried by the spacecraft mother ship is set. The deployment orbit height of the spacecraft mother ship is set, a Lambert problem of the sub-spacecraft released by the spacecraft mother ship and a target spacecraft is established, the sub-spacecraft rendezvous range boundary is solved according to the speed increment capacity of the sub-spacecraft, and a sub-spacecraft rendezvous range database is constructed with the orbit plane angle as input and the sub-spacecraft rendezvous range boundary as output. The minimum rendezvous transfer phase range of all the sub-spacecraft carried by a single spacecraft mother ship is calculated by interpolation using the sub-spacecraft rendezvous range database, and the initial deployment orbit interval covered by the spacecraft mother ship is determined. The process of determining the spacecraft mother ship deployment range is repeated until the corresponding spacecraft mother ship orbit interval of all the target spacecraft is determined.

Description

TECHNICAL FIELD

[0001] The application relates to a multi-spacecraft rendezvous orbit interval determination method, in particular to a deployment orbit interval determination method suitable for a spacecraft mother ship capable of releasing multiple sub-spacecraft for rendezvous with multiple targets, and belongs to the technical field of aerospace. BACKGROUND

[0002] The initial orbit interval determination technology is of great significance in the multi-target rendezvous mission of a spacecraft. The technology not only gives each mission spacecraft a position interval capable of realizing rendezvous and docking, but also evaluates the total number of spacecrafts required to complete the multi-target rendezvous mission, which is a key to ensuring the smooth completion of the mission. The current multi-target rendezvous mission planning technology mainly faces the object with multiple transfer maneuver capabilities. The task scene of releasing multiple sub-spacecraft from a spacecraft mother ship to complete multi-target rendezvous is less studied. However, with the continuous growth of potential task targets and the development and maturity of small satellite technology, it will become a trend for the spacecraft mother ship to release multiple sub-spacecraft to complete the rendezvous or fly-by of multiple targets in the future. In addition, compared with the traditional optimal deployment position, the form of giving all positions satisfying the rendezvous constraint condition in the form of orbit interval is more conducive to engineering practice. Based on this, the patent proposes a multi-spacecraft rendezvous orbit interval determination method for the task planning problem of the spacecraft mother ship releasing multiple sub-spacecraft to rendezvous with multiple targets. The method not only realizes the initial deployment position determination of the spacecraft mother ship, but also evaluates the number of spacecraft mother ships required in the multi-target scene according to the capability of the sub-spacecraft, and meets the demand of more spacecraft on-orbit service tasks.

[0003] Among the developed methods for determining the initial deployment position of a spacecraft rendezvous mission, the first technology [1] (see: Zhu Xiaoyu, Qiao Bing, Zhang Qingzhan, Jin Yongqiang, Tan Yinglong. Space fuel station deployment problem of on-orbit refueling task of circular orbit spacecraft [J]. China space science and technology, 2017, 37(03): 35-43.) gives an on-orbit refueling task scheduling and optimization algorithm based on clustering analysis. The immune genetic algorithm is used to give a reference site selection position for the refueling task scheduling space fuel station. However, this method cannot give the range of the site selection position in the form of a feasible interval, which brings difficulties to the actual deployment. SUMMARY

[0004] The technical problem to be solved by the multi-spacecraft rendezvous orbit interval determination method disclosed by the application is: for any number of target spacecrafts with orbit altitudes in a certain range and orbit inclinations close to each other, the rendezvous is sequentially performed in the form of a mission in which a plurality of spacecraft motherships carry a plurality of sub-spacecraft, the number of spacecraft motherships required is given through planning, and the initial deployment position range of each spacecraft mothership in the rendezvous mission is determined.

[0005] The object of the application is achieved by the following technical solutions:

[0006] The multi-spacecraft rendezvous orbit interval determination method disclosed by the application selects any number of spacecrafts near a certain nominal orbit and with a small angle between orbit planes as targets, takes the mission mode in which a spacecraft mother ship releases a plurality of sub-spacecraft at the same time after reaching the deployment position and makes the sub-spacecraft rendezvous with the target spacecrafts at the same time, sets the maximum number of sub-spacecraft that can be carried by the spacecraft mother ship according to the mission scale and the carrying capacity of the spacecraft mother ship, sets the deployment orbit altitude of the spacecraft mother ship according to the actual mission requirements, establishes the Lambert problem of the rendezvous between the sub-spacecraft released by the spacecraft mother ship and the target spacecrafts, solves the rendezvous range boundary of the sub-spacecraft according to the speed increment capacity of the sub-spacecraft, constructs the sub-spacecraft rendezvous range database with the angle between orbit planes as input and the rendezvous range boundary of the sub-spacecraft as output, and performs interpolation calculation on the minimum rendezvous transfer phase range of all sub-spacecraft carried by a single spacecraft mother ship by using the sub-spacecraft rendezvous range database, so as to determine the initial deployment orbit interval that can be covered by the spacecraft mother ship. The process of determining the deployment range of the spacecraft mother ship is repeated until the orbit interval of the corresponding spacecraft mother ship of all target spacecrafts is determined, that is, the multi-spacecraft rendezvous orbit interval determination is realized.

[0007] The multi-spacecraft rendezvous orbit interval determination method disclosed by the application comprises the following steps:

[0008] Step one: The position of the target spacecraft is described by classical orbital elements. The selected target spacecraft should be approximately on the same circular orbit, i.e., all target spacecrafts are near a nominal orbital altitude, and the orbital plane angle between any two target spacecrafts is small. According to the task scale and the carrying capacity of the spacecraft mother ship, the maximum number of sub-spacecraft that the spacecraft mother ship can carry is set. The task mode is that the spacecraft mother ship releases multiple sub-spacecraft at the same time after reaching the deployment location, and the sub-spacecrafts simultaneously rendezvous with the target spacecrafts. In the subsequent steps, the number of spacecraft mother ships required to complete the rendezvous with all target spacecrafts is planned, and the initial deployment orbit interval of each spacecraft mother ship is determined accordingly.

[0009] The positions of the target spacecrafts are described by classical orbital elements. The orbital elements and epoch time of all targets are obtained. The number of target spacecrafts is denoted as N max . The maximum number of sub-spacecraft that a single spacecraft mother ship can carry is denoted as n max . The velocity increment of each sub-spacecraft carried by the spacecraft mother ship is denoted as Δv max . The maximum transfer time of a single sub-spacecraft is equal to the task time constraint, denoted as tof max . As a preferred option, the orbital plane angle between any two target spacecrafts should be within 8°.

[0010] Step two: The deployment orbital altitude of the spacecraft mother ship is set according to the actual task requirements, and the rendezvous problem of the sub-spacecraft released by the spacecraft mother ship with the target spacecrafts is established. Combining the orbital plane angle between the sub-spacecraft and the target spacecraft, the Lambert problem of the sub-spacecraft rendezvous with the target spacecraft is solved, and the sub-spacecraft rendezvous range boundary is obtained according to the velocity increment capability of the sub-spacecraft. A sub-spacecraft rendezvous range database is constructed, with the orbital plane angle as input and the sub-spacecraft rendezvous range boundary as output. Since the target spacecraft positions are represented by considering the orbital plane angle in addition to the nominal orbit, the accuracy of determining the initial deployment orbit interval of the spacecraft mother ship in the subsequent steps can be improved. In addition, the sub-spacecraft rendezvous range database is constructed offline in advance, which can improve the computational efficiency of determining the initial deployment orbit interval of the spacecraft mother ship in steps three to five.

[0011] Step 2.1: The required velocity increment for rendezvous under different phase differences and orbital plane angles is iteratively solved under the maximum transfer time, obtaining the corresponding relationship between the transfer phase difference, the orbital plane angle, and the transfer velocity increment.

[0012] The phase difference is discretized in the range of -180° to 180°, denoted as δ p . The orbital plane angle is discretized in the range of 0° to 8°, denoted as δ i . The Lambert problem for spacecraft rendezvous is constructed:

[0013] Δv = Lambert(tof max , δ i , δ p ) (1)

[0014] As a preferred, Gauss algorithm is selected to solve the Lambert problem of spacecraft rendezvous. When the orbital angle δ i is given, by repeatedly solving equation (1) with different phase differences δ p , the corresponding relationship between the phase difference, the orbital plane angle and the velocity increment under the current spacecraft altitude and the maximum rendezvous time constraint is obtained, which is denoted by function f(·) as follows:

[0015] Δv = f(δ p , δ i ) (2)

[0016] Step 2.2: According to the velocity increment constraint of the sub-spacecraft, the equation is constructed and solved to obtain the boundary values of the rendezvous phase range of the sub-spacecraft, and the sub-spacecraft rendezvous range database is constructed with the orbital plane angle as the input and the boundary of the sub-spacecraft rendezvous range as the output.

[0017] The velocity increment Δv max of the sub-spacecraft is brought into the corresponding relationship of the transfer phase difference, the orbital plane angle and the transfer velocity increment obtained in step 2.1 to obtain the following equation:

[0018] Δv max = f(δ p , δ i ) (3)

[0019] Where the phase difference δ p is the unknown to be solved. Δv max is the given upper limit of the velocity increment, δ i takes the discrete values within the range of step two, and all are known. By interpolation and numerical root finding method, two solutions δ i and δ p0,L of equation (3) under the given orbital plane angle δ p0,R are calculated, which are the left boundary and the right boundary of the rendezvous range of the sub-spacecraft under the transfer time constraint, the velocity increment constraint and the deployment orbit altitude given in step one. The left boundary δ p0,L and the right boundary δ p0,R solved under the same orbital plane angle are denoted as the rendezvous number pair (δ p0,L , δ p0,R ) of the sub-spacecraft, and the relationship between the number pair and the orbital plane angle is denoted by function g(·) as follows:

[0020] (δ p0,L , δ p0,R ) = g(δ i) (4)

[0021] The corresponding relationship in formula (4) is a sub-aircraft rendezvous range database.

[0022] Step three: Project the actual position of the target spacecraft along the geocentric connecting line direction onto the nominal orbit to obtain the relative phase of the target spacecraft on the nominal orbit, establish a target pool containing all target orbit elements and relative phases, and sort them in ascending order according to the relative phase of the spacecraft; set the deployment orbit altitude of the spacecraft mother ship according to the actual task requirements, and set the orbit inclination of the spacecraft mother ship as the nominal orbit inclination of the target spacecraft; select the corresponding number of target spacecraft in the target pool according to the number of sub-aircraft that a single spacecraft mother ship can carry, and use the sub-aircraft rendezvous range database established in step two to interpolate and calculate the rendezvous range of each sub-aircraft at the orbit plane angle with the target spacecraft. Since the target spacecraft position is represented by the nominal orbit and the relative phase, compared with the description using orbit elements, the number of variables required to describe the problem can be reduced under the premise of ensuring high accuracy, and the calculation efficiency of the orbit interval determination is improved. In addition, the influence of the orbit plane angle on the required velocity increment is considered by the database interpolation calculation method, which improves the calculation efficiency of the rendezvous velocity increment under the premise of ensuring the calculation accuracy of the sub-aircraft rendezvous range.

[0023] Step 3.1: Calculate the target relative position according to the target orbit elements obtained in step one and sort them.

[0024] Project the actual position of the target spacecraft along the geocentric connecting line direction onto the nominal orbit. For the target spacecraft with GEO as the nominal orbit, the relative phase representation and calculation method will be given in the embodiments.

[0025] Sort the relative phases of all target spacecraft calculated according to the above process in ascending order, and establish a target pool containing all target orbit elements and relative phases. The relative phase of the kth target in the target pool is denoted as

[0026] Step 3.2: According to the deployment orbit altitude requirement of the spacecraft mother ship, deploy the spacecraft mother ship on the corresponding circular orbit to determine the semi-major axis, eccentricity and orbit inclination in the orbit elements.

[0027] According to the deployment orbit altitude requirement of the spacecraft mother ship, directly determine the semi-major axis in the orbit elements of the spacecraft mother ship.

[0028] According to the number of sub-aircraft carried by the spacecraft mother ship, take the first n max target orbit elements in the target pool established in step 3.1, take the orbit inclination of the nominal orbit as the deployment orbit inclination of the spacecraft mother ship, and set the remaining four orbit elements of the spacecraft mother ship to zero.

[0029] Step 3.3: According to the sub-spacecraft rendezvous range database obtained in step 2, the rendezvous range of all sub-spacecraft carried by the spacecraft mother ship at the maximum orbital plane angle is respectively interpolated and calculated.

[0030] The maximum orbital plane angle between the spacecraft mother ship in step 3.2 and the first n max target in the target pool is denoted as δ i,max , and the sub-spacecraft rendezvous range boundary when the orbital plane angle is δ i,max is interpolated and calculated by the sub-spacecraft rendezvous range database of formula (4), and the left boundary and the right boundary are respectively denoted as δ p ' 0,L and δ p ' 0,R .

[0031] Step 4: According to the sub-spacecraft rendezvous range boundary obtained in step 3, combined with the number of targets in the target pool and the relative phase relationship, the relative phase of the first target in the current target pool is subtracted by the left boundary value of the sub-spacecraft rendezvous range as the right boundary of the spacecraft mother ship deployment phase range. Find the target spacecraft in the target pool whose relative phase does not exceed the right boundary of the spacecraft mother ship deployment phase range and whose number in the current target pool is less than or equal to the number of sub-spacecraft that the spacecraft mother ship can carry, and subtract the right boundary value of the sub-spacecraft rendezvous range from the relative phase as the left boundary of the spacecraft mother ship deployment phase range. According to the task execution time, the corresponding Greenwich hour angle is calculated, the spacecraft mother ship deployment range expressed by the relative phase is converted into the true perigee angle range in the orbital elements, and the determination of the orbital interval of the spacecraft mother ship is realized.

[0032] The right boundary of the spacecraft mother ship deployment phase is calculated according to the relative phase of the target and the left boundary value of the sub-spacecraft rendezvous range, as follows:

[0033]

[0034] Wherein, is the relative phase of the first target in the current target pool, S R represents the right boundary of the reachable phase. The relative phase of the last target in the target pool is denoted as δ p,end , and the number of targets that the sub-spacecraft released by the current spacecraft mother ship can rendezvous is denoted as n' max .

[0035] When S R ≥ δ p,end , let n' max = N max ; when S R < δ p,endAt that time, starting from k=1, k is increased sequentially while comparing the relative phases of targets in the target pool, until a k is found that makes k such that If true, let n′ max =k.

[0036] At this time, if n′ max >n max Let n′ max =n max .

[0037] The left boundary of the deployment phase of the spacecraft mothership is calculated as follows:

[0038]

[0039] in Represents the n′-th target in the current target pool max The relative phase corresponding to each target.

[0040] Calculate the Green's hour angle at the start of the rendezvous mission, and convert the deployment phase range of the spacecraft mothership into the corresponding true anomaly angle range of orbital elements, as follows:

[0041] θ L =S L +gst (7)

[0042] θ R =S R +gst (8)

[0043] Where, θ L and θ R represents the left and right boundaries of the true anomaly angle range of the spacecraft mothership, respectively, and gst represents the Green's time angle at the start of the rendezvous mission. According to equations (7) and (8), the initial deployment positions of the spacecraft mothership when releasing multiple sub-spacecraft to complete the rendezvous mission can be calculated, thus determining the orbital range of the spacecraft mothership.

[0044] Step 5: Remove the targets assigned to the spacecraft mothership and corresponding sub-spacecraft for rendezvous from the target pool, and reconstruct the target pool in ascending order of the relative phase of the remaining targets. Repeat steps 3 and 4 until there are no remaining targets in the target pool. This completes the mission mode in which the spacecraft mothership arrives at the deployment position and simultaneously releases multiple sub-spacecraft to rendezvous with the target spacecraft. The allocation of all spacecraft motherships and the determination of the deployment orbital range of the spacecraft motherships enable the sub-spacecraft to rendezvous with the target spacecraft at any position of the spacecraft mothership within its respective orbital range. This expands the flexibility of multi-spacecraft target rendezvous missions and meets the needs of more spacecraft on-orbit service missions.

[0045] Beneficial effects:

[0046] 1. The multi-spacecraft rendezvous orbit position interval determination method disclosed in the present application, when representing the position of the target spacecraft, considers the orbital plane angle on the basis of the nominal orbit, which facilitates improving the accuracy of the initial deployment orbit position interval determination of the spacecraft mother ship in the subsequent steps.

[0047] 2. The multi-spacecraft rendezvous orbit position interval determination method disclosed in the present application considers the influence of the orbital plane angle on the required velocity increment for rendezvous through the database interpolation calculation method, which improves the calculation efficiency of the required velocity increment for rendezvous on the premise of ensuring the calculation accuracy of the rendezvous range of the sub-spacecraft.

[0048] 3. The multi-spacecraft rendezvous orbit position interval determination method disclosed in the present application, since the position of the target spacecraft is represented by the nominal orbit and the relative phase, compared with the description using the orbital elements, the number of variables required for description can be reduced on the premise of ensuring high accuracy, thereby improving the calculation efficiency of the orbit position interval determination.

[0049] 4. The multi-spacecraft rendezvous orbit position interval determination method disclosed in the present application, the rendezvous range database of the sub-spacecraft is pre-offline constructed, which can improve the calculation efficiency of the initial deployment orbit position interval determination of the spacecraft mother ship.

[0050] 5. The multi-spacecraft rendezvous orbit position interval determination method disclosed in the present application, the multi-target rendezvous task is completed by adopting the task form of the spacecraft mother ship carrying the sub-spacecraft, the spacecraft mother ship can be reserved on the initial deployment orbit for tasks such as relay communication and guidance of the sub-spacecraft, thereby reducing the system complexity of the sub-spacecraft, and further enabling the rendezvous task of a large number of targets to be completed at a lower cost.

[0051] 6. The multi-spacecraft rendezvous orbit position interval determination method disclosed in the present application, by giving the deployment orbit position interval of the spacecraft mother ship, the spacecraft mother ship can release the sub-spacecraft at any position in the range, and the rendezvous between the sub-spacecraft and the target spacecraft can be realized, thereby expanding the flexibility of the multi-spacecraft target rendezvous task and meeting the more on-orbit service task requirements of the spacecraft. BRIEF DESCRIPTION OF DRAWINGS

[0052] Figure 1 is a flowchart of the multi-spacecraft rendezvous orbit position interval determination method disclosed in the present application;

[0053] Figure 2 is a schematic diagram of solving the rendezvous range according to the database in embodiment 1;

[0054] Figure 3 is a schematic diagram of the orbit position interval and task allocation result of the spacecraft mother ship in embodiment 1. DETAILED DESCRIPTION

[0055] In order to better illustrate the purposes and advantages of the present application, the following is a simulation analysis of a GEO multi-target rendezvous mission planning problem, and the present application is explained in detail.

[0056] Embodiment 1:

[0057] As Figure 1 shown, the multi-spacecraft rendezvous orbit interval determination method disclosed in the embodiment, the specific implementation steps are as follows:

[0058] Step one: describe the position of the target spacecraft with classical orbital elements, select the target spacecraft to be approximately on the same circular orbit, that is, satisfy all target spacecrafts are near a nominal orbit altitude, and the orbital plane angle between any target spacecrafts is small. According to the task scale and the carrying capacity of the spacecraft mother ship, set the maximum number of sub-spacecraft that the spacecraft mother ship can carry. The task mode is that the spacecraft mother ship releases multiple sub-spacecraft at the same time after reaching the deployment position and makes them rendezvous with the target spacecraft at the same time. In the subsequent steps, the number of spacecraft mother ships required to complete all target spacecraft rendezvous is planned, and the orbit interval of each spacecraft mother ship on the nominal orbit is determined accordingly.

[0059] The position of the target spacecraft is described by classical orbital elements, the orbital elements and epoch time of all targets are obtained, the number of target spacecrafts is denoted as N max , the maximum number of sub-spacecraft that a single spacecraft mother ship can carry is denoted as n max , the velocity increment of each sub-spacecraft carried by the spacecraft mother ship is equal and denoted as Δv max , and the maximum transfer time of a single sub-spacecraft is equal to the task time constraint and denoted as tof max . As a preferred, the orbital plane angle between any two of the selected target spacecrafts should be within 8°.

[0060] Step two: set the deployment orbit altitude of the spacecraft mother ship according to the actual task requirements, establish the rendezvous problem of the sub-spacecraft released by the spacecraft mother ship and the target spacecraft. Combined with the orbital plane angle, solve the Lambert problem of spacecraft rendezvous, and then solve the sub-spacecraft rendezvous range boundary according to the velocity increment capability of the sub-spacecraft, to construct a sub-spacecraft rendezvous range database with the orbital plane angle as input and the sub-spacecraft rendezvous range boundary as output. When representing the position of the target spacecraft, the orbital plane angle is considered in addition to the nominal orbit, which facilitates improving the accuracy of determining the initial deployment orbit interval of the spacecraft mother ship in the subsequent steps. In addition, the sub-spacecraft rendezvous range database is constructed offline in advance, which can improve the calculation efficiency of determining the initial deployment orbit interval of the spacecraft mother ship in subsequent steps three to five.

[0061] Step 2.1: Obtain the corresponding relationship among the transfer phase difference, the orbital plane angle and the transfer velocity increment by traversing the solution of the required velocity increment of the rendezvous under different phase differences and orbital plane angles at the maximum transfer time.

[0062] Discretize the phase difference in the range of -180-180°, denoted as δ p Discretize the orbital plane angle in the range of 0-8°, denoted as δ i . Construct the Lambert problem of the spacecraft rendezvous:

[0063] Δv = Lambert(tof max , δ i , δ p ) (9)

[0064] As a preferred, the Gauss algorithm is selected to solve the Lambert problem of the spacecraft rendezvous. When the orbital angle δ i is given, the equation (9) is repeatedly solved by inputting different phase differences δ p to obtain the corresponding relationship among the phase difference, the orbital plane angle and the velocity increment under the constraints of the current spacecraft altitude and the maximum rendezvous time, which is denoted as a function f(·) as follows:

[0065] Δv = f(δ p , δ i ) (10)

[0066] Step 2.2: According to the velocity increment constraint of the sub-spacecraft, the equation is constructed and solved to obtain the boundary values of the phase range of the sub-spacecraft rendezvous, and the sub-spacecraft rendezvous range database is constructed with the orbital plane angle as the input and the boundary of the sub-spacecraft rendezvous range as the output.

[0067] The velocity increment Δv max of the sub-spacecraft is brought into the corresponding relationship among the transfer phase difference, the orbital plane angle and the transfer velocity increment obtained in step 2.1 to obtain the following equation:

[0068] Δv max = f(δ p , δ i ) (11)

[0069] Where the phase difference δ p is an unknown to be solved. Δv max is the given upper limit of the velocity increment, δ i takes the discrete values in the range of step two, and all are known. The two solutions δ i and δ p0,L of equation (11) under the given orbital plane angle δ p0,R are calculated by the interpolation and numerical root finding method., and the right boundary of the rendezvous range of the sub-spacecraft under the transfer time constraint, the velocity increment constraint, and the deployment orbit altitude given in step one. The left boundary δ p0,L and the right boundary δ p0,R are denoted as the rendezvous number pair (δ p0,L , δ p0,R ) of the sub-spacecraft, and the relationship between the number pair and the orbit plane angle is expressed by a function g(·) as follows:

[0070] (δ p0,L , δ p0,R ) = g(δ i ) (12)

[0071] The corresponding relationship in equation (12) is the rendezvous range database of the sub-spacecraft.

[0072] Step three: Project the actual positions of the target spacecrafts along the geocentric connecting line direction onto the nominal orbit to obtain the relative phases of the target spacecrafts on the nominal orbit, establish a target pool containing all the target spacecraft orbit elements and relative phases, and sort the target pool in ascending order according to the spacecraft relative phases; set the deployment orbit altitude of the spacecraft mother ship according to the actual mission requirements, and set the orbit inclination of the spacecraft mother ship to be the nominal orbit inclination of the target spacecrafts; select a corresponding number of target spacecrafts in the target pool according to the number of sub-spacecrafts that can be carried by a single spacecraft mother ship, and use the sub-spacecraft rendezvous range database established in step two to interpolate and calculate the rendezvous range of each sub-spacecraft under the orbit plane angle thereof and the target spacecraft. Since the positions of the target spacecrafts are represented by the nominal orbit and the relative phase, compared with the description using orbit elements, the number of variables required to describe the problem can be reduced under the premise of ensuring high accuracy, and the calculation efficiency of the orbit interval determination can be improved. In addition, the influence of the orbit plane angle on the required velocity increment for rendezvous is considered by the database interpolation calculation method, which improves the calculation efficiency of the rendezvous velocity increment under the premise of ensuring the calculation accuracy of the sub-spacecraft rendezvous range.

[0073] Step 3.1: Calculate the target relative positions according to the target orbit elements obtained in step one and sort them.

[0074] In this embodiment, the GEO target is taken as an example to give the representation and calculation method of the target relative phase. According to the orbit elements of each target, the longitude and latitude of the target are obtained by Kepler orbit recursion for one orbit period from the mission start time, and the longitude of the target when it crosses the equator is obtained by interpolation. The longitude value is taken as the relative phase of the target, which is used to reflect the target position and the relative phase relationship between the targets.

[0075] Sort the relative phases calculated according to the above process of all target spacecraft in ascending order, establish a target pool containing all target orbital elements and relative phases, and record the relative phase of the kth target in the target pool as

[0076] Step 3.2: According to the deployment orbit altitude requirement of the spacecraft mother ship, deploy the spacecraft mother ship on the corresponding circular orbit, and determine the semi-major axis, eccentricity and orbit inclination in the orbital elements.

[0077] According to the deployment orbit altitude requirement of the spacecraft mother ship, directly determine the semi-major axis in the orbital elements of the spacecraft mother ship.

[0078] According to the number of sub-aircraft carried by the spacecraft mother ship, take the orbital elements of the first n max targets in the target pool established in step 3.1, take the orbit inclination of the nominal orbit as the deployment orbit inclination of the spacecraft mother ship, and set the remaining four orbital elements of the spacecraft mother ship to 0.

[0079] Step 3.3: According to the sub-aircraft intersection range database obtained in step two, respectively interpolate the intersection range of all sub-aircraft carried by the spacecraft mother ship under the maximum orbit plane angle.

[0080] The maximum orbit plane angle between the spacecraft mother ship in step 3.2 and the first n max targets in the target pool is recorded as δ i,max , and the sub-aircraft intersection range boundary when the orbit plane angle is δ i,max is calculated by interpolating the sub-aircraft intersection range database of formula (12), and the left boundary and right boundary are recorded as δ p ′ 0,L and δ p ′ 0,R .

[0081] Step four: According to the sub-aircraft intersection range boundary obtained in step three, combined with the number of targets in the target pool and the relative phase relationship, subtract the left boundary value of the sub-aircraft intersection range from the relative phase of the first target in the current target pool as the right boundary of the spacecraft mother ship deployment phase range. Find the target spacecraft whose relative phase does not exceed the right boundary of the spacecraft mother ship deployment phase range and whose number in the current target pool is less than or equal to the number of sub-aircraft that the spacecraft mother ship can carry, and subtract the right boundary value of the sub-aircraft intersection range from the relative phase as the left boundary of the spacecraft mother ship deployment phase range. According to the task execution time, calculate the corresponding Greenwich hour angle, convert the spacecraft mother ship deployment range expressed by the relative phase into the true anomaly angle range in the orbital elements, and realize the determination of the orbit interval of the spacecraft mother ship.

[0082] The right boundary of the spacecraft mothership's deployment phase is calculated based on the target's relative phase and the left boundary value of the sub-vehicle's rendezvous range, as follows:

[0083]

[0084] in, S represents the relative phase of the first target in the current target pool. R This represents the right boundary of the reachable phase. The relative phase of the last target in the target pool is denoted as δ. p,end The number of targets that the child spacecraft released from the current spacecraft mothership can rendezvous with is denoted as n′. max .

[0085] When S R ≥δ p,end When, let n′ max =N max When S R <δ p,end At that time, starting from k=1, k is increased sequentially while comparing the relative phases of targets in the target pool, until a k is found that makes k such that If true, then n′ max =k.

[0086] At this time, if n′ max >n max Let n′ max =n max .

[0087] The left boundary of the deployment phase of the spacecraft mothership is calculated as follows:

[0088]

[0089] in Represents the n′-th target in the current target pool max The relative phase corresponding to each target.

[0090] Calculate the Green's hour angle at the start of the rendezvous mission, and convert the deployment phase range of the spacecraft mothership into the corresponding true anomaly angle range of orbital elements, as follows:

[0091] θ L =S L +gst (15)

[0092] θ R =S R +gst (16)

[0093] Where, θ L and θ Rrespectively represent the left and right boundaries of the true anomaly range of the spacecraft mother ship, and gst represents the Greenwich hour angle at the beginning of the rendezvous mission. According to formula (15) and formula (16), the initial deployment position of the spacecraft mother ship releasing multiple sub-spacecraft to complete the rendezvous mission can be calculated, and the determination of the spacecraft mother ship orbit interval is realized.

[0094] Step five: remove the targets for which the spacecraft mother ship and the corresponding sub-spacecraft have been scheduled to perform the rendezvous mission from the target pool, reconstruct the target pool arranged in ascending order of the relative phase of the remaining targets, and repeat steps three and four until there are no remaining targets in the target pool, i.e. the spacecraft mother ship reaches the deployment position and releases multiple sub-spacecraft at the same time and makes them rendezvous with the target spacecraft at the same time in this mission mode. The allocation of all spacecraft mother ships and the determination of the spacecraft mother ship deployment orbit interval enable the sub-spacecraft to rendezvous with the target spacecraft when the spacecraft mother ship releases the sub-spacecraft at any position in the respective orbit interval, thereby expanding the flexibility of the multi-spacecraft target rendezvous mission and meeting more on-orbit servicing mission requirements.

[0095] To verify the feasibility of the method, the spacecraft mother ship is deployed on a circular orbit with an orbital height of 35988.1 km, the upper limit of the transfer time of a single sub-spacecraft is set to 5 hours, the upper limit of the velocity increment is set to 1.2 km / s, the spacecraft mother ship can carry a maximum of 5 sub-spacecraft, and the Earth radius is 6378.14 km. 20 targets are randomly given on a circular orbit with an altitude of 35788.1 km, and the relative phase of the target distribution is shown in Figure 3 The initial time of the mission is set to UTC time 7:00 on July 15, 2025. The initial orbit interval of the spacecraft mother ship releasing multiple sub-spacecraft to rendezvous with the target is calculated using the proposed method, and the range of the single sub-spacecraft that can rendezvous is solved by using the numerical method in step two of embodiment 1 as shown in Figure 2

[0096] The rendezvous transfer range database of the sub-spacecraft under different target orbit plane angle calculated according to the above initial conditions is shown in Table 1.

[0097] Table 1 Rendezvous transfer range of sub-spacecraft under different target orbit inclination difference

[0098] Track surface included angle / deg Intersection range left boundary / deg Intersection range right boundary / deg 0 -13.42 13.56 2 -13.33 13.43 4 -13.05 13.07 6 -12.59 12.46 8 -11.94 11.63

[0099] According to the branching and stopping conditions in steps four and five, the required number of spacecraft mother ships and their orbit intervals are obtained as shown in Table 2.

[0100] Table 2 Determination results of the orbit interval of the multi-target rendezvous spacecraft mother ship

[0101] ​

[0102]

[0103] The initial orbital range of all spacecraft motherships is as follows: Figure 3 As shown, different shapes are used to mark the target allocation results and the orbital range of the spacecraft mothership. (Refer to Table 2 and...) Figure 3 It can be seen that five mother spacecraft carrying daughter spacecraft are needed to complete the rendezvous and docking with 20 GEO targets, and the calculated orbital range is relatively reasonable. Using the spacecraft multi-target rendezvous orbital range determination method proposed in this invention to plan the above mission scenario, there is no significant computational overhead except for the database generation step. Furthermore, the generated database can be reused for any number of targets and their specific locations, demonstrating the computational efficiency advantage of the method proposed in this invention.

[0104] 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 a position interval of a multi-spacecraft rendezvous, characterized in that: Comprising the following steps, Step one: describe the position of target spacecraft with classical orbit elements, select the target spacecraft to be approximately on the same circular orbit, that is, all target spacecrafts are near a nominal orbit altitude, and the orbital plane angle between any target spacecrafts should be within 8°; according to the task scale and the carrying capacity of spacecraft mother ship, set the maximum number of sub-spacecraft that the spacecraft mother ship can carry; the task mode is that the spacecraft mother ship releases multiple sub-spacecraft at the same time after reaching the deployment location and makes them rendezvous with the target spacecraft at the same time, plan the number of spacecraft mother ships required to complete the rendezvous of all target spacecrafts in the subsequent steps, and determine the initial deployment orbit interval of each spacecraft mother ship accordingly; Step two: set the deployment orbit altitude of the spacecraft mother ship according to the actual task requirements, establish the rendezvous problem of the sub-spacecraft released by the spacecraft mother ship and the target spacecraft; combine the orbital plane angle between the sub-spacecraft and the target spacecraft, solve the Lambert problem of the sub-spacecraft and the target spacecraft rendezvous, and then solve the sub-spacecraft rendezvous range boundary according to the velocity increment capability of the sub-spacecraft, to construct a sub-spacecraft rendezvous range database with the orbital plane angle as input and the sub-spacecraft rendezvous range boundary as output; since the position of the target spacecraft is represented by the nominal orbit and the orbital plane angle, the accuracy of determining the initial deployment orbit interval of the spacecraft mother ship in the subsequent steps can be improved; in addition, the sub-spacecraft rendezvous range database is constructed offline in advance, which can improve the calculation efficiency of determining the initial deployment orbit interval of the spacecraft mother ship in steps three to five; Step three: project the actual position of the target spacecraft along the geocentric connecting line to the nominal orbit to obtain the relative phase of the target spacecraft on the nominal orbit, establish a target pool containing the orbit elements and relative phases of all target spacecrafts, and sort them in ascending order according to the relative phase of the spacecraft; set the deployment orbit altitude of the spacecraft mother ship according to the actual task requirements, and set the orbit inclination of the spacecraft mother ship to the nominal orbit inclination of the target spacecraft; select the corresponding number of target spacecrafts in the target pool according to the number of sub-spacecraft that a single spacecraft mother ship can carry, and use the sub-spacecraft rendezvous range database established in step two to interpolate and calculate the rendezvous range of each sub-spacecraft under the orbital plane angle between it and the target spacecraft; since the position of the target spacecraft is represented by the nominal orbit and the relative phase, compared with using orbit elements to describe, the number of variables required to describe the problem can be reduced under the premise of ensuring high accuracy, and the calculation efficiency of the orbit interval determination can be improved; in addition, the influence of the orbital plane angle on the velocity increment required for rendezvous is considered through database interpolation calculation, which improves the calculation efficiency of the rendezvous velocity increment under the premise of ensuring the calculation accuracy of the sub-spacecraft rendezvous range; Step four: according to the sub-aircraft rendezvous range boundary obtained in step three, combined with the number of targets in the target pool and the relative phase relationship, the relative phase of the first target in the current target pool is subtracted from the left boundary value of the sub-aircraft rendezvous range as the right boundary of the spacecraft mother ship deployment phase range; find out the target spacecraft in the target pool whose relative phase does not exceed the right boundary of the spacecraft mother ship deployment phase range and whose number in the current target pool is less than or equal to the number of sub-aircraft that the spacecraft mother ship can carry, and subtract the right boundary value of the sub-aircraft rendezvous range from the relative phase as the left boundary of the spacecraft mother ship deployment phase range; according to the task execution time, calculate the corresponding Greenwich hour angle, convert the spacecraft mother ship deployment range represented by the relative phase into the true perihelion angle range in the orbital elements, and realize the determination of the orbital interval of the spacecraft mother ship; Step five: remove the targets that have arranged the spacecraft mother ship and the corresponding sub-aircraft to perform the rendezvous task from the target pool, reconstruct the target pool arranged in ascending order of the relative phase of the remaining targets, repeat steps three and four until there is no remaining target in the target pool, that is, the spacecraft mother ship reaches the deployment position and releases multiple sub-aircraft at the same time and makes them rendezvous with the target spacecraft simultaneously. In this mode of task, the allocation of all spacecraft mother ships and the determination of the deployment orbit interval of the spacecraft mother ship enable the spacecraft mother ship to release sub-aircraft at any position in the respective orbit interval, which can realize the rendezvous of the sub-aircraft with the target spacecraft, thereby expanding the flexibility of the multi-spacecraft target rendezvous task and meeting more on-orbit service task requirements.

2. The method of claim 1, wherein: Step one is implemented by, The position of the target spacecraft is described by classical orbit elements, and the orbit elements and epoch time of all targets are obtained, and the number of target spacecraft is denoted as N max ; the number of sub-spacecraft that can be carried by a single spacecraft mother ship is denoted as n max ; the velocity increment of each sub-spacecraft carried by the spacecraft mother ship is equal, and is denoted as Δv max ; and the maximum transfer time of a single sub-spacecraft is equal to the mission time constraint, and is denoted as tof max .

3. The method of claim 2, wherein: Step two is implemented by, Step 2.1: under the maximum transfer time, the required velocity increment under different phase differences and orbit plane angles is solved by iteration, and the corresponding relationship among the transfer phase difference, the orbit plane angle and the transfer velocity increment is obtained; Discrete phase difference in the range -180 to 180°, denoted δ p Discrete orbital plane angle in the range 0 to 8°, denoted δ i ; Lambert problem for spacecraft rendezvous: Δv = Lambert(tof max , δ i , δ p ) (1) Given the orbital angle δ i At that time, by introducing different phase differences δ p By repeatedly solving equation (1), the corresponding relationship between the phase difference, the orbital plane angle, and the velocity increment under the constraints of the current aircraft altitude and the maximum rendezvous time is obtained, which is expressed by the function f(·) as follows: Δv = f(δ p ,δ i ) (2) Step 2.2: according to the sub-aircraft velocity increment constraint, an equation is constructed and solved to obtain the boundary values of the sub-aircraft rendezvous phase range, and a sub-aircraft rendezvous range database is constructed with the orbit plane angle as the input and the sub-aircraft rendezvous range boundary as the output; The velocity increment Δv of the sub-spacecraft max Substituting the transfer phase difference, the orbital plane angle and the transfer velocity increment correspondence obtained in step 2.1, the following equation is obtained: Δv max = f(δ p , δ i ) (3) Where the phase difference δ p Let Δv be the unknown variable to be solved. max Given the upper limit of the velocity increment, δ i The discrete values ​​within the range of step two are all known; the angle δ between the points of reference on the given orbital plane is calculated using interpolation and numerical root-finding methods. i The two solutions δ p0,L and δ p0,R This refers to the left and right boundaries of the intersecting range of the sub-vehicle under the given transfer time constraint, velocity increment constraint, and deployment orbit altitude in step one; the left boundary δ is obtained by solving the angle between the same orbital planes. p0,L and right boundary δ p0,R Let the number of rendezvous pairs of sub-spacecraft be denoted as δ. p0,L ,δ p0,R If the angle between this pair and the orbital plane is given by the function g(·), then the relationship between them is as follows: (δ p0,L ,δ p0,R ) = g(δ i ) (4), The corresponding relationship in formula (4) is the sub-aircraft rendezvous range database.

4. The method of claim 3, wherein: Step three is implemented by, Step 3.1: according to the target orbital elements obtained in step one, the target relative position is calculated and sorted; The actual position of the target spacecraft is projected onto the nominal orbit along the geocentric connecting line direction, and the relative phase representation and calculation method for the target spacecraft with GEO as the nominal orbit; according to the orbital elements of each target, a Kepler orbit is recursively calculated for one orbit period from the task start time, the longitude and latitude of the target within this period are obtained, and the longitude of the target passing through the equator is interpolated to obtain the relative phase of the target, which is used to reflect the relative phase relationship between the target position and the target; The relative phases calculated for all target spacecraft according to the above procedure are sorted in ascending order, a target pool containing all target orbital elements and relative phases is established, and the relative phase of the kth target in the target pool is denoted as l k ; Step 3.2: according to the deployment orbit height requirement of the spacecraft mother ship, the spacecraft mother ship is deployed on the corresponding circular orbit, and the semi-major axis, eccentricity and orbit inclination in the orbital elements are determined; According to the deployment orbit height requirement of the spacecraft mother ship, the semi-major axis in the orbital elements is directly determined; According to the number of sub-spacecraft carried by the spacecraft mother ship, take the first n max target orbit elements in the target pool established in step 3.1, take the orbit inclination of the nominal orbit as the deployment orbit inclination of the spacecraft mother ship, and set the remaining 4 orbit elements of the spacecraft mother ship to 0; Step 3.3: According to the sub-spacecraft intersection range database obtained in step 2, the intersection range of each sub-spacecraft carried by the spacecraft mother ship at the maximum orbital plane angle is calculated by interpolation; The maximum orbital plane angle between the spacecraft mother ship in step 3.2 and the first n targets in the target pool is denoted as δ max The orbital plane angle δ i,max is calculated by the sub-spacecraft intersection range database of equation (4) to find the sub-spacecraft intersection range boundary when the orbital plane angle is δ i,max The left and right boundaries of the sub-spacecraft intersection range are denoted as δ' p0,L and δ' p0,R , respectively.

5. The method of claim 4, wherein: The fourth step is implemented by, The right boundary of the deployment phase of the spacecraft mother ship is calculated according to the relative phase of the target and the left boundary value of the intersection range of the sub-spacecraft, as follows: S R = l1- δ' p0,L (5) wherein, l1 is the relative phase of the first target in the current target pool, S R represents the right boundary of the reachable phase; the relative phase of the last target in the target pool is recorded as δ p,end , and the number of targets that can be rendezvoused by the sub-spacecraft released by the current space vehicle mother ship is recorded as n′ max ; When S R ≥ δ p,end , let n′ max = N max ; when S R < δ p,end , increase k one by one from k = 1, and compare the relative phases of the targets in the target pool until a k is found such that l k ≤ S R < l k+1 , and let n′ max = k; At this time, if n' max > n max , let n' max = n max ; The left boundary of the deployment phase of the spacecraft mother ship is calculated as follows: wherein represents the relative phase corresponding to then'th max target in the current target pool. According to the Greenwich hour angle at the intersection task start time, the deployment phase range of the spacecraft mother ship is converted into the corresponding orbital element true anomaly angle range, as follows: θ L = S L + gst (7) θ R = S R + gst (8) where θ L and θ R respectively represent the left and right boundaries of the true anomaly angle range of the spacecraft mother ship, and gst represents the Greenwich hour angle at the beginning of the rendezvous mission; the initial deployment position of the spacecraft mother ship releasing multiple sub-spacecraft to complete the rendezvous mission can be calculated according to formula (7) and formula (8), so as to determine the orbit interval of the spacecraft mother ship.

6. The method of claim 5, wherein: The Gauss algorithm is selected to solve the Lambert problem of spacecraft intersection.

Images