A mission planning method for multi-target on-orbit delivery
By optimizing the delivery time and orbital parameters of the main spacecraft, the orbital offset problem during multi-target on-orbit delivery in giant constellations is solved, ensuring the stable convergence of the sub-platform and the target spacecraft is reduced, and the cost is reduced.
Patent Information
- Application Number
- CN202410662876.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-05-27
- Publication Date
- 2025-08-15
- Estimated Expiration
- 2044-05-27
AI Technical Summary
The prior art is difficult to effectively solve the orbital offset problem caused by the perturbation of the recoil volume during multi-target delivery in orbit in giant constellations, resulting in the convergence distance between the sub-platform and the target spacecraft being too large and unable to successfully converge.
By calculating the delivery time series of the main spacecraft on the standard orbit, optimizing the departure time and free flight time of the sub-platform, using the momentum conservation theorem to update the main spacecraft orbit parameters, combining the Lambert problem and Hohmann transfer orbit, optimizing the delivery scheme to stabilize the convergence distance.
The stability of the convergence distance between the sub-platform and the target spacecraft during multiple delivery is achieved, ensuring the success of the intersection and reducing the mission cost.
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Figure CN118505088B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of spacecraft supply delivery, and in particular to a mission planning method for multi-target on-orbit delivery. Background Art
[0002] On-orbit servicing is an important guarantee for improving the operational reliability and extending the service life of spacecraft. With the development of mega-constellations, existing technologies are unable to meet the increasing demand for resupply missions at a low cost.
[0003] Propellant-free delivery orbital maneuvering technology uses rotational separation to achieve relative velocity, allowing the delivered spacecraft to enter the predetermined orbit. Since delivery does not consume propellant, this method can effectively reduce mission costs.
[0004] However, in the process of the delivery spacecraft (referred to as the main spacecraft) sending the supply materials (referred to as the sub-platform) into the transfer orbit, it will inevitably be affected by the recoil perturbation, resulting in orbital deviation.
[0005] Due to the large number of satellites in a mega-constellation, the increasing number of launches will cause this deviation to exceed acceptable limits. If the launch is still planned based on the undeflected orbit (referred to as the standard orbit), the rendezvous distance between the sub-platform and the resupply spacecraft (referred to as the target spacecraft) will be too large, making successful rendezvous impossible. Therefore, mission planning methods for multi-target on-orbit delivery are particularly important. Summary of the Invention
[0006] The present invention aims to provide a mission planning method for multi-target on-orbit delivery. This method addresses the existing technical problem of excessive deviations due to the large number of satellites in a mega-constellation and the increasing number of delivery attempts. If delivery planning is still performed according to standard orbits, the rendezvous distance between the sub-platform and the target spacecraft is too large, making successful rendezvous impossible.
[0007] To solve the above technical problems, the present invention specifically provides a mission planning method for multi-target on-orbit delivery, comprising the following steps:
[0008] Calculate the launch time series t of the main spacecraft in the standard orbit hi ,(i=1,2,3,…,N), N is the total number of target spacecraft that need to be delivered;
[0009] Sort the obtained time and send the time series t hi , (i=1,2,3,…,N) are sorted in ascending order to determine the actual delivery order;
[0010] Create a new Server object entity for the main spacecraft and a Target entity for the target spacecraft, and set the class attribute parameters according to their initial orbit information;
[0011] According to the sorting rules, the following steps are executed repeatedly until all target spacecraft are replenished:
[0012] Optimize the single delivery and get the departure time t of the sub-platform i and the duration of free flight t fi ;
[0013] The orbital parameters of the main spacecraft and the target spacecraft are set to t i and t fi The corresponding parameters of the moment;
[0014] Given the absolute velocity of the sub-platform at the time of departure, the orbital elements and position velocity vector of the main spacecraft are updated according to the law of conservation of momentum, and the orbital parameters of the main spacecraft are updated to the corresponding parameters after launch;
[0015] Among them, t i Indicates the time when the sub-platform departs, t fi Indicates the duration of the sub-platform's free flight.
[0016] As a preferred solution of the present invention, the method for calculating the launch time sequence of the main spacecraft on the standard orbit is:
[0017] In the Hohmann transfer, the phase difference between the departure and arrival positions of each sub-platform transfer relative to the central celestial body is π, and the corresponding flight time t fh for:
[0018]
[0019] Where μ is the gravitational constant of the Earth;
[0020] At the same time, the angular velocities of the main spacecraft and the target spacecraft in their respective orbits are
[0021]
[0022] The time t at which target spacecraft No. i is required to be delivered i , we need to know its initial phase θ i0 and the initial phase θ0 of the main spacecraft;
[0023] In terms of kinematics, the phase difference between the arrival time of the target spacecraft on the sub-platform and the departure time of the main spacecraft is required to be π, that is, it satisfies:
[0024] ω2(t i +t fh )+θi0 -ω1t i -θ0=(2n+1)π,n=±1,±2,±3,…
[0025] This equation is a simple system of linear equations with a remainder. Its corresponding solutions under different n values can be easily obtained using methods such as Newton's method. In general, it is sufficient to set n = 0.
[0026] As a preferred solution of the present invention, the objective function required for optimizing a single delivery is named OptThrow. The function input t i and t fi , the relative speed Δv required for output delivery i , the calculation method includes the following steps:
[0027] Find t i +t fi The orbital elements of the main spacecraft at that moment;
[0028] Using the orbit element conversion algorithm, the plane orbit elements are converted into position and velocity vector outputs to obtain the absolute position r of the main spacecraft at the time of delivery di ;
[0029] Find t fi Orbital elements of the target spacecraft at that moment;
[0030] Using the orbit element conversion algorithm, the plane orbit elements are converted into position and velocity vector outputs to obtain the absolute position r of the target spacecraft at the time of merging with the sub-platform ai ;
[0031] Known r di and r ai , and the transfer time t is known fi , the transfer orbit is required, which is the Lambert problem in orbital dynamics. The Lamberthub library can be called to obtain the velocity vector v of the sub-platform di and the velocity vector v at the moment of convergence ai .
[0032] According to Δv i =||v di -v1||, find Δv i , which is the relative speed required for output delivery. i the speed of the moment;
[0033] The optimization process of the OptThrow function can be implemented through the minimize function in the Scipy library.
[0034] As a preferred embodiment of the present invention, ti The orbital elements of the main spacecraft at time t fi The method for calculating the orbital elements of the target spacecraft at a given moment is:
[0035] It is known that at time t, the orbital elements of the spacecraft are: a, e, θ and θ ω0 ;
[0036] At time t+Δt, a, e, and θ remain unchanged. According to the Kepler equation, the true perigee angle θ ω The calculation process is as follows:
[0037] Calculate the time tt when the spacecraft passes the perigee s :
[0038]
[0039] Using Newton's method, solve the variable E in the following equation, which is the eccentric perigee angle at time:
[0040]
[0041] Convert the eccentric perigee angle E at time t+Δt into the true perigee angle θ ω :
[0042]
[0043] As a preferred solution of the present invention, the orbit element conversion algorithm includes a process of converting from orbit elements to position velocity vectors and a process of converting from position velocity vectors to orbit elements;
[0044] The process of converting from orbital elements to position and velocity vectors consists of the following steps:
[0045] Calculate the semi-major axis p = a(1-e 2 );
[0046] According to the ellipse formula in polar coordinates, calculate the distance ||r|| between the spacecraft and the center of the earth:
[0047]
[0048] Calculate the position vector in rectangular coordinates:
[0049] x=∣∣r∣∣cosθ, y=∣∣r∣∣sinθ;
[0050] Calculate the velocity vector in polar coordinates:
[0051]
[0052] Convert the velocity vector in polar coordinate system to rectangular coordinate system:
[0053]
[0054] The process of converting position and velocity vectors to orbital elements consists of the following steps:
[0055] According to the sum of the kinetic energy and potential energy of the spacecraft in the gravitational field of the central celestial body, the orbital semi-major axis a is calculated:
[0056]
[0057] According to the value of angular momentum H, calculate the eccentricity e:
[0058]
[0059] At the same time, the corresponding semi-permeable diameter p = a(1-e 2 );
[0060] Calculate the radial component v r :
[0061]
[0062] θ is obtained by calculating the trigonometric function corresponding to the true anomaly, where:
[0063]
[0064] According to sinθ and cosθ, the angle calculation module can be called to obtain the θ value.
[0065] As a preferred solution of the present invention, the angle calculation module is:
[0066]
[0067] Compared with the prior art, the present invention has the following beneficial effects:
[0068] The multi-target on-orbit delivery mission planning method of the present invention can calculate and update the position of the main spacecraft after each delivery of the sub-platform by the main spacecraft, so as to re-plan the next delivery route. Even after multiple deliveries, the convergence distance between the sub-platform and the target spacecraft remains stable, which facilitates the intersection of the sub-platform and the target spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS
[0069] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other implementation drawings based on the provided drawings without inventive effort.
[0070] Figure 1 Schematic diagram of the mission scenario in which the main spacecraft delivers a sub-platform to the target spacecraft in the present invention.
[0071] Figure 2 Flowchart of the multiple delivery optimization algorithm in the present invention. DETAILED DESCRIPTION
[0072] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.
[0073] The present invention specifically provides a mission planning method for multi-target on-orbit delivery, comprising the following steps:
[0074] Step 1: Task scenario description:
[0075] like Figure 1 As shown in the figure, at the beginning of the mission, the main spacecraft is in a circular orbit with a radius of r1, and the target spacecraft is in a circular orbit with a radius of r2. The two circular orbits are in the same plane. The main spacecraft can launch the sub-platform into a transfer orbit by rotating it apart. After a period of flight, the sub-platform reaches the target spacecraft and performs an autonomous rendezvous and docking, thereby resupplying the target spacecraft.
[0076] During the delivery process, the presence of reaction momentum will cause the orbit of the main spacecraft to deviate from the standard orbit. Therefore, the calculation of the delivery plan needs to take the influence of orbital deviation into account.
[0077] Step 2: Calculate the standard orbit delivery plan:
[0078] This step aims to provide a delivery plan when the main spacecraft is always operating in the standard orbit, which is used as the initial value of the optimization algorithm in steps five and six.
[0079] According to the knowledge of orbital dynamics, when transferring between two circular orbits with different radii, the most fuel-efficient way is the Hohmann transfer, that is, the transfer is tangent to the circular orbit at both departure and arrival.
[0080] In the Hohmann transfer, the phase difference between the departure and arrival positions of each sub-platform transfer relative to the central celestial body (the Earth) is π. The corresponding flight time t fh for:
[0081]
[0082] where μ is the gravitational constant of the Earth.
[0083] At the same time, the angular velocities of the host spacecraft and the target spacecraft in their respective orbits are:
[0084]
[0085] The time t at which target spacecraft No. i is required to be delivered i , we need to know its initial phase θ i0 and the initial phase θ0 of the main spacecraft.
[0086] In terms of kinematics, the phase difference between the arrival time of the target spacecraft on the sub-platform and the departure time of the main spacecraft is required to be π, that is, it satisfies:
[0087] ω2(t i +t fh )+θ i0 -ω1t i -θ0=(2n+1)π,n=±1,±2,±3,…
[0088] This is a simple system of linear equations with a cofactor. Using methods such as Newton's method, we can easily find the corresponding solutions for different values of n. In general, we can just set n = 0.
[0089] Step 3: Orbital dynamics calculation module:
[0090] This step aims to use object-oriented thinking to establish a two-dimensional orbital dynamics program module. The orbital dynamics program module specifically includes the following modules:
[0091] Angle calculation module:
[0092] In programs, it is often necessary to inversely calculate the corresponding angle based on the value of a trigonometric function. Due to the range of inverse trigonometric functions, it is necessary to determine the angle based on both the sine and cosine values. The calculation method is:
[0093]
[0094] Track element conversion module:
[0095] In the two-dimensional case, the orbital elements of a spacecraft in space can be expressed in two ways: the plane orbit elements (semi-major axis a, eccentricity e, polar angle θ in polar coordinates and the angle θ between the perigee position phase and the polar axis) ω ) and position velocity vector (position vector r and velocity vector v).
[0096] The plane orbit elements include four: semi-major axis a, eccentricity e, polar angle θ in polar coordinate system and the angle θ between the perigee position phase and the polar axis. ω .
[0097] The position and velocity vectors consist of two vectors: the position vector r and the velocity vector v, both expressed in a rectangular coordinate system:
[0098] r=[x,y],v=[v x ,v y ];
[0099] The process of converting from orbital elements to position and velocity vectors is as follows:
[0100] (1) Calculate the semi-major axis p = a(1-e 2 );
[0101] (2) Calculate the distance between the spacecraft and the center of the earth ||r|| according to the ellipse formula in polar coordinates:
[0102]
[0103] (3) Calculate the position vector in the rectangular coordinate system:
[0104] x=∣∣r∣∣cosθ, y=∣∣r∣∣sinθ;
[0105] (4) Calculate the velocity vector in the polar coordinate system:
[0106]
[0107] (5) Convert the velocity vector in the polar coordinate system into a rectangular coordinate system:
[0108]
[0109] The calculation process from position velocity vector to orbital element number is as follows:
[0110] (1) Calculate the orbital semi-major axis a based on the sum of the kinetic energy and potential energy of the spacecraft in the gravitational field of the central celestial body:
[0111]
[0112] (2) Calculate the eccentricity e based on the value of angular momentum H:
[0113]
[0114] At the same time, the corresponding semi-permeable diameter p = a(1-e 2 )
[0115] (3) Calculate the radial component v r:
[0116]
[0117] (4) Calculate the trigonometric function corresponding to the true anomaly to find θ, where
[0118]
[0119] According to sinθ and cosθ, the angle calculation module can be called to obtain the θ value.
[0120] Orbit prediction module:
[0121] This module can give the orbital elements of the spacecraft after Δt.
[0122] It is known that at time t, the orbital elements of the spacecraft are: a, e, θ and θ ω0 , at time t+Δt, a, e, and θ remain unchanged, but the true perigee angle θ ω Calculation needs to be performed according to the Kepler equation.
[0123] The calculation process is as follows:
[0124] (1) Calculate the time tt when the spacecraft passes the perigee s
[0125]
[0126] (2) Using Newton's method, solve the variable E in the following equation, which is the perigee angle at time
[0127]
[0128] (3) Convert the eccentric perigee angle E at time t+Δt into the true perigee angle θ ω :
[0129]
[0130] Step 4: Program object structure:
[0131] Using object-oriented programming principles, we designed three classes: the base spacecraft class SpaceCraft, the main spacecraft class Server, and the target spacecraft class Target. In subsequent calculations, if we need to generate a main spacecraft, we simply define an instance of the main spacecraft based on the SpaceCraft class. Object-oriented programming is a common encapsulation concept in programming.
[0132] Implement three objects: the base spacecraft class SpaceCraft, the main spacecraft class Server, and the target spacecraft class Target, which contain the following methods, properties, and inheritance relationships:
[0133] (1) Spacecraft base class SpaceCraft
[0134] property:
[0135] t: the moment of the spacecraft in the scene;
[0136] a, e, θ, and θ ω : The orbital element corresponding to the spacecraft at time t;
[0137] Position vector r and velocity vector v;
[0138] method:
[0139] orb2proj: Uses orbital element conversion algorithm to convert plane orbital elements into position and velocity vector output;
[0140] proj2orb: Uses the orbit element conversion algorithm to convert position and velocity vectors into plane orbit element output;
[0141] orbPred: uses the orbit prediction module to output the orbit elements at time t+Δt;
[0142] timeTravel: Sets the spacecraft's orbital elements and position velocity vectors to the values corresponding to time t+Δt.
[0143] (2) Main spacecraft class Server: inherited from SpaceCraft;
[0144] New properties:
[0145] m_server, m0: the mass of the main spacecraft and sub-platform;
[0146] New methods:
[0147] Throw: Description of the delivery process. Given the absolute velocity of the sub-platform at the time of departure, according to the law of conservation of momentum, the orbital elements and position velocity vector of the main spacecraft itself are updated.
[0148] (3) Target spacecraft class Target: inherited from SpaceCraft.
[0149] Step 5: Single delivery optimization algorithm
[0150] After the orbits of the main spacecraft and the target spacecraft are given, a delivery is determined by two parameters: the time t at which the sub-platform departs; iand the duration of free flight t fi . t i Determines the absolute position r of the main spacecraft at the time of launch di , t fi Determine the absolute position r of the target spacecraft and the sub-platform at the moment of rendezvous ai .
[0151] In the connection di and r ai In the elliptical orbit cluster, the flight time is limited to t fi Therefore, in the delivery process, the minimum delivery plan can be obtained by optimizing t i and t fi to achieve.
[0152] The objective function required for the optimization process is named OptThrow. The function input t i and t fi , the relative speed Δv required for output delivery i The calculation process is as follows:
[0153] (1) According to the orbital dynamics module described in step 4, t i The orbital elements of the main spacecraft at this moment can be obtained by the orbPred method of the Server class. The orbital elements can be input into orb2proj to obtain r di , the same process is performed on the target spacecraft class Target to obtain r ai .
[0154] (2) Known r di and r ai , and the transfer time t is known fi , requiring the transfer orbit, which is the Lambert problem in orbital dynamics. The Lamberthub library can be called to obtain the velocity vector v of the sub-platform di and the velocity vector v at the moment of convergence ai .
[0155] (3) According to Δv i =||v di -v1||, find Δv i , which is the relative speed required for output delivery. i The speed of time.
[0156] The optimization process of the OptThrow function can be implemented through the minimize function in the Scipy library.
[0157] Step 6: Multiple Delivery Optimization Algorithm
[0158] The algorithm process for overall delivery planning is as follows: Figure 2 As shown:
[0159] (1) According to step 2, calculate the delivery time sequence t of the main spacecraft on the standard orbit hi ,(i=1,2,3,…,N), N is the total number of target spacecraft that need to be delivered.
[0160] (2) Sort the obtained time and send it into time series t hi , (i=1,2,3,…,N) are sorted in ascending order to determine the actual delivery order.
[0161] (3) Create a new Server object entity for the main spacecraft and a Target entity for the target spacecraft, and set the class attribute parameters according to their initial orbit information.
[0162] (4) According to the sorting rules, the following steps are executed repeatedly until all target spacecraft are replenished:
[0163] Perform the single delivery optimization process in step 5 to obtain the departure time t of the sub-platform i and the duration of free flight t fi ;
[0164] By using the timeTravel method, the orbital parameters of the main spacecraft and the target spacecraft are set to t i and t fi The corresponding parameters of the moment;
[0165] The throw method is used to update the orbital parameters of the main spacecraft to the corresponding parameters after launch.
[0166] The multi-target on-orbit delivery mission planning method of the present invention can calculate and update the position of the main spacecraft after each delivery of the sub-platform by the main spacecraft, so as to re-plan the next delivery route. Even after multiple deliveries, the convergence distance between the sub-platform and the target spacecraft remains stable, which facilitates the intersection of the sub-platform and the target spacecraft.
[0167] The above embodiments are merely exemplary embodiments of the present application and are not intended to limit the scope of the present application. The scope of protection of the present application is defined by the claims. Those skilled in the art may make various modifications or equivalent substitutions to the present application within the essence and scope of protection of the present application, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present application.
Claims
1. A mission planning method for multi-target on-orbit delivery, characterized in that: The following steps are involved: Calculate the sub-platform delivery plan when the main spacecraft always operates in the standard orbit: Calculate the launch time series t of the main spacecraft in the standard orbit hi ,(i=1,2,3,…,N), N is the total number of target spacecraft that need to be resupplied; For the delivery time series t hi , (i=1,2,3,…,N) are sorted in ascending order to determine the actual delivery order; According to the sorting order, the following steps are repeated until all target spacecraft are replenished: Optimize a single delivery and get the optimized sub-platform departure time t i and the duration of free flight t fi ; The orbital parameters of the main spacecraft and the target spacecraft are set to t i and t i +t fi The corresponding parameters of the moment; Update the orbital elements and position velocity vector of the main spacecraft itself, and update the orbital parameters of the main spacecraft to the corresponding parameters after launch; Among them, t i Indicates the time when the sub-platform departs, t fi Indicates the duration of free flight of the sub-platform; The method of single delivery optimization is: input t into the objective function OptThrow required for single delivery optimization i and t fi , output the relative speed Δv required for the delivery sub-platform i , the calculation method includes the following steps: Find t i Plane orbit elements of the main spacecraft at that moment; Using the orbit element conversion algorithm, the plane orbit elements are converted into position and velocity vector outputs to obtain the absolute position r of the main spacecraft at the time of delivery di ; Find t i +t fi Plane orbit elements of the target spacecraft at that moment; Using the orbit element conversion algorithm, the plane orbit elements are converted into position and velocity vector outputs to obtain the absolute position r of the target spacecraft at the time of merging with the sub-platform ai ; Known r di and r ai , and the duration of the sub-platform's free flight t is known fi , we can get the unique sub-platform delivery transfer orbit, and call the Lamberthub library to get the sub-platform departure velocity vector v di and the velocity vector v at the moment of convergence ai ; According to Δv i =||v di -v1||, find Δv i , which is the relative speed required for the delivery sub-platform, where v1 is the main spacecraft at t i the speed of the moment; The minimize function in the Scipy library can be used to i and t fi Optimize to optimize the delivery trajectory.
2. The method for planning a multi-target on-orbit delivery mission according to claim 1, wherein: The method for calculating the delivery time series of the main spacecraft in the standard orbit is: In the Hohmann transfer, the phase difference between the departure and arrival positions of each sub-platform transfer relative to the central celestial body is π, and the corresponding flight time t fh for: Where μ is the gravitational constant of the Earth; r1 and r2 represent the orbital radii of the host spacecraft and the target spacecraft at the initial moment, respectively; At the same time, the angular velocities of the host spacecraft and the target spacecraft in their respective orbits are: In terms of kinematics, the phase difference between the arrival time of the target spacecraft on the sub-platform and the departure time of the main spacecraft is required to be π, that is, it satisfies: ω2(t i +t fh )+θ i0 -ω1t i -θ0=(2n+1)π,n=±1,±2,±3,… The Newton method can be used to obtain the corresponding solution under different n values, and the time t for delivering the target spacecraft No. i can be obtained. i ; Among them, θ i0 is the initial phase of the target spacecraft No. i, and θ0 is the initial phase of the master spacecraft.
3. The method for planning a multi-target on-orbit delivery mission according to claim 1, wherein: The orbital element conversion algorithm includes the process of converting from orbital elements to position velocity vectors and the process of converting from position velocity vectors to orbital elements; The process of converting from orbital elements to position and velocity vectors consists of the following steps: Calculate the semi-diameter p = a(1-e 2 ); According to the ellipse formula in polar coordinates, calculate the distance ||r|| between the spacecraft and the center of the earth: Calculate the velocity vector in polar coordinates: Convert the velocity vector in polar coordinate system to rectangular coordinate system: The process of converting position and velocity vectors to orbital elements consists of the following steps: According to the sum of the kinetic energy and potential energy D of the spacecraft under the gravitational field of the central celestial body, the orbital semi-major axis a is calculated as: According to the value of angular momentum H, calculate the eccentricity e: At the same time, the corresponding semi-permeable diameter p = a(1-e 2 ); Calculate the radial component v r : θ is obtained by calculating the trigonometric function corresponding to the true anomaly, where: According to sinθ and cosθ, the angle calculation module is called to obtain the θ value.
4. The method for planning a multi-target on-orbit delivery mission according to claim 3, wherein: The angle calculation module is: