A GEO Multi-Spacecraft Cooperative On-Orbit Refueling Mission Planning Method

Abstract

The present invention relates to the technical field of on-orbit servicing of spacecraft, and specifically to a method for mission planning of cooperative on-orbit refueling for multiple GEO spacecraft. The key points of its technical solution include: 1. Establish an orbit transfer model based on the method of attitude and phase adjustment maneuvers to reveal the relationship between the velocity increment and time of spacecraft orbit transfer; 2. Establish a two-layer optimization model for cooperative on-orbit refueling mission planning to determine the mission time range on the basis of minimizing fuel consumption; 3. Use a two-layer optimization algorithm to efficiently solve the optimization model, and the branch and bound algorithm and the fast elitist multi-objective genetic algorithm are respectively adopted for the inner and outer layers. The method of the present invention breaks through the limitations of the traditional many-to-many on-orbit refueling strategy, allows multiple service spacecraft to cooperate to complete the same refueling mission, reduces the fuel consumption and time cost of the on-orbit refueling mission, and the result is close to the Pareto optimal state. The present invention fully considers various constraints such as dynamic scheduling and payload limitations, and is closer to the actual engineering requirements.

Description

Technical Field

[0001] The present invention relates to the technical field of on-orbit servicing of spacecraft, and particularly to a method for planning GEO multi-spacecraft collaborative on-orbit refueling missions. Background Art

[0002] With the development of technology, the field of on-orbit servicing of spacecraft has received extensive attention globally. On-orbit refueling of spacecraft, rather than directly replacing fuel-depleted spacecraft, as a low-risk on-orbit service, has the advantages of reducing launch weight, extending the lifespan of spacecraft, and improving system efficiency. However, on-orbit refueling missions for large-scale satellite constellations exhibit characteristics such as high demand and high requirements for the payload capacity of servicing spacecraft. Providing on-orbit refueling services to multiple spacecraft in a single mission can not only improve operational efficiency but also greatly enhance economic benefits. How to achieve the optimal on-orbit refueling mission planning has become a key factor in maximizing benefits.

[0003] In existing on-orbit refueling mission planning methods, including one-to-many and many-to-many scenarios, the fuel payload capacity of a single servicing spacecraft is limited, severely restricting the number of target spacecraft it can service. Moreover, the same refueling mission is only allowed to be completed by a single servicing spacecraft. When the demand of target spacecraft is large, the servicing spacecraft has to make multiple round trips to the fuel station, increasing fuel consumption and mission time. Therefore, the GEO multi-spacecraft on-orbit refueling method and its mission planning problem are currently technical challenges that need to be urgently overcome. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the present invention provides a method for planning GEO multi-spacecraft collaborative on-orbit refueling missions to solve the problems raised in the background art.

[0005] The above technical objectives of the present invention are achieved through the following technical solutions:

[0006] A method for planning GEO multi-spacecraft collaborative on-orbit refueling missions includes the following steps:

[0007] Step 1: Establish an orbit transfer model based on the method of attitude and phase adjustment maneuvers to reveal the relationship between the orbit transfer velocity increment and time of the spacecraft;

[0008] Step 2: Establish a two-layer optimization model for on-orbit refueling mission planning to determine the mission time range on the basis of minimizing fuel consumption;

[0009] Step 3: Use a two-layer optimization algorithm to efficiently solve the optimization model. The B&B algorithm and the NSGA-II algorithm are respectively used for the inner and outer layers to obtain the optimal service sequence of servicing spacecraft, decision variable set, fuel consumption, and mission time.

[0010] Further, the above Step 1 includes the following contents:

[0011] Using multiple service spacecraft and multiple fuel stations to complete the refueling tasks for multiple target spacecraft is the target satellite constellation is the th target spacecraft is the number of target spacecraft

[0012] is the service satellite constellation is the th service spacecraft is the number of service spacecraft

[0013] is the fuel station is the th fuel station is the number of fuel stations

[0014] Under given mission parameters, the service spacecraft departs from the fuel station and performs orbital transfer until it rendezvouses and docks with the target spacecraft with depleted fuel and completes the refueling task

[0015] If the fuel carried by a single service spacecraft is insufficient, it can return to the fuel station to replenish fuel and then continue to perform the mission or cooperate with other service spacecraft to complete it

[0016] After all tasks are completed, the service spacecraft needs to return to the fuel station

[0017] The relationship between the velocity increment of orbital maneuver and fuel consumption is:

[0018] ;

[0019] where is fuel consumption is the velocity increment is the mass of the service spacecraft is the gravitational acceleration is the specific impulse of the spacecraft propellant

[0020] The fuel consumption of orbital maneuver is positively correlated with the velocity increment

[0021] Therefore, solving the optimal orbital maneuver is transformed into optimizing the number of transfer circles of the service spacecraft in the phasing orbit

[0022] Since the orbital plane can be adjusted during the phasing maneuver stage, the time for the service spacecraft to adjust the orbital plane is already included in the phasing maneuver time, so only the optimal maneuver in the phasing maneuver stage needs to be solved

[0023] is the decision variable, representing the service spacecraft After servicing the target spacecraft is it necessary to return to the fuel station for refueling?

[0024] When, after the servicing spacecraft has completed the refueling mission, it does not need to return to the fuel station for refueling, When, after the servicing spacecraft has completed the refueling mission, it needs to return to the fuel station for refueling.

[0025] Furthermore, step 1 further includes:

[0026] When the servicing spacecraft still has sufficient fuel after completing the current mission, that is When, the servicing spacecraft performs a double-pulse maneuver. The number of transfer orbits of the servicing spacecraft and the target spacecraft satisfies When the velocity increment consumed by the orbital transfer of the servicing spacecraft is minimized, at this time and satisfy the following equation:

[0027] ;

[0028] Where the function is the floor function, is the upper limit of the completion time of a single mission, is the start time of a single mission, is the refueling time of a single mission, is the period of the geosynchronous orbit, is the phasing angle and ;

[0029] After determining the number of transfer orbits and the phasing orbit can be determined;

[0030] When the fuel of the servicing spacecraft is insufficient to continue the subsequent mission after completing the current mission, or all refueling missions are completed, that is When, the servicing spacecraft performs two double-pulse maneuvers. The two numbers of transfer orbits are respectively equal to the number of transfer orbits of the target spacecraft and the fuel station, satisfying , The velocity increment of the orbital transfer of the servicing spacecraft is minimized. Let At this time, the optimal number of transfer orbits satisfies the following equation:

[0031] ;

[0032] Where is the single refueling time, is the orbital period of the fuel station, is the phasing angle of the first double-pulse maneuver, is the phase modulation angle for the second double-pulse maneuver;

[0033] After determining the number of transfer orbits, the phase modulation orbit can be determined;

[0034] After determining the phase modulation orbit for each of the two cases, the minimum velocity increment required for the orbit maneuver can be calculated through the relationship between the velocity increment and fuel consumption of the orbit maneuver.

[0035] Furthermore, step 2 includes the following content:

[0036] The state variables of the servicing spacecraft , including the following five cases:

[0037] : The servicing spacecraft is refueling the target spacecraft;

[0038] : The servicing spacecraft is in the orbit transfer process of rendezvousing and docking with the target spacecraft;

[0039] : The servicing spacecraft is replenishing fuel at the fuel station;

[0040] : The servicing spacecraft is in the orbit transfer process of returning to the fuel station;

[0041] : The servicing spacecraft has completed all refueling tasks and returned to the initial position.

[0042] Furthermore, step 2 also includes:

[0043] After a certain servicing spacecraft sends a collaborative refueling request, the remaining servicing spacecraft meet the preconditions for collaborative refueling if they are in the orbit transfer process, that is ;

[0044] Establish a two-layer optimization model for on-orbit refueling mission planning;

[0045] ;

[0046] where is the refueling sequence of the servicing spacecraft, is the refueling sequence of the servicing spacecraft of, is the th task in the refueling sequence;

[0047] is the time allocation for each orbit maneuver of the servicing spacecraft, where is the time allocation for each orbit maneuver of the servicing spacecraft of, For the servicing spacecraft The time required to maneuver from the current target position to the target in the refueling sequence ;

[0048] is the set of decision variables for the servicing satellite constellation, For the servicing spacecraft is the set of decision variables;

[0049] is the set of the number of services for the servicing satellite constellation, For the servicing spacecraft is the set of the number of services;

[0050] is the total fuel consumption;

[0051] For the many-to-many on-orbit refueling mission, is the time when the latest task among multiple servicing spacecraft is completed;

[0052] is the servicing refueling constraint for spacecraft cooperation. All tasks must be completed, and each target spacecraft can be serviced by multiple servicing spacecraft;

[0053] is the servicing spacecraft orbit maneuver rendezvous time constraint;

[0054] and is the servicing spacecraft dynamic mission time constraint, is the minimum start time of the current mission, is the maximum completion time of the current mission, is the completion time of the previous mission when the servicing spacecraft executes the mission ; and respectively represent the minimum and maximum time intervals for executing the mission ;

[0055] is the requirement constraint for the target spacecraft ;

[0056] is the fuel station replenishment constraint. When the servicing spacecraft carries insufficient fuel, it returns to the fuel station for replenishment and returns to the fuel station after all refueling tasks are completed. ;

[0057] Furthermore, the specific process of step 3 is as follows:

[0058] Solve using a two-layer optimization algorithm. For the variables 、 and , optimize using the NSGA-II algorithm, and the variables , and together form a chromosome , where adopts the sequential encoding method, adopts the integer encoding method. Since the number of transfer orbits of the service spacecraft in the phasing orbit must be an integer, also adopts the integer encoding method;

[0059] The variable is solved using the B&B algorithm. After the variable is initially generated, solutions that do not meet the constraint conditions need to be optimized and eliminated during the refueling process.

[0060] Furthermore, the collaborative refueling algorithm process in step 3 is as follows:

[0061] Input: mission variables;

[0062] Output: updated mission variables and objective function values;

[0063] 1: Initialize parameters

[0064] 2: for do

[0065] 3: for do

[0066] 4: if then

[0067] 5: if then

[0068] 6: Calculate the fuel consumption , and find the optimal collaborative service spacecraft

[0069] 7: Update the variables

[0070] 8: else

[0071] 9: Return refueling after refueling station replenishment

[0072] 10: Calculate the fuel consumption , and update the variables

[0073] 11: end if

[0074] 12: else

[0075] 13: Calculate the fuel consumption , and update the variables

[0076] 14: end if

[0077] 15:

[0078] 16: end for

[0079] 17:

[0080] end for.

[0081] Furthermore, the outer-layer optimization algorithm process of step 3 is as follows:

[0082] Input: Task variable;

[0083] Output: Updated task variable and objective function value;

[0084] 1: Set the number of population individuals to , initialize the population

[0085] 2: The number of iterations is ,

[0086] 3: for do

[0087] 4: Calculate the objective function values of the individuals in the population according to the collaborative refueling algorithm in

[0088] 5: Calculate all non-dominated fronts of

[0089] 6: Retain some of the optimal individuals and create an offspring population through selection, crossover, and mutation

[0090] 7: Update the population

[0091] 8:

[0092] end for.

[0093] In summary, the present invention mainly has the following beneficial effects:

[0094] 1. The present invention breaks through the limitations of the traditional many-to-many in-orbit refueling strategy and proposes a collaborative in-orbit refueling strategy. When the service spacecraft carries insufficient fuel, it allows the service spacecraft to return to the fuel station to replenish fuel or cooperate with other service spacecraft to complete the refueling task, effectively reducing the number of times the service spacecraft travels back and forth to the fuel station, reducing fuel consumption and mission time.

[0095] ​2. The algorithm proposed by the present invention is different from the existing algorithms. Considering various constraints, especially dynamic scheduling and payload limitations, the proposed strategy is closer to the actual engineering requirements, having important engineering application value and practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] Figure 1 is a schematic diagram of multi - to - multi in - orbit refueling for GEO satellite constellations of the present invention;

[0097] Figure 2 is a graph showing the relationship between the velocity increment required for the phasing maneuver of the service spacecraft and time in the present invention;

[0098] Figure 3 is the optimal path diagram of service spacecraft 1 in a specific example of the present invention;

[0099] Figure 4 is the optimal path diagram of service spacecraft 2 in a specific example of the present invention;

[0100] Figure 5 is the optimal path diagram of service spacecraft 3 in a specific example of the present invention;

[0101] Figure 6 is the mission timing diagram of service spacecraft in a specific example of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0102] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of protection of the present invention.

[0103] The following embodiments are used to illustrate the present invention, but cannot be used to limit the scope of protection of the present invention. The conditions in the embodiments can be further adjusted according to specific conditions. Any simple improvement of the method of the present invention under the premise of the concept of the present invention belongs to the scope of protection required by the present invention.

[0104] Embodiment 1

[0105] A method for mission planning of cooperative in - orbit refueling of multiple GEO spacecraft, the mission scenario is as Figure 1 shown:

[0106] There are multiple target spacecraft on the GEO orbit that need to be refueled in - orbit. At the same time, there is a fuel station on the GEO orbit, and a certain amount of fuel is stored in the fuel station. Multiple service spacecraft start from the fuel station respectively and perform refueling tasks;

[0107] When the fuel carried by a single service spacecraft is insufficient, it can return to the fuel station or cooperate with other service spacecraft to perform refueling tasks;

[0108] To achieve the maximum economic benefit, it is required that the fuel consumed by the service spacecraft's transfer orbit is minimized and the mission time is the shortest.

[0109] The present invention provides an optimal mission plan for this mission, including the service order sequence of service spacecraft, the decision variable set, fuel consumption, and mission time;

[0110] In this example, 20 target spacecraft, 3 fuel stations, and 3 service spacecraft on the GEO orbit are selected, and the specific parameters are shown in Table 1 and Table 2;

[0111] The operating period of the GEO orbit is approximated as 86400 s (1 day), and this is used as the time unit;

[0112] The upper limit of the single orbit transfer time of the service spacecraft is set to 15 days, and the refueling time of the target spacecraft and the replenishment time of the fuel station are both set to 2 days;

[0113] The dry weight of the service spacecraft , specific impulse ;

[0114] The gravitational acceleration is taken as ;

[0115] The present invention provides a method for planning a GEO multi-spacecraft cooperative on-orbit refueling mission, and the specific steps are as follows:

[0116] Step 1: Establish an orbit transfer model based on the plane adjustment and phase adjustment maneuver method to reveal the relationship between the orbital transfer velocity increment of the spacecraft and time:

[0117] In this example, the target satellite group is , is the th target spacecraft, is the number of target spacecraft;

[0118] is the service satellite group, is the th service spacecraft, is the number of service spacecraft;

[0119] is the fuel station, is the th fuel station, is the number of fuel stations;

[0120] Table 1 GEO target spacecraft parameters

[0121]

[0122] Table 2 Parameters of the GEO service spacecraft

[0123]

[0124] The relationship between the velocity increment and fuel consumption for orbital maneuver is as follows:

[0125] ;

[0126] where is the fuel consumption, is the velocity increment, is the mass of the service spacecraft, is the acceleration due to gravity, is the specific impulse of the spacecraft propellant;

[0127] The fuel consumption for orbital maneuver is positively correlated with the velocity increment, as shown in Figure 2 ;

[0128] Therefore, solving the optimal orbital maneuver is transformed into optimizing the number of transfer loops of the service spacecraft in the phasing orbit;

[0129] The velocity increment includes the velocity increment required for the plane adjustment maneuver and the velocity increment required for the phasing maneuver. The calculation method is as follows:

[0130] The velocity increment required for the plane adjustment maneuver:

[0131] ;

[0132] where is the orbital velocity of the service spacecraft, calculated by obtained , and are the orbital inclinations of the service spacecraft and the target spacecraft respectively, and are the right ascensions of the ascending nodes of the service spacecraft and the target spacecraft respectively;

[0133] For the phasing maneuver, the semi-major axis of the phasing orbit satisfies:

[0134] ;

[0135] where and are the respective number of orbits of the service spacecraft and the target spacecraft, is the radius of the geosynchronous orbit, is the phasing angle and ;

[0136] Then the speed increment required for phase modulation is:

[0137] ;

[0138] Where is the standard gravitational parameter. For the Earth, it is the product of the Earth's mass and the gravitational constant;

[0139] Since the adjustment of the orbital plane can be carried out during the phase modulation maneuver phase, the time for the servicing spacecraft to adjust the orbital plane has been included in the phase modulation maneuver time. Therefore, only the optimal maneuver during the phase modulation maneuver phase needs to be solved;

[0140] is a decision variable, representing the servicing spacecraft after servicing the target spacecraft whether it needs to return to the fuel station to replenish fuel;

[0141] When, the servicing spacecraft does not need to return to the fuel station to replenish fuel after completing the refueling mission, When, the servicing spacecraft needs to return to the fuel station to replenish fuel after completing the refueling mission;

[0142] When the servicing spacecraft still has sufficient fuel after completing the current mission, that is When, the servicing spacecraft performs a two-pulse maneuver, and the number of transfer orbits of the servicing spacecraft and the target spacecraft satisfy When the speed increment consumed by the orbital transfer of the servicing spacecraft is the smallest, at this time and satisfy the following equation:

[0143] ;

[0144] Where The function is the floor function, is the upper limit of the completion time of a single mission, is the start time of a single mission, is the refueling time of a single mission, is the period of the geosynchronous orbit, is the phase modulation angle and ;

[0145] After determining the number of transfer orbits and the phase modulation orbit can be determined.

[0146] When the fuel of the servicing spacecraft is not enough to continue the subsequent mission after completing the current mission, or all refueling missions are completed, that is When the time is right, the service spacecraft conducts two double-pulse maneuvers. The number of transfer orbits for the two times is equal to the number of transfer orbits of the target spacecraft and the fuel station respectively, satisfying , the minimum orbital transfer velocity increment of the service spacecraft. Let , at this time, the optimal number of transfer orbits satisfies the following equation:

[0147] ;

[0148] where is the time for single refueling, is the orbital period of the fuel station, is the phase adjustment angle of the first double-pulse maneuver, is the phase adjustment angle of the second double-pulse maneuver;

[0149] After determining the number of transfer orbits, the phase adjustment orbit can be determined;

[0150] The calculation method of the number of transfer orbits is as follows:

[0151] and are positive numbers. By establishing the Lagrange equation to solve and , the established Lagrange equation is:

[0152] ;

[0153] Take the partial derivatives of , and , there is , and the solution is:

[0154] , , and the second-order partial derivative value is greater than 0;

[0155] The minimum number of transfer orbits is: , ;

[0156] After determining the phase adjustment orbit, the minimum velocity increment required for the orbital maneuver can be calculated through the relationship between the velocity increment and fuel consumption of the orbital maneuver.

[0157] Step 2: Establish a two-layer optimization model for the on-orbit refueling mission planning, and determine the mission time range on the basis of minimizing the fuel consumption;

[0158] The state variables of the service spacecraft include the following five situations:

[0159] (1) : The service spacecraft is refueling the target spacecraft;

[0160] (2) : During the orbital transfer process of the servicing spacecraft for rendezvous and docking with the target spacecraft;

[0161] (3) : The servicing spacecraft is refueling at the fuel station;

[0162] (4) : During the orbital transfer process of the servicing spacecraft returning to the fuel station;

[0163] (5) : The servicing spacecraft has completed all refueling tasks and returned to the initial position.

[0164] After a certain servicing spacecraft issues a collaborative refueling request, the remaining servicing spacecraft meet the preconditions for collaborative refueling if they are in the orbital transfer process, that is ;

[0165] In the double-layer optimization model, it mainly includes collaborative refueling constraints, payload constraints, and mission time constraints. The constraint conditions are as follows:

[0166] (1) Collaborative refueling constraints: All tasks must be completed, and each target can be serviced by multiple servicing spacecraft: ;

[0167] Where represents the target being serviced by the servicing spacecraft ; conversely means the target not being serviced by the servicing spacecraft ;

[0168] (2) Servicing spacecraft orbital maneuver rendezvous time constraint: The orbital maneuver time of the servicing spacecraft each time does not exceed , ;

[0169] (3) Target spacecraft fuel demand constraint: The fuel demand of the target spacecraft cannot exceed , ;

[0170] (4) Servicing spacecraft dynamic mission time constraint: Assume the execution time of the previous task of the servicing spacecraft for performing task is

[0171] ;

[0172] where is the execution time of the mission , is the minimum start time of the current mission is the maximum completion time of the current mission represents the minimum time interval for executing the mission , represents the maximum time interval for executing the mission ;

[0173] (5) Payload constraint of the service spacecraft: When the service spacecraft executes the mission each time, the fuel carried shall not exceed the payload upper limit , and the fuel carried shall be greater than the payload lower limit , that is, to ensure the normal operation of the service spacecraft in orbit ;

[0174] (6) Fuel station replenishment constraint: After the service spacecraft completes all refueling missions, it needs to return to the fuel station, or when the fuel carried is insufficient to continue the refueling mission, it needs to return to the fuel station for replenishment: ;

[0175] Establish a two - layer optimization model for the on - orbit refueling mission planning:

[0176] ;

[0177] where is the refueling sequence of the service spacecraft, where is the refueling sequence of the service spacecraft , is the th mission in the refueling sequence;;

[0178] is the time allocation for each orbital maneuver of the service spacecraft, where is the time allocation for each orbital maneuver of the service spacecraft , is the time required for the service spacecraft to maneuver from the current target position orbit to the target in the refueling sequence ;

[0179] is the decision variable set of the service satellite constellation is the decision variable set of the service spacecraft ;

[0180] is the service quantity set of the service satellite constellation is the service spacecraft Set of service quantities;

[0181] is the total fuel consumption;

[0182] For the many-to-many in-orbit refueling mission, is the time when the task is completed latest among multiple service spacecraft;

[0183] The inner-layer optimization model is to solve the optimal cooperation scheme for a single solution, and the outer-layer optimization model is to explore the solution space. The optimal in-orbit refueling scheme is continuously iteratively solved through the established two-layer optimization model;

[0184] Step 3: Use the two-layer optimization algorithm to efficiently solve the optimization model. The B&B algorithm and the NSGA-II algorithm are respectively used for the inner and outer layers to obtain the optimal service sequence sequence of service spacecraft, the decision variable set, the fuel consumption, and the task time;

[0185] When using the two-layer optimization algorithm for solution, for variables , and , the NSGA-II algorithm is used for optimization. Variables , and together form a chromosome , where adopts the sequential encoding method, adopts the integer encoding method. Since the number of transfer orbits of the service spacecraft in the phasing orbit must be an integer, also adopts the integer encoding method;

[0186] Variable is solved by the B&B algorithm. After variable is initially generated, solutions that do not meet the constraint conditions need to be optimized and eliminated during the refueling process;

[0187] The cooperative refueling algorithm finds the optimal cooperative service spacecraft by dynamically adjusting the task variables to minimize the fuel consumption and complete the task. The outer loop traverses the task set, and the inner loop processes the specific execution of each task. The algorithm flow is as follows:

[0188]

[0189] The outer-layer optimization algorithm is based on the NSGA-II algorithm. By iteratively optimizing the task variables, a set of non-dominated solutions (Pareto front) is found. The algorithm flow is as follows:

[0190]

[0191] The population size of the algorithm is set to 100, and the number of iterations is 100.

[0192] In this example, the fuel requirement of the target spacecraft is set to 250 kg. The optimization objectives and objective function values in this scenario are shown in Table 3. The optimal paths of the three servicing spacecraft are respectively as Figure 3 , 4 , and 5, and the mission time sequence is as Figure 6 shown.

[0193] In the optimization results, the mission variables are , representing that the three servicing spacecraft respectively perform 7, 5, and 8 refueling tasks of their own;

[0194] Among them, the optimal path of servicing spacecraft 1 is , being its decision variable. The specific mission description is as follows: as Figure 3 shown, servicing spacecraft 1 initially departs from fuel station 1, refuels targets #6, #18, and #17 in sequence, then returns to the fuel station to replenish fuel, continues to refuel targets #5 and #4, and then performs a collaborative refueling mission with servicing spacecraft 3, that is, refuels target #14, and then returns to the fuel station to replenish fuel, and then refuels targets #7 and #3, and finally returns to the initial position;

[0195] The optimal path of servicing spacecraft 2 , and the decision variable is . The specific mission description is as follows: as Figure 4 shown, servicing spacecraft 2 initially departs from fuel station 2, refuels targets #2, #1, and #19 in sequence, then returns to fuel station 2 to replenish fuel, and then performs a collaborative refueling mission with servicing spacecraft 3, that is, refuels target #16, continues to refuel targets #20 and #8, and finally returns to the initial position;

[0196] The optimal path of servicing spacecraft 3 is , being its decision variable. The specific mission description is as follows: as Figure 5 shown, servicing spacecraft 3 initially departs from fuel station 3 and refuels targets #9, #15, and #16 of the spacecraft in sequence. At this time, since the fuel in servicing spacecraft 3 is not enough to complete the #16 mission, it returns to fuel station 3 to replenish fuel midway during the refueling mission for target #16, and then refuels targets #11, #12, and #14. Similarly, the fuel in servicing spacecraft 3 is not enough to complete the #14 mission, so it returns to the fuel station midway during the refueling mission for target #14.

[0197] The fuel consumption of the entire refueling mission for orbital transfer is 1533.7 kg, and the time required to complete the mission is 68 days;

[0198] When other conditions are the same, when the fuel requirement of the target spacecraft is greater than a certain value, the collaborative refueling method has certain advantages in reducing fuel consumption and mission time;

[0199] Table 3 Optimization Objectives and Objective Function Values

[0200]

[0201] Those skilled in the art of this technology can understand that, unless otherwise defined, all terms used herein (including technical terms and scientific terms) have the same meaning as the general understanding of those of ordinary skill in the field to which this invention belongs. It should also be understood that terms such as those defined in a general dictionary should be understood to have a meaning consistent with the meaning in the context of the prior art, and will not be interpreted in an idealized or overly formal sense unless defined as here.

[0202] The specific embodiments described above have further elaborated on the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only for the specific embodiments of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for planning GEO multi-spacecraft collaborative in-orbit refueling missions, characterized in that, It includes the following steps: Step 1: Establish an orbit transfer model based on the phasing and attitude control method of the spacecraft, and reveal the relationship between the velocity increment and time of spacecraft orbit transfer; Step 2: Establish a two-layer optimization model for on-orbit refueling mission planning, and determine the mission time range on the basis of minimizing fuel consumption: Using multiple service spacecraft and multiple fuel stations to complete the refueling tasks of multiple target spacecraft, R = {r j | j ∈ 1, 2, …, n} is the target satellite group, r j is the j-th target spacecraft, and n is the number of target spacecraft; Q = {q i | i ∈ 1, 2, …, m} is the service satellite constellation, q i is the i-th service spacecraft, and m is the number of service spacecraft; F = {f k | k ∈ 1, 2, …, l} is the fuel station, f k is the k-th fuel station, and l is the number of fuel stations; Under given mission parameters, the service spacecraft departs from the fuel station and performs orbit transfer until the service spacecraft rendezvouses and docks with the target spacecraft with depleted fuel and completes the refueling mission; If the fuel carried by a single service spacecraft is insufficient, it can return to the fuel station to replenish fuel and then continue to perform the mission or cooperate with other service spacecraft to complete it; After all missions are completed, the service spacecraft needs to return to the fuel station; The state variables G of the service spacecraft = {G1, G2, G3, G4, G5}, including the following five situations: G1: The service spacecraft is refueling the target spacecraft; G2: The service spacecraft is in the orbit transfer process of rendezvousing and docking with the target spacecraft; G3: The service spacecraft is replenishing fuel at the fuel station; G4: The service spacecraft is in the orbit transfer process of returning to the fuel station; G5: The service spacecraft has completed all refueling missions and returned to the initial position; After a certain service spacecraft issues a cooperative refueling request, the remaining service spacecraft meet the preconditions for cooperative refueling if they are in the orbit transfer process, that is, G = {G2, G4, G5}; Establish a two-layer optimization model for on-orbit refueling mission planning; Find X,T,S,H Min Z1 = dM fuel , Z2 = dT 0 < t ij ≤ T max ET j <t j ≤LT j M min ≤M i ≤M max S.t. 0 < dm j < M j x ij ∈{0,1} i∈{1,2,...,m},j∈{1,2,...,n} where X = {X1, X2, …, X m} is the refueling sequence of the service spacecraft, and X m = {x1, x2, …, x p} is the refueling sequence of the m-th service spacecraft, and x p is the p-th task in the refueling sequence; T = {T1, T2, …, T m} is the time allocation for each orbital maneuver of the servicing spacecraft, where T m = {t i1 , t i2 , …, t ip} is the time allocation for each orbital maneuver of servicing spacecraft m, and t ip is the time required for servicing spacecraft i to maneuver from the current target position orbit to target p in the refueling sequence; S = {S1, S2, …, S m} is the decision variable set of the service star cluster, and S m is the decision variable set of the service spacecraft m; H = {H1, H2, …, H m} is the set of the number of services of the service satellite constellation, and H m is the set of the number of services of the service spacecraft m; Z1 = dM fuel is the total fuel consumption; For many-to-many on-orbit refueling missions, Z2 = dT is the time when the latest mission is completed among multiple service spacecraft; x ij For the collaborative refueling constraints of spacecraft, x ij = 1 indicates that service spacecraft i refuels target spacecraft j, x ij = 0 indicates that service spacecraft i does not refuel target spacecraft j. All tasks must be completed, and each target spacecraft can be served by multiple service spacecraft; T max is the time constraint for the orbital maneuver rendezvous of the service spacecraft; ET j and LT j To serve the dynamic mission time constraint of the service spacecraft, is the minimum start time of the current mission, is the maximum completion time of the current mission, TP j is the completion time of the previous mission for the service spacecraft to execute mission j, and represent the minimum and maximum time intervals for executing mission j, t j is the execution time of mission j; M i is the fuel constraint carried by service spacecraft i, M min and M max respectively represent the minimum and maximum fuel quantities carried; M j is the requirement constraint for the target spacecraft j, dm j is the fuel demand of the target spacecraft j; S ij For the fuel station replenishment constraint, when the service spacecraft i runs out of fuel, it returns to the fuel station j for replenishment and returns to the fuel station after all refueling tasks are completed; Step 3: Use the two-layer optimization algorithm to efficiently solve the optimization model. The B&B algorithm and NSGA-II algorithm are respectively used for the inner and outer layers to obtain the optimal service sequence of the service spacecraft, decision variable set, fuel consumption, and mission time.

2. The GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, wherein, The content of the said Step 1 includes: The relational expression between the velocity increment and fuel consumption of orbit maneuver is: where Δm is the fuel consumption, Δv ij is the velocity increment, m is the mass of the servicing spacecraft, g0 is the acceleration due to gravity, and I sp is the specific impulse of the spacecraft propellant; The fuel consumption of orbit maneuver is positively correlated with the velocity increment; Therefore, solving the optimal orbit maneuver is transformed into optimizing the number of transfer loops of the service spacecraft in the phasing orbit; Since the orbit plane can be adjusted during the phasing maneuver stage, the time for the service spacecraft to adjust the orbit plane has been included in the phasing maneuver time, so only the optimal maneuver in the phasing maneuver stage needs to be solved; S ij is a decision variable, representing whether the servicing spacecraft i needs to return to the fuel station for refueling after servicing the target spacecraft j; S ij When S = 0, after the servicing spacecraft completes the refueling mission, it does not need to return to the fuel station for refueling. ij When S = 1, after the servicing spacecraft completes the refueling mission, it needs to return to the fuel station for refueling.

3. A method for planning GEO multi-spacecraft collaborative on-orbit refueling missions according to claim 2, characterized in that, The said Step 1 also includes: When the servicing spacecraft still has sufficient fuel after completing the current mission, i.e., S ij = 0, the servicing spacecraft performs a double-pulse maneuver. The number of transfer orbits of the servicing spacecraft and the target spacecraft satisfies N s = N t when the velocity increment consumed by the orbit transfer of the servicing spacecraft is minimized. At this time, N s and N t satisfy the following equation where the floor[] function is the floor function, LT is the upper limit of the single-task completion time, ET is the start time of the single task, and Δt fuel is the refueling time for a single task, T t is the period of the geosynchronous orbit, and Δθ is the phase modulation angle and Δθ ∈ (-π, π]; After determining the number of transfer turns N s and N t the phase modulation orbit can be determined; When the fuel of the servicing spacecraft is insufficient to continue the subsequent tasks after completing the current task, or all refueling tasks are completed, i.e., S ij = 1, the servicing spacecraft performs two dual-pulse maneuvers. The number of transfer orbits for the two times is equal to the number of transfer orbits of the target spacecraft and the fuel station respectively, satisfying N s1 = N t 、N s2 = N f The orbital transfer velocity increment of the servicing spacecraft is minimized. Let N s = N s1 + N s2 , and the optimal number of transfer orbits satisfies the following equation where Δt fill is the single refueling time, T f is the orbital period of the fuel station, Δθ1 is the phase adjustment angle of the first double-pulse maneuver, and Δθ2 is the phase adjustment angle of the second double-pulse maneuver; After determining the number of transfer loops, the phasing orbit can be determined; For each of the two situations, after determining the phasing orbit, the minimum velocity increment required for orbit maneuver can be calculated through the relational expression between the velocity increment and fuel consumption of orbit maneuver.

4. A GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, characterized in that, The specific process of the said Step 3 is: Use the two-layer optimization algorithm to solve. For variables X, H, and T, use the NSGA-II algorithm for optimization. Variables X, H, and T together form chromosome Ch = [X, H, T], where X uses sequential coding, H uses integer coding. Since the number of transfer loops of the service spacecraft in the phasing orbit must be an integer, T also uses integer coding; The variable S is solved using the B&B algorithm. After the initial generation of the variable S, it is necessary to optimize and eliminate the solutions that do not meet the constraint conditions during the refueling process.

5. A method for planning GEO multi-spacecraft collaborative in-orbit refueling missions according to claim 1, characterized in that, The collaborative refueling algorithm process of step 3 is as follows: Input: Task variables; Output: Updated task variables and objective function values; 1: Initialize parameters k, l = 1 2: for k ≤ n do 3: for l ≤ m do 4: if M i ≤dm j then 5: if then 6: Calculate the burnup dM fuel , and find the optimal cooperative service spacecraft 7: Update variables 8: else 9: Return refueling after refueling at the fuel station 10: Calculate the burnup dM fuel , update the variable 11: end if 12: else 13: Calculate burnup dM fuel , update variables 14: end if 15：l＝l+1 16: end for 17：l＝l+1 18: end for.

6. The GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, wherein The outer optimization algorithm process of step 3 is as follows: Input: Task variables; Output: Updated task variables and objective function values; 1: Set the number of individuals in the population to N and initialize the population R t 2: The number of iterations is Gen, i = 1 3: for i ≤ Gen do 4: Calculate the objective function values of individuals in population R according to the collaborative annotation algorithm t in it 5: Calculate R t for all non-dominated fronts 6: Retain some of the best individuals and create a subpopulation through selection, crossover, and mutation 7: Update the population 8: i = i + 1 9: end for.

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