GEO multi-spacecraft cooperative on-orbit refueling task planning method

Abstract

The invention relates to the technical field of spacecraft on-orbit service, in particular to a GEO multi-spacecraft cooperative on-orbit refueling task planning method, which is characterized by comprising the following steps of: 1, establishing an orbit transfer model based on a surface and phase modulation maneuvering method, and revealing a relationship between spacecraft orbit transfer speed increment and time; 2, establishing a double-layer optimization model for collaborative on-orbit refueling task planning, and determining a task time range on the basis of minimum fuel consumption; 3, efficiently solving the optimization model by utilizing a double-layer optimization algorithm, wherein a branch and bound algorithm and a fast elite multi-objective genetic algorithm are respectively adopted in an inner layer and an outer layer; according to the method, the limitation of a traditional many-to-many on-orbit refueling strategy is broken through, multiple service spacecrafts are allowed to cooperate to complete the same refueling task, the fuel consumption and time cost of the on-orbit refueling task are reduced, the result is close to the Pareto optimal state, the constraints of multiple aspects such as dynamic scheduling and effective load limitation are fully considered, and the method is suitable for large-scale popularization and application. And actual engineering requirements are met.

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 advantages such as reducing launch weight, extending the lifespan of spacecraft, and improving system efficiency. However, on-orbit refueling missions for large-scale satellite constellations are characterized by high demand and high requirements for the payload capacity of service spacecraft. Providing on-orbit refueling services for 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, the fuel payload capacity of a single service spacecraft is limited, severely restricting the number of target spacecraft it can serve. Moreover, the same refueling mission is only allowed to be completed by a single service spacecraft. When the demand for target spacecraft is large, the service spacecraft has to make multiple round trips to the fuel station, increasing fuel consumption and lengthening the mission time. Therefore, the on-orbit refueling method for GEO multi-spacecraft and its mission planning problem are currently technical challenges that need to be overcome urgently. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, 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 attitude and phase adjustment maneuver method 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, adopting the B&B algorithm and the NSGA-II algorithm for the inner and outer layers respectively to obtain the optimal service sequence of service spacecraft, decision variable set, fuel consumption, and mission time.

[0010] Furthermore, the above Step 1 includes the following content:

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

[0012] is the service 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 the 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 mission

[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 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, the time for the service spacecraft to adjust the orbital plane is 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 Whether it is necessary to return to the fuel station for refueling after servicing the target spacecraft ;

[0024] When, after the servicing spacecraft completes the refueling mission, it does not need to return to the fuel station for refueling, When, after the servicing spacecraft completes 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 orbit 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 not enough 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 number of transfer orbits of the two times is equal to the number of transfer orbits of the target spacecraft and the fuel station respectively, satisfying , The velocity increment of the orbit 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] Further, 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 process of orbit transfer during rendezvous and docking with the target spacecraft;

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

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

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

[0042] Further, step 2 also includes:

[0043] 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 process of orbit transfer, 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 collaboration. 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 for the servicing spacecraft to execute 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] Use a two-layer optimization algorithm to solve. For the variables 、 and Optimize using the NSGA-II algorithm. The variables , and together form a chromosome . Among them, uses the sequential encoding method, uses the integer encoding method. Since the number of transfer orbits of the service spacecraft in the phasing orbit must be an integer, also uses 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 fueling process.

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

[0061] Input: Task variables;

[0062] Output: Updated task 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 to refueling after refueling at the fuel station

[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 variables;

[0083] Output: Updated task variables and objective function values;

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

[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, and 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 It is a schematic diagram of multi - to - multi in - orbit refueling for GEO satellite constellations of the present invention;

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

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

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

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

[0101] Figure 6 It is a mission timing diagram of the service spacecraft in a specific example of the present invention. Detailed Embodiment

[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 in conjunction with 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 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 to the method of the present invention under the premise of the concept of the present invention falls within 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, and the mission scenario is as Figure 1 shown:

[0106] There are multiple target spacecraft in the GEO orbit that need to be refueled in orbit. At the same time, a fuel station is set up in 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 in the 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 sequence sequence of the service spacecraft, the decision variable set, the fuel consumption and the 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 , the specific impulse ;

[0114] The gravitational acceleration is taken as ;

[0115] The present invention provides a method for planning the on-orbit refueling mission of multiple GEO spacecraft in cooperation, 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 velocity increment and time of the spacecraft orbit transfer:

[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 relational expression between the velocity increment and fuel consumption for orbital maneuver is:

[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 plane adjustment maneuver and the velocity increment required for phasing maneuver, and the calculation method is:

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

[0131] ;

[0132] where is the orbital velocity of the service spacecraft, calculated from obtained by calculation , 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, the time for the service 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 needs to be solved;

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

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

[0142] When the service spacecraft still has sufficient fuel after completing the current mission, that is, When, the service spacecraft performs a two-pulse maneuver, and the number of transfer orbits of the service spacecraft and the target spacecraft satisfy When the speed increment consumed by the orbital transfer of the service 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 service spacecraft is insufficient to continue the subsequent mission after completing the current mission, or all refueling missions are completed, that is, When the time is up, the service spacecraft performs 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 orbital transfer velocity increment of the service spacecraft is minimized. Let , and at this time, the optimal number of transfer orbits satisfies the following equation:

[0147] ;

[0148] Among them 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 Lagrangian equation to solve and , the established Lagrangian equation is:

[0152] ;

[0153] Taking the partial derivatives of , and , we have , 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 constraint: 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 is not 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 for the servicing spacecraft to execute task is , then the mission time constraint can be expressed as:

[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 constraints of the service spacecraft: When the service spacecraft executes a 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, it meets the normal operation of the service spacecraft in orbit ;

[0174] (6) Fuel station replenishment constraints: After the service spacecraft completes all refueling missions, it needs to return to the fuel station, or when the fuel carried is not enough 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 many-to-many in-orbit refueling missions, is the time when the latest mission is completed 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 obtained through iterative solution of 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, decision variable set, fuel consumption, and mission time;

[0185] Use the two-layer optimization algorithm to solve. For variables , and , the NSGA-II algorithm is used for optimization. Variables , and together form a chromosome , where adopts the sequential coding method, adopts the integer coding method. Since the number of transfer circles of the service spacecraft in the phasing orbit must be an integer, also adopts the integer coding 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 mission variables to minimize fuel consumption and complete the mission. The outer loop traverses the mission set, and the inner loop processes the specific execution of each mission. The algorithm flow is as follows:

[0188]

[0189] The outer-layer optimization algorithm is based on the NSGA-II algorithm. By iteratively optimizing the mission 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 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 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 Figure 5 shown, servicing spacecraft 3 initially departs from fuel station 3 and refuels target spacecraft #9, #15, and #16 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 halfway through the refueling mission for #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 halfway through the refueling mission for #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 the present technology can understand that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the art to which the present 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 with an idealized or overly formal meaning unless defined as such herein.

[0202] The specific embodiments described above have further elaborated on the objectives, technical solutions, and beneficial effects of the present invention. It should be understood that the above description is only 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 GEO multi-spacecraft collaborative on-orbit refueling mission planning method, characterized in that: The following steps are involved: Step 1: Establish an orbit transfer model based on the face and phase adjustment method to reveal the relationship between the spacecraft orbit transfer velocity increment and time; Step 2: Establish a two-level optimization model for on-orbit refueling mission planning and determine the mission time range based on minimizing fuel consumption; Step 3: Use a two-layer optimization algorithm to efficiently solve the optimization model. The inner and outer layers use the B&B algorithm and the NSGA-Ⅱ algorithm respectively to obtain the optimal service order sequence, decision variable set, fuel consumption, and mission time for the service spacecraft.

2. A GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, characterized in that: The step 1 includes the following contents: Use multiple service spacecraft and multiple fuel stations to complete the refueling mission of multiple target spacecraft. For the target constellation, For the target spacecraft, is the number of target spacecraft; To serve the constellation, For the Service spacecraft, Number of spacecraft to be serviced; For fuel stations, For the Fuel stations, 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 fuel-depleted target spacecraft and completes the refueling mission; If a single service spacecraft does not carry enough fuel, it can return to the fuel station to refuel and continue to perform its mission or collaborate with other service spacecraft to complete the mission; After all tasks are completed, the service spacecraft needs to return to the fuel station; The relationship between the velocity increment and fuel consumption of orbital maneuvers is: ； Among them is Fuel consumption, is the velocity increment, is the mass of the serviced spacecraft, is the acceleration due to gravity, is the spacecraft propellant specific impulse; The fuel consumption of orbital maneuvers is positively correlated with the velocity increment; Therefore, solving the optimal orbital maneuver is transformed into optimizing the number of transfer circles of the service spacecraft in the phase adjustment orbit; Since the orbital plane can be adjusted during the phase adjustment maneuvering phase, the time for the service spacecraft to adjust the orbital plane is included in the phase adjustment maneuvering time, so it is only necessary to solve the optimal maneuver during the phase adjustment maneuvering phase. is the decision variable, representing the service spacecraft Servicing the target spacecraft Do you need to return to the fuel station to refuel? When the service spacecraft completes the refueling mission, it does not need to return to the fuel station to refuel. When the service spacecraft completes the refueling mission, it needs to return to the fuel station to refuel.

3. A GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, characterized in that: The step 1 also includes: When the service spacecraft has completed its current mission and still has sufficient fuel, When the service spacecraft performs a double-pulse maneuver, the number of turns of the service spacecraft and the number of turns of the target spacecraft meet When the service spacecraft orbit transfer consumption speed increment is the smallest, and Satisfies the following equation ； in The function is a floor function. The time limit for completing a single task. is the start time of a single task, Add time to a single task. is the period of the geosynchronous orbit, is the phase modulation angle and ; Determining the number of transfer turns and After that, the phase modulation orbit can be determined; When the service spacecraft completes its current mission and the fuel is insufficient to complete the subsequent mission, or all refueling tasks are completed, When the service spacecraft performs two double-pulse maneuvers, the number of transfer circles of the two times is equal to the number of transfer circles of the target spacecraft and the number of transfer circles of the fuel station, respectively, to meet , The orbit transfer velocity increment of the service spacecraft is the smallest, , at this time the optimal number of transfer cycles satisfies the following equation ； in The time for a single refueling. is the orbital period of the fuel station, is the phasing angle of the first double-pulse maneuver, is the phasing angle of the second double-pulse maneuver; After determining the number of transfer turns, the phase modulation orbit can be determined; After the phase adjustment orbit is determined in each of the two cases, the minimum speed increment required for orbital maneuvering can be calculated by the relationship between the speed increment and fuel consumption of orbital maneuvering.

4. A GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, characterized in that: The step 2 includes the following contents: Service spacecraft state variables , including the following five situations: : The service spacecraft is refueling the target spacecraft; : The service spacecraft is in the process of orbit transfer during rendezvous and docking with the target spacecraft; : The service spacecraft is refueling at the fuel station; : The serviced spacecraft is in the process of orbit transfer on its way back to the fuel station; :The service spacecraft has completed all refueling tasks and returned to its initial position.

5. The GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1 is characterized in that: The step 2 also includes: After a service spacecraft issues a collaborative refueling request, the other service spacecraft, if they are in the process of orbit transfer, meet the preconditions for collaborative refueling, that is, ; Establish a two-level optimization model for on-orbit refueling mission planning; ； in To service the spacecraft's refueling sequence, Servicing spacecraft The injection sequence, The first tasks; The time allocation for each orbital maneuver of the servicing spacecraft is Servicing spacecraft The time allocation for each orbital maneuver, Servicing spacecraft Maneuver from the current target position orbit to the target in the refueling sequence Time required; is the set of decision variables serving the constellation, Servicing spacecraft The set of decision variables; is the service quantity set of the service constellation, Servicing spacecraft The number of services set; is the total fuel consumption; For many-to-many on-orbit refueling missions, The latest time for multiple service spacecraft to complete their mission; Add constraints to spacecraft collaboration, all tasks must be completed, and each target spacecraft can be served by multiple service spacecraft; To provide time constraints for orbital maneuver rendezvous with service spacecraft; and To serve the dynamic mission time constraints of spacecraft, is the minimum start time of the current task, is the maximum completion time of the current task, Servicing spacecraft missions The completion time of the predecessor task, and Represents the execution of tasks The minimum and maximum time intervals; The requirements constraints for the target spacecraft; The fuel station refueling constraint requires that the service spacecraft returns to the fuel station for refueling when the fuel it carries is insufficient, and returns to the fuel station after all refueling tasks are completed.

6. A GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, characterized in that: The specific process of step 3 is as follows: A two-layer optimization algorithm is used to solve the problem. , and , using NSGA-Ⅱ algorithm for optimization, variables , and Together they form chromosomes ,in Using sequential coding, Integer encoding is used, because the number of transfer circles of the service spacecraft in the phase adjustment orbit must be an integer. The same integer encoding method is used; variable The B&B algorithm is used to solve the problem. After the initial generation, it is necessary to optimize during the filling process to eliminate solutions that do not meet the constraints.

7. A GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1, characterized in that: The collaborative filling algorithm process of step 3 is as follows: Input: task variables; Output: updated task variables and objective function values; 1: Initialization parameters ; 2: for do 3: for do 4: if then 5: if then 6: Calculate fuel consumption , find the optimal collaborative service spacecraft 7: Update variables 8: else 9: Return to the fuel station for refueling 10: Calculate fuel consumption , update the variable 11: end if 12: else 13: Calculate fuel consumption , update the variable 14: end if 15： ； 16: end for 17： ； 18: end for.

8. The GEO multi-spacecraft collaborative on-orbit refueling mission planning method according to claim 1 is characterized in that: The outer optimization algorithm flow 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 , initialize the population ; 2: The number of iterations is , ; 3: for do; 4: Calculate the population according to the collaborative injection algorithm The objective function value of the individual 5: Calculation All non-dominated frontiers 6: Keep some of the best individuals and create offspring populations through selection, crossover and mutation 7: Update population 8： ； 9: end for.

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