Low-thrust on-orbit maintenance method, device, equipment and medium based on fuel optimization

Abstract

The present invention provides a method, device, equipment and medium for maintaining low thrust on orbit based on fuel optimization, which belongs to the field of spacecraft orbital dynamics and control technology. The method may include: obtaining a predicted orbital state corresponding to each extrapolated time point within a set extrapolation time period based on an initial orbital state of a satellite; obtaining the osculating orbit element number of each extrapolated time point according to the predicted orbital state corresponding to each extrapolated time point; selecting a target extrapolated time point from all extrapolated time points based on the difference between the osculating orbit elements of all extrapolated time points and the average element number of a calibrated orbit; obtaining the orbital state of the starting point of the satellite's orbital maneuvering segment according to the osculating orbital element number of the target extrapolated time point, and obtaining the orbital state of the ending point of the satellite's orbital maneuvering segment through a genetic algorithm according to the orbital state of the starting point; and obtaining a thrust sequence for maintaining low thrust on orbit with fuel optimization using the orbital state of the ending point of the orbital maneuvering segment.

Description

Technical Field

[0001] The embodiments of the present disclosure relate to the field of spacecraft orbital dynamics and control technology, and in particular to a method, device, equipment and medium for maintaining low thrust on-orbit based on fuel optimization. Background Art

[0002] In order to achieve low latency and low attenuation, stackable flat-panel satellites mostly operate in low orbits. Therefore, they will be affected by various perturbations in near-Earth space, and the accuracy of the satellite position vector and velocity vector is limited. Even if the orbit is designed based on a high-precision dynamic model, it will gradually deviate after a period of time. Therefore, regular orbit maintenance becomes inevitable.

[0003] At present, orbit maintenance usually adopts chemical propulsion, which can meet the needs of various tasks. However, chemical propulsion has low specific impulse and high fuel consumption, making it difficult to achieve long-term orbit maintenance tasks. At the same time, chemical propulsion has large thrust, which is suitable for pulse maneuvers and has limited accuracy. With the continuous development and application of electric propulsion, relying on the high specific impulse and switch controllable characteristics of electric propulsion, long-term orbit maintenance with high accuracy and low fuel consumption can be better achieved. However, it only considers the semi-major axis deviation and descending node deviation, and is not suitable for orbit maintenance that also requires orbit inclination and eccentricity. Summary of the invention

[0004] In view of this, the embodiments of the present disclosure hope to provide a low-thrust on-orbit maintenance method, device, equipment and medium based on fuel optimization, which can perform orbit maintenance on multiple orbital elements, improve the accuracy of orbit maintenance, and orbit maintenance based on fuel optimization, which is suitable for long-term missions with limited fuel carrying capacity.

[0005] The technical solution of the embodiment of the present disclosure is implemented as follows:

[0006] In a first aspect, an embodiment of the present disclosure provides a low-thrust on-orbit maintenance method based on fuel optimization, comprising:

[0007] Based on the initial orbital state of the satellite, extrapolation is performed at equal time intervals within a set extrapolation duration to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation duration;

[0008] Obtaining the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point;

[0009] Based on the difference between the osculating orbit elements of all extrapolated time points and the average element number of the calibration orbit, a target extrapolated time point is selected from all extrapolated time points;

[0010] Acquire the orbit state of the starting point of the orbit maneuvering segment of the satellite according to the osculating orbit element number at the target extrapolated time point, and acquire the orbit state of the ending point of the orbit maneuvering segment of the satellite through a genetic algorithm according to the orbit state of the starting point;

[0011] The orbital state of the end point of the orbital maneuvering segment is used to obtain a thrust sequence with optimal fuel for low-thrust on-orbit maintenance.

[0012] In a second aspect, an embodiment of the present disclosure provides a low-thrust on-orbit maintenance device based on fuel optimization, the low-thrust on-orbit maintenance device based on fuel optimization comprises: an extrapolation part, a first acquisition part, a selection part, a second acquisition part and a maintenance part; wherein,

[0013] The extrapolation part is configured to perform extrapolation at equal time intervals within a set extrapolation duration based on the initial orbital state of the satellite to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation duration;

[0014] The first acquisition part is configured to acquire the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point;

[0015] The selection part is configured to select a target extrapolation time point from all extrapolation time points based on the difference between the osculating orbit elements of all extrapolation time points and the average element number of the calibration orbit;

[0016] The second acquisition part is configured to acquire the orbit state of the starting point of the orbit maneuvering segment of the satellite according to the osculating orbit element number of the target extrapolated time point, and obtain the orbit state of the ending point of the orbit maneuvering segment of the satellite through a genetic algorithm according to the orbit state of the starting point;

[0017] The maintenance section is configured to utilize the orbital state of the end point of the orbital maneuvering segment to obtain a thrust sequence with the best fuel for low-thrust on-orbit maintenance.

[0018] In a third aspect, an embodiment of the present disclosure provides a computing device, the computing device comprising: a memory and a processor; wherein:

[0019] The memory is used to store a computer program that can be run on the processor;

[0020] The processor is used to execute the low-thrust on-orbit maintenance method based on fuel optimization described in the first aspect when running the computer program.

[0021] In a fourth aspect, an embodiment of the present disclosure provides a computer-readable storage medium storing at least one instruction, wherein the at least one instruction is used to be executed by a processor to implement the low-thrust on-orbit maintenance method based on fuel optimization as described in the first aspect.

[0022] The disclosed embodiments provide a method, device, equipment and medium for maintaining low thrust on-orbit based on fuel optimization. The real-time orbital state of the satellite in the earth-fixed coordinate system is periodically obtained by onboard sensors and transmitted to the computing equipment on the ground. The technical solution only occupies the computing resources on the ground and does not rely on the ground measurement and control resources. Therefore, real-time intervention and control on the ground are not required, which reduces the delay caused by waiting for ground instructions, and can achieve rapid response to changes in the satellite orbital state to adjust the satellite's orbit in time. The osculating orbital element number of each extrapolated time point is obtained according to the predicted orbital state corresponding to each extrapolated time point within the set extrapolation duration. The osculating orbital element number is not limited to the orbital maintenance of a single element of the semi-major axis and orbital inclination, which improves the accuracy of satellite orbit maintenance. The thrust sequence for low thrust on-orbit maintenance with fuel optimization is obtained according to the orbital state of the end point of the orbital maneuvering segment, which can be suitable for long-term missions with limited fuel carrying capacity. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A flow chart of a low-thrust on-orbit maintenance method based on fuel optimization provided in an embodiment of the present disclosure;

[0024] Figure 2 The detection cycle provided by the embodiment of the present disclosure , Extrapolation duration and equal time intervals The relationship diagram between

[0025] Figure 3 A detailed flow chart of a low-thrust on-orbit maintenance method based on fuel optimization provided in an embodiment of the present disclosure;

[0026] Figure 4 A schematic diagram of a low-thrust on-orbit sustaining device based on fuel optimization provided by an embodiment of the present disclosure;

[0027] Figure 5 A schematic diagram of the hardware structure of a computing device provided in an embodiment of the present disclosure. DETAILED DESCRIPTION

[0028] The technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure.

[0029] Chemical propulsion is usually used for orbit maintenance, but it has low specific impulse and high fuel consumption, making it difficult to achieve long-term orbit maintenance tasks. Although electric propulsion can achieve long-term orbit maintenance with high accuracy and low fuel consumption, in some examples, only the semi-major axis deviation and descending node deviation are considered, which is not suitable for satellite orbit maintenance that also has requirements for orbital inclination and eccentricity. Based on this, the embodiments of the present disclosure hope to provide a technical solution for in-orbit maintenance based on low thrust and fuel optimization. This technical solution can solve the problem of satellites being limited by their flat-panel configuration and carrying limited fuel, and can meet the needs of long-term orbit maintenance under the influence of the atmosphere, gravitational perturbations, solar radiation pressure, etc. See. Figure 1 , which shows a low-thrust on-orbit maintenance method based on fuel optimization provided by an embodiment of the present disclosure, the method comprising:

[0030] S101: Based on the initial orbital state of the satellite, extrapolation is performed at equal time intervals within a set extrapolation time period to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation time period.

[0031] Exemplarily, the initial orbital state of the satellite can be characterized by a position state vector and a velocity state vector. The extrapolation duration is the total duration used for orbital state extrapolation, that is, the length of time calculated backward from the moment corresponding to the initial orbital state, which is used to predict the orbital state of the satellite in the future. Sampling is performed at equal time intervals within the extrapolation duration to obtain extrapolated time points within the period. For each extrapolated time point, extrapolation can be performed based on the initial orbital state to obtain the predicted orbital state corresponding to each extrapolated time point. It should be noted that the predicted orbital state is the orbital state within the extrapolation duration based on the initial orbital state without performing any orbit maintenance operation.

[0032] S102: Obtain the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point.

[0033] The osculating orbit elements are usually called orbit elements or Kepler orbit elements, which are a set of orbital parameters used to describe the motion state of the satellite in orbit and the deviation information from the predetermined orbit or calibrated orbit. According to the motion state and deviation information, it is determined whether the satellite needs to be orbitally maneuvered and the orbital maneuver is designed to achieve fuel optimization. The motion state includes the satellite's current orbit state and predicted orbit state. The osculating orbit elements include semi-major axis, eccentricity, orbit inclination, right ascension of ascending node, true anomaly and perigee angular distance.

[0034] S103: Select a target extrapolation time point from all extrapolation time points based on the differences between the osculating orbit elements of all extrapolation time points and the average element number of the calibration orbit.

[0035] The calibration orbit is the expected orbit that the satellite should follow, and the average number of calibration orbit elements is the benchmark for orbit maintenance. The osculating orbit element difference represents the deviation between the osculating orbit element at each extrapolated time point and the average number of calibration orbit elements. The first extrapolated time point at which the osculating orbit element difference is greater than a set threshold is determined as the target extrapolated time point, and the target extrapolated time point is the starting time point for the satellite orbit maneuver.

[0036] S104: Obtain the orbital state of the starting point of the satellite's orbital maneuvering segment according to the osculating orbital elements at the target extrapolated time point, and obtain the orbital state of the ending point of the satellite's orbital maneuvering segment through a genetic algorithm according to the orbital state of the starting point.

[0037] Exemplarily, the orbital maneuvering phase is a specific period of time during which a satellite is subjected to a specific motion adjustment in orbit, and the adjustment generally involves changing the satellite's speed by applying thrust to change its orbital parameters, such as orbital altitude, orbital inclination, orbital phase, etc. In the field of aerospace, orbital maneuvers generally refer to intentional changes to the orbit of a satellite or other spacecraft to achieve a specific orbital adjustment or correction. The adjustment may be directed to at least one of the orbital parameters such as orbital altitude, orbital inclination, orbital shape (such as eccentricity) or orbital phase (such as true anomaly). Based on the above adjustments, the satellite can remain on a predetermined orbit or be transferred from one orbit to another. However, in the present disclosure, the orbital maneuver is only used to maintain the satellite on its current orbit.

[0038] S105: Utilizing the orbital state of the end point of the orbital maneuvering segment, a thrust sequence with optimal fuel for low-thrust on-orbit maintenance is obtained.

[0039] According to the description of the above scheme, the real-time orbital state of the satellite in the earth-fixed coordinate system is periodically obtained by the onboard sensor and transmitted to the computing device on the ground. This technical scheme only occupies the computing resources on the ground and does not rely on the ground measurement and control resources. Therefore, there is no need for real-time intervention and control from the ground, which reduces the delay caused by waiting for ground instructions, and can achieve rapid response to changes in the satellite orbital state to adjust the satellite's orbit in time. According to the predicted orbital state corresponding to each extrapolated time point within the set extrapolation duration, the osculating orbital element number of each extrapolated time point is obtained, and the osculating orbital element number is not limited to the orbit maintenance of a single element of the semi-major axis and orbital inclination, which improves the accuracy of satellite orbit maintenance. According to the orbital state of the end point of the orbital maneuvering segment, the thrust sequence for small thrust on-orbit maintenance with optimal fuel is obtained, which can be suitable for long-term missions with limited fuel carrying.

[0040] against Figure 1In some possible implementations of the technical solution shown, the initial orbital state based on the satellite is extrapolated at equal time intervals within a set extrapolation duration to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation duration, including:

[0041] The real-time orbit state obtained by the onboard sensor is converted into coordinates to obtain the initial orbit state of the satellite;

[0042] The initial orbital state is extrapolated through a high-fidelity orbital dynamics model to obtain a predicted orbital state corresponding to each extrapolation time point within a set extrapolation duration.

[0043] For the above implementation, in some examples, the coordinate conversion of the real-time orbit state acquired by the onboard sensor to obtain the initial orbit state of the satellite includes:

[0044] The real-time orbit status of the satellite in the earth-fixed coordinate system is periodically obtained through onboard sensors;

[0045] The real-time orbit state of the satellite in the earth-fixed coordinate system is transformed to obtain the initial orbit state in the J2000 inertial system.

[0046] In the above example, every cycle The satellite's real-time orbit state in the Earth-fixed coordinate system is obtained through onboard sensors, that is, the real-time position state vector and the real-time velocity state vector. It is a detection period to determine whether orbital maneuvers are needed in the future. The value is determined according to the speed of orbital deviation. The shorter the orbit maintenance period, the longer the orbital maneuver. The smaller the value, the larger the value. Not too large, the specific choice is ,in, is the orbit maintenance period. For low-Earth orbit, The value of is between 1.5 hours and 2 hours. is the average value of the historical orbital maneuvering interval, which is generally more than 5 orbit maintenance cycles. In some examples, coordinate conversion is a basic operation in a space mission, which converts the orbital state of the satellite from one reference system to another reference system to eliminate the influence of factors such as the rotation of the earth, ensuring that the calculation and analysis of the satellite orbital state are carried out in a stable and unified reference frame, thereby improving the accuracy and reliability of orbit prediction. In the present disclosure, the real-time orbital state of the satellite is converted from the earth-fixed coordinate system to the J2000 inertial system, wherein the earth-fixed coordinate system, i.e., the geocentric inertial system, is a coordinate system centered on the center of mass of the earth, parallel to the axis of rotation of the earth, but ignoring the rotation of the earth. In this coordinate system, the position and velocity of the satellite are relative to the center of mass of the earth, but the coordinate system rotates with the rotation of the earth. The J2000 inertial system is fixed and does not change with the rotation of the earth. Therefore, conversion to the J2000 inertial system can reduce the dynamic error caused by the rotation of the earth, and the coordinate system is suitable for long-term orbit prediction and analysis.

[0047] For the above implementation, in some examples, the extrapolating the initial orbital state by a high-fidelity orbital dynamics model to obtain a predicted orbital state corresponding to each extrapolation time point within a set extrapolation duration includes:

[0048] Build high-fidelity orbital dynamics models to describe satellite motion;

[0049] Determining the time step of the high-fidelity orbital dynamics model according to a set extrapolation duration and a set equal time interval duration within the extrapolation duration;

[0050] The initial orbit state is integrated through the high-fidelity orbit dynamics model according to the time step to obtain the predicted orbit state corresponding to each extrapolation time point within the set extrapolation duration.

[0051] For the above example, a high-fidelity orbital dynamics model for describing satellite motion is established based on Newton's laws of motion and the law of universal gravitation. The high-fidelity orbital dynamics model takes into account factors such as the earth's gravity, the gravitational influence of other celestial bodies, the earth's non-spherical perturbation, solar radiation pressure, and atmospheric resistance. Among them, the high-fidelity orbital dynamics model for describing satellite motion is:

[0052]

[0053] in, 、 , are the position, velocity and acceleration of the satellite in the J2000 inertial system; , , They are the satellite positions in the J2000 inertial system. Position components in the x, y, and z directions; , , are the satellite speeds in the J2000 inertial system Velocity components in the x, y, and z directions; , , are the satellite acceleration in the J2000 inertial system The acceleration components in the x, y, and z directions; is the gravitational constant; is the non-spherical perturbation of the Earth; is the radius of the Earth; , , is the gravitational perturbation component of higher order gravitational perturbation in the x, y, and z axis directions; , , are the components of the perturbations in the x, y, and z axis directions except for the solar pressure perturbation and the atmospheric drag perturbation gravity.

[0054] In some examples, after establishing a high-fidelity orbital dynamics model for describing satellite motion, a specific implementation method for determining the time step of the high-fidelity orbital dynamics model is as follows: Figure 2 Specifically, the extrapolation duration is determined according to the track maintenance strategy, and the extrapolation duration is expressed as It indicates the total time used for orbital state extrapolation, that is, the length of time calculated backward from the current moment, which is used to predict the orbital state of the satellite in the future. The determination of needs to comprehensively consider the influence of factors such as satellite orbit characteristics, maneuvering requirements, computing resources and model accuracy. Due to the difference between the high-fidelity orbital dynamics model and the actual orbit, The value of should not be too large. If the orbital maneuver is too long, it will cause a delay in the execution of the orbital maneuver. In addition, sufficient time must be provided to prepare and execute the orbital maneuver. If the orbital maneuver is too short, it will not provide enough preparation time. Considering the perturbations to which the satellite is subject, such as atmospheric drag and the non-spherical perturbations of the Earth, It needs to be long enough to be able to predict the orbit changes of the satellite for a period of time in the future and to be able to predict the long-term impact of the perturbations on the satellite orbit. Every cycle The extrapolation time of the orbital state after yes multiples of. The value should not be greater than Too many, and according to The value of is adjusted to ensure timely update of orbital status and timely execution of orbital maneuvers. The value is 1.1 times of , which can provide a sufficient time window to predict the future orbital state while avoiding over-prediction, thereby reducing the consumption of computing resources. For the extrapolation time The time intervals between the internal points are used to form a series of extrapolated time points, where the extrapolated time points represent the predicted positions of the satellite at different times in the future. Decided in The frequency of taking points within the time period, The value of should be small enough to capture subtle changes in the orbit, and small Values ​​can also provide a more detailed orbital description, but increase the computational effort. and equal time intervals , determine the time step for integral calculation of the initial orbital state, the selection of the time step needs to strike a balance between calculation accuracy and calculation efficiency. After determining the time step of the high-fidelity orbital dynamics model, the high-fidelity orbital dynamics model starts from the initial orbital state and gradually performs integral calculation according to the time step to obtain the duration of each equal time interval The orbital state at that time, that is, the position state vector and velocity state vector of the satellite at each extrapolation time point, repeats the above integral calculation process until the set extrapolation time is reached , the duration of each equal time interval obtained The orbital states at the locations are recorded and sorted to form a data set of a sequence of extrapolated time points, thereby obtaining the predicted orbital state corresponding to each extrapolated time point.

[0055] against Figure 1 In some possible implementations of the technical solution shown, obtaining the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point includes:

[0056] Obtaining an angular momentum vector and orbital energy according to the predicted orbital state corresponding to each extrapolated time point;

[0057] The number of osculating orbital elements at each extrapolated time point is obtained according to the angular momentum vector and the orbital energy.

[0058] For the above implementation, the angular momentum is a quantity describing the rotational motion of an object around a certain point, and the orbital energy can also be generally referred to as mechanical energy, which is used to describe the total energy of the satellite's motion in orbit, including kinetic energy and potential energy. According to the angular momentum vector and the orbital energy, the osculating orbit elements at each extrapolated time point are obtained, and the osculating orbit elements include the semi-major axis, eccentricity, orbital inclination, ascending node right ascension, true anomaly and perigee angular distance, wherein the semi-major axis in the osculating orbit elements is half of the major axis of the orbit, which determines the size of the orbit. The eccentricity is a parameter used to describe the shape of the orbit, 0 represents a circular orbit, and greater than 0 represents an elliptical orbit. The orbital inclination is the inclination angle of the orbital plane relative to the reference plane, and the reference plane is usually the equatorial plane of the earth. The ascending node right ascension is the angular position of the ascending node, which is the intersection line of the orbital plane and the reference plane. The true anomaly is the angle from the ascending node to the current position of the satellite in orbit. The perigee angular distance is the angle from the perigee to the current position of the satellite in orbit.

[0059] For the above implementation, in some examples, obtaining the angular momentum vector and the orbital energy according to the predicted orbital state corresponding to each extrapolated time point includes:

[0060] According to the position state vector in the predicted orbit state corresponding to each extrapolated time point and the velocity state vector Get the angular momentum vector and orbital energy for:

[0061]

[0062] in, , , are the angular momentum scalar of the satellite in the J2000 inertial system Angular momentum components on the x, y, and z axes;

[0063]

[0064] in, is the velocity state vector At the moment i scalar at ; is the gravitational constant; is the semi-major axis.

[0065] For the above implementation, in some examples, obtaining the number of osculating orbit elements at each extrapolated time point according to the angular momentum vector and the orbit energy includes:

[0066] According to the angular momentum vector and orbital energy The number of osculating orbit elements at each extrapolated time point is obtained as:

[0067] Semi-major axis: ;in, is the gravitational constant; For at the moment i The position state scalar at ; is the velocity state vector At the moment i The velocity scalar at ;

[0068] Eccentricity: ;in, is the semi-major axis; is the gravitational constant; For at the moment i The angular momentum scalar at ;

[0069] Orbital inclination: ;in, , , are the angular momentum components on the x, y, and z axes in the J2000 inertial system;

[0070] Ascending node right ascension: ;in, , are the angular momentum components on the x and y axes in the J2000 inertial system respectively;

[0071] True anomaly: ;in, is the semi-diameter; For at the moment i The position state scalar at ; is the eccentricity;

[0072] Perigee angular distance: ;in, is the orbital argument Expression of For at the moment i The position state vector at ; is the equatorial projection after rotation A unit vector in space; is the true anomaly angle.

[0073] For the above implementation, since the angular momentum vector In the J2000 inertial system, the equatorial projection differs from the right ascension of the ascending node by 90°. In some examples, the specific calculation process of the right ascension of the ascending node is:

[0074] Set the angular momentum vector Equatorial projection in J2000 inertial system ;

[0075] The equatorial projection Rotate 90° counterclockwise to obtain the equatorial projection after rotation for:

[0076] ;

[0077] According to the equatorial projection after rotation The right ascension of the ascending node is obtained as:

[0078] ;in, , They are the angular momentum scalars in the J2000 inertial system. Angular momentum components on the x, y axis.

[0079] In some examples, the true anomaly angle represents the angle from the ascending node to the current position of the satellite. With position state scalar , Semi-diameter The relationship is:

[0080]

[0081] According to the above formula, the true anomaly angle is calculated as:

[0082]

[0083] in, is the semi-diameter; ; is the gravitational constant; is the angular momentum scalar; is the eccentricity.

[0084] In some examples, the perigee angular distance represents the angle from the perigee to the current position of the satellite, and the relationship between the perigee angular distance, the orbital argument, and the true anomaly angle is:

[0085]

[0086] According to the equatorial projection after rotation Get its unit vector in space for:

[0087]

[0088] According to the unit vector The orbital argument is obtained as:

[0089]

[0090] Substituting the orbital argument into , the perigee angular distance is obtained as:

[0091]

[0092] in, For at the moment i The position state vector at ; is the equatorial projection after rotation A unit vector in space; is the true anomaly angle.

[0093] against Figure 1 In the technical solution shown in the figure, in some possible implementations, the target extrapolation time point is selected from all extrapolation time points based on the difference between the osculating orbit elements at all extrapolation time points and the average elements of the calibration orbit. Specifically, in the orbit maintenance strategy, the step of judging whether orbit maneuvers are required is crucial because it determines when and how to adjust the orbit of the satellite. The specific implementation of the judgment process is as follows: First, define the average elements of the calibration orbit or the reference orbit as , the calibration orbit is the expected orbit that the satellite should follow, and the average element of the calibration orbit is the benchmark for orbit maintenance. Secondly, the difference between the osculating orbit elements at all extrapolated time points and the average element of the calibration orbit is calculated, that is, the difference between the semi-major axis, eccentricity, orbit inclination, right ascension of the ascending node, and perigee angular distance in the osculating orbit elements and the average element of the calibration orbit is calculated. The difference between the osculating orbit elements for:

[0094]

[0095] in, is the semi-major axis, is the eccentricity, is the orbital inclination, is the right ascension of the ascending node, is the angular distance of perigee.

[0096] Then, the difference of the number of osculating orbit elements is Compare with the set threshold to determine whether it is necessary to perform orbital maneuvers on the satellite. The set threshold is the acceptable range of orbital deviation. If the difference in the number of osculating orbit elements at each extrapolated time point is within the set threshold, it is considered that no orbital maneuver is required for the satellite at each extrapolated time point. If the difference in the number of osculating orbit elements at one or more extrapolated time points is greater than the set threshold, it is considered that an orbital maneuver is required for the satellite, and the first extrapolated time point at which the difference in the number of osculating orbit elements at all extrapolated time points is greater than the set threshold is selected as the target extrapolated time point.

[0097] against Figure 1 In some possible implementations of the technical solution shown, the step of obtaining the orbit state of the starting point of the orbit maneuvering segment of the satellite according to the osculating orbit element at the target extrapolated time point, and obtaining the orbit state of the ending point of the orbit maneuvering segment of the satellite through a genetic algorithm according to the orbit state of the starting point includes:

[0098] Establish an inverse quintic polynomial orbit model;

[0099] Based on the inverse quintic polynomial orbit model, according to the orbit state of the starting point of the orbit maneuvering segment corresponding to the target extrapolated time point, the orbit state of the ending point of the orbit maneuvering segment is obtained through a genetic algorithm.

[0100] For the above implementation, the inverse quintic polynomial orbit model is established. For example, when implementing the orbital maneuver, a new cylindrical coordinate system needs to be established according to the orbital state of the starting point to facilitate the representation and calculation of orbital parameters. In the cylindrical coordinate system, the xy plane is the initial orbital plane, the starting x-axis direction is consistent with the position state vector of the satellite, the y-axis is determined by the right-hand rule, and the z-axis direction is the angular momentum direction. The cylindrical coordinate system is used to represent the orbital state of the starting point and the orbital parameters of the predicted orbital state. Since the orbital parameters of the predicted orbital state are is fixed, but the true anomaly angle Can be The true anomaly angle can be adjusted within this range to optimize fuel consumption. Based on the shape algorithm of the inverse quintic polynomial, the orbit state of the corresponding points at the start and end, that is, the orbit state of the starting point and the predicted orbit state are transferred to the cylindrical coordinate system to obtain the corresponding orbit parameters. The cylindrical coordinate form of the orbit parameter of the orbit state of the starting point is , the cylindrical coordinate form of the orbital parameters of the predicted orbital state is According to the definition of the cylindrical coordinate system, ,in, and are the radial components of cylindrical coordinates of the initial and final positions respectively; and are the cylindrical coordinate radial components of the initial and final velocities, respectively; and are the cylindrical coordinate polar angle components of the initial and final positions respectively; and are the cylindrical coordinate polar angle components of the initial and final velocities respectively; and are the vertical components of the cylindrical coordinates of the initial and final positions respectively; and are the cylindrical coordinate vertical components of the initial and final velocities, respectively.

[0101] In some examples, a specific implementation method of obtaining analytical parameters of the inverse quintic polynomial in the cylindrical coordinate system according to the orbital parameters to determine the inverse quintic polynomial orbital model is:

[0102] It is assumed that the cylindrical coordinate radial component of the satellite position relative to the central celestial body during the transition from the orbit state of the starting point to the predicted orbit state The inverse quintic polynomial satisfied is:

[0103]

[0104] in, is the radial component of the cylindrical coordinates of the satellite relative to the central celestial body; are the analytical parameters of the inverse quintic polynomial respectively; is the cylindrical coordinate polar angle component of the position during the transfer process;

[0105] Assuming that the z-axis direction is a high-order polynomial, the high-order polynomial is:

[0106]

[0107] in, is an integer greater than or equal to 3; is the vertical component of the cylindrical coordinates of the position during the transfer process; is the cylindrical coordinate vertical component of the velocity during the transfer process; , , , are the analytical parameters of the high-order polynomials respectively; is the cylindrical coordinate polar angle component of the position during the transfer process; It is the first-order derivative of the cylindrical coordinate polar angle component of the position during the transfer process with respect to time.

[0108] For the above example, the core concept of the shape algorithm of the inverse quintic polynomial is to first assume that the orbit satisfies the analytical expression of the inverse quintic polynomial during the orbit state transition. The analytical expression of the inverse quintic polynomial is used to describe the change in the orbit shape. All analytical parameters are determined by the orbit state of the starting point and the predicted orbit state that is ultimately expected to be achieved, and a unique analytical orbit is obtained. Based on the above core concept, first, it is assumed that the inverse quintic polynomial orbit model is satisfied during the orbit transfer process. This assumption allows the orbit shape to be optimized by adjusting the analytical parameters of the polynomial. Secondly, determining the inverse quintic polynomial orbit model is to obtain the analytical parameters of the inverse quintic polynomial based on the orbit parameters of the starting point orbit state and the predicted orbit state. And the analytical parameters of the high-order polynomial in the z-axis direction , , , To determine the inverse quintic polynomial orbit model, the process of obtaining analytical parameters is:

[0109] The radial component of the cylindrical coordinates of the satellite relative to the central celestial body The time derivative of the inverse quintic polynomial is obtained for:

[0110]

[0111] The obtained Substitute the flight direction angle The equation satisfied is obtained as follows:

[0112]

[0113] The derivatives are:

[0114]

[0115] Since the inverse quintic polynomial provides the initial value for the subsequent Gaussian pseudospectral method, the dynamics does not need to be too precise. When other perturbations are ignored, the satellite's dynamic equation in polar coordinates under the central gravitational field and small thrust is as follows:

[0116]

[0117] in, is the radial component of the cylindrical coordinates of the satellite relative to the central celestial body; is the first-order derivative of the cylindrical coordinate polar angle component of the position during the transfer process with respect to time; is the gravitational constant; is the thrust acceleration; is the thrust direction angle, i.e., the angle between the thrust vector and the tangent direction in the polar coordinate system;

[0118] according to , and obtain the following formula:

[0119]

[0120] During the orbit transfer process, the direction of the small thrust will generally cause the satellite's energy to decrease or increase the fastest. Therefore, it is assumed that the direction of the thrust during the flight is always the same as or opposite to the direction of the speed, that is:

[0121] ,in, is the thrust direction angle; is the flight direction angle; is 0 or 1;

[0122] Further simplification gives:

[0123]

[0124] According to the starting point orbit state, the predicted orbit state and the above formula, the following equation is obtained:

[0125]

[0126] Get the analytical parameters of the inverse quintic polynomial They are:

[0127]

[0128] Substitute the starting point orbit state, the position of the predicted orbit state, and the cylindrical coordinate vertical component of the velocity into the high-order polynomial to obtain:

[0129]

[0130] Get the analytical parameters of the high-order polynomial in the z-axis direction , , , They are:

[0131]

[0132] in, is the flight direction angle; is the phase angle of the orbit state at the starting point relative to the predicted orbit state, which varies with the true anomaly of the orbital element The amount of change; , are the polar angle components of the velocity in the starting point orbit state and the predicted orbit state in cylindrical coordinates respectively; is the flight direction angle of the starting point; is the flight direction angle of the end point.

[0133] It should be noted that an inverse quintic polynomial orbit model is constructed based on the determined starting point orbit state and the predicted orbit state. Through the inverse quintic polynomial orbit model, an optimal orbit transfer path is found between the starting point orbit state and the predicted orbit state, that is, the ending point orbit state, based on the shape algorithm of the inverse quintic polynomial. The orbit transfer path is approximated by an inverse quintic polynomial, and the true anomaly with optimal fuel consumption is found through a genetic algorithm.

[0134] For the above implementation, in some examples, the step of obtaining the orbit state of the end point of the orbit maneuvering segment by a genetic algorithm based on the inverse quintic polynomial orbit model and the orbit state of the start point of the orbit maneuvering segment corresponding to the target extrapolated time point includes:

[0135] Obtaining thrust acceleration in a cylindrical coordinate system according to the inverse quintic polynomial orbit model and its analytical parameters;

[0136] The fuel consumption is obtained according to the thrust acceleration, and the orbital state of the end point of the orbital maneuvering segment is obtained according to the fuel consumption.

[0137] In some examples, obtaining the thrust acceleration in a cylindrical coordinate system according to the inverse quintic polynomial orbit model and its analytical parameters includes:

[0138] The thrust acceleration in the cylindrical coordinate plane is obtained according to the inverse quintic polynomial orbit model and its analytical parameters. for:

[0139]

[0140] Thrust acceleration in the z-axis direction for:

[0141]

[0142] in, is the gravitational constant; is the radial component of the cylindrical coordinates of the satellite relative to the central celestial body; is the flight direction angle; and The first-order derivative and the second-order derivative of the cylindrical coordinate polar angle component of the position during the transfer process between the orbit state of the starting point and the predicted orbit state with respect to time; is an integer greater than or equal to 3; are the analytical parameters of the inverse quintic polynomial respectively; , , , are the analytical parameters of the high-order polynomials.

[0143] In some examples, obtaining fuel consumption according to the thrust acceleration, and obtaining the end point orbit state of the orbital maneuvering segment according to the fuel consumption includes:

[0144] The total thrust acceleration is obtained according to the thrust acceleration in the cylindrical coordinate plane and the thrust acceleration in the z-axis direction;

[0145] integrating the total thrust acceleration to obtain a fuel consumption;

[0146] According to the fuel consumption, the optimal true anomaly angle of fuel is obtained through a genetic algorithm to determine the orbital parameters corresponding to the end point of the orbital maneuver, and the corresponding end point orbital state is obtained according to the orbital parameters.

[0147] In some examples, the total thrust acceleration obtained according to the thrust acceleration in the cylindrical coordinate plane and the thrust acceleration in the z-axis direction is:

[0148]

[0149] In some examples, the total thrust acceleration is integrated to obtain the fuel consumption for:

[0150]

[0151] in, is the phase angle of the orbit state at the starting point relative to the predicted orbit state, which varies with the true anomaly of the orbital element The amount of change; is the cylindrical coordinate polar angle component of the position during the transfer process; is the first-order derivative of the cylindrical coordinate polar angle component of the position during the transfer process with respect to time; is the total thrust acceleration.

[0152] For the above example, the analytical parameters of the inverse quintic polynomial orbit model are obtained according to the orbital parameters of the starting point orbit and the predicted orbit, and the required thrust acceleration is calculated using the inverse quintic polynomial orbit model and the analytical parameters, thereby evaluating the total fuel consumption. The genetic algorithm is used to iteratively search for the true anomaly that can minimize the fuel consumption based on the total fuel consumption. Based on the true anomaly obtained by the search, the orbital parameters corresponding to the end point of the orbital maneuver are determined, and then the orbital state of the end point of the orbital maneuver segment is obtained according to the orbital parameters.

[0153] against Figure 1In some possible implementations of the technical solution shown, the use of the orbital state of the end point of the orbital maneuvering segment to obtain a thrust sequence with the best fuel for low-thrust on-orbit maintenance includes:

[0154] According to the orbital state of the end point of the orbital maneuvering phase, a thrust sequence with optimal fuel for small thrust on-orbit maintenance is obtained by Gaussian pseudo-spectral method.

[0155] For the above implementation, in some examples, obtaining a thrust sequence for low-thrust on-orbit maintenance with fuel optimization by using a Gaussian pseudo-spectral method according to the orbital state of the end point of the orbital maneuvering segment includes:

[0156] Acquiring a starting orbital state vector according to the orbital state of the end point of the orbital maneuvering segment;

[0157] The Gaussian nodes selected in the orbit maneuvering segment are used as discrete time points, and based on the initial orbit state vector, the orbit state vector and the control vector at each discrete time point are discretized to construct a nonlinear programming model;

[0158] Obtaining the constraint conditions of the nonlinear programming model according to the orbital state vector and the control vector at each discrete time point; wherein the constraint conditions include dynamic constraint conditions, boundary constraint conditions, thrust constraint conditions and fuel optimization constraint conditions;

[0159] Based on the constraints formed by combining the dynamic constraints, boundary constraints, thrust constraints and fuel optimization constraints, a fuel-optimal thrust sequence for low-thrust on-orbit maintenance is obtained through the nonlinear programming model.

[0160] For the above implementation, in some examples, the Gaussian nodes selected in the orbital maneuvering segment are used as discrete time points, and based on the initial orbital state vector, the orbital state vector and the control vector at each discrete time point are discretized to construct a nonlinear programming model, including:

[0161] Mapping a time interval consisting of a start time and an end time of the orbital maneuvering segment of the satellite to obtain a mapping interval, and selecting Gaussian nodes on the mapping interval as discrete time points;

[0162] Based on the initial orbital state vector, the orbital state vector and the control vector of the orbital maneuvering segment are discretized at the discrete time points to obtain a discretized nonlinear programming model.

[0163] For the above example, the orbital state vector and control vector of the orbital maneuvering phase of the satellite are discretized using the Gauss Pseudospectral Method (GPSM) based on the starting orbital state vector, wherein the orbital state vector includes a position state vector and a velocity state vector, and the control vector is a thrust vector. The start time and end time of the satellite in the orbital maneuvering phase are set to and , the start time , End time The time zone Map to In the interval, The time in the interval is recorded as In the mapping interval Select Gaussian nodes are used as discrete time points for discretization processing, and the orbital state vector of the orbital maneuvering segment is discretized at the discrete time points as , the control vector is discretized into .

[0164] In some examples, based on the nonlinear programming model, the design variables at each discrete time point are obtained as follows:

[0165]

[0166] in, is the 6-dimensional orbital state vector; is a 3D control vector; It is the end time of the satellite's orbital maneuvering phase.

[0167] The orbit state at each discrete time point is obtained as:

[0168]

[0169] in, It's time time after mapping; represents the orbital state vector Any dimension in The value of the moment; is the Lagrange interpolation basis function, and the Lagrange interpolation basis function is:

[0170]

[0171] in, ; for right The derivative of and for different time points.

[0172] For the above example, the Lagrange interpolation basis function is used to interpolate from the discrete time points to construct a continuous function model, so that the system state at any time point can be predicted and analyzed. In the present disclosure, a continuous function model is constructed based on known discrete time points (such as Gaussian nodes in the Gaussian pseudospectral method) to describe the change of system state (such as position and speed) over time.

[0173] For the above implementation, in some examples, obtaining the constraint conditions of the nonlinear programming model according to the track state vector and the control vector at each discrete time point includes:

[0174] The orbital state of each discrete time point is calculated in time Taking the derivative at , we get the following formula:

[0175]

[0176] in, ; for right The derivative of for right The second derivative of k and is the number of Gaussian nodes;

[0177] The dynamic constraint conditions obtained according to the track state vector and control vector at each offline time point are:

[0178]

[0179] in, is the differential equation for the orbital state vector The time variable is t Convert to in the form of for:

[0180] ,in, are natural forces, including gravity and perturbations; is the control vector.

[0181] The boundary constraints are obtained according to the orbit state of the end point of the orbit maneuvering segment:

[0182]

[0183] in, and are the initial orbit vector and the ending point orbit vector respectively; For the k The quadrature coefficients at the Gaussian nodes.

[0184] According to the relationship between the thrust acceleration at the Gaussian node and the maximum thrust acceleration of the satellite engine, the thrust constraint is:

[0185] ,in, is the maximum thrust acceleration of the engine, For the k The thrust acceleration at each Gaussian node.

[0186] Obtain optimal fuel constraints based on fuel consumption, including:

[0187] The fuel consumption By performing quadrature, the optimal fuel constraint is obtained as follows:

[0188]

[0189] in, , They are the start time and end time of the satellite’s orbital maneuvering phase, respectively; According to the start time, end time and time of the orbital maneuvering segment in the mapping interval The thrust acceleration obtained.

[0190] In some examples, obtaining the boundary constraint condition according to the orbit state of the end point of the orbit maneuvering segment includes:

[0191] When the orbit state of the end point of the orbit maneuvering segment satisfies the following formula, the boundary constraint condition is obtained:

[0192]

[0193] Transform the equation to obtain:

[0194]

[0195] in, ; For the k The quadrature coefficients at the Gaussian nodes; ; ; for n Legendre polynomial of order exist Right The derivative of

[0196] The boundary constraints are:

[0197]

[0198] in, and are the initial orbit vector and the ending point orbit vector respectively; For the k The quadrature coefficients at the Gaussian nodes.

[0199] For the above example, the constraints specifically include dynamic constraints satisfied at each discrete time point, boundary constraints satisfied by the orbital states at the starting point and the ending point of orbit maintenance, thrust constraints that satisfy the maximum thrust limit of the engine, and fuel optimality constraints satisfied by the total fuel consumption.

[0200] In some examples, the constraints based on the combined constraints of the dynamic constraints, boundary constraints, thrust constraints and fuel optimization constraints are obtained through the nonlinear programming model using a numerical optimization algorithm, such as a gradient descent method, a Newton method or a quasi-Newton method, to obtain a thrust sequence with optimal fuel for on-orbit maintenance with small thrust. Through multiple iterations, the orbit state vector and control variables are continuously updated until convergence conditions are met. Lagrange interpolation or other methods are used to interpolate from the discrete time points to the states of continuous time points, thereby obtaining a thrust sequence with optimal fuel for on-orbit maintenance with small thrust.

[0201] Combination Figure 1 The technical solution shown is described in detail with a specific embodiment Figure 1 The technical solution shown in Figure 3 , which shows a detailed flow chart of a low-thrust on-orbit maintenance method based on fuel optimization provided by an embodiment of the present disclosure, such as Figure 3 As shown, the specific steps are as follows:

[0202] S301: Obtain the real-time orbit status of the satellite through the onboard sensor and transmit it to the ground;

[0203] Every cycle The real-time orbit state of the satellite in the earth-fixed coordinate system is obtained and transmitted to the computing device on the ground so as to calculate and process the real-time orbit state.

[0204] S302: performing coordinate transformation on the real-time orbit state to obtain an initial orbit state;

[0205] The real-time orbital state of the satellite is converted from the Earth-fixed coordinate system to the J2000 inertial system to eliminate the influence of factors such as the Earth's rotation, thereby ensuring that the calculation and analysis of the satellite's orbital state are carried out in a stable and unified reference frame.

[0206] S303: extrapolating a set extrapolation time according to the initial orbit state to obtain a predicted orbit state;

[0207] The specific implementation method of extrapolating based on the initial orbital state is detailed in the above content and will not be repeated here.

[0208] S304: taking points according to the set equal time intervals on the extrapolated time to obtain the number of osculating orbit elements at each extrapolated time point;

[0209] set up For the extrapolation time The time interval of the internal points is used to form a series of extrapolated time points. The high-fidelity orbital dynamics model starts from the initial orbit state and gradually performs integral calculations according to the time step to obtain the time interval of each equal time interval. The orbital state at The orbital states at each extrapolation time point are recorded and sorted to form a data set of an extrapolation sequence. The number of osculating orbit elements at each extrapolation time point is obtained according to the predicted orbital state corresponding to each extrapolation time point.

[0210] S305: Determine whether orbital maneuvering is required. If orbital maneuvering is required, jump to step S306; otherwise, jump to step S301;

[0211] The specific implementation method for determining whether it is necessary to perform orbital maneuvers on the satellite is detailed in the above content and will not be repeated here.

[0212] S306: searching the orbit state after the orbit maneuver by using a genetic algorithm;

[0213] Using genetic algorithms or other optimization methods, the required speed change, thrust size, direction and duration are obtained according to the orbital state of the starting point, and the optimal true anomaly angle for fuel is obtained, so as to obtain the orbital parameters after the maneuver and its corresponding orbital state of the end point. This process requires multiple iterative optimizations to ensure that the maneuver plan minimizes fuel consumption while meeting the orbital adjustment requirements.

[0214] S307: Obtain the thrust sequence that is optimal for fuel.

[0215] The thrust sequence with the best fuel for maintaining low thrust on orbit is obtained by Gaussian pseudospectral method. The thrust sequence is applied to the satellite, and the orbital maneuver is performed. During the execution, the actual orbital state change of the satellite is monitored and adjusted when necessary to ensure the accuracy of the orbital maneuver. Through the above process, the satellite's orbit can be effectively maintained and adjusted to meet the mission requirements and cope with the influence of various perturbation factors.

[0216] Based on the same inventive concept as the above technical solution, see Figure 4 , which shows a low-thrust on-orbit maintenance device 400 based on fuel optimization provided by an embodiment of the present disclosure, the low-thrust on-orbit maintenance device 400 based on fuel optimization includes: an extrapolation part 401, a first acquisition part 402, a selection part 403, a second acquisition part 404 and a maintenance part 405; wherein,

[0217] The extrapolation part 401 is configured to perform extrapolation at equal time intervals within a set extrapolation duration based on the initial orbital state of the satellite to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation duration;

[0218] The first acquisition part 402 is configured to acquire the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point;

[0219] The selection part 403 is configured to select a target extrapolation time point from all extrapolation time points based on the difference between the number of osculating orbit elements at all extrapolation time points and the average number of calibrated orbit elements;

[0220] The second acquisition part 404 is configured to acquire the orbit state of the starting point of the orbit maneuvering segment of the satellite according to the osculating orbit element number of the target extrapolated time point, and obtain the orbit state of the ending point of the orbit maneuvering segment of the satellite through a genetic algorithm according to the orbit state of the starting point;

[0221] The maintenance section 405 is configured to utilize the orbital state of the end point of the orbital maneuvering segment to obtain a thrust sequence with the best fuel for low-thrust on-orbit maintenance.

[0222] In some examples, the extrapolation portion 401 is configured as follows:

[0223] The real-time orbit state obtained by the onboard sensor is converted into coordinates to obtain the initial orbit state of the satellite;

[0224] The initial orbital state is extrapolated through a high-fidelity orbital dynamics model to obtain a predicted orbital state corresponding to each extrapolation time point within a set extrapolation duration.

[0225] In some examples, the extrapolation portion 401 is configured as follows:

[0226] Build high-fidelity orbital dynamics models to describe satellite motion;

[0227] Determining the time step of the high-fidelity orbital dynamics model according to a set extrapolation duration and a set equal time interval duration within the extrapolation duration;

[0228] The initial orbit state is integrated through the high-fidelity orbit dynamics model according to the time step to obtain the predicted orbit state corresponding to each extrapolation time point within the set extrapolation duration.

[0229] In some examples, the first acquisition part 402 is configured to:

[0230] Obtaining an angular momentum vector and orbital energy according to the predicted orbital state corresponding to each extrapolated time point;

[0231] The number of osculating orbital elements at each extrapolated time point is obtained according to the angular momentum vector and the orbital energy.

[0232] In some examples, the second obtaining portion 404 is configured to:

[0233] Establish an inverse quintic polynomial orbit model;

[0234] Based on the inverse quintic polynomial orbit model, according to the orbit state of the starting point of the orbit maneuvering segment corresponding to the target extrapolated time point, the orbit state of the ending point of the orbit maneuvering segment is obtained through a genetic algorithm.

[0235] In some examples, the maintaining portion 405 is configured to:

[0236] According to the orbital state of the end point of the orbital maneuvering phase, a thrust sequence with optimal fuel for small thrust on-orbit maintenance is obtained by Gaussian pseudo-spectral method.

[0237] In some examples, the maintaining portion 405 is configured to:

[0238] Acquiring a starting orbital state vector according to the orbital state of the end point of the orbital maneuvering segment;

[0239] The Gaussian nodes selected in the orbit maneuvering segment are used as discrete time points, and based on the initial orbit state vector, the orbit state vector and the control vector at each discrete time point are discretized to construct a nonlinear programming model;

[0240] Obtaining the constraint conditions of the nonlinear programming model according to the orbital state vector and the control vector at each discrete time point; wherein the constraint conditions include dynamic constraint conditions, boundary constraint conditions, thrust constraint conditions and fuel optimization constraint conditions;

[0241] Based on the constraints formed by combining the dynamic constraints, boundary constraints, thrust constraints and fuel optimization constraints, a fuel-optimal thrust sequence for low-thrust on-orbit maintenance is obtained through the nonlinear programming model.

[0242] It can be understood that the exemplary technical solution of the low-thrust on-orbit maintenance device 400 based on fuel optimization and the technical solution of the low-thrust on-orbit maintenance method based on fuel optimization belong to the same concept, therefore, the details not described in detail in the technical solution of the low-thrust on-orbit maintenance device 400 based on fuel optimization can be referred to the description of the technical solution of the low-thrust on-orbit maintenance method based on fuel optimization. This embodiment of the disclosure will not be elaborated on this.

[0243] Please refer to Figure 5 , which shows a schematic diagram of the hardware structure of a computing device provided by an exemplary embodiment of the present disclosure. In some examples, the computing device may be at least one of a smart phone, a smart watch, a desktop computer, a laptop, a virtual reality terminal, an augmented reality terminal, a wireless terminal, and a laptop. The computing device has a communication function and can access a wired network or a wireless network. The computing device may generally refer to one of a plurality of terminals, and those skilled in the art may know that the number of the above terminals may be more or less. In some examples, the computing device may receive data based on a fuel-optimal low-thrust on-orbit maintenance method based on the connected wired network or wireless network. It can be understood that the computing device undertakes the calculation and processing work of the technical solution of the present disclosure, and the embodiments of the present disclosure are not limited to this.

[0244] like Figure 5 As shown, the computing device in the present disclosure may include one or more of the following components: a processor 510 and a memory 520 .

[0245] Optionally, the processor 510 uses various interfaces and lines to connect various parts within the entire computing device, and executes various functions of the computing device and processes data by running or executing instructions, programs, code sets or instruction sets stored in the memory 520, and calling data stored in the memory 520. Optionally, the processor 510 can be implemented in at least one hardware form of digital signal processing (DSP), field programmable gate array (FPGA), and programmable logic array (PLA). The processor 510 can integrate one or a combination of a central processing unit (CPU), a graphics processing unit (GPU), a neural network processor (NPU), and a baseband chip. Among them, the CPU mainly processes the operating system, user interface, and application programs; the GPU is responsible for rendering and drawing the content that needs to be displayed on the touch display; the NPU is used to implement artificial intelligence (AI) functions; and the baseband chip is used to process wireless communications. It is understandable that the above baseband chip may not be integrated into the processor 510, but may be implemented by a separate chip.

[0246] The memory 520 may include a random access memory (RAM) or a read-only memory (ROM). Optionally, the memory 520 includes a non-transitory computer-readable storage medium. The memory 520 may be used to store instructions, programs, codes, code sets, or instruction sets. The memory 520 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as a touch function, a sound playback function, an image playback function, etc.), instructions for implementing the above various method embodiments, etc.; the data storage area may store data created according to the use of the computing device, etc.

[0247] In addition, those skilled in the art can understand that the structure of the computing device shown in the above drawings does not constitute a limitation on the computing device, and the computing device may include more or fewer components than shown in the figure, or combine certain components, or arrange the components differently. For example, the computing device also includes a display screen, a camera assembly, a microphone, a speaker, a radio frequency circuit, an input unit, a sensor (such as an acceleration sensor, an angular velocity sensor, an optical fiber sensor, etc.), an audio circuit, a WiFi module, a power supply, a Bluetooth module and other components, which will not be described in detail here.

[0248] An embodiment of the present disclosure also provides a computer-readable storage medium storing at least one instruction, wherein the at least one instruction is used to be executed by a processor to implement the low-thrust on-orbit maintenance method based on fuel optimization as described in the above embodiments.

[0249] An embodiment of the present disclosure also provides a computer program product, which includes computer instructions, which are stored in a computer-readable storage medium; a processor of a computing device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computing device executes to implement the low-thrust on-orbit maintenance method based on fuel optimization as described in the above-mentioned embodiments.

[0250] Those skilled in the art should be aware that in one or more of the above examples, the functions described in the embodiments of the present disclosure can be implemented with hardware, software, firmware, or any combination thereof. When implemented using software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium. Computer-readable media include computer-readable storage media and communication media, wherein the communication media include any media that facilitates the transmission of a computer program from one place to another. The readable storage medium can be any available medium that can be accessed by a general or special-purpose computer.

[0251] The above description is only a specific implementation mode of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present disclosure, which should be included in the protection scope of the present disclosure.

Claims

1. A low-thrust on-orbit maintenance method based on fuel optimization, characterized in that: The method comprises: Based on the initial orbital state of the satellite, extrapolation is performed at equal time intervals within a set extrapolation duration to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation duration; Obtaining the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point; Based on the difference between the osculating orbit elements of all extrapolated time points and the average element number of the calibration orbit, a target extrapolated time point is selected from all extrapolated time points; Acquire the orbit state of the starting point of the orbit maneuvering segment of the satellite according to the osculating orbit element number at the target extrapolated time point, and acquire the orbit state of the ending point of the orbit maneuvering segment of the satellite through a genetic algorithm according to the orbit state of the starting point; The orbit state of the end point of the orbital maneuvering segment is used to obtain a thrust sequence with the best fuel for low-thrust on-orbit maintenance; The initial orbital state based on the satellite is extrapolated at equal time intervals within a set extrapolation duration to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation duration, including: The real-time orbit state obtained by the onboard sensor is converted into coordinates to obtain the initial orbit state of the satellite; Extrapolating the initial orbital state through a high-fidelity orbital dynamics model to obtain a predicted orbital state corresponding to each extrapolation time point within a set extrapolation time period; The obtaining the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point includes: Obtaining an angular momentum vector and orbital energy according to the predicted orbital state corresponding to each extrapolated time point; Obtaining the number of osculating orbital elements at each extrapolated time point according to the angular momentum vector and the orbital energy; The step of obtaining the orbit state of the starting point of the orbit maneuvering segment of the satellite according to the osculating orbit element number at the target extrapolated time point, and obtaining the orbit state of the ending point of the orbit maneuvering segment of the satellite through a genetic algorithm according to the orbit state of the starting point includes: Establish an inverse quintic polynomial orbit model; Based on the inverse quintic polynomial orbit model, according to the orbit state of the starting point of the orbit maneuvering segment corresponding to the target extrapolated time point, the orbit state of the ending point of the orbit maneuvering segment is obtained by a genetic algorithm; The method of utilizing the orbital state of the end point of the orbital maneuvering segment to obtain a thrust sequence with optimal fuel for low-thrust on-orbit maintenance comprises: According to the orbital state of the end point of the orbital maneuvering phase, a thrust sequence with optimal fuel for small thrust on-orbit maintenance is obtained by Gaussian pseudo-spectral method.

2. The method according to claim 1, characterized in that: The extrapolating the initial orbital state by the high-fidelity orbital dynamics model to obtain a predicted orbital state corresponding to each extrapolation time point within a set extrapolation time period includes: Build high-fidelity orbital dynamics models to describe satellite motion; Determining the time step of the high-fidelity orbital dynamics model according to a set extrapolation duration and a set equal time interval duration within the extrapolation duration; The initial orbit state is integrated through the high-fidelity orbit dynamics model according to the time step to obtain the predicted orbit state corresponding to each extrapolation time point within the set extrapolation duration.

3. The method according to claim 1, characterized in that The method of obtaining a thrust sequence for low-thrust on-orbit maintenance with fuel optimization by using a Gaussian pseudo-spectral method according to the orbital state of the end point of the orbital maneuvering segment includes: Acquiring a starting orbital state vector according to the orbital state of the end point of the orbital maneuvering segment; The Gaussian nodes selected in the orbit maneuvering segment are used as discrete time points, and based on the initial orbit state vector, the orbit state vector and the control vector at each discrete time point are discretized to construct a nonlinear programming model; Obtaining the constraint conditions of the nonlinear programming model according to the orbital state vector and the control vector at each discrete time point; wherein the constraint conditions include dynamic constraint conditions, boundary constraint conditions, thrust constraint conditions and fuel optimization constraint conditions; Based on the constraints formed by combining the dynamic constraints, boundary constraints, thrust constraints and fuel optimization constraints, a fuel-optimal thrust sequence for low-thrust on-orbit maintenance is obtained through the nonlinear programming model.

4. A low-thrust on-orbit sustaining device based on fuel optimization, characterized in that: The low-thrust on-orbit maintenance device based on fuel optimization includes: an extrapolation part, a first acquisition part, a selection part, a second acquisition part and a maintenance part; wherein, The extrapolation part is configured to perform extrapolation at equal time intervals within a set extrapolation duration based on the initial orbital state of the satellite to obtain a predicted orbital state corresponding to each extrapolation time point within the extrapolation duration; The first acquisition part is configured to acquire the number of osculating orbit elements at each extrapolated time point according to the predicted orbit state corresponding to each extrapolated time point; The selection part is configured to select a target extrapolation time point from all extrapolation time points based on the difference between the osculating orbit elements of all extrapolation time points and the average element number of the calibration orbit; The second acquisition part is configured to acquire the orbit state of the starting point of the orbit maneuvering segment of the satellite according to the osculating orbit element number of the target extrapolated time point, and obtain the orbit state of the ending point of the orbit maneuvering segment of the satellite through a genetic algorithm according to the orbit state of the starting point; The maintenance section is configured to obtain a thrust sequence with the best fuel for low-thrust on-orbit maintenance by utilizing the orbital state of the end point of the orbital maneuvering segment; Wherein, the extrapolation part is further configured as follows: The real-time orbit state obtained by the onboard sensor is converted into coordinates to obtain the initial orbit state of the satellite; Extrapolating the initial orbital state through a high-fidelity orbital dynamics model to obtain a predicted orbital state corresponding to each extrapolation time point within a set extrapolation time period; The first acquisition part is further configured as follows: Obtaining an angular momentum vector and orbital energy according to the predicted orbital state corresponding to each extrapolated time point; Obtaining the number of osculating orbital elements at each extrapolated time point according to the angular momentum vector and the orbital energy; The second acquisition part is further configured as follows: Establish an inverse quintic polynomial orbit model; Based on the inverse quintic polynomial orbit model, according to the orbit state of the starting point of the orbit maneuvering segment corresponding to the target extrapolated time point, the orbit state of the ending point of the orbit maneuvering segment is obtained by a genetic algorithm; The maintenance part is configured as follows: According to the orbital state of the end point of the orbital maneuvering phase, a thrust sequence with optimal fuel for small thrust on-orbit maintenance is obtained by Gaussian pseudo-spectral method.

5. A computing device, characterized in that: The computing device comprises: a processor and a memory; wherein, The memory is used to store a computer program that can be run on the processor; The processor is used to execute the low-thrust on-orbit maintenance method based on fuel optimization as described in any one of claims 1 to 3 when running the computer program.

6. A computer-readable storage medium, characterized in that: The readable storage medium stores at least one instruction, and the at least one instruction is used to be executed by a processor to implement the low-thrust on-orbit maintenance method based on fuel optimization as described in any one of claims 1 to 3.

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