A low-thrust continuous thrust orbit transfer optimization method based on piecewise constant yaw angle strategy

Abstract

This invention discloses an optimization method for low-thrust transfer between circular orbits based on piecewise constant yaw angle guidance, belonging to the field of spacecraft orbit control technology. The implementation method of this invention is as follows: the low-thrust transfer process is divided into a transfer segment, a drift segment, and an adjustment segment; a piecewise constant yaw angle guidance strategy is proposed, using latitude argument angles α, β, γ as switching points, dividing each orbital period into four arc segments, maintaining a constant yaw angle and thrust switching state within each arc segment; based on the Gaussian perturbation equation, analytical solutions are derived for the long-term changes of the orbital semi-major axis, orbital inclination, and right ascension of the ascending node under this strategy and perturbation influence; the parameters of the optimal drift orbit are estimated based on the impulse assumption; a mixed-integer nonlinear programming model is established with the objective of minimizing the total velocity increment, and based on the dynamic relationship that "inclination changes are only generated by the thrust of arc segment 1," the model is transformed into several nonlinear programming sub-problems for solution, obtaining near-optimal guidance parameters. This invention avoids tedious numerical integration, significantly improves the efficiency of orbit design and optimization, and the resulting transfer scheme has fuel consumption close to the theoretical optimum. Moreover, the algorithm is robust and suitable for rapid orbit design tasks such as large-scale constellation deployment.

Description

Technical Field

[0001] This invention relates to a low-thrust continuous thrust orbit transfer optimization method based on a piecewise constant yaw angle strategy, belonging to the field of spacecraft orbital dynamics and control. Background Technology

[0002] In recent years, electric propulsion technology has been increasingly applied to missions such as orbit transfer, position holding, and interplanetary transfer due to its advantages of low power consumption, high specific impulse, fast response, lightweight design, and cost-effectiveness. With the deployment of large-scale constellations like Starlink, the demand for low-thrust orbit transfers is growing. However, traditional low-thrust orbit optimization methods (such as direct and indirect methods) often face problems such as convergence difficulties and high computational load, especially when multiple orbit transfers and frequent yaw angle adjustments are involved, resulting in low computational efficiency and difficulty in meeting real-time mission planning requirements. Existing methods, such as segmented yaw strategies, can reduce the frequency of attitude adjustments, but still cannot balance orbit transfer optimality with computational efficiency. To improve the efficiency and real-time performance of low-thrust transfers between circular orbits, this invention proposes an optimization method for low-thrust transfers between circular orbits based on segmented constant yaw angle guidance. By establishing analytical expressions for changes in orbital elements, the optimization problem is transformed into a nonlinear programming problem, significantly reducing computational load and achieving fast near-optimal trajectory design. Summary of the Invention

[0003] This invention provides an optimization method for low-thrust transfer of circular orbits based on segmented constant yaw angle and analytical propagation, an electronic device, and a computer-readable storage medium, to reduce the computational complexity of orbit transfer design and achieve near-optimal fuel consumption.

[0004] In a first aspect, embodiments of the present invention provide an optimization method for low-thrust transfer in circular orbits based on segmented constant yaw angles and analytical propagation, comprising the following steps:

[0005] The orbital transfer is divided into a transfer phase, a drift phase, and an adjustment phase, utilizing Earth's... Perturbation enables natural drift correction for RAAN;

[0006] Each orbital period is divided into four latitudinal argument intervals, maintaining a constant yaw angle and thrust magnitude within each interval while satisfying symmetry constraints;

[0007] Based on the near-circular orbit assumption and Perturbation is used to establish the average equations of motion for the semi-major axis, inclination, and right ascension of the ascending node, and to derive their analytical solutions;

[0008] A mixed-integer nonlinear programming model is constructed with the objective of minimizing the total speed increment, including thrust switching variables, yaw angle variables, time variables, and switching angle variables;

[0009] By estimating drift trajectory parameters and decomposing integer variables, the mixed integer nonlinear programming problem is transformed into multiple nonlinear programming subproblems, which are then solved and compared to obtain the optimal guidance parameters.

[0010] In the drift segment, the RAAN drift rate of the drift trajectory Calculated by the following formula:

[0011]

[0012] in The coefficient of Earth's oblateness. Earth's radius, denoted as the Earth's gravitational constant, a as the semi-major axis of the orbit, and I as the orbital inclination.

[0013] The four latitudinal argument intervals are defined as follows:

[0014] Arc 1:

[0015] Arc 2:

[0016] Arc 3:

[0017] Arc 4:

[0018] in For the switching angle, the constant yaw angle of each arc segment satisfies:

[0019] ,

[0020] The thrust switch states of each arc segment satisfy the following:

[0021] ,

[0022] in , 1 indicates on, 0 indicates off. This is the maximum thrust acceleration.

[0023] The average equations of motion for the semi-major axis, inclination, and right ascension of the ascending node of the orbit are as follows:

[0024]

[0025]

[0026]

[0027] in, For orbital velocity, It is a constant. , , , The expression is as follows:

[0028]

[0029]

[0030]

[0031]

[0032] The analytical solution for the semi-major axis of the orbit is:

[0033]

[0034] in For time, The initial orbital velocity, and The specific expression is as follows:

[0035]

[0036]

[0037] in This is the semi-major axis of the initial orbit.

[0038] The performance metrics of the optimization model That is, the total velocity increment, expressed as:

[0039]

[0040] in The final time of the orbital transfer. These are the thrust switching variables for the transfer and adjustment phases, respectively. and Their switching angles are respectively. For a period of time, To adjust the start time of the phase, This represents the total time for orbital transfer.

[0041] The drift trajectory parameters: semi-major axis of the drift trajectory and drift track inclination It is obtained by solving the Kuhn-Tucker condition equations based on the impulse assumption, which contain information about the variation of the semi-major axis. Change in orbital inclination and Lagrange multipliers The equation. The integer variable decomposition method is: to decompose the four common combinations of the thrust switch variable. The original problem is decomposed into four independent nonlinear programming subproblems, and the combination is as follows:

[0042]

[0043] The vector elements represent the thrust switch states of the first arc segment of the transfer segment, the second arc segment of the transfer segment, the first arc segment of the adjustment segment, and the second arc segment of the adjustment segment, respectively.

[0044] Secondly, embodiments of the present invention also provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements an optimization method for low-thrust transfer between circular orbits based on piecewise constant yaw angle guidance.

[0045] Thirdly, embodiments of the present invention also provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements an optimization method for low-thrust transfer between circular orbits based on piecewise constant yaw angle guidance.

[0046] Compared with existing technologies, the low-thrust transfer optimization method for circular orbits based on segmented constant yaw angle and analytical propagation provided by this invention has the following significant advantages:

[0047] 1. High computational efficiency: By deriving and applying the analytical solution of the average change of orbital elements, the time-consuming numerical integration process is completely avoided, which improves the calculation speed of multi-cycle, long-period transfer trajectories by several orders of magnitude, meeting the requirements of rapid mission design.

[0048] 2. Excellent optimization performance: The proposed segmented constant yaw angle strategy is more flexible than the fixed switching point strategy and can better coordinate changes in semi-major axis, inclination angle, and RAAN. Simulation results show that the fuel consumption obtained by this method is very close to the theoretical pulse optimal estimate and outperforms similar methods in existing literature.

[0049] 3. Strong engineering applicability: The method transforms the complex mixed-integer optimization problem into a nonlinear programming problem with a small number of design variables through drift trajectory estimation, resulting in a stable and reliable solution. The output guidance parameters (constant yaw angle, fixed switching point) are simple and clear, making them easy to implement on satellite.

[0050] 4. High robustness: Monte Carlo simulations show that under different transfer times and different orbital differences, this method can stably provide near-optimal solutions, demonstrating good robustness and adaptability.

[0051] In summary, this invention provides a complete and practical solution for achieving rapid and fuel-efficient orbital transfer of spacecraft, and is particularly suitable for the deployment, reconfiguration, and maintenance of large-scale constellations. Attached Figure Description

[0052] Figure 1 Schematic diagram of the orbital rotation problem;

[0053] Figure 2. Schematic diagram of the RAAN rate of change as a function of the semi-major axis and the orbital inclination angle;

[0054] Figure 3 A schematic diagram illustrating the process of orbital transfer using a drift track;

[0055] Figure 4 Schematic diagram of segmented constant yaw angle maneuver strategy;

[0056] Figure 5 shows the simulation results of Example 1;

[0057] Figure 6 shows the simulation results of Example 2;

[0058] Figure 7 shows the simulation results of Example 3;

[0059] Figure 8 shows the simulation results of Example 4;

[0060] Figure 9 The diagram showing the changes in orbital elements in Example 1;

[0061] Figure 10 The diagram showing the variation of yaw angle with latitude angle during the transfer and adjustment phases in Example 1;

[0062] Figure 11 The diagram showing the changes in orbital elements in Example 2;

[0063] Figure 12 The diagram showing the variation of yaw angle with latitude angle during the transfer and adjustment phases in Example 2; Detailed Implementation

[0064] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0065] This invention provides an optimization method for low-thrust transfer on circular orbits based on piecewise constant yaw angles and analytical propagation, comprising the following steps:

[0066] Step 1: Description of the orbital transfer problem and segmented transfer strategy

[0067] This invention considers as follows Figure 1 The orbital transfer problem shown, Figure 1 In This represents the change in the right ascension of the ascending node (RAAN). Considering that both the initial and target orbits are near-circular, they deviate from each other in terms of semi-major axis, orbital inclination, and RAAN. To save fuel and avoid direct maneuvering to correct RAAN deviations, this invention employs a three-stage transfer strategy: a transfer stage, a drift stage, and an adjustment stage. In the transfer stage, continuous thrust is used to adjust the spacecraft's semi-major axis and inclination, guiding it into a specific drift orbit. In this orbit, the spacecraft relies on Earth... The long-term RAAN drift rate difference generated by the perturbation force naturally eliminates the RAAN deviation from the target orbit. The variation of the RAAN drift rate with the semi-major axis and inclination angle is shown in Figure 2. Finally, continuous thrust is applied again during the adjustment phase, causing the spacecraft to enter the target orbit from the drift orbit. The RAAN drift rate of the drift orbit is affected by... The perturbation effect is calculated using the following formula:

[0068] (1)

[0069] in This represents the drift rate of RAAN. The coefficient of Earth's oblateness. Earth's radius, The gravitational constant of Earth, For the semi-major axis of the track, This represents the track inclination angle.

[0070] By adjusting the semi-major axis variation and The change in tilt angle can change the change in drift rate. The relationship is shown in Figure 2, which illustrates the different combinations of semi-major axis and tilt angle. The change graph. The relationship is obtained by taking the total differential of equation (1):

[0071] (2)

[0072] Where the partial derivatives and The specific expressions are given by equations (3) and (4):

[0073] (3)

[0074] (4)

[0075] Based on this relationship, a specific RAAN deviation can be identified. and total transfer time Design appropriate drift trajectory parameters The drift trajectory and transfer process are illustrated in the diagram below. Figure 3 As shown.

[0076] Step 2, Piece-by-Piece Constant Yaw Angle Maneuver Strategy

[0077] This invention proposes a novel piecewise constant yaw angle guidance strategy, such as... Figure 4 As shown. Figure 4 A schematic diagram of the segmented constant yaw angle maneuvering strategy of the present invention is shown. The diagram shows the yaw angle within four specific latitudinal argument intervals (defined as shown in equation (4)) using one orbital period as the unit. And thrust magnitude Maintaining constancy and satisfying symmetry conditions, this strategy sets a constant yaw angle and thrust magnitude within four specific latitudinal argument intervals, using one orbital period as the unit. Specifically, four switching point latitudinal arguments are defined: , , , Divide one orbital period into four arc segments:

[0078] Arc 1:

[0079] Arc 2:

[0080] Arc 3:

[0081] Arc 4:

[0082] Yaw angle within each arc segment And the magnitude of thrust acceleration To maintain constancy, and to simplify the design while maintaining symmetry, let the yaw angles of arc segment 3 and arc segment 1, and arc segment 4 and arc segment 2 be equal in magnitude and opposite in direction, i.e.:

[0083]

[0084]

[0085] At the same time, the thrust switch states of the corresponding arc segments are the same, that is...

[0086]

[0087]

[0088] in These are binary thrust switch variables (1 indicates on, 0 indicates off). This is the maximum thrust acceleration (determined by engine performance).

[0089] Therefore, the yaw angle within one cycle and thrust acceleration This can be expressed as:

[0090] (5)

[0091] in and These are the constant yaw angles for the first and second intervals, respectively, and have... , The switching angle (defining the latitude argument of the switching point).

[0092] Step 3: Average Equation of Motion and Analytical Solution

[0093] Under the near-circular orbit assumption, combined with the above maneuvering strategies and The perturbation effect is addressed by averaging the Gaussian perturbation equation over one orbital period, yielding the description of the semi-major axis. ,inclination Right ascension of ascending node Long-term average equation of motion:

[0094] (6)

[0095] (7)

[0096] (8-a)

[0097] in, For orbital velocity, It is a constant. , , , The expression is as follows:

[0098] (8-b)

[0099] (8-c)

[0100] (8-d)

[0101] (8-e)

[0102] Step 3.1, Analytical solution of the semi-major axis of the orbit

[0103] Based on equations (6)-(8), the analytical solution of the orbital elements as a function of time is obtained by integration, where the analytical solution of the semi-major axis is:

[0104] (9-a)

[0105] in For time, The initial orbital velocity, and The specific expression is as follows:

[0106] (9-b)

[0107] (9-c)

[0108] in This is the semi-major axis of the initial orbit.

[0109] Step 3.2, Analytical Solution of Track Inclination

[0110] The analytical solution for the orbital inclination angle is based on Whether it is 0 (i.e. whether the semi-major axis has changed) depends on two cases:

[0111] 1. When the semi-major axis remains unchanged, that is... The analytical solution for the orbital inclination angle can be expressed as:

[0112] (10-a)

[0113] in The initial orbital inclination angle, for

[0114] (10-b)

[0115] 2. When the semi-major axis of the orbit changes with time, that is... The rate of change of the orbital inclination can be expressed as:

[0116] (11-a)

[0117] in for

[0118] (11-b)

[0119] Integrating equation (11) above, we get:

[0120] (12-a)

[0121] in

[0122] (12-b)

[0123] (12-c)

[0124] Step 3.3, Analytical Solution of Right Ascension of Ascending Node

[0125] According to the semi-major axis and tilt angle Whether it changes or not, the analytical solutions for the right ascension of the ascending node fall into four categories:

[0126] 1. When and When all values ​​are constant, the analytical solution for the right ascension of the ascending node can be expressed as:

[0127] (13)

[0128] in The initial ascending node is the right ascension.

[0129] 2. When It is a constant value. The analytical solution for the right ascension of the ascending node as it changes over time can be expressed as:

[0130] (14)

[0131] 3. When Over time, When the right ascension of the ascending node is constant, the analytical solution can be expressed as:

[0132] (15)

[0133] in The initial orbital inclination angle, for

[0134]

[0135] 4. When and When both change with time, the analytical solution for the right ascension of the ascending node can be expressed as:

[0136] (16)

[0137] and As shown in equations (12-b) and (12-c) respectively.

[0138] The analytical solutions described in step 3 avoid tedious numerical integration and can directly and quickly calculate long-term orbital evolution, providing an efficient tool for subsequent optimization. Simulations under four typical conditions (as shown in Figures 5-8) demonstrate that the analytical solutions are completely consistent with the numerical integration results, verifying their accuracy and effectiveness and providing an efficient and reliable tool for subsequent optimization.

[0139] Step 4: Optimize Problem Modeling and Solution

[0140] This invention constructs the entire low-thrust orbital transfer problem as an optimization problem with the objective of minimizing the total velocity increment. To solve this optimization problem, a mixed-integer nonlinear programming (MINLP) model is first established, where the design variables include:

[0141] 1. Thrust switch variable in the transfer section and Thrust switch variable of the adjustment section and ;

[0142] 2. Yaw angle variable during the transfer segment and yaw angle variable in the adjustment segment and ;

[0143] 3. Time of the transfer segment Adjustment period ;

[0144] 4. Switching angle of the transfer segment The switching angle of the adjustment segment .

[0145] The performance index of this optimization problem is the total velocity increment. Its specific expression is as follows:

[0146] (17)

[0147] in The final time of the orbital transfer. The constraints of this optimization problem include time sequence constraints:

[0148] (18)

[0149] Switching angle range constraints:

[0150] (19)

[0151] Yaw angle range constraints:

[0152] (20)

[0153] Terminal track element equation constraint:

[0154] (twenty one)

[0155] Among the terminal constraints , and The calculation will be performed using the analytical solution given in step 3.

[0156] After establishing the MINLP model, to reduce the solution complexity, it is first necessary to estimate the semi-major axis of the optimal drift trajectory based on the impulse assumption. and orbital inclination Then, an optimization problem is established with the objective of minimizing the total pulse velocity increment and RAAN deviation correction as an equality constraint. This is achieved by solving the following Kuhn-Tucker condition equations:

[0157] (twenty two)

[0158] (twenty three)

[0159] (twenty four)

[0160] (25)

[0161] Or an analytical solution in the following specific case:

[0162] (26)

[0163] To obtain the optimal semi-major axis change required from the initial trajectory to the drift trajectory. and orbital inclination change Therefore, it is determined by equation (61). and In equation (26) For Lagrange multipliers, , , .

[0164] Finally, using the obtained drift trajectory parameters and The MINLP model established above can be simplified and transformed into a more easily solvable nonlinear programming problem. Combining equations (7) and (8-b) above, the track inclination angle can be determined. long-term rate of change It only relates to the parameters of arc segment 1:

[0165] (27)

[0166] From the above formula, it can be seen that in order for the tilt angle to change, the following conditions must be met. Due to yaw angle Available Optimize the selection within the range, and you will always find one that makes... of Therefore, the necessary and sufficient condition for achieving the tilt angle change is the thrust switch flag of arc segment 1. .

[0167] Based on the aforementioned deterministic relationships, some integer variables (thrust switch variables) in the MINLP model can be fixed, thereby decomposing the problem. Define an integer variable vector. , to integer variables , , and By fixing the four common combinations, the original MINLP problem is decomposed into four independent nonlinear programming (NLP) problems:

[0168] (28)

[0169] Each fixed Substituting these variables into the original MINLP model, the original model is transformed into a purely nonlinear programming problem with fewer design variables. The main design variables in this NLP model include the yaw angle of each segment. , , , Switching angle , End time of transfer segment and adjustment period start time The performance index remains the total speed increment shown in equation (17). The constraints include the time, angle, and terminal equation constraints in the original equations (18)-(21), as well as the newly added drift trajectory approximation constraints:

[0170] (29)

[0171] in and This represents the upper limit of the allowable error.

[0172] Solve each of the four NLP sub-problems separately and compare the obtained optimal performance index values. , among which The minimum solution yields the globally optimal or near-optimal guidance parameters, including the yaw angles for each segment. Switching angle End time of transfer segment and adjustment period start time .

[0173] Example 1: Orbit transfer with only RAAN deviation

[0174] This embodiment considers a transfer scenario where the initial and target orbits have the same semi-major axis and inclination, with only a RAAN deviation. The parameters of the initial and target orbits are shown in Table 1.

[0175] Table 1. Track parameters of Example 1

[0176]

[0177] Step 1: Drift Track Design. Using the drift track estimation method based on the impulse assumption from Step 4, the optimal drift track parameters shown in Equation (26) are solved, and the changes in the semi-major axis, track inclination, and RAAN are obtained:

[0178] (30-a)

[0179] (30-b)

[0180] (30-c)

[0181] Semi-major axis of the drift track track inclination .

[0182] Step 2: MINLP Model Establishment and Simplification. Based on the drift trajectory parameters, the MINLP model is transformed into four NLP subproblems, whose integer variable combinations are shown in Equation (28).

[0183] Step 3: Solve the nonlinear programming problem. Use the sequential quadratic programming algorithm to solve the four NLP subproblems respectively, and obtain the optimal performance index for each subproblem. As shown in Table 2.

[0184] Table 2. Results of velocity increments for each sub-problem in Example 1

[0185]

[0186] Comparing the results in the table above, we can see that when The total velocity increment is the smallest at that time, which is 492.193 m / s.

[0187] Step 4: Guide Parameter Extraction. Based on the conclusions of Step 3, corresponding... The guiding parameters are shown in Table 3.

[0188] Table 3. Track parameters of Example 1

[0189]

[0190] Step 5: Trajectory Simulation Verification. Using the above guidance parameters, combined with the analytical solution formulas given in Step 3 (such as Equation (18) for the semi-major axis, Equation (22) for the inclination angle, and Equation (28) for RAAN), the trajectory elements changing with time are calculated as follows: Figure 9 As shown in the figure. In this embodiment, the variation of the yaw angle of the transfer segment and the adjustment segment with the latitude argument u is as follows: Figure 10 As shown, solid lines represent thrust activation, and dashed lines represent thrust deactivation. It can be seen that during the transfer phase, the yaw angle is mainly set near the ascending node to efficiently adjust the roll angle; during the adjustment phase, the RAAN is mainly adjusted near the inverse node. Simulation results show that, in the total time... Within a day, the spacecraft successfully transferred from its initial orbit to its target orbit, and the terminal constraints met the accuracy requirements.

[0191] Example 2: Track transfer with simultaneous deviations in semi-major axis, inclination angle, and RAAN.

[0192] This embodiment considers the general case where the initial orbit deviates from the target orbit in terms of semi-major axis, inclination, and RAAN. The orbital parameters are shown in Table 4.

[0193] Table 4. Track parameters for Example 2

[0194]

[0195] Step 1: Drift track design. Solve the nonlinear equations (Kuhn-Tucker conditions) consisting of equations (22)–(25) to obtain the changes in the semi-major axis, inclination angle, and RAAN of the track:

[0196] (30-a)

[0197] (30-b)

[0198] Semi-major axis of the drift track track inclination .

[0199] Step 2: Optimization Solution and Results. Using the same optimization process as in Example 1, the four NLP subproblems are solved to obtain the optimal combination of integer variables. The minimum total velocity increment is 561.251 m / s.

[0200] Step 3: Guidance Parameters and Trajectory. The optimal guidance parameters are shown in Table 5, and the orbital elements change over time as follows: Figure 11 As shown, the yaw angle varies with the latitude angle as follows: Figure 12 As shown.

[0201] Table 5. Track parameters for Example 2

[0202]

[0203] Example 3: Monte Carlo Robustness Verification

[0204] To verify the robustness and near-optimal performance of this method under different transition times, Monte Carlo simulations were conducted. The transition time was set... The change from 100 days to 300 days applies to each... The drift trajectory was redesigned and the optimization problem was solved. The optimization results corresponding to different transition times are shown in Table 6.

[0205] Table 6 Optimization results at different transfer times

[0206]

[0207] Simulation results show that the optimal combination of integer variables is 0 for all transition times. This demonstrates the consistency of the strategy proposed in this invention. Furthermore, the optimized total velocity increment is very close to the optimal pulse estimate, with an error within 1%, verifying the near-optimal nature of this method. Simultaneously, as the transition time increases, the difference between the actual optimized solution and the pulse estimate gradually decreases.

[0208] The above embodiments demonstrate that the method proposed in this invention can effectively design low-thrust transfer trajectories under different orbital deviations and transfer times, with fuel consumption close to the theoretical optimum, high computational efficiency, and good engineering applicability and robustness.

[0209] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A low-thrust transfer optimization method for circular orbits based on piecewise constant yaw angle and analytical propagation, characterized in that, Includes the following steps: The orbital transfer is divided into a transfer phase, a drift phase, and an adjustment phase, utilizing Earth's... Perturbation enables natural drift correction for RAAN; Each orbital period is divided into four latitudinal argument intervals, maintaining a constant yaw angle and thrust magnitude within each interval while satisfying symmetry constraints; Based on the near-circular orbit assumption and Perturbation is used to establish the average equations of motion for the semi-major axis, inclination, and right ascension of the ascending node, and to derive their analytical solutions; A mixed-integer nonlinear programming model is constructed with the objective of minimizing the total speed increment, including thrust switching variables, yaw angle variables, time variables, and switching angle variables; By estimating drift trajectory parameters and decomposing integer variables, the mixed integer nonlinear programming problem is transformed into multiple nonlinear programming subproblems, which are then solved and compared to obtain the optimal guidance parameters.

2. The method according to claim 1, characterized in that, In the drift segment, the RAAN drift rate of the drift trajectory Calculated by the following formula: in The coefficient of Earth's oblateness. Earth's radius, denoted as the Earth's gravitational constant, a as the semi-major axis of the orbit, and I as the orbital inclination.

3. The method according to claim 1, characterized in that, The four latitudinal argument intervals are defined as follows: Arc 1: Arc 2: Arc 3: Arc 4: in For the switching angle, the constant yaw angle of each arc segment satisfies: ， The thrust switch states of each arc segment satisfy the following: ， in , 1 indicates on, 0 indicates off. This is the maximum thrust acceleration.

4. The method according to claim 1, characterized in that, The average equations of motion for the semi-major axis, inclination, and right ascension of the ascending node of the orbit are as follows: in, For orbital velocity, It is a constant. , , , The expression is as follows:

5. The method according to claim 4, characterized in that, The analytical solution for the semi-major axis of the orbit is: in For time, The initial orbital velocity, and The specific expression is as follows: in This is the semi-major axis of the initial orbit.

6. The method according to claim 1, characterized in that, The performance metrics of the optimization model That is, the total velocity increment, expressed as: in The final time of the orbital transfer. These are the thrust switching variables for the transfer and adjustment phases, respectively. and Their switching angles are respectively. For a period of time, To adjust the start time of the phase, This represents the total time for orbital transfer.

7. The method according to claim 1, characterized in that, The drift trajectory parameters: semi-major axis of the drift trajectory and drift track inclination It is obtained by solving the Kuhn-Tucker condition equations based on the impulse assumption, which contain information about the variation of the semi-major axis. Change in orbital inclination and Lagrange multipliers The equation.

8. The method according to claim 1, characterized in that, The integer variable decomposition method is as follows: four common combinations of the thrust switch variable... The original problem is decomposed into four independent nonlinear programming subproblems, and the combination is as follows: The vector elements represent the thrust switch states of the first arc segment of the transfer segment, the second arc segment of the transfer segment, the first arc segment of the adjustment segment, and the second arc segment of the adjustment segment, respectively.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the low-thrust transfer optimization method between circular orbits based on piecewise constant yaw angle guidance as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the low-thrust transfer optimization method between circular orbits based on piecewise constant yaw angle guidance as described in any one of claims 1 to 8.

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