Limited-thrust spacecraft proximity rendezvous guidance method

Abstract

The application discloses a spacecraft rendezvous guidance method based on limited thrust, and belongs to the technical field of spacecraft guidance. The application aims at the problem that the existing autonomous approach method of a spacecraft in a close distance guidance stage cannot simultaneously consider fuel consumption and hardware cost. The method comprises the following steps: calculating a theoretical speed increment of a current task stage; judging a state of a thruster according to a preset period during the execution of the task stage; if the thruster is in a propelling state, calculating a residual speed increment by combining the theoretical speed increment and a single-period speed increment of the thruster; until the current residual speed increment is less than a set threshold value, determining that the thruster is in a non-propelling state; then recalculating the theoretical speed increment, comparing the theoretical speed increment with a track safety belt threshold value, and judging whether a tracking spacecraft exceeds a safety belt range; if yes, updating a task state, and controlling the thruster to perform propelling, so as to correct a transfer orbit, until the task stage is ended. The application realizes high-precision guidance control.

Description

Technical Field

[0001] This invention relates to a spacecraft approach and rendezvous guidance method based on limited thrust, belonging to the field of spacecraft guidance technology. Background Technology

[0002] Existing autonomous approach methods for spacecraft during close-range guidance include: dual-multipulse guidance based on CW / TH (circular / elliptical orbit) equations, artificial potential function method, optimal control / model predictive control method, and state-space based control method, etc.

[0003] The dual-multipulse guidance method based on the CW / TH equations utilizes the analytical solutions of the CW (circular orbit) or TH (elliptical orbit) equations to calculate the required velocity pulses based on the current relative navigation state and the desired terminal state (usually constant relative position and zero relative velocity). The dual-pulse method requires calculating an initial pulse and a terminal pulse to achieve a two-point transfer, representing open-loop programming. The multipulse method divides the entire approach process into multiple stages, applying a pulse in each stage, similar to closed-loop control. This method is theoretically mature and computationally efficient (especially the analytical form), but it heavily relies on the accuracy of the dynamic model (ignoring perturbation and nonlinearity), resulting in significant errors in long-duration, long-distance, or high-precision missions.

[0004] The artificial potential function method, inspired by physics, transforms path planning into a motion problem within a "virtual force field." By artificially designing gravitational and repulsive fields, a "potential energy well" is created at the target point, guiding the spacecraft towards the target. Simultaneously, "potential energy peaks" are established around obstacles (such as sensitive parts of the target spacecraft, space debris) and no-fly zones, generating repulsive potentials to ensure spacecraft safety. Under the combined force of the attractive and repulsive potentials, the spacecraft automatically plans a safe, collision-free path. This method naturally handles obstacle avoidance problems, offering high safety, good real-time performance, and relatively simple computation. However, the potential field parameters are complex to design, difficult to update in real time, have poor generalization ability, and unreasonable parameters may lead to local optima or oscillations. Furthermore, rigorously proving its theoretical stability is also challenging.

[0005] In optimal control / model predictive control methods, optimal control represents a performance index (such as minimum fuel consumption or shortest time) as a mathematical functional. Optimal control uses optimization algorithms (such as genetic algorithms or sequential quadratic programming) to find the optimal pulse sequence or optimal control law under constraints such as optimal fuel consumption or fixed time. However, this is often difficult to solve online. Model predictive control is a rolling implementation of optimal control. Based on the current state and the dynamic model, it predicts the system's state evolution over a future period. That is, it solves a finite open-loop optimization problem to obtain a series of future control commands that optimize the predicted trajectory (such as minimizing fuel consumption) and satisfy all constraints (such as obstacle avoidance or thruster limitations). Then, only the first optimized control command is executed. In the next cycle, the state is updated with new measurements, and prediction and optimization are repeated, forming a closed-loop feedback. This method is highly robust to errors and disturbances and has optimal performance, but it has a very heavy computational burden and requires high computing power.

[0006] State-space control methods include PID control and sliding mode control. They are conceptually simple and easy to implement, but require discretization and consume a great deal of fuel. Summary of the Invention

[0007] To address the issue that existing autonomous approach methods for close-range guidance of spacecraft cannot simultaneously balance fuel consumption and hardware costs, this invention provides a spacecraft approach rendezvous guidance method based on limited thrust.

[0008] The present invention provides a spacecraft approach and rendezvous guidance method based on finite thrust, comprising:

[0009] When the tracking spacecraft enters the mission phase, the theoretical velocity increment for the current mission phase is calculated based on the current state and the expected terminal state of the tracking spacecraft.

[0010] During the mission phase, the thruster status is assessed at preset intervals. If the thruster is in motion, the remaining velocity increment is calculated by combining the theoretical velocity increment of the current mission phase with the single-cycle velocity increment of the thruster. The remaining velocity increment is determined to be less than a set threshold, at which point the thruster is in a non-propelling state. The theoretical velocity increment is then recalculated, and the tracking spacecraft is checked against the current theoretical velocity increment and the trajectory safety zone threshold to determine if it has exceeded the safety zone range. If so, the mission status is updated, and the thrusters are controlled to propel the spacecraft to correct the transfer trajectory until the mission phase ends, achieving a close rendezvous with the tracking spacecraft.

[0011] The beneficial effects of this invention are as follows: The method of this invention achieves limited thrust guidance based on the trajectory safety belt, which has lower hardware cost and complexity, higher accuracy compared to dual-pulse CW guidance, and minimal increase in fuel consumption; compared to multi-pulse CW guidance, it has no pulse number requirement and higher autonomy; compared to optimal control, it can meet higher calculation speed and real-time requirements.

[0012] The method of this invention combines CW dual-pulse guidance and trajectory correction safety belt to achieve high-precision guidance and control with limited thrust that cannot implement "pulse" (thruster execution time > mission time / 100). It has the characteristics of low hardware requirements, wide applicability and high real-time performance and accuracy. Attached Figure Description

[0013] Figure 1 This is a flowchart of the spacecraft rendezvous guidance method based on limited thrust described in this invention;

[0014] Figure 2 This is a graph showing the change in the relative positions of the tracking spacecraft and the target spacecraft over time in scenario 1 of the simulation experiment.

[0015] Figure 3 This is a graph showing the change in the relative positions of the tracking spacecraft and the target spacecraft over time in scenario 1 of the simulation experiment;

[0016] Figure 4 This is a graph showing the change in the relative velocity between the tracking spacecraft and the target spacecraft over time in scenario 1 of the simulation experiment.

[0017] Figure 5 This is a graph showing the change in the relative velocity between the tracking spacecraft and the target spacecraft over time in scenario 1 of the simulation experiment.

[0018] Figure 6 This is a graph showing the change in the thrust execution of the tracking spacecraft over time under scenario 1 in the simulation experiment;

[0019] Figure 7 This is a graph showing the change in the relative positions of the tracking spacecraft and the target spacecraft over time in scenario 2 of the simulation experiment.

[0020] Figure 8 This is a graph showing the change in the relative positions of the tracking spacecraft and the target spacecraft over time in scenario 2 of the simulation experiment;

[0021] Figure 9 This is a graph showing the change in the relative positions of the tracking spacecraft and the target spacecraft over time in scenario 3 of the simulation experiment.

[0022] Figure 10 This is a graph showing the change in the relative positions of the tracking spacecraft and the target spacecraft over time in scenario 3 of the simulation experiment;

[0023] Figure 11 This is a graph showing the change of the relative position over time during 100 target shots in a simulation experiment;

[0024] Figure 12 It is the change of the end position of the target over time in 100 shots in the simulation experiment;

[0025] Figure 13 It is a three-dimensional spatial distribution diagram of the end positions of 100 shots in a simulation experiment;

[0026] Figure 14 This is a graph showing the relative velocity changing over time during 100 target shots in a simulation experiment.

[0027] Figure 15 This is a graph showing the change of the relative velocity at the end of the target over time during 100 shots in a simulation experiment. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Specific Implementation Method 1: Combination Figure 1 As shown, the present invention provides a spacecraft approach and rendezvous guidance method based on finite thrust, comprising:

[0030] When the tracking spacecraft enters the mission phase, the theoretical velocity increment for the current mission phase is calculated based on the current state and the expected terminal state of the tracking spacecraft.

[0031] During the mission phase, the thruster status is assessed at preset intervals. If the thruster is in motion, the remaining velocity increment is calculated by combining the theoretical velocity increment of the current mission phase with the single-cycle velocity increment of the thruster. The remaining velocity increment is determined to be less than a set threshold, at which point the thruster is in a non-propelling state. The theoretical velocity increment is then recalculated, and the tracking spacecraft is checked against the current theoretical velocity increment and the trajectory safety zone threshold to determine if it has exceeded the safety zone range. If so, the mission status is updated, and the thrusters are controlled to propel the spacecraft to correct the transfer trajectory until the mission phase ends, achieving a close rendezvous with the tracking spacecraft.

[0032] In this embodiment, a data input module can be used to receive information transmitted by the satellite computer, including onboard time, mission start and end timestamps, relative position, velocity, theoretical thrust, etc. The information sources include inter-satellite communication, ground-based data transfer, etc.

[0033] The remaining speed increment can be calculated in the current cycle using the remaining speed increment calculated in the previous control cycle and the theoretical single-cycle speed increment.

[0034] Furthermore, the theoretical velocity increment is calculated based on the CW equation and its analytical solution in the target orbit coordinate system.

[0035] The method for calculating the theoretical velocity increment based on the CW equation and its analytical solution in the target orbit coordinate system is as follows:

[0036] ,

[0037] In the formula , , To track the X, Y, and Z coordinates of the spacecraft in the target orbit coordinate system, To track the spacecraft's average orbital angular velocity, To track the X-axis acceleration of the spacecraft, To track the spacecraft's Y-axis acceleration, To track the Z-axis acceleration of the spacecraft; This is the vector pointing from the target spacecraft to the tracking spacecraft in the LVLH coordinate system (target orbit coordinate system);

[0038]

[0039] ,

[0040] In the formula To track the spacecraft's initial velocity increment, , , To track the spacecraft's initial position using the X, Y, and Z axis coordinates, , , To track the X, Y, and Z coordinates of the spacecraft's terminal position, For the orbital change time, To track the velocity increments at the end of a spacecraft's lifecycle;

[0041] As an intermediate variable:

[0042] ;

[0043] ,

[0044] In the formula This represents the theoretical speed increment.

[0045] Calculate the orbit change time based on the current onboard time and the end timestamp. for:

[0046] ,

[0047] In the formula To track the spacecraft's start time, To track the deadline of spacecraft.

[0048] Furthermore, determining whether the tracked spacecraft has exceeded the safety belt range includes determining whether it has exceeded the in-plane trajectory safety belt threshold based on the CW equation:

[0049] ,

[0050] In the formula This represents the X-axis component of the current remaining velocity increment when the thruster is not in a propulsive state. This represents the Y-axis component of the current remaining velocity increment when the thruster is not in a propulsive state. The safety belt threshold for in-plane trajectory is based on the CW equation.

[0051] Determining whether a tracked spacecraft has exceeded the safety belt range also includes determining whether it has exceeded the out-of-plane trajectory safety belt threshold based on the CW equation:

[0052] ,

[0053] This represents the Z-axis component of the current remaining velocity increment when the thruster is not in a propulsive state. The safety belt threshold for out-of-plane trajectory is based on the CW equation.

[0054] A state update module can be used for mission state updates. It determines whether an update is needed based on the various state variables of the current cycle, including whether to execute a velocity increment based on whether the satellite has exceeded the trajectory safety zone, whether to update the storage module, and whether to update thruster switching commands. Under the assumption of undisturbed CW equations, the calculated velocity increment is always 0 when the satellite is on the correct transfer path. If the velocity increment is not equal to 0, it means the satellite has deviated from the desired transfer orbit, and a larger velocity increment indicates a greater deviation. Therefore, the boundary can be corrected by manually selecting the safety zone.

[0055] In this embodiment, a status judgment module is used to judge the mission status of the tracking spacecraft. If the mission phase has not been entered, the system waits for the mission status to be updated until the mission phase is entered.

[0056] The status judgment module can determine the task flow to be entered based on the status variables of the current cycle, including whether to enter / exit the task, whether it is in a certain stage of the task, whether it is progressing, whether to calculate the speed increment, etc.

[0057] During the mission phase, the thruster status is determined by combining the thruster's historical propulsion status.

[0058] If the tracked spacecraft goes beyond the safety belt range, a thruster activation command is generated, and the mission status is updated; otherwise, a thruster deactivation command is generated, and the mission status is updated.

[0059] The thruster activation and deactivation commands are transmitted to the spacecraft computer for thruster control.

[0060] The required data can be stored using a storage module; the thruster switching commands can be output to the spacecraft computer using a data output module.

[0061] In this embodiment, the data received by the data input module may include three types:

[0062] Time-related parameters: onboard real-time time, mission start timestamp, mission end timestamp, used for subsequent calculation of orbit change duration;

[0063] Motion state parameters: relative position and relative velocity of the target in the LVLH coordinate system, which provide the basic state variables for velocity increment calculation;

[0064] Thrust parameters: Theoretical thrust values ​​of the thruster, adapted to finite thrust characteristics, used for incremental updates of remaining velocity.

[0065] In this embodiment, data input requires no additional sensors or ground intervention, relying solely on routine onboard data interaction, demonstrating the advantages of hardware simplification.

[0066] The four core components of this implementation method—state determination, velocity increment calculation, remaining velocity increment calculation, and state update—serve as the decision center, and their collaborative logic is as follows:

[0067] First, the status judgment module makes a preliminary judgment on the current task status: if the task has not entered the task stage, it returns to the data input module to wait for triggering; if the task has entered the task stage, it further judges whether it is in the process of execution and whether speed increment calculation needs to be started (such as the first time entering the task or periodic update node), and sends a trigger signal to the corresponding module.

[0068] When the velocity increment calculation is triggered, the velocity increment calculation module can call the time and relative motion state parameters cached in the storage module, calculate the theoretical velocity increment required from the current state to the desired end state (constant relative position, zero relative velocity) based on the analytical solution of the CW equation in the target LVLH system, and pass the result to the remaining velocity increment calculation module.

[0069] If the current process is in progress, the remaining velocity increment calculation module can combine the remaining velocity increment of the previous cycle with the theoretical thrust of the current cycle to update the remaining velocity increment at the end of the current cycle in real time, and synchronize the update results to the status update module and the storage module.

[0070] The status update module, as the core decision-making node, reads the theoretical speed increment from the speed increment calculation module or the real-time remaining speed increment from the remaining speed increment calculation module; it also calls the trajectory safety belt threshold from the storage module, for example, selectable... It determines whether the current remaining speed increment exceeds the seat belt range: if it does, it generates a thruster activation command; if it does not exceed the range, it generates a thruster deactivation command, and updates the mission stage status (such as advancing, waiting to advance) and writes it to the storage module.

[0071] The storage module serves as a data cache throughout the process, storing information including: the original input parameters, the theoretical and remaining speed increments during the calculation process, the trajectory safety belt threshold, and task status markers, such as task started or progress execution, ensuring the continuity of data interaction between modules and the accuracy of periodic updates.

[0072] The data output module is the endpoint of the process. It receives the thruster on / off commands generated by the status update module and transmits them directly to the space station computer. The space station computer then controls the thrusters to perform the corresponding actions, completing the closed loop from decision-making to execution.

[0073] This implementation improves guidance for finite thrust, making it more realistic compared to traditional CW dual / multi-pulse guidance strategies. Since the main calculations still involve analytical solutions to the CW equations, real-time performance and computational simplicity are preserved.

[0074] Compared to traditional CW dual / multi-pulse guidance strategies, it offers better accuracy and robustness, which is verified through simulation experiments below:

[0075] Simulation experiment: Simulation duration 3000s, step size 1s.

[0076] Table 1. Various parameters in the simulation

[0077]

[0078] The errors of the unknown perturbation force and position velocity are simulated using random numbers:

[0079] Table 2 Random Number Parameters

[0080]

[0081] The simulation results are as follows:

[0082] Table 3 Number of 6 orbital elements for the two spacecraft

[0083]

[0084] At this point, taking the scenario described in Table 3 as Scenario 1, the initial relative position of the tracking spacecraft in the target LVLH coordinate system is: Meters. Choose a seatbelt:

[0085] Table 4 Seat belt parameters

[0086]

[0087] Based on the above parameters, simulation verification is carried out under the basic initial state, such as... Figures 2 to 6 As shown, Figure 2 and Figure 3 The study presents the trend of the relative position of the tracked spacecraft within the LVLH system over time in autonomous maneuver mode. It shows that after the terminal maneuver, the X, Y, and Z axis positions did not fluctuate significantly, and the overall trajectory closely followed the expected transfer channel; the corresponding change in relative velocity can be observed through... Figure 4 and Figure 5 The two sets of curves further confirm this, with the relative speed of XYZ at the end remaining within a relatively small range, demonstrating the restraining effect of the track safety belt on speed deviation; while Figure 6 The thrust variation curve intuitively reflects the execution logic of limited thrust. The thruster only starts when the speed increment exceeds the seat belt threshold, with no redundant thrust output, balancing guidance accuracy and fuel economy.

[0088] Furthermore, to verify the adaptability of the method of the present invention under different initial conditions, differentiated scenarios 2 and 3 were set by modifying the true perimeter angle of the tracked spacecraft, with simulated initial relative positions as follows: Mihe The trajectory changes and thruster performance under three scenarios are as follows: Figures 2 to 10 As shown; Figure 7 and Figure 8 The trajectory changes corresponding to scenario 2 are shown. Even if the Y-axis position deviates significantly in the initial stage, the position gradually returns to a reasonable range in the later stage under the correction logic of the trajectory safety belt. Figure 9 and Figure 10 The trajectory curve for scenario 3 shows that the three-axis positions remain stable throughout, without any loss of control or significant deviation, proving that the method of this invention can be adapted to the guidance requirements of various initial relative position scenarios.

[0089] To further verify the robustness of the method of the present invention under perturbation scenarios, a target shooting test was conducted in the neighborhood of scenario 1. Figure 11 and Figure 12 It presents the trajectory distribution under different initial states in the neighborhood. Even with initial disturbances, each trajectory can complete the maneuver through periodic correction. Figure 13 The scatter plot of the terminal positions visually demonstrates the final position convergence effect. The terminal positions of all test samples are concentrated in a small range, with no outliers with excessive dispersion.

[0090] To smoothly begin the next phase, it is necessary to advance the approximate range of the final velocity, as described above regarding the firing speed. Figure 14 and Figure 15 As shown.

[0091] The numerical simulation accuracy of the relative position at the end of the final thrust, starting from within the neighborhood during the autonomous approach process of the tracking spacecraft, has been verified as follows:

[0092] Table 5 Performance Compliance Statistics of Autonomous Approach Model

[0093]

[0094] Table 5 shows the deviation between the tracked spacecraft's position and the desired position at the end of the final propulsion, which clarifies the terminal guidance accuracy boundaries of the method of this invention: the fluctuation range of the X-axis and Y-axis terminal positions is controlled within ±5m, the overall position converges within a square with a side length of 10m, and the Z-axis position is stably maintained within the preset range of 99~104m. This accuracy index fully meets the mission requirements of the close-range guidance phase of the spacecraft, ensuring that the tracked spacecraft accurately arrives at the designated area near the target, laying a stable position foundation for the subsequent rendezvous and docking phase; at the same time, the terminal velocity is also maintained in a low fluctuation range without significant velocity deviation, avoiding interference with subsequent missions.

[0095] Overall, this simulation tested the method from three dimensions: basic initial state verification, multi-initial position adaptation verification, and neighborhood perturbation robustness verification. Under basic conditions, the method demonstrated by this invention can achieve precise control of limited thrust through a trajectory safety band, with both trajectory and velocity conforming to expectations. In multi-initial position scenarios, stable maneuvers were completed under different initial relative states without significant deviations. Neighborhood target shooting tests proved that the method of this invention has good anti-interference capabilities against initial perturbations, with both terminal position and velocity converging to the required range. The series of simulations fully demonstrates that the method of this invention retains the computational simplicity and real-time performance of traditional CW guidance, while overcoming the shortcomings of traditional CW dual / multi-pulse guidance, such as reliance on ideal pulse assumptions and susceptibility to initial errors, through limited thrust and trajectory safety band design. Furthermore, it achieves superior guidance accuracy and engineering practicality without requiring high computational power.

[0096] The method of this invention is applied to autonomous rendezvous and docking of spacecraft, and is suitable for autonomous rendezvous and docking missions between spacecraft, which autonomously approach each other through the close-range guidance phase of the spacecraft.

[0097] In summary, the method of this invention abandons the assumption of ideal pulse thrust in traditional CW guidance and constructs a full-process correction mechanism adapted to the characteristics of actual thrusters. It sequentially acquires basic information such as onboard time and relative position / velocity through a data input module, determines the current mission stage through a state judgment module, generates theoretical velocity increments based on the analytical solution of the CW equations through a velocity increment calculation module, updates the remaining correction amount after thrust output in real time through a remaining velocity increment calculation module, and coordinates with a state update module and a trajectory safety belt to determine whether correction is triggered. This achieves dynamic trajectory correction under limited thrust, preserving the computational simplicity of the CW equations while solving the problem of mismatch between ideal pulses and actual thruster characteristics.

[0098] This invention, based on the dynamic characteristics of the CW equation, directly correlates the trajectory safety zone with the velocity increment, forming an in-plane and out-of-plane classification and monitoring system. The principle is as follows: under the assumption of an undisturbed CW equation, the velocity increment value is positively correlated with the degree of trajectory deviation. Based on this, in-plane and out-of-plane trajectory safety zones are designed. By setting velocity increment correction boundaries, it accurately identifies whether trajectory deviation requires thrust correction, avoiding the problems of complex parameter design and susceptibility to local optima in traditional artificial potential function methods, while simultaneously improving the targeting and correction accuracy of trajectory monitoring.

[0099] A pulse-free guidance mechanism based on periodic state updates: This invention breaks away from the dependence of traditional multi-pulse CW guidance on a fixed number of pulses, constructing a closed-loop update system based on the control cycle. The principle is as follows: Within each control cycle, the state update module dynamically updates the data in the storage module and the thruster switching commands by combining the current remaining velocity increment, the trajectory safety belt threshold, and the thruster execution state. Trajectory control is achieved solely through a periodic judgment-correction-update cycle, without the need for pre-dividing pulse stages and counts. Compared to the staged control and computationally burdensome optimal control of multi-pulse guidance, this mechanism enhances the autonomy of the guidance process, eliminates the need for preset pulse parameters, ensures real-time performance through periodic lightweight computation, and reduces the computational requirements.

[0100] The finite thrust correction method of this invention is adapted to the characteristics of actual thrusters, reducing the impact of initial errors and improving guidance accuracy and practicality. On one hand, it directly adopts a finite thrust mode that conforms to the characteristics of actual thrusters, avoiding the disconnect between ideal pulse assumptions and engineering practice. On the other hand, it enables the remaining velocity increment calculation step and the state update step to work in tandem: within each control cycle, the correction amount is updated in real time based on the remaining velocity increment of the previous cycle and the theoretical thrust, and the terminal accuracy is only related to the velocity increment of the last correction, rather than depending on the initial state parameters. This ensures that the terminal position is always controlled within a reasonable range, significantly reducing the impact of initial errors on accuracy compared to traditional CW dual-pulse guidance, while avoiding the pulse number constraints of multi-pulse guidance, thus improving engineering practicality.

[0101] This invention has low computational resource consumption and strong real-time performance: it simplifies calculations by relying on CW analytical solutions to meet the real-time control requirements of the close-range guidance segment. Based on the analytical solution of the CW equation and a modular, lightweight process, this method simplifies calculations while stably achieving the control objective. First, the velocity increment calculation directly uses the analytical solution of the CW equation in the target LVLH system. This analytical solution has a clear formula; only known parameters such as onboard time, mission end timestamp (for calculating orbit change time), current relative position / velocity, and desired terminal relative position / velocity need to be substituted to directly solve for the required velocity increment. No complex iterations or additional optimization steps are required, significantly simplifying the calculation process and fundamentally reducing the computational burden. Second, the overall technical process is divided into independent steps such as data input, state judgment, increment calculation, and state update. Each control cycle only requires three core operations: remaining velocity increment update, trajectory safety zone threshold judgment, and thruster switch command output. There are no redundant calculation steps, and the data interaction logic is clear. Simulation verification shows that this method can stably complete the full-cycle guidance and control under conventional onboard computing power conditions. It not only meets the real-time requirements of the close-range guidance phase but also ensures the terminal accuracy of tracking the spacecraft, precisely achieving the core control objective of the spacecraft autonomously approaching to a specified range near the target.

[0102] This invention features low hardware cost and low complexity: It reduces cost and complexity by using a finite thrust thruster and a simplified hardware interface, thus lowering the difficulty of engineering implementation. On one hand, it only requires an on / off controlled finite thrust thruster, eliminating the need for an additional thrust feedback module. On the other hand, the interaction between the system and the spaceborne computer involves only the input of conventional data such as timestamps, relative position / velocity, and theoretical thrust, as well as the output of thruster switching commands. The interface logic is simple, requiring no complex hardware adaptation circuits. Simultaneously, the storage module only needs to store a small number of key parameters (such as remaining velocity increment and safety belt threshold), eliminating the need for large-capacity storage hardware. This significantly reduces hardware procurement and integration costs, while minimizing hardware failure points, improving system reliability, and making it more suitable for the payload and cost constraints of small and medium-sized spacecraft.

[0103] In the method of this invention, the target orbit coordinate system (LVLH coordinate system) is an inertial coordinate system established with the target spacecraft as the origin. The CW equations, also known as the circular orbit relative motion equations, are linearized dynamic equations describing the relative motion between two spacecraft operating in near-Earth circular orbits. Their core characteristic is that they can be solved analytically. The TH equations are an extension of the CW equations, applicable to describing the relative motion of spacecraft in elliptical orbits, and are also linearized dynamic equations.

[0104] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method of limited-thrust based spacecraft proximity rendezvous guidance, characterized by, The method comprises the following steps: calculating a theoretical velocity increment of the current task phase according to the current state of the tracking spacecraft and the expected end state when the tracking spacecraft enters the task phase; judging the state of the thruster at a preset period during the execution of the task phase; if the thruster is in the propelling state, calculating a current residual velocity increment in combination with the theoretical velocity increment of the current task phase and the single-period velocity increment of the thruster; until the current residual velocity increment is less than a set threshold, determining that the thruster is in the non-propelling state; then recalculating the theoretical velocity increment, judging whether the tracking spacecraft exceeds the safety belt range according to the current theoretical velocity increment and the trajectory safety belt threshold, if yes, updating the task state and controlling the thruster to propel to correct the transfer orbit until the task phase ends, so as to realize the rendezvous of the tracking spacecraft.

2. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 1, wherein the theoretical velocity increment is calculated based on the C-W equation and its analytical solution in the target orbit coordinate system.

3. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 2, wherein the method for calculating the theoretical velocity increment based on the C-W equation and its analytical solution in the target orbit coordinate system is as follows:

4. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 3, wherein the method for calculating the theoretical velocity increment based on the C-W equation and its analytical solution in the target orbit coordinate system is as follows:

5. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 4, wherein judging whether the tracking spacecraft exceeds the safety belt range comprises judging whether the tracking spacecraft exceeds the in-plane trajectory safety belt threshold based on the C-W equation: ， In the formula , , is the X-axis, Y-axis, Z-axis coordinate of the tracking spacecraft in the target orbit coordinate system, is the average angular velocity of the orbit of the tracking spacecraft, is the X-axis acceleration of the tracking spacecraft, is the Y-axis acceleration of the tracking spacecraft, is the Z-axis acceleration of the tracking spacecraft; ， wherein is the initial position of the tracking spacecraft in X, Y, Z axes, , , is the initial position of the tracking spacecraft in X, Y, Z axes, , , is the final position of the tracking spacecraft in X, Y, Z axes, is the time of orbit transfer, is the final velocity increment of the tracking spacecraft; For intermediate variables: ； ， In the formula is the theoretical speed increment.

6. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 5, wherein judging whether the tracking spacecraft exceeds the safety belt range further comprises judging whether the tracking spacecraft exceeds the out-of-plane trajectory safety belt threshold based on the C-W equation: Time of deorbit is: ， In the formula t0 is the start time of the spacecraft, t1 is the end time of the spacecraft.

7. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 6, wherein the state judgment module is used to judge the task state of the tracking spacecraft, and if the tracking spacecraft has not entered the task phase, the method waits for the update of the task state until the tracking spacecraft enters the task phase.

8. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 1, wherein if the tracking spacecraft exceeds the safety belt range, a thruster opening instruction is generated, and the task state is updated; otherwise, a thruster closing instruction is generated, and the task state is updated. ， wherein X-axis component of the current residual velocity increment for the thruster in the non-propulsive state, Y-axis component of the current residual velocity increment for the thruster in the non-propulsive state, C-W equation-based in-plane trajectory safety band threshold.

9. The limited-propulsion-based spacecraft rendezvous guidance method according to claim 8, wherein the thruster opening instruction and the thruster closing instruction are transmitted to the spacecraft computer to control the thruster. ​ ， Z-axis component of the current remaining speed increment for the thruster in the non-propulsive state, Out-of-plane trajectory safety belt threshold based on C-W equation. ​ ​ ​ ​ ​ ​

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