An ultra-low earth orbit satellite pose cooperative control method and system based on aerodynamic force

Abstract

This invention provides a method and system for coordinated attitude control of ultra-low Earth orbit (UEO) satellites based on aerodynamics, relating to the field of spacecraft control technology. The method includes: obtaining the relative position error of the secondary satellite and the attitude error of the primary satellite based on real-time state data; determining the control mode of the secondary satellite based on the relative position error and the attitude error of the primary satellite; when the control mode is position control, constructing a sliding mode surface and solving it using a composite reaching law to determine the target deflection angle; when the control mode is attitude control, determining the desired control torque of the secondary satellite, constructing a first-order decaying differential equation based on the desired control torque, and determining the target deflection angle using a local Jacobian matrix and the first-order decaying differential equation; and driving the aerodynamic actuators of the secondary satellite to perform coordinated attitude control actions relative to the primary satellite based on the target deflection angle. This invention improves the control accuracy for aerodynamic UEO satellite attitude control.

Description

Technical Field

[0001] This invention relates to the field of spacecraft control technology, and more specifically, to a method and system for coordinated attitude control of ultra-low orbit satellites based on aerodynamics. Background Technology

[0002] Ultra-low Earth orbit (ULE) satellites, due to their low orbital altitude, offer significant advantages in remote sensing observation, communication speed, and launch cost, making them a key research focus in the aerospace field. Current ULE satellite control schemes primarily employ a parallel joint control architecture for relative position (orbit) and attitude, simultaneously outputting orbital control drag and attitude torque via aerodynamic solar panels.

[0003] In related technologies, the drastic fluctuations in atmospheric density in the ultra-low Earth orbit (UEO) environment can severely disturb satellite operation, leading to strong nonlinear coupling between attitude dynamics and formation relative orbital dynamics. Furthermore, aerodynamic solar panels must also consider attitude control. Therefore, in parallel control mode, the two types of control commands compete for the degrees of freedom of the actuators, resulting in solar panel torque saturation and mutual interference in control loops, causing high-frequency chattering of control quantities. In addition, traditional aerodynamic force distribution requires inverting and solving nonlinear aerodynamic equations, which are easily affected by atmospheric conditions, leading to computational divergence. This makes it impossible to guarantee satellite attitude or achieve convergence of formation relative positions, rendering UEO satellites unsuitable for diverse on-orbit missions. Summary of the Invention

[0004] The problem addressed by this invention is how to improve the control accuracy of aerodynamic ultra-low orbit satellite attitude.

[0005] To address the aforementioned problems, this invention provides a method and system for coordinated attitude control of ultra-low orbit satellites based on aerodynamics.

[0006] In a first aspect, the present invention provides a method for coordinated attitude control of ultra-low Earth orbit satellites based on aerodynamics, comprising: The real-time status data of the secondary satellite in the ultra-low orbit satellite formation is obtained, and based on the real-time status data, the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite are obtained. The control mode of the secondary satellite is determined by comparing the relative position error and the local satellite attitude error with a preset relative position threshold and a preset attitude alignment threshold, respectively. When the control mode is the position control mode, a sliding surface is constructed based on the relative motion state variables of the secondary star in the orbital plane and the expected relative trajectory of the secondary star; based on the sliding surface, the expected aerodynamic drag of the secondary star is obtained by combining the composite reaching law; the expected aerodynamic drag is converted into the target deflection angle of the aerodynamic actuator of the secondary star. When the control mode is attitude control mode, the angular velocity error of the secondary satellite is determined based on the real-time status data, and the desired control torque of the secondary satellite is determined based on the attitude error of the primary satellite and the angular velocity error. A first-order decaying differential equation is constructed based on the desired control torque and the actual aerodynamic torque of the secondary satellite, and the target deflection angle of the aerodynamic actuator of the secondary satellite is determined based on the first-order decaying differential equation using the local Jacobian matrix. Based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode, the aerodynamic actuator of the secondary satellite is driven to perform attitude coordination control actions relative to the primary satellite.

[0007] Optionally, the real-time status data includes the relative position of the secondary satellite relative to the primary satellite and the actual attitude quaternion of the secondary satellite. The step of acquiring the real-time status data of the secondary satellite in the ultra-low orbit satellite formation, and obtaining the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite based on the real-time status data, includes: Obtain the relative position of the secondary star with respect to the primary star and the actual attitude quaternion; The relative position error of the formation is determined based on the relative position and the preset expected relative trajectory of the secondary star; Based on the actual attitude quaternion of the secondary satellite and the expected attitude quaternion of the secondary satellite, the attitude quaternion error is determined, and the attitude quaternion error is used as the attitude error of the local satellite.

[0008] Optionally, the attitude control mode includes an attitude maneuver mode and an attitude stabilization mode, and the preset relative position threshold includes a first threshold and a second threshold, wherein the first threshold is less than the second threshold; The step of determining the control mode of the secondary satellite by comparing the relative position error and the local satellite attitude error with preset relative position thresholds and preset attitude alignment thresholds, respectively, includes: When the relative position error is less than or equal to the first threshold, the control mode is determined to be the attitude maneuver mode; When the relative position error is greater than or equal to the second threshold, the control mode is determined to be the attitude stabilization mode; When the relative position error is greater than the first threshold and less than the second threshold, and the local satellite attitude error is less than the preset attitude alignment threshold, the control mode is determined to be the position control mode.

[0009] Optionally, constructing the sliding surface based on the relative motion state variables of the secondary star within the orbital plane and the desired relative trajectory of the secondary star includes: The tracking error is determined based on the relative motion state variables and the desired relative trajectory; Based on the tracking error, and combined with the preset sliding surface parameter matrix, the sliding surface is constructed.

[0010] Optionally, the step of calculating the desired aerodynamic drag of the secondary star based on the sliding surface and in conjunction with the composite reaching law includes: Differentiating the sliding surface yields the dynamic equation of the sliding surface; The differential aerodynamic acceleration along the orbit of the secondary star is obtained by solving the equivalent relationship between the dynamic equation of the sliding surface and the composite approach law. The desired aerodynamic drag is determined based on the differential aerodynamic acceleration along the orbit and the mass of the secondary satellite.

[0011] Optionally, converting the desired aerodynamic drag into a target deflection angle of the sub-satellite's aerodynamic actuator includes: The drag tracking error is determined based on the expected aerodynamic drag and the actual aerodynamic drag of the secondary satellite. Based on the resistance tracking error, an error dynamic convergence equation is determined, and based on the error dynamic convergence equation, the convergence requirement of the resistance tracking error is mapped to the deflection angle change rate of the pneumatic actuator. The target deflection angle is obtained by numerically integrating the rate of change of the deflection angle.

[0012] Optionally, the real-time status data includes the actual angular velocity of the secondary satellite. The step of determining the angular velocity error of the secondary satellite based on the real-time status data, and determining the desired control torque of the secondary satellite based on the attitude error of the local satellite and the angular velocity error, includes: Obtain the desired target attitude of the secondary satellite; wherein, when the control mode is the attitude maneuver mode, the mission pointing attitude is taken as the desired target attitude, and when the control mode is the attitude stabilization mode, the orbital coordinate system attitude is taken as the desired target attitude. The angular velocity error is determined based on the actual angular velocity and the expected angular velocity corresponding to the desired target attitude; The desired control torque is obtained by linearly combining the proportional term of the local satellite attitude error, the differential term of the angular velocity error, and the integral term of the local satellite attitude error.

[0013] Optionally, the step of constructing a first-order decaying differential equation based on the desired control torque and the actual aerodynamic torque of the secondary satellite, and determining the target deflection angle of the aerodynamic actuator of the secondary satellite using the local Jacobian matrix and the first-order decaying differential equation, includes: The torque tracking error is determined based on the desired control torque and the actual aerodynamic torque. Based on the torque tracking error, construct the first-order decay differential equation; The time derivative of the torque tracking error is calculated, and combined with the local Jacobian matrix, a mapping relationship is established between the rate of change of the torque tracking error and the rate of change of the deflection angle of the pneumatic actuator. The deflection angle change rate of the pneumatic actuator is obtained by simultaneously solving the first-order decay differential equation and the mapping relationship. The target deflection angle is obtained by integrating the rate of change of the deflection angle.

[0014] Optionally, driving the pneumatic actuator of the secondary satellite to perform attitude-coordinated control actions relative to the primary satellite based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode includes: The pneumatic actuator adjusts the deflection angle of the secondary satellite's aerodynamic sails according to the target deflection angle in the attitude control mode or the target deflection angle in the position control mode, thereby controlling the secondary satellite's attitude or its formation position relative to the primary satellite.

[0015] Secondly, the present invention provides an aerodynamic-based ultra-low orbit satellite attitude cooperative control system applied to the aerodynamic-based ultra-low orbit satellite attitude cooperative control method described above, comprising: The error calculation unit is used to acquire the real-time status data of the secondary satellite in the ultra-low orbit satellite formation, and based on the real-time status data, to obtain the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite. The mode determination unit is used to determine the control mode of the secondary satellite by comparing the relative position error and the local satellite attitude error with a preset relative position threshold and a preset attitude alignment threshold, respectively. The position control unit is used to construct a sliding surface based on the relative motion state variables of the secondary satellite in the orbital plane and the expected relative trajectory of the secondary satellite when the control mode is position control mode; to calculate the expected aerodynamic drag of the secondary satellite based on the sliding surface and the composite reaching law; and to convert the expected aerodynamic drag into the target deflection angle of the aerodynamic actuator of the secondary satellite. An attitude control unit is used to determine the angular velocity error of the secondary satellite based on the real-time status data when the control mode is attitude control mode, and to determine the desired control torque of the secondary satellite based on the attitude error of the primary satellite and the angular velocity error; to construct a first-order decaying differential equation based on the desired control torque and the actual aerodynamic torque of the secondary satellite, and to determine the target deflection angle of the aerodynamic actuator of the secondary satellite based on the first-order decaying differential equation using the local Jacobian matrix; An execution unit is used to drive the pneumatic actuator of the secondary satellite to perform attitude coordination control actions relative to the primary satellite, based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode.

[0016] The present invention relates to an aerodynamic-based ultra-low orbit satellite attitude cooperative control method and system. First, by acquiring real-time state data of the secondary satellite relative to the primary satellite, the relative position error of the formation and the attitude error of the primary satellite are calculated. Then, based on the comparison results of the relative position error and attitude error with preset thresholds, the system dynamically determines whether the secondary satellite should be in position control mode or attitude control mode. This achieves time-division decoupling of attitude and orbit control, fundamentally avoiding torque saturation and loop interference caused by the competition between two types of commands for the degrees of freedom of the actuators in parallel control mode, thus eliminating the root cause of high-frequency chattering in the control quantity. When in position control mode, a sliding surface is constructed using the relative motion state variables within the orbital plane and the desired trajectory. The desired aerodynamic drag is then calculated using a composite reaching law and directly converted into the target deflection angle of the solar panel, thus eliminating the need for nonlinear aerodynamic equations. The inverse process effectively overcomes the computational divergence problem caused by atmospheric random perturbations, while the strong robustness of sliding mode control ensures high-precision convergence of the relative positions of the formation. When in attitude control mode, the desired control torque is determined by introducing angular velocity error and local satellite attitude error. Based on the desired control torque and actual aerodynamic torque, a first-order decaying differential equation is constructed. The torque tracking error is smoothly mapped to the solar panel deflection angle through the local Jacobian matrix, making the attitude adjustment process smooth and without overshoot. Finally, the aerodynamic actuator is driven to perform attitude coordination control according to the target deflection angle, enabling the secondary satellite to adaptively switch control strategies according to the real-time state. This not only ensures the accuracy of attitude maneuvering but also achieves high-precision convergence of the relative positions of the formation, thereby significantly improving the attitude control accuracy of ultra-low orbit satellites for aerodynamic forces and enabling it to adapt to diverse on-orbit missions. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of an aerodynamic-based ultra-low orbit satellite attitude cooperative control system according to another embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0019] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0020] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0021] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0022] Combination Figure 1 As shown in the figure, an embodiment of the present invention provides a method for coordinated attitude control of ultra-low orbit satellites based on aerodynamics, comprising: The real-time status data of the secondary satellite in the ultra-low orbit satellite formation is obtained, and based on the real-time status data, the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite are obtained.

[0023] Specifically, by acquiring real-time status data of secondary satellites in a VLEO satellite formation and extracting the relative position error of the formation and the attitude error of the primary satellite, the geometric deviation of the formation configuration and the pointing deviation of the satellite itself can be quantified. This quantification process is the foundation for mode decision-making and control law calculation. Only by obtaining the relative position deviation between the secondary satellite and the primary satellite, as well as the attitude deviation of the secondary satellite itself, can it be determined whether the formation is within a safety margin and whether the attitude meets the aerodynamic drag modulation conditions. This allows for the determination of which control strategy to adopt to correct the deviation, ultimately achieving the adjustment of the VLEO satellite's attitude.

[0024] The control mode of the secondary satellite is determined by comparing the relative position error and the attitude error of the local satellite with a preset relative position threshold and a preset attitude alignment threshold, respectively.

[0025] Specifically, the determination of the secondary satellite's control mode aims to achieve time-sharing switching of attitude and orbit control tasks, thereby avoiding command conflicts in parallel control modes. Specifically, by comparing the relative position error and the satellite's attitude error with preset relative position thresholds and attitude alignment thresholds, respectively, the safety level of the formation configuration and the degree of attitude alignment can be dynamically assessed, thus determining whether the secondary satellite should perform position control or attitude control at the current moment. Utilizing the timescale difference between rapidly changing attitude dynamics and slowly changing orbital dynamics, different control priorities can be assigned under different safety margins. For example, when the relative position deviation is small, attitude maneuvering tasks are prioritized; when the deviation approaches the safety boundary, attitude correction is forced; and position control mode is only switched in when the attitude is stable and the position is in the hysteresis range. This decouples the strong attitude and orbit coupling, preventing two types of control commands from competing for the same set of aerodynamic actuators and avoiding torque saturation and high-frequency chattering.

[0026] When the control mode is the position control mode, a sliding surface is constructed based on the relative motion state variables of the secondary star in the orbital plane and the expected relative trajectory of the secondary star; based on the sliding surface, the expected aerodynamic drag of the secondary star is obtained by combining the composite reaching law; the expected aerodynamic drag is converted into the target deflection angle of the aerodynamic actuator of the secondary star.

[0027] Specifically, when the position control mode is determined, a sliding mode surface is constructed using the deviation between the relative motion state variables of the secondary satellite within the orbital plane and the desired relative trajectory. A composite reaching law is then introduced to calculate the desired aerodynamic drag. This sliding mode variable structure control process effectively overcomes nonlinear disturbances such as severe fluctuations in atmospheric density at very low Earth orbit, ensuring the robustness of formation position convergence. Subsequently, the desired aerodynamic drag is directly mapped to the target deflection angle of the aerodynamic panels, avoiding the computational divergence problem caused by inverting and solving the nonlinear aerodynamic equations in traditional methods. Without relying on traditional propellant consumption, precise differential aerodynamic drag is generated solely by adjusting the deflection angle of the panels, thereby driving the secondary satellite to maintain or reconstruct its formation configuration relative to the primary satellite, achieving high-precision relative position convergence.

[0028] When the control mode is attitude control mode, the angular velocity error of the secondary satellite is determined based on the real-time status data, and the desired control torque of the secondary satellite is determined based on the attitude error of the primary satellite and the angular velocity error. A first-order decaying differential equation is constructed based on the desired control torque and the actual aerodynamic torque of the secondary satellite, and the target deflection angle of the aerodynamic actuator of the secondary satellite is determined based on the first-order decaying differential equation using the local Jacobian matrix.

[0029] Specifically, when attitude control mode is selected, the angular velocity error of the secondary satellite is first acquired and combined with the attitude error of the local satellite as input. The desired control torque is then determined through a control algorithm to ensure tracking of the desired target attitude. Subsequently, a first-order decaying differential equation is constructed based on the deviation between the desired control torque and the actual aerodynamic torque to define the exponential convergence dynamics of the torque tracking error. The desired dynamics are then mapped to the yaw angular velocity of the solar panel using a local Jacobian matrix. The target yaw angle is obtained through integration, rather than by directly providing a jump angle. This avoids abrupt changes in angle commands, enabling the aerodynamic solar panel to respond smoothly to attitude control commands, avoiding drastic angle jumps and torque chattering. This eliminates high-frequency oscillations during attitude control and ensures a rapid return to the minimum drag attitude in stable attitude mode, effectively reducing the adverse effects of aerodynamic disturbances on the orbit.

[0030] Based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode, the aerodynamic actuator of the secondary satellite is driven to perform attitude coordination control actions relative to the primary satellite.

[0031] Specifically, by sending the target deflection angle to the aerodynamic actuators (drive devices for the aerodynamic sails) of the secondary satellite, the sails are precisely deflected to the specified angle, thereby changing the sails' frontal area and angle of attack, and generating the desired aerodynamic drag or aerodynamic torque in real time. The aerodynamic effects directly act on the secondary satellite, adjusting its relative position to the primary satellite and its own attitude pointing. This physically transforms the control commands, enabling the secondary satellite to adaptively generate the required aerodynamic control quantities according to the control mode, thus achieving real-time, closed-loop adjustment of the formation configuration and attitude, completing the entire-link attitude coordination control from state perception to command calculation to physical execution.

[0032] The aerodynamic-based ultra-low orbit satellite attitude cooperative control method of this invention first acquires real-time state data of the secondary satellite relative to the primary satellite, calculates the formation relative position error and the primary satellite's attitude error, and then dynamically determines whether the secondary satellite should be in position control mode or attitude control mode based on the comparison results of the relative position error and attitude error with preset thresholds. This achieves time-division decoupling of attitude and orbit control, fundamentally avoiding torque saturation and loop interference caused by the competition between two types of commands for the degrees of freedom of the actuator in parallel control mode, and eliminating the root cause of high-frequency chattering in the control quantity. When in position control mode, a sliding surface is constructed using the relative motion state variables in the orbital plane and the desired trajectory, and the desired aerodynamic drag is calculated by combining the composite reaching law, which is then directly converted into the target deflection angle of the solar panel, thus eliminating the need for nonlinear aerodynamic equations. Inverse calculation effectively overcomes the computational divergence problem caused by atmospheric random perturbations, while the strong robustness of sliding mode control ensures high-precision convergence of the formation's relative position. When in attitude control mode, angular velocity error and local satellite attitude error are introduced to jointly determine the desired control torque. Based on the desired control torque and actual aerodynamic torque, a first-order decaying differential equation is constructed. The torque tracking error is smoothly mapped to the solar panel deflection angle through a local Jacobian matrix, making the attitude adjustment process smooth and without overshoot. Finally, the aerodynamic actuator is driven to perform attitude coordination control according to the target deflection angle, enabling the secondary satellite to adaptively switch control strategies according to the real-time state. This not only ensures the accuracy of attitude maneuvering but also achieves high-precision convergence of the formation's relative position, thereby significantly improving the attitude control accuracy of ultra-low orbit satellites for aerodynamic forces and enabling it to adapt to diverse on-orbit missions.

[0033] Optionally, the real-time status data includes the relative position of the secondary satellite relative to the primary satellite and the actual attitude quaternion of the secondary satellite. The step of acquiring the real-time status data of the secondary satellite in the ultra-low orbit satellite formation, and obtaining the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite based on the real-time status data, includes: Obtain the relative position of the secondary star with respect to the primary star and the actual attitude quaternion; The relative position error of the formation is determined based on the relative position and the preset expected relative trajectory of the secondary star; Based on the actual attitude quaternion of the secondary satellite and the expected attitude quaternion of the secondary satellite, the attitude quaternion error is determined, and the attitude quaternion error is used as the attitude error of the local satellite.

[0034] Specifically, when acquiring real-time status data of secondary satellites in a VLEO satellite formation, the relative position vector of the secondary satellite relative to the primary satellite is collected using an onboard GPS receiver or inter-satellite link measurement equipment. Simultaneously, the attitude quaternions of the secondary satellite are obtained using a star sensor and gyroscope combined measurement unit. This relative position is compared with a pre-set desired relative trajectory of the secondary satellite, and the Euclidean distance between them is calculated to determine the formation relative position error. The desired relative trajectory is typically a nominal configuration that meets the requirements of the formation flight mission, such as a Leplander formation trajectory with the primary satellite as the origin. For attitude information, the actual attitude quaternions and the desired attitude quaternions of the secondary satellite are calculated using the quaternion multiplication rule to obtain the attitude quaternion error. This attitude quaternion error is used as the satellite's attitude error for subsequent command calculations in attitude control modes.

[0035] Specifically, according to the generalized multiplication rules of quaternions, the attitude error of this satellite is defined as: ; in, This is the attitude error of the satellite. For the desired quaternion, The actual attitude quaternion. Through the above steps, the original state data is transformed into two key control deviations: the formation relative position error and the local satellite attitude error. This provides clear and quantified inputs for the mode decision of the pose-coupled state machine and algorithms such as sliding mode control and PID control.

[0036] In this embodiment of the invention, the original relative position measurement data and attitude measurement data are converted into formation relative position error and local satellite attitude error, providing the basic input for subsequent adaptive switching of control modes and calculation of control laws. Based on the comparison between the relative position and the preset desired trajectory, the degree of deviation of the formation configuration can be quantified in real time; and based on the error calculation between the actual attitude quaternion and the desired attitude quaternion, the current pointing deviation of the secondary satellite can be described. This significantly improves the calculation accuracy and stability of subsequent control algorithms.

[0037] Optionally, the attitude control mode includes an attitude maneuver mode and an attitude stabilization mode, and the preset relative position threshold includes a first threshold and a second threshold, wherein the first threshold is less than the second threshold; The step of determining the control mode of the secondary satellite by comparing the relative position error and the local satellite attitude error with preset relative position thresholds and preset attitude alignment thresholds, respectively, includes: When the relative position error is less than or equal to the first threshold, the control mode is determined to be the attitude maneuver mode; When the relative position error is greater than or equal to the second threshold, the control mode is determined to be the attitude stabilization mode; When the relative position error is greater than the first threshold and less than the second threshold, and the local satellite attitude error is less than the preset attitude alignment threshold, the control mode is determined to be the position control mode.

[0038] Specifically, during the formation flight of ultra-low orbit satellites, based on preset relative position thresholds and preset attitude alignment thresholds, the preset relative position thresholds include a first threshold and a second threshold, where the first threshold is less than the second threshold. The first threshold corresponds to the lower boundary between the attitude maneuvering mode and the position control mode, and the second threshold corresponds to the upper boundary between the attitude stabilization mode and the position control mode. The attitude alignment threshold is used to determine whether the secondary satellite's attitude has reached a stable aerodynamic configuration. The formation relative position error of the secondary satellite relative to the primary satellite and the secondary satellite's local attitude error, calculated in real time, are compared with the above three thresholds. Specifically: when the relative position error is less than or equal to the first threshold, it indicates that the current formation configuration has a high safety margin, and the secondary satellite is in the offline maneuvering phase. At this time, the control mode is determined to be the attitude maneuvering mode. In the attitude maneuvering mode, the secondary satellite can freely track the desired spatial pointing attitude, and the aerodynamic sails are only used to fit the attitude control torque, while the longitudinal aerodynamic drag serves as a natural disturbance in the orbital dynamics. When the relative position error is greater than or equal to the second threshold, it indicates that the formation configuration has approached the safety boundary and there is a risk of divergence. The secondary satellite needs to enter the attitude stabilization phase. At this time, the control mode is set to attitude stabilization mode, and the aerodynamic panels are forced to be mobilized first for attitude correction. Orbital control authority is revoked, and the secondary satellite is driven to maneuver to the minimum drag attitude that coincides with the orbital coordinate system. When the relative position error is between the first and second thresholds, that is, greater than the first threshold and less than the second threshold, and the attitude error of the satellite is less than the preset attitude alignment threshold, it indicates that the secondary satellite has recovered to a stable aerodynamic configuration and the relative position is within the hysteresis range. At this time, the control mode is set to position control mode, and the outer ring relative position controller officially takes over the control degrees of freedom of the panels. By adjusting the deflection angle of each panel, the desired aerodynamic drag is tracked and the formation configuration is corrected. This forms a state machine control architecture with hysteresis characteristics. The first and second thresholds are not equal, which avoids frequent oscillations of the relative position error near the boundary, which would cause repeated switching of the control mode, thus ensuring the stability of the system operation.

[0039] In this embodiment of the invention, by determining the mode based on dual thresholds and attitude alignment thresholds, the control mode can be adaptively divided into attitude maneuver mode, attitude stabilization mode and position control mode according to the different intervals of the relative position error of the secondary satellite and the convergence state of the attitude error of the primary satellite. This realizes time-division decoupling and smooth switching between the fast attitude change subsystem and the slow orbit change subsystem. Under the premise of ensuring high-precision convergence of the relative position of the ultra-low orbit satellite formation and configuration safety, the control efficiency of aerodynamic forces is maximized and the ineffective energy loss is reduced.

[0040] Optionally, constructing the sliding surface based on the relative motion state variables of the secondary star within the orbital plane and the desired relative trajectory of the secondary star includes: The tracking error is determined based on the relative motion state variables and the desired relative trajectory; Based on the tracking error, and combined with the preset sliding surface parameter matrix, the sliding surface is constructed.

[0041] Specifically, the extracted relative motion state variables coupled within the orbital plane are represented as follows: ; Among them, among them, and These represent the radial and orbital components of the secondary star's relative position to the primary star within the orbital plane, respectively. and These correspond to the relative velocity components in the radial and orbital directions, respectively. Furthermore, based on the desired relative trajectory pre-planned for the secondary satellite during the formation flight mission, it is expressed as: ; in, and These represent the expected relative position components of the secondary star with respect to the primary star in the radial and along-the-orbit directions within the orbital plane. and These represent the desired relative velocity components in the radial and along-track directions, respectively. The relative motion state variables are... relative trajectory with expectation Subtracting each component individually yields the tracking error, which is expressed as follows: ; in, To track the error, a linear sliding surface is constructed based on the tracking error: ; in, For sliding surface, The preset sliding surface parameter matrix is ​​used to construct the linear sliding surface of the system. Its core function is to define the convergence dynamics of the system error. The function of the sliding surface synthesizes the multidimensional tracking error into a scalar index, when... When the value approaches zero, the tracking error will follow the parameters defined by the preset sliding surface parameter matrix. The defined linear relationship converges to zero, thus providing a clear objective for the design of subsequent sliding mode control laws.

[0042] In this embodiment of the invention, the high-dimensional relative motion state (position and velocity deviation) of the secondary satellite within the orbital plane is transformed into a comprehensive sliding surface, providing an effective control target for the subsequent solution of the sliding mode control law. There is no need to invert and solve complex nonlinear aerodynamic equations; the sliding surface can be constructed simply through linear combination, resulting in high computational efficiency and numerical stability. When the state lies on the sliding surface, the sliding control is completely invariant to uncertainties such as external atmospheric density fluctuations and perturbations. Therefore, it can significantly improve the accuracy and robustness of formation relative position control in complex environments such as ultra-low Earth orbit, ensuring that the secondary satellite can still accurately track the desired relative trajectory under severe disturbances, achieving high-precision maintenance and reconstruction of the formation configuration.

[0043] Optionally, the step of calculating the desired aerodynamic drag of the secondary star based on the sliding surface and in conjunction with the composite reaching law includes: Differentiating the sliding surface yields the dynamic equation of the sliding surface; The differential aerodynamic acceleration along the orbit of the secondary star is obtained by solving the equivalent relationship between the dynamic equation of the sliding surface and the composite approach law. The desired aerodynamic drag is determined based on the differential aerodynamic acceleration along the orbit and the mass of the secondary satellite.

[0044] Specifically, in position control mode, based on the constructed sliding surface, the time derivative of the sliding surface is first calculated to obtain the dynamic equation of the sliding surface: ; in, To preset the sliding surface parameter matrix, The system matrix for the secondary star, The system input matrix for the secondary star. For relative motion state variables, For the differential aerodynamic acceleration along the orbit of the secondary satellite, Let be the derivative of the desired relative trajectory with respect to time. Let be the time derivative of the sliding mode face.

[0045] in, ; n is the average angular velocity of the secondary star's orbit.

[0046] To overcome the disturbances of the complex environment of ultra-low Earth orbit and ensure the dynamic quality during the approach phase, a composite approach law combining constant velocity and exponential approach is introduced, resulting in: ; in, For symbolic functions, This is a switching gain mechanism used to overcome bounded uncertainties such as atmospheric density fluctuations and perturbations. To approximate the velocity gain, used to determine the exponential reaching term. The convergence rate, Let be the time derivative of the sliding mode face. Let be the sliding surface. Solving the above equations yields the differential aerodynamic acceleration along the track: ; in, To preset the sliding surface parameter matrix, The system input matrix for the secondary star. The system matrix for the secondary star, For relative motion state variables, Let be the derivative of the desired relative trajectory with respect to time. For symbolic functions, For sliding surface, To approximate the speed gain, To switch the gain. Finally, according to Newton's second law, the differential aerodynamic acceleration along the orbit is multiplied by the mass of the secondary star to obtain the desired aerodynamic drag, which is the target value for subsequent aerodynamic force distribution.

[0047] In this embodiment of the invention, the dynamics of the sliding surface are organically combined with the composite approach law to calculate the differential aerodynamic acceleration along the track and further obtain the desired aerodynamic drag. This achieves high-precision and robust control of the relative position of the formation under complex disturbances in the ultra-low orbit environment, and significantly improves the anti-disturbance capability, computational stability and control accuracy of the aerodynamic ultra-low orbit satellite attitude control system.

[0048] Optionally, converting the desired aerodynamic drag into a target deflection angle of the sub-satellite's aerodynamic actuator includes: The drag tracking error is determined based on the expected aerodynamic drag and the actual aerodynamic drag of the secondary satellite. Based on the resistance tracking error, an error dynamic convergence equation is determined, and based on the error dynamic convergence equation, the convergence requirement of the resistance tracking error is mapped to the deflection angle change rate of the pneumatic actuator. The target deflection angle is obtained by numerically integrating the rate of change of the deflection angle.

[0049] Specifically, after calculating the desired aerodynamic drag, it needs to be converted into the physical deflection angle of the sail. Since the aerodynamic drag coefficient mapping is highly nonlinear, traditional solutions are prone to divergence; therefore, a dynamic aerodynamic drag fitting and allocation strategy without inverse solutions is proposed. Specifically, the drag tracking error is determined based on the desired aerodynamic drag and the actual aerodynamic drag of the secondary satellite: ; in, For the desired aerodynamic drag, For actual aerodynamic drag, This represents the resistance tracking error.

[0050] Based on the resistance tracking error, a dynamic convergence equation combining linear and higher-order nonlinear terms is constructed to achieve rapid convergence of large errors and smooth approximation of small errors: ; in, The derivative of the resistance tracking error with respect to time. For linear gain, It is a nonlinear gain, and .

[0051] Based on the dynamic convergence equation of the error, the convergence requirement of the drag tracking error is mapped to the rate of change of the deflection angle of the pneumatic actuator. Here, assuming that the rate of change of the upper-level command is small, the closed-loop approximation requirement can be directly mapped to the rate of change of the deflection angle: ; in, The deflection angle of the pneumatic actuator. The rate of change of deflection angle. Atmospheric density, This is the aerodynamic drag coefficient. The derivative of the aerodynamic drag coefficient, For the differential of the deflection angle of the pneumatic actuator, This is the partial derivative of the aerodynamic drag coefficient with respect to the deflection angle. This represents the velocity of the secondary star relative to the atmosphere.

[0052] By continuously integrating the rate of change of the deflection angle, the required target physical deflection angle can be dynamically updated in real time, avoiding the complex process of inverting nonlinear algebraic equations.

[0053] In this embodiment of the invention, an inverse-solution-free aerodynamic force allocation strategy directly converts the desired aerodynamic drag into the target deflection angle of the aerodynamic sail, avoiding the numerical divergence problem caused by inverting the nonlinear aerodynamic equations in traditional methods, thus significantly improving the stability and computational efficiency of control allocation. Specifically, a drag tracking error is defined and a nonlinear error dynamic convergence equation containing cubic terms is constructed, achieving a variable gain control effect of rapid approximation with large errors and smooth convergence with small errors, ensuring both transient response speed and avoiding overshoot and oscillation. The error convergence requirement is mapped to the partial derivative of drag with respect to the deflection angle as a command for the rate of change of the sail deflection angle, and then the target deflection angle is obtained through numerical integration. This transforms the static nonlinear algebraic problem into a dynamic first-order differential tracking problem. Even when there are uncertainties or fluctuations in aerodynamic parameters, the integration stage can play a smoothing and filtering role, allowing the sail deflection angle command to change continuously, thereby eliminating mechanical shock and energy consumption caused by command jumps.

[0054] Optionally, the real-time status data includes the actual angular velocity of the secondary satellite. The step of determining the angular velocity error of the secondary satellite based on the real-time status data, and determining the desired control torque of the secondary satellite based on the attitude error of the local satellite and the angular velocity error, includes: Obtain the desired target attitude of the secondary satellite; wherein, when the control mode is the attitude maneuver mode, the mission pointing attitude is taken as the desired target attitude, and when the control mode is the attitude stabilization mode, the orbital coordinate system attitude is taken as the desired target attitude. The angular velocity error is determined based on the actual angular velocity and the expected angular velocity corresponding to the desired target attitude; The desired control torque is obtained by linearly combining the proportional term of the local satellite attitude error, the differential term of the angular velocity error, and the integral term of the local satellite attitude error.

[0055] Specifically, firstly, the desired target attitude is determined based on the control mode type: when the control mode is attitude maneuvering mode, the mission pointing attitude is taken as the desired target attitude. This mission pointing attitude is pre-set according to the specific on-orbit mission requirements, such as pointing towards the Earth during Earth observation, pointing towards the primary satellite during inter-satellite communication, or pointing towards a specific space. When the control mode is attitude stabilization mode, the orbital coordinate system attitude is taken as the desired target attitude, ensuring that the secondary satellite's body coordinate system coincides with the LVLH coordinate system to achieve the minimum aerodynamic drag configuration. After determining the desired target attitude, the corresponding desired attitude quaternion is obtained. and expected angular velocity (The expected angular velocity in attitude maneuver mode is given by mission planning; the expected angular velocity in attitude stabilization mode is equal to the orbital angular velocity.) Obtain the actual angular velocity of the secondary satellite. (Measured by a gyroscope), the actual angular velocity is subtracted from the expected angular velocity to obtain the angular velocity error: ; in, For angular velocity error, This is the attitude error of the satellite. To preset the sliding surface parameter matrix, The actual angular velocity of the secondary star. The expected angular velocity of the secondary star. It is the direction cosine transfer matrix from the target system to the local system, generated by the attitude quaternion error (local satellite attitude error).

[0056] Define angular velocity error as ;in, , , These are the angular velocity errors around the X-axis (usually the roll axis), the Y-axis (usually the pitch axis), and the Z-axis (usually the yaw axis), respectively. The attitude error of this satellite is defined as... ,in, , , , These are the scalar component of the attitude quaternion error (local satellite attitude error), the rotational component of the attitude quaternion error (local satellite attitude error) about the X-axis (roll axis) of the secondary satellite body, the rotational component of the attitude quaternion error (local satellite attitude error) about the Y-axis (pitch axis) of the secondary satellite body, and the rotational component of the attitude quaternion error (local satellite attitude error) about the Z-axis (yaw axis) of the secondary satellite body.

[0057] Furthermore, when describing the dynamic evolution of attitude error, it is necessary to establish the differential relationship between the attitude quaternion error (local satellite attitude error) and the angular velocity error. Among these, Let be the direction cosine transfer matrix from the target system to the home system generated by the attitude quaternion error (home satellite attitude error). After coordinate transformation and simplification by differentiation, the differential equation of the attitude quaternion error is highly isomorphic to the absolute kinematics equation in algebraic structure. Its matrix expansion form for numerical solution is: ; in, , , , These are the time variation rates of the scalar component of the attitude quaternion error (local satellite attitude error), the time variation rates of the rotational component around the X-axis of the secondary satellite body, the time variation rates of the rotational component around the Y-axis of the secondary satellite body, and the time variation rates of the rotational component around the Z-axis of the secondary satellite body, respectively.

[0058] This can then be expressed as: ; in, This represents the vector component of the attitude quaternion error (local satellite attitude error). , This is the time rate of change of the vector component of the attitude quaternion error (local satellite attitude error). For angular velocity error, It is a 3×3 identity matrix. It is the antisymmetric matrix (cross product matrix) of the vector part of the attitude quaternion error (local satellite attitude error). It is the transpose of the vector part of the attitude quaternion error (local satellite attitude error).

[0059] In the above error equation, the scalar part of the attitude quaternion error represents the principal rotation angle deviation between the current system attitude and the target attitude; when the closed-loop system tends to stabilize, it should satisfy... and .

[0060] In the outer loop control, a PID control algorithm combining quaternion and angular velocity feedback is adopted. The proportional term of the satellite's attitude error, the derivative term of the angular velocity error, and the integral term of the satellite's attitude error are linearly combined to calculate the desired control torque under ideal conditions: ; in, To achieve the desired control torque, , , These are the diagonally positive definite proportional, differential, and integral gain matrices, respectively. This is the attitude error of the satellite. This is the integral term for the attitude error of this satellite. This is a proportional term for the attitude error of this satellite. This is the differential term of the angular velocity error.

[0061] In this embodiment of the invention, the desired target attitude is adaptively selected according to different attitude control modes, so that the same PID control framework can simultaneously meet two very different control requirements: mission-oriented maneuvering and minimum drag attitude return, which significantly improves the flexibility and adaptability of the control system.

[0062] Optionally, the step of constructing a first-order decaying differential equation based on the desired control torque and the actual aerodynamic torque of the secondary satellite, and determining the target deflection angle of the aerodynamic actuator of the secondary satellite using the local Jacobian matrix and the first-order decaying differential equation, includes: The torque tracking error is determined based on the desired control torque and the actual aerodynamic torque. Based on the torque tracking error, construct the first-order decay differential equation; The time derivative of the torque tracking error is calculated, and combined with the local Jacobian matrix, a mapping relationship is established between the rate of change of the torque tracking error and the rate of change of the deflection angle of the pneumatic actuator. The deflection angle change rate of the pneumatic actuator is obtained by simultaneously solving the first-order decay differential equation and the mapping relationship. The target deflection angle is obtained by integrating the rate of change of the deflection angle.

[0063] Specifically, to ensure that the inner ring aerodynamic torque quickly tracks the outer ring command, the torque tracking error is defined as: ; in, For torque tracking error, For the inner ring aerodynamic torque of the secondary star, To determine the desired control torque, construct a first-order decay differential equation for the error vector: ; in, Let be the derivative of the torque tracking error with respect to time, and represent the rate of change of the torque tracking error. For gain scalar, This represents the torque tracking error. By taking the time derivative of the torque tracking error, the static nonlinear algebraic equation is transformed into a mapping relationship between the yaw rate and the rate of change of the torque tracking error: ; in, The local Jacobian matrix of the system characterizes the sensitivity of the output torque to small changes in the sail deflection angle. Let be the derivative of the torque tracking error with respect to time, and represent the rate of change of the torque tracking error. This represents the rate of change of the deflection angle.

[0064] To address the inherent analytical redundancy of non-matrix systems, a pseudo-inverse matrix is ​​introduced to obtain the deflection angle change rate that satisfies the torque tracking requirement: ; in, It is the pseudo-inverse of the local Jacobian matrix. For gain scalar, For torque tracking error, Let be the rate of change of the yaw angle. Then, by numerically integrating the rate of change of the yaw angle, the target yaw angle driving the sail can be obtained.

[0065] Furthermore, unlike kinematic models that only focus on changes in spatial geometric orientation, attitude dynamics centers on revealing the dynamic response mechanism of a spacecraft's rotational state to external torques. Based on the rigid body angular momentum theorem and Euler's equations, the absolute attitude dynamic evolution of the secondary star in inertial space can be constructed in the following matrix differential form: ; in, For the inner ring aerodynamic torque of the secondary star, The actual angular acceleration (actual angular velocity) of the secondary star (derivative with respect to time) The actual angular velocity of the secondary star. The antisymmetric matrix of the actual angular velocity of the secondary star. Let be the rotational inertia matrix of the secondary star.

[0066] In this embodiment of the invention, the first-order exponential decay requirement of torque tracking error is combined with the physical mapping of the solar panel deflection angular velocity, which realizes smooth and jitter-free tracking of the desired control torque. This significantly improves the response quality of the attitude control mode and the mechanical life of the actuator. Even in both attitude maneuvering and attitude stabilization modes, it can achieve fast, smooth and reliable torque output, effectively ensuring the pointing accuracy and configuration safety of the satellite.

[0067] Optionally, driving the pneumatic actuator of the secondary satellite to perform attitude-coordinated control actions relative to the primary satellite based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode includes: The pneumatic actuator adjusts the deflection angle of the secondary satellite's aerodynamic sails according to the target deflection angle in the attitude control mode or the target deflection angle in the position control mode, thereby controlling the secondary satellite's attitude or its formation position relative to the primary satellite.

[0068] Specifically, the aerodynamic actuators of the secondary satellite—namely, the four aerodynamic sails symmetrically mounted on the four sides of the satellite body and their driving devices—adjust the actual deflection angle of each sail according to the target deflection angle. When the target deflection angle originates from the position control mode, the sail deflection primarily alters the effective windward area and aerodynamic drag coefficient along the orbital direction, thereby generating the desired differential aerodynamic drag. This drag acts on the secondary satellite's center of mass, propelling the secondary satellite relative to the primary satellite in the radial and orbital directions within the orbital plane, thus achieving control of the formation's relative position. When the target deflection angle originates from the attitude control mode, the sail deflection primarily alters the angle of attack of each sail relative to the satellite body, generating a three-axis aerodynamic torque around the satellite's center of mass. This torque drives the secondary satellite to rotate around its center of mass, causing the secondary satellite's actual attitude quaternion to approach the desired target attitude quaternion, thereby achieving attitude maneuvering or attitude stabilization.

[0069] In this embodiment of the invention, the target deflection angle is physicalized as the actual angle deflection of the aerodynamic solar panels. This allows the secondary satellite to simultaneously achieve attitude adjustment and formation position maintenance / reconfiguration without consuming any propellant, relying solely on the aerodynamic forces generated by the interaction between the atmosphere and the solar panels. Since the target deflection angle originates from sliding mode variable structure control (position mode) or torque tracking control based on first-order decay differential equations and local Jacobian matrices (attitude mode), the commands themselves have been smoothed and designed to resist disturbances. Therefore, driving the solar panels to deflect will not produce drastic jumps or high-frequency jitter, effectively reducing mechanical wear and energy loss of the actuators. Simultaneously, the same set of aerodynamic solar panels switches the target deflection angle calculation strategy according to different control modes, achieving dynamic time-sharing coordination of attitude and orbit control tasks, fundamentally avoiding command conflicts and torque saturation problems under parallel control. Ultimately, the secondary satellite can track the desired relative trajectory and desired target attitude with high precision in the complex atmospheric environment of ultra-low Earth orbit (ULE), significantly improving the safety, stability, and mission adaptability of formation flight, and providing a reliable attitude control execution means for long-term on-orbit operation of ULE satellites.

[0070] Combination Figure 2 As shown, another embodiment of the present invention provides an aerodynamic-based ultra-low orbit satellite attitude cooperative control system applied to the aerodynamic-based ultra-low orbit satellite attitude cooperative control method described above, comprising: The error calculation unit is used to acquire the real-time status data of the secondary satellite in the ultra-low orbit satellite formation, and based on the real-time status data, to obtain the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite. The mode determination unit is used to determine the control mode of the secondary satellite by comparing the relative position error and the local satellite attitude error with a preset relative position threshold and a preset attitude alignment threshold, respectively. The position control unit is used to construct a sliding surface based on the relative motion state variables of the secondary satellite in the orbital plane and the expected relative trajectory of the secondary satellite when the control mode is position control mode; to calculate the expected aerodynamic drag of the secondary satellite based on the sliding surface and the composite reaching law; and to convert the expected aerodynamic drag into the target deflection angle of the aerodynamic actuator of the secondary satellite. An attitude control unit is used to determine the angular velocity error of the secondary satellite based on the real-time status data when the control mode is attitude control mode, and to determine the desired control torque of the secondary satellite based on the attitude error of the primary satellite and the angular velocity error; to construct a first-order decaying differential equation based on the desired control torque and the actual aerodynamic torque of the secondary satellite, and to determine the target deflection angle of the aerodynamic actuator of the secondary satellite based on the first-order decaying differential equation using the local Jacobian matrix; An execution unit is used to drive the pneumatic actuator of the secondary satellite to perform attitude coordination control actions relative to the primary satellite, based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode.

[0071] The aerodynamic-based ultra-low orbit satellite attitude cooperative control system of the present invention has the same advantages over the prior art as the aforementioned aerodynamic-based ultra-low orbit satellite attitude cooperative control method, and will not be repeated here.

[0072] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for coordinated attitude control of ultra-low Earth orbit satellites based on aerodynamics, characterized in that, include: The real-time status data of the secondary satellite in the ultra-low orbit satellite formation is obtained, and based on the real-time status data, the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite are obtained. The control mode of the secondary satellite is determined by comparing the relative position error and the local satellite attitude error with a preset relative position threshold and a preset attitude alignment threshold, respectively. When the control mode is the position control mode, a sliding surface is constructed based on the relative motion state variables of the secondary star in the orbital plane and the expected relative trajectory of the secondary star; based on the sliding surface, the expected aerodynamic drag of the secondary star is obtained by combining the composite reaching law; the expected aerodynamic drag is converted into the target deflection angle of the aerodynamic actuator of the secondary star. When the control mode is attitude control mode, the angular velocity error of the secondary satellite is determined based on the real-time status data, and the desired control torque of the secondary satellite is determined based on the attitude error of the primary satellite and the angular velocity error. Based on the desired control torque and the actual aerodynamic torque of the sub-satellite, a first-order decay differential equation is constructed, and the target deflection angle of the aerodynamic actuator of the sub-satellite is determined by the local Jacobian matrix according to the first-order decay differential equation. Based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode, the aerodynamic actuator of the secondary satellite is driven to perform attitude coordination control actions relative to the primary satellite.

2. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 1, characterized in that, The real-time status data includes the relative position of the secondary satellite relative to the primary satellite and the actual attitude quaternion of the secondary satellite. The process of acquiring the real-time status data of the secondary satellite in the ultra-low orbit satellite formation, and obtaining the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite based on the real-time status data, includes: Obtain the relative position of the secondary star with respect to the primary star and the actual attitude quaternion; The relative position error of the formation is determined based on the relative position and the preset expected relative trajectory of the secondary star; Based on the actual attitude quaternion of the secondary satellite and the expected attitude quaternion of the secondary satellite, the attitude quaternion error is determined, and the attitude quaternion error is used as the attitude error of the local satellite.

3. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 1, characterized in that, The attitude control mode includes an attitude maneuver mode and an attitude stabilization mode, and the preset relative position threshold includes a first threshold and a second threshold, wherein the first threshold is less than the second threshold. The step of determining the control mode of the secondary satellite by comparing the relative position error and the local satellite attitude error with preset relative position thresholds and preset attitude alignment thresholds, respectively, includes: When the relative position error is less than or equal to the first threshold, the control mode is determined to be the attitude maneuver mode; When the relative position error is greater than or equal to the second threshold, the control mode is determined to be the attitude stabilization mode; When the relative position error is greater than the first threshold and less than the second threshold, and the local satellite attitude error is less than the preset attitude alignment threshold, the control mode is determined to be the position control mode.

4. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 1, characterized in that, The step of constructing a sliding surface based on the relative motion state variables of the secondary star within the orbital plane and the desired relative trajectory of the secondary star includes: The tracking error is determined based on the relative motion state variables and the desired relative trajectory; Based on the tracking error, and combined with the preset sliding surface parameter matrix, the sliding surface is constructed.

5. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 1, characterized in that, The desired aerodynamic drag of the secondary star is obtained by solving the problem based on the sliding surface and in conjunction with the composite reaching law, including: Differentiating the sliding surface yields the dynamic equation of the sliding surface; The differential aerodynamic acceleration along the orbit of the secondary star is obtained by solving the equivalent relationship between the dynamic equation of the sliding surface and the composite approach law. The desired aerodynamic drag is determined based on the differential aerodynamic acceleration along the orbit and the mass of the secondary satellite.

6. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 1, characterized in that, The step of converting the desired aerodynamic drag into a target deflection angle of the aerodynamic actuator of the secondary satellite includes: The drag tracking error is determined based on the expected aerodynamic drag and the actual aerodynamic drag of the secondary satellite. Based on the resistance tracking error, an error dynamic convergence equation is determined, and based on the error dynamic convergence equation, the convergence requirement of the resistance tracking error is mapped to the deflection angle change rate of the pneumatic actuator. The target deflection angle is obtained by numerically integrating the rate of change of the deflection angle.

7. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 3, characterized in that, The real-time status data includes the actual angular velocity of the secondary satellite. The step of determining the angular velocity error of the secondary satellite based on the real-time status data, and determining the desired control torque of the secondary satellite based on the attitude error of the primary satellite and the angular velocity error, includes: Obtain the desired target attitude of the secondary satellite; wherein, when the control mode is the attitude maneuver mode, the mission pointing attitude is taken as the desired target attitude, and when the control mode is the attitude stabilization mode, the orbital coordinate system attitude is taken as the desired target attitude. The angular velocity error is determined based on the actual angular velocity and the expected angular velocity corresponding to the desired target attitude; The desired control torque is obtained by linearly combining the proportional term of the local satellite attitude error, the differential term of the angular velocity error, and the integral term of the local satellite attitude error.

8. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 1, characterized in that, The process of constructing a first-order decaying differential equation based on the desired control torque and the actual aerodynamic torque of the secondary satellite, and determining the target deflection angle of the aerodynamic actuator of the secondary satellite using the local Jacobian matrix and the first-order decaying differential equation, includes: The torque tracking error is determined based on the desired control torque and the actual aerodynamic torque. Based on the torque tracking error, construct the first-order decay differential equation; The time derivative of the torque tracking error is calculated, and combined with the local Jacobian matrix, a mapping relationship is established between the rate of change of the torque tracking error and the rate of change of the deflection angle of the pneumatic actuator. The deflection angle change rate of the pneumatic actuator is obtained by simultaneously solving the first-order decay differential equation and the mapping relationship. The target deflection angle is obtained by integrating the rate of change of the deflection angle.

9. The aerodynamic-based ultra-low orbit satellite attitude cooperative control method according to claim 1, characterized in that, The step of driving the pneumatic actuator of the secondary satellite to perform attitude coordination control actions relative to the primary satellite based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode includes: The pneumatic actuator adjusts the deflection angle of the secondary satellite's aerodynamic sails according to the target deflection angle in the attitude control mode or the target deflection angle in the position control mode, thereby controlling the secondary satellite's attitude or its formation position relative to the primary satellite.

10. An aerodynamic-based ultra-low orbit satellite attitude cooperative control system applied to the aerodynamic-based ultra-low orbit satellite attitude cooperative control method as described in claim 1, characterized in that, include: The error calculation unit is used to acquire the real-time status data of the secondary satellite in the ultra-low orbit satellite formation, and based on the real-time status data, to obtain the formation relative position error of the secondary satellite relative to the primary satellite in the ultra-low orbit satellite formation and the local attitude error of the secondary satellite. The mode determination unit is used to determine the control mode of the secondary satellite by comparing the relative position error and the local satellite attitude error with a preset relative position threshold and a preset attitude alignment threshold, respectively. The position control unit is used to construct a sliding surface based on the relative motion state variables of the secondary satellite in the orbital plane and the expected relative trajectory of the secondary satellite when the control mode is position control mode; to calculate the expected aerodynamic drag of the secondary satellite based on the sliding surface and the composite reaching law; and to convert the expected aerodynamic drag into the target deflection angle of the aerodynamic actuator of the secondary satellite. An attitude control unit is used to determine the angular velocity error of the secondary satellite based on the real-time status data when the control mode is attitude control mode, and to determine the desired control torque of the secondary satellite based on the attitude error of the primary satellite and the angular velocity error. Based on the desired control torque and the actual aerodynamic torque of the sub-satellite, a first-order decay differential equation is constructed, and the target deflection angle of the aerodynamic actuator of the sub-satellite is determined by the local Jacobian matrix according to the first-order decay differential equation. An execution unit is used to drive the pneumatic actuator of the secondary satellite to perform attitude coordination control actions relative to the primary satellite, based on the target deflection angle in the attitude control mode or the target deflection angle in the position control mode.

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