Freight airship reentry and recovery attitude cooperative control method

By combining federated Kalman filtering and adaptive sliding mode controller with pseudo-inverse method to optimize command allocation, the problems of attitude control adaptability and actuator coordination efficiency during the reentry of cargo spacecraft were solved, achieving improved attitude estimation accuracy and reduced fuel consumption, thus ensuring the stability and accuracy of the reentry process.

CN121349134APending Publication Date: 2026-01-16ZIWEI YUTONG TECHNOLOGY EQUIPMENT (WUXI) CO LTD
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Patent Information

Application Number
CN202511500398.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-10-21
Publication Date
2026-01-16

AI Technical Summary

Technical Problem

In existing technologies, the attitude control of cargo spacecraft during reentry has fixed parameters that are difficult to adapt to environmental changes, resulting in attitude overshoot or oscillation, frequent actuator movements, high fuel consumption, increased hardware costs, lack of targeted control objectives, insufficient attitude stability, and low efficiency of actuator coordination.

Method used

A federated Kalman filter algorithm is used to fuse data from multiple sensors to design an adaptive sliding mode controller. The pseudo-inverse method and weighted least squares method are combined for command allocation, and the control strategy is dynamically adjusted. The reentry process is subdivided into multi-stage optimization, and the propulsion system and aerodynamic control surfaces work together to provide real-time feedback on adjustment parameters.

Benefits of technology

It improves the accuracy of attitude estimation and the adaptability of the control algorithm, reduces fuel consumption and hardware costs, enhances the robustness of attitude control and the collaborative efficiency of actuators, and ensures the attitude stability and accuracy of the reentry process.

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Abstract

The invention discloses a freight spaceship reentry recovery attitude cooperative control method. The method comprises the following steps: S1, determining key attitude indexes in a freight spaceship reentry recovery process; s2, collecting atmospheric environment parameters in a reentry process, and meanwhile, obtaining earth gravitational field distribution data to provide environment input for a subsequent attitude control algorithm; s3, based on the Newton's second law and the Euler equation, establishing a kinetic model of the freight spaceship, establishing an attitude kinematics model by adopting a quaternion method or an Euler angle method, and establishing an execution mechanism model for a propulsion system of the freight spaceship; through sub-filter local estimation and main filter global weighting, noise and abnormal values are effectively filtered, attitude estimation precision is improved, instruction distribution adopts a pseudo-inverse method in combination with a weighted least square method, an initial instruction is obtained through the pseudo-inverse method, then secondary optimization is performed in combination with execution mechanism constraints, instruction oversaturation is avoided, and attitude estimation accuracy is improved. Extra redundant execution mechanisms are not needed, and the hardware cost is reduced.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of cargo spacecraft, and particularly relates to a cargo spacecraft reentry recovery attitude cooperative control method. BACKGROUND

[0002] In the prior art, the traditional attitude control mostly adopts the PID control with fixed parameters or the conventional sliding mode control, and has two core limitations: one is that when facing complex disturbances such as sudden change of atmospheric density (for example, the atmospheric density fluctuation at the height of 20-80 km reaches 3 orders of magnitude) and uneven earth gravity field in the reentry process, the fixed parameters are difficult to dynamically match the environmental changes, and attitude overshoot or oscillation is prone to occur; the other is that the switching gain of the conventional sliding mode control needs to be artificially preset, and cannot be adaptively adjusted according to the error, resulting in prominent "chattering problem" and possibly causing frequent action of the actuator and shortening the service life.

[0003] The existing technology of the actuator control mostly has the problem of "functional fragmentation": either over-reliance on the propulsion system throughout the reentry (such as using the attitude of the thruster throughout the reentry), resulting in an increase of 30%-50% in fuel consumption and a reduction in the effective payload capacity of the spacecraft; or over-reliance on the aerodynamic control surface (such as forcibly using the flap in the low atmospheric density area at a height of >60 km), resulting in an increased risk of attitude control failure due to insufficient aerodynamic moment. In addition, the instruction distribution link often adopts the "average distribution" or "fixed priority" strategy, without considering the constraints of the actuator (such as the maximum thrust of the thruster and the deflection limit of the rudder surface), and is prone to instruction oversaturation, which requires additional redundant actuators and increases the hardware cost.

[0004] The existing technology has a rough stage division for the reentry process (mostly only divided into "reentry segment" and "landing segment"), and the control target and parameter setting lack pertinence: for example, in the middle segment (30-50 km) with the most intense aerodynamic heating, the same control gain as the initial segment is still used, resulting in insufficient attitude stability and possibly causing damage to the spacecraft structure due to uneven aerodynamic heating; in the landing phase of the final segment, the parameters are not optimized for the landing attitude accuracy (such as the pitch angle needs to be controlled within -5°±1° to ensure the landing cushion), and the landing attitude deviation is prone to exceed the tolerance. SUMMARY

[0005] The purpose of the present application is to provide a cargo spacecraft reentry recovery attitude cooperative control method, which has stronger adaptability of the control algorithm, significantly improved anti-interference and robustness, and more efficient cooperation of the actuator, and more accurate multi-stage dynamic optimization.

[0006] To achieve the above purpose, the present application provides the following technical scheme: a cargo spacecraft reentry recovery attitude cooperative control method, comprising the following specific steps: S1, clearly defining the key attitude indicators in the reentry recovery process of the cargo spacecraft; S2. Collect atmospheric environmental parameters during reentry and acquire data on the distribution of Earth's gravity field to provide environmental input for subsequent attitude control algorithms. S3. Based on Newton's second law and Euler's equations, establish a dynamic model of the cargo spacecraft, and use the quaternion method or Euler angle method to establish an attitude kinematic model. For the propulsion system of the cargo spacecraft, establish its actuator model. S4. Activate the attitude measurement sensors on the cargo spacecraft, collect the raw data of each sensor according to the set sampling frequency (e.g., IMU sampling frequency is 100Hz, star sensor sampling frequency is 10Hz), and transmit the data to the data processing unit. S5. The data processing unit preprocesses the raw data; S6. The Federated Kalman Filter algorithm is used to fuse the preprocessed multi-sensor data to obtain more accurate and reliable spacecraft attitude information; S7. An attitude controller is designed using the Adaptive Sliding Mode Control (ASMC) algorithm. S8. The pseudo-inverse method combined with the weighted least squares method is used to distribute control commands, and the total control torque generated by the attitude controller is distributed to each actuator. S9. The control commands allocated to each actuator (such as the thrust magnitude of the thruster and the deflection angle of the control surface) are transmitted to the corresponding actuator drive unit. The drive unit controls the actuator to move according to the command, generates the corresponding control torque, and realizes the adjustment of the spacecraft attitude.

[0007] Preferably, the key attitude indicators in S1 specifically include the following indicators: The allowable error range of attitude angles (roll angle, pitch angle, yaw angle) (e.g., roll angle error not exceeding ±2°, pitch angle error not exceeding ±1.5°, yaw angle error not exceeding ±2°), attitude angular velocity limits (e.g., angular velocity of each axis not exceeding ±5° / s), and reentry trajectory parameters (e.g., reentry angle, reentry velocity, reentry altitude range).

[0008] Preferably, in step S2, the atmospheric environmental parameters are specifically: Atmospheric density, atmospheric temperature, wind speed, and wind direction parameters at different altitudes.

[0009] Preferably, the dynamic model is as follows: Translation equations: ; In the formula: For the mass of the spacecraft, For the rate of change of velocity, Due to Earth's gravity, Aerodynamic force; Equation of rotation: ; In the formula: J is the moment of inertia matrix, The rate of change of angular velocity, Where ω is the attitude angular velocity, Ma is the aerodynamic torque, and Mc is the control torque; The posture kinematic model is as follows: ; In the formula: q is a quaternion, The rate of change of the quaternion.

[0010] Preferably, the data processing unit preprocesses the raw data, specifically by: S50. Use the Kalman filter algorithm to remove noise from the IMU data; S51. Use timestamp alignment to synchronize data from each sensor; S52, adopting a system based on The outlier detection method of the criteria is used to detect outliers in preprocessed sensor data.

[0011] Preferably, the fusion of multi-sensor data in step S6 involves the following steps: S60. Different types of sensors are divided into multiple subsystems, such as IMU-star sensor subsystem, IMU-sun sensor subsystem, and IMU-magnetometer subsystem, with each subsystem corresponding to a sub-filter; S61. Each sub-filter uses the corresponding sensor data to perform local state estimation according to the Kalman filter algorithm, and obtains the local attitude estimate. Covariance Matrix ; S62. The main filter receives the local estimation results from each sub-filter and, based on the reliability of each sub-filter, uses a weighted fusion method to obtain the global attitude estimate. .

[0012] Preferably, the attitude controller is designed in step S7, and the specific design steps are as follows: S70, Select attitude angle error ( For the desired attitude angle, (actual attitude angle) and attitude angular velocity error ( For the desired attitude angular velocity, Define the sliding surface (for attitude angular velocity); S71, on the sliding surface By differentiating the sliding surface and setting it equal to 0, the equivalent control law is derived. ,in These are equivalent control commands used to achieve ideal tracking in the system; S72, Design Switching Control Law ,in To switch the gain, The sign function is used. The switching gain is adjusted via an adaptive law. , making It can automatically adjust based on system errors, avoiding the chattering problem of traditional sliding mode control. The adaptive law design is... ,in For adaptive gain; S73. The overall control law is the sum of the equivalent control law and the switching control law, that is... .

[0013] Compared with the prior art, the beneficial effects of the present invention are: (1) This application effectively filters noise and outliers by local estimation of sub-filters and global weighting of main filters, thereby improving attitude estimation accuracy. Even if a sensor fails temporarily, data reliability can still be guaranteed through the cooperation of other sensors.

[0014] (2) In this application, instruction allocation adopts a combination of pseudo-inverse method and weighted least squares method. The initial instruction is obtained first through pseudo-inverse method, and then secondary optimization is performed in combination with the constraints of the execution mechanism to avoid instruction oversaturation. No additional redundant execution mechanism is required, and the hardware cost is reduced.

[0015] (3) The parameters of each stage of this application are linked by real-time attitude feedback and online adjustment. For example, when the atmospheric density changes suddenly in the middle section, the efficiency matrix updates the aerodynamic control surface coefficient in real time to ensure that the control strategy always adapts to the current environment. Attached Figure Description

[0016] Fig. 1 This is a schematic diagram of the overall method flow of the present invention; Fig. 2 This is a schematic diagram of the raw data preprocessing process in this invention; Fig. 3 This is a schematic diagram of the multi-sensor data fusion process in this invention. Detailed Implementation

[0017] 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.

[0018] Please see Figs. 1-3 This invention provides a technical solution: a method for coordinated attitude control of cargo spacecraft reentry and recovery, comprising the following specific steps: Step 1: Identify the key attitude parameters during the reentry and recovery process of the cargo spacecraft, specifically including the following parameters: The allowable error range of attitude angles (roll angle, pitch angle, yaw angle) (e.g., roll angle error not exceeding ±2°, pitch angle error not exceeding ±1.5°, yaw angle error not exceeding ±2°), attitude angular velocity limits (e.g., angular velocity of each axis not exceeding ±5° / s), and reentry trajectory parameters (e.g., reentry angle, reentry velocity, reentry altitude range). Step 2: Collect atmospheric environmental parameters during reentry. Specifically, atmospheric environmental parameters include atmospheric density, atmospheric temperature, wind speed, and wind direction at different altitudes. At the same time, acquire data on the distribution of Earth's gravity field to provide environmental input for subsequent attitude control algorithms. Step 3: Based on Newton's second law and Euler's equations, establish a dynamic model of the cargo spacecraft. Use the quaternion method or Euler angle method to establish an attitude kinematic model. For the propulsion system of the cargo spacecraft, establish a model of its actuators. The dynamic model is as follows: Translation equations: ; In the formula: For the mass of the spacecraft, For the rate of change of velocity, Due to Earth's gravity, Aerodynamic force; Equation of rotation: ; In the formula: J is the moment of inertia matrix, The rate of change of angular velocity, Here, ω represents the attitude angular velocity, Ma represents the aerodynamic torque, and Mc represents the control torque. The posture kinematic model is as follows: ; In the formula: q is a quaternion, Rate of change of quaternions Step 4: Activate the attitude measurement sensors on the cargo spacecraft. The attitude measurement sensors include an inertial measurement unit (IMU, used to measure attitude angular velocity and linear acceleration), a star sensor (used to measure the spacecraft's attitude relative to a star), a sun sensor (used to measure the attitude relative to the sun in near-Earth orbit and the initial reentry phase), and a magnetometer (used to measure the strength of the Earth's magnetic field to help determine the attitude), etc. Collect the raw data from each sensor according to the set sampling frequency (e.g., the IMU sampling frequency is 100Hz, and the star sensor sampling frequency is 10Hz), and transmit the data to the data processing unit. Step 5, the data processing unit pre-processes the original data; Specifically, Step 50, Kalman Filter algorithm is used to remove noise from IMU data; First, the state equation and the observation equation of the IMU are established. The state equation considers the drift characteristics of the IMU, and the observation equation is based on the measurement values of the IMU. Through the prediction and update steps, the noise-free attitude angular velocity and linear acceleration are estimated. The specific algorithm flow is as follows: Prediction step: ; ; Wherein: is the prior state estimation value at time k, is the state transition matrix, is the posterior state estimation value at time k-1, is the input matrix, is the input value, is the prior covariance matrix at time k, is the posterior covariance matrix at time k-1, is the process noise covariance matrix.

[0019] Update step: ; ; Wherein: is the Kalman gain, is the observation matrix, is the observation value at time k, is the observation noise covariance matrix, is the posterior state estimation at time k, is the posterior covariance matrix at time k, and I is the unit matrix.

[0020] Step 51, due to the different sampling frequencies of different sensors, the time stamp alignment method is used to synchronize the data of each sensor. Taking the sampling time of the star sensor as the reference, the data of the IMU, the sun sensor, the magnetometer and other sensors are adjusted to the same time point through interpolation or extrapolation, to ensure the accuracy of subsequent data fusion; Step 52, based on The outlier detection method of the criterion detects the pretreated sensor data, calculates the mean μ and the standard deviation σ of each sensor data, and determines that an outlier exists if a data point is outside the range [μ-3σ, μ+3σ]. For outliers, the linear interpolation method of normal data at adjacent time points is used for replacement, and if multiple outliers appear continuously, the backup sensor data is started.

[0021] Step 6, the federated Kalman filter (Federated Kalman Filter) algorithm is used to fuse the pretreated multi-sensor data, and more accurate and reliable spacecraft attitude information is obtained; The specific steps are as follows: Step 60, different types of sensors are divided into multiple subsystems, such as IMU-star sensor subsystem, IMU-sun sensor subsystem, and IMU-magnetometer subsystem, each of which corresponds to a sub-filter; Step 61, each sub-filter uses the corresponding sensor data to perform local state estimation according to the Kalman filter algorithm, and obtains the local attitude estimation value and the covariance matrix , is the sub-filter number; Step 62, the main filter receives the local estimation results of each sub-filter, and according to the reliability of each sub-filter, a weighted fusion method is used to obtain the global attitude estimation value , wherein ; , n is the number of sub-filters, and the global covariance matrix is updated at the same time.

[0022] Step 7, an adaptive sliding mode control (Adaptive Sliding Mode Control, ASMC) algorithm is used to design an attitude controller; The specific design steps are as follows: Step 70, select the attitude angle error ( is the desired attitude angle, is the actual attitude angle) and the attitude angular velocity error ( is the desired attitude angular velocity, is the attitude angular velocity), and define a sliding surface; Step 71, on the sliding surface , the equivalent control law is derived by taking the derivative of the sliding surface and setting it to 0, wherein is the equivalent control command, which is used to realize the ideal tracking of the system; Step 72, design a switching control law , wherein is the switching gain, is the sign function. The switching gain is adjusted by the adaptive law such that can be automatically adjusted according to the system error, avoiding the chattering problem of traditional sliding mode control. The adaptive law is designed as where is the adaptive gain; Step 73, the total control law is the sum of the equivalent control law and the switching control law, i.e. .

[0023] Step 8, the pseudo-inverse method combined with the weighted least squares method is used for control command distribution, and the total control torque generated by the attitude controller is distributed to each actuator; An actuator effectiveness matrix is established: assuming that the cargo spaceship has m actuators, the components of the control torque generated by each actuator on each coordinate axis form the effectiveness matrix .

[0024] Solving the initial command: according to the total control torque demand Mc, the pseudo-inverse method is used to solve the initial actuator command where is the pseudo-inverse of the effectiveness matrix B.

[0025] Checking the initial command whether it meets the constraints of the actuators (such as the maximum thrust limit of the thrusters and the maximum deflection angle limit of the rudders). If the constraints are met, the is taken as the final actuator command; if the constraints are not met, the weighted least squares method is used to solve the actuator command u that minimizes the performance index under the premise of meeting the constraints, where W is the weighting matrix used to adjust the importance of the control torque on each coordinate axis. The optimization problem of the performance index can be converted into a quadratic programming problem with constraints, which is solved by the Lagrange multiplier method or numerical optimization algorithms (such as the interior point method).

[0026] Step 9, the actuator commands (such as the thrust size of the thrusters and the deflection angle of the rudders) obtained by the control command distribution are transmitted to the corresponding actuator driving units, and the driving units control the actuators to act according to the commands, generating corresponding control torques to adjust the attitude of the spaceship.

[0027] In summary: The present application adopts adaptive sliding mode control (ASMC), which designs The adaptive law of the sliding mode control makes the switching gain k able to be adjusted in real time according to the sliding mode surface s (reflecting the integrated state of the attitude error and the angular velocity error): when the attitude error is large, k is automatically increased to improve the response speed and quickly offset the disturbance; when the error is reduced, k is automatically reduced to suppress the chattering. At the same time, combined with the multi-sensor data fusion of the federal Kalman filter, compared with the single sensor dependence in the prior art (such as relying only on the IMU which is easy to be affected by drift) or simple weighted fusion, the local estimation of the sub-filter and the global weighting of the main filter (the weight is dynamically determined by the covariance matrix) can effectively filter the noise and abnormal values, and the attitude estimation accuracy is improved by more than 30%, even if a sensor temporarily fails (such as the sun sensor being blocked by clouds), the data reliability can still be ensured through the cooperation of other sensors.

[0028] The present application solves the above problems through a phased cooperative strategy + dynamic command allocation: in the initial reentry stage (height > 80km), the propulsion system is mainly used, and the aerodynamic control surface is used as a supplement, and the attitude is quickly adjusted by using the thruster; in the middle stage (20-80km), the weights of the two are dynamically adjusted according to the change of atmospheric density, the aerodynamic control surface efficiency is improved, and the use of the thruster is gradually reduced, and the fuel consumption is reduced by more than 25% compared with the prior art; in the final stage (height < 20km), the aerodynamic control surface is mainly used, and the propulsion system is only used for fine tuning, taking into account the accuracy and economy. At the same time, the command allocation adopts the "pseudo-inverse method + weighted least squares method", the initial command is obtained by the pseudo-inverse method, and then the secondary optimization is carried out combined with the execution mechanism constraint, avoiding the command oversaturation, without additional redundant execution mechanism, and the hardware cost is reduced by 15%-20%.

[0029] The reentry process of the present application is divided into an initial stage (> 80km), a middle stage (20-80km), and a final stage (< 20km), and each stage is designed with exclusive control targets and parameters: the initial stage takes "trajectory tracking" as the core, sets the weight of the trajectory-related coordinate axis in the weight matrix W to 5 (others are 1), to ensure rapid entry into the predetermined trajectory; the middle stage focuses on "suppressing aerodynamic heating", adjusts the pitch angle to control the aerodynamic drag, and gradually reduces the sliding mode control gain k from 10 to 3 to balance the response speed and stability; the final stage takes "landing accuracy" as the target, sets the weight of the landing attitude-related coordinate axis to 6 (others ≤ 2), and reduces the sliding mode control gain k to 1, so that the attitude control error is reduced to within ±0.5°, which is 67% higher than the accuracy of ±1.5° in the prior art. In addition, the parameters of each stage are linked through "real-time attitude feedback + online adjustment", such as when the atmospheric density suddenly changes in the middle stage, the aerodynamic control surface coefficient is updated in real time to ensure that the control strategy is always adapted to the current environment.

[0030] While embodiments of the application have been shown and described, it is to be understood that the embodiments described are merely exemplary of the principles and application of the present application. Numerous modifications and adaptions can be effected without departing from the spirit and scope of the present application, which is not limited to the exact construction and arrangement described. It is intended, therefore, to cover all modifications and adaptions that fall within the scope of the claims and their equivalents.

Claims

1. A method for cooperative control of reentry and recovery attitude of a cargo spacecraft, characterized in that, The method comprises the following specific steps: S1, determining key attitude indexes in the reentry and recovery process of the cargo spaceship; S2, collecting atmospheric environment parameters in the reentry process, and obtaining earth gravity field distribution data, to provide environmental inputs for subsequent attitude control algorithms; S3, establishing a dynamics model of the cargo spaceship based on Newton's second law and Euler's equation, establishing an attitude kinematics model by using a quaternion method or an Euler angle method, and establishing an actuator model of the propulsion system of the cargo spaceship; S4, starting attitude measurement sensors on the cargo spaceship, collecting original data of each sensor according to a set sampling frequency, and transmitting the data to a data processing unit; S5, the data processing unit pre-processes the original data; S6, fusing the pre-processed multi-sensor data by using a federated Kalman filtering algorithm to obtain more accurate and reliable spaceship attitude information; S7, designing an attitude controller by using an adaptive sliding mode control algorithm; S8, distributing control commands by using a pseudo-inverse method combined with a weighted least squares method, and distributing the total control torque generated by the attitude controller to each actuator; S9, transmitting the actuator commands obtained by distributing the control commands to the corresponding actuator driving units, and driving the actuator to act according to the commands to generate corresponding control torques, thereby adjusting the attitude of the spaceship.

2. The method of cooperative control of re-entry and recovery attitude of a cargo spacecraft according to claim 1, characterized in that, The key attitude indexes in S1 specifically include the following indexes: an allowable error range of the attitude angle, an attitude angular velocity limit, and reentry trajectory parameters.

3. The method of cooperative control of re-entry and recovery attitude of a cargo spacecraft according to claim 1, characterized in that, In S2, the atmospheric environment parameters specifically include: atmospheric density parameters, atmospheric temperature parameters, wind speed parameters, and wind direction parameters at different altitudes.

4. The method of cooperative control of re-entry and recovery attitude of a cargo spacecraft according to claim 1, characterized in that, The dynamics model is: Translational equations: ; where: is the mass of the spacecraft, is the rate of change of velocity, is the Earth's gravitational force, is the aerodynamic force; Equation of rotation: ; where J is the moment of inertia matrix, is the angular rate of change, is the attitude angular rate, Ma is the aerodynamic moment, and Mc is the control moment. The attitude kinematics model is: ; where: q is a quaternion, is the rate of change of the quaternion.

5. The method of cooperative control of re-entry and recovery attitude of a cargo spacecraft according to claim 1, characterized in that, The data processing unit pre-processes the original data, specifically: S50, removing noise from IMU data by using a Kalman filtering algorithm; S51, synchronizing sensor data by using a time stamp alignment method; S52, adopt the outlier detection method based on criteria to detect the pre-processed sensor data.

6. The method of cooperative control of re-entry and recovery attitude of a cargo spacecraft according to claim 1, characterized in that, In S6, the multi-sensor data are fused, and the specific steps are as follows: S60, dividing different types of sensors into multiple subsystems, such as an IMU-star sensor subsystem, an IMU-sun sensor subsystem, and an IMU-magnetometer subsystem, each of which corresponds to a sub-filter; S61, each sub-filter utilizes the corresponding sensor data to perform local state estimation according to the Kalman filtering algorithm, and obtains a local attitude estimation value and a covariance matrix ; S62, the main filter receives the local estimation results of each sub-filter, and obtains a global attitude estimation value by using a weighted fusion method according to the reliabilities of the sub-filters .

7. The method of cooperative control of re-entry and recovery attitude of a cargo spacecraft according to claim 1, characterized in that, In S7, the attitude controller is designed, and the specific design steps are as follows: S70, selecting a pose angle error and a pose angular velocity error , defining a sliding surface S71、On the slip surface , the equivalent control law is derived by taking the derivative of the slip surface and setting it equal to 0 ; S72, design switching control law , adjust switching gain by adaptive law , adaptive law is designed as ; S73, the total control law is the sum of the equivalent control law and the switching control law.