Satellite attitude control demonstration system in simulated weightlessness environment

Abstract

The application discloses a satellite attitude control demonstration system in a simulated weightless environment, which comprises a cubic robot and a three-axis rotating table; the three-axis rotating table comprises a fixed part, and outer, middle and inner rings are sequentially arranged in the fixed part; the inner ring is a cubic frame, and the cubic robot is embedded in the inner ring; the inner ring is rotationally connected with the middle ring, the middle ring is arranged in the inner part of the outer ring, and axial interference is generated between the inner ring and the middle ring and between the middle ring and the outer ring; the inner ring rotates around an X axis to realize rolling motion, the middle ring rotates around a Y axis to realize pitching motion, and the outer ring rotates around a Z axis to realize yawing motion, so that the cubic robot is freely rotated around the X, Y and Z axes, and three-dimensional attitude motion of the satellite in the weightless environment is simulated; during the free rotation of the cubic robot around the X, Y and Z axes, friction torque is generated due to the axial interference, the friction torque offsets eccentric torque caused by the gravity center deviation, and interference suppression is realized.

Description

Technical Field

[0001] This invention relates to embedded system measurement and control technology, belonging to the field of spacecraft ground simulation test and attitude control, specifically to a satellite attitude control demonstration system under simulated weightlessness. Background Technology

[0002] Chinese invention patent application CN118486227A discloses an air-floating satellite attitude control demonstration system and its control method, comprising a main body and an air-floating simulation structure. The system measures attitude data via an attitude measurement module, transmits this data to a host computer via a communication module, receives control commands from the host computer via the communication module, calculates the target angle based on the host computer control commands and the measured attitude data, and sends control commands to the actuator. The actuator drives the device to adjust the attitude to achieve the target angle, and the control module controls the deployment and retraction of the solar panels. The air-floating simulation structure includes an air pump, an air-floating platform, and a spherical shell. The main body is installed inside the spherical shell, and the air pump inflates the inside of the air-floating platform to form an air film on its surface, creating a micro-friction environment to simulate a weightless environment.

[0003] However, the above solution has the following shortcomings:

[0004] (1) When using an air-bearing platform to simulate weightlessness, there are complex turbulence and other disturbances in the airflow at the contact surface. At the same time, due to the offset between the center of gravity and the center of rotation of the simulated satellite, an unbalanced gravitational torque is generated. These disturbances are large and exceed the allowable limit, and their characteristics are time-varying, making them difficult to balance and cancel out.

[0005] (2) Using a single IMU module as the sensing module has problems such as heading angle drift and insufficient accuracy, which makes the ground simulation effect still not ideal;

[0006] (3) Using a two-layer PID controller to control the motor speed and realize the attitude control function has limited robustness to control error and nonlinear disturbance. Summary of the Invention

[0007] Purpose of the invention: The purpose of this invention is to provide a satellite attitude control demonstration system that simulates weightlessness. This system uses frictional torque to counteract the eccentric torque caused by the shift of the center of gravity, thereby achieving interference suppression.

[0008] Technical Solution: This invention provides a satellite attitude control demonstration system simulating a weightless environment, comprising a cubic robot and a three-axis rotary table. The three-axis rotary table includes a base and a ring-shaped fixing component vertically mounted above the base. The fixing component contains an outer ring, a middle ring, and an inner ring arranged sequentially. The inner ring is a cubic frame, and the cubic robot is embedded within it. The inner ring is rotatably connected to the middle ring via an inner ring bracket. The middle ring is mounted inside the outer ring via a connector and bearings. Axial interference occurs between the inner and middle rings, and between the middle and outer rings. The inner ring rotates around the X-axis to achieve roll motion, the middle ring rotates around the Y-axis to achieve pitch motion, and the outer ring rotates around the Z-axis to achieve yaw motion, enabling the cubic robot to rotate freely around the X, Y, and Z axes, thereby simulating the three-dimensional attitude motion of a satellite in a weightless environment. During the free rotation of the cubic robot around the X, Y, and Z axes, axial interference generates frictional torque, which counteracts the eccentric torque caused by the shift in the center of gravity, thus suppressing interference.

[0009] Furthermore, the cube robot is shaped like a cube, with an attitude sensing system fixed on the upper surface of the cube, a motherboard fixedly installed inside the cube, a main controller mounted on the motherboard, and a control execution system mounted on the inner wall of the cube. The main controller is used to process the attitude data measured by the attitude sensing system and generate control commands. The control execution system performs actions according to the control commands to achieve satellite attitude adjustment.

[0010] Furthermore, the attitude perception system includes an IMU board and a simulated star sensor, wherein the IMU board integrates an inertial measurement unit; the IMU board and the simulated star sensor are on the same plane; the inertial measurement unit is used to measure the raw three-axis angular velocity data in the coordinate system of the satellite model in real time, as IMU angular velocity data; the simulated star sensor is used to observe visual attitude data; the simulated star sensor is equipped with a simulated star sensor controller, which acquires the current visual attitude data observed by the simulated star sensor, calculates the current visual attitude data, and sends the calculated current visual attitude data to the main controller.

[0011] Furthermore, the main controller acquires IMU angular velocity data measured by the inertial measurement unit and current rotational speed values ​​fed back by the three momentum wheel motor drivers. The main controller also receives the calculated current visual attitude data from the analog star sensor controller. The main controller has a built-in attitude calculation and fusion program that calculates the IMU angular velocity data. The calculated IMU angular velocity data and the calculated current visual attitude data are input to the error state Kalman filter for data fusion to obtain the optimal estimated unit quaternion. Based on the optimal estimated unit quaternion, the real-time estimated value of the optimal three-axis attitude angle of the satellite model at the current moment is obtained. The attitude calculation and fusion program compares the optimal estimated unit quaternion with the preset target attitude quaternion to obtain the error quaternion. At the same time, it uses the process noise covariance combined with the error state discrete dynamic equation to calculate the Kalman gain. The attitude error is obtained using the Kalman gain and the error quaternion.

[0012] Furthermore, the main controller has a built-in momentum output calculation and control program. In the momentum output calculation and control program, the disturbance state observer estimates the lumped disturbance in real time and inputs the real-time estimated value, attitude error and angular velocity together to the saturated sliding mode controller. The saturated sliding mode controller calculates the three-axis control torque vector required to make the system state converge to the sliding surface. Through the coordinate transfer matrix determined by the orthogonal installation geometry, the three-axis control torque vector is converted into the target speed command of the three momentum wheels.

[0013] Furthermore, the perturbation state observer is designed as follows:

[0014] Based on the conservation of total angular momentum, the dynamic equations of the cubic robot (1) are established as follows:

[0015]

[0016] in, This is the three-axis control torque vector; Here is the rotational inertia matrix; Control the target angular velocity; These are known nonlinear terms in the dynamic equations; For total disturbance; total disturbance As the quantity to be estimated, a perturbation state observer is designed by treating the total perturbation as an extended state:

[0017] ;

[0018] in, This is the three-axis control torque vector; This is an estimate of the angular velocity of the cubic robot; This is the estimated total disturbance. This represents the angular velocity estimation error.

[0019] The nonlinear function is defined as follows: , .

[0020] Furthermore, the calculation formula for the three-axis control torque vector is as follows:

[0021] ;

[0022] in, This is the three-axis control torque vector; These are known nonlinear terms in the dynamic equations; For lumped interference; Here is the rotational inertia matrix; The robust gain matrix; This is the boundary layer thickness vector.

[0023] Furthermore, the control execution system includes three motors and three momentum wheels. Each motor and momentum wheel constitutes a set of execution mechanisms, and the three sets of execution mechanisms are respectively installed inside the three mutually orthogonal surfaces of the cube robot.

[0024] Furthermore, the cube robot is equipped with a fixed power supply system, which includes a camera board battery and a motherboard battery. The camera board battery powers the analog star sensor, and the motherboard battery powers the motherboard.

[0025] Furthermore, the motherboard is equipped with a communication system, which includes a built-in Bluetooth module and a built-in WIFI module; the built-in Bluetooth module is used to input the current attitude data observed by the simulated star sensor into the attitude calculation and fusion program; the built-in WIFI module is wirelessly connected to an external host computer system.

[0026] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0027] (1) The present invention uses a three-axis rotary table to replace the traditional air-floating platform. The cubic robot can rotate freely around the X, Y and Z axes through a three-layer orthogonal frame formed by the outer ring, middle ring and inner ring. It can also simulate the three-dimensional posture motion in the microgravity environment of space. The frictional torque is generated by the axial interference between the inner ring and the middle ring, and between the middle ring and the outer ring. The frictional torque cancels the eccentric torque caused by the center of gravity shift, thus achieving interference suppression.

[0028] (2) In order to further improve the attitude measurement accuracy and overcome the problem of heading angle drift of a single IMU, this invention introduces a simulated star sensor, integrates the inertial measurement unit (IMU) with the simulated star sensor, and realizes the data fusion of inertial navigation and visual guidance through the error state Kalman filter (ESKF). This enables the demonstration system to have the advantages of high dynamic response (200Hz sampling rate) of IMU and absolute heading reference (30Hz update rate) of simulated star sensor, thereby simulating high-precision integrated navigation attitude determination of satellite under ground conditions.

[0029] (3) This invention innovatively designs a sliding mode control strategy based on a disturbance state observer, which solves the nonlinear coupling and internal and external disturbances in the demonstration system. The study combines the characteristics of the system itself with multiple disturbances and strong nonlinearity, and selects the robust sliding mode control strategy as the main control strategy. At the same time, based on the physical model of the system, a disturbance state observer is designed to cancel the disturbances and nonlinear terms, so as to achieve feedback linearization. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the overall structure of the present invention;

[0031] Figure 2 for Figure 1 Front view of the inner and outer rings and the fastener in the same vertical plane;

[0032] Figure 3 This is a front view of the three-axis rotary table in this invention;

[0033] Figure 4 for Figure 1 A schematic diagram of the structure of the Neutral Robot;

[0034] Figure 5 for Figure 4 Structural diagram with the front side removed;

[0035] Figure 6 This is a schematic diagram illustrating the working principle of the cubic robot in this invention.

[0036] Figure 7 This is a flowchart illustrating the attitude calculation and fusion process in this invention;

[0037] Figure 8 This is a flowchart illustrating the momentum output calculation and control program in this invention.

[0038] Figure 9 This is a schematic diagram of the host computer interface in this invention. Detailed Implementation

[0039] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0040] like Figure 1-3 As shown, this invention presents a satellite attitude control demonstration system under simulated weightlessness. It simulates the weightless state of a satellite in space, demonstrating basic attitude adjustment and control functions. This invention uses a three-axis rotary table to create a weightless environment for the satellite, constructing a satellite attitude measurement and control system within a cubic space. By measuring the satellite's attitude and controlling its attitude changes, the system can control the satellite to adjust to any set attitude; under external interference, it can quickly restore a stable attitude. The system includes a cubic robot 1 and a three-axis rotary table 2. This invention uses an STM32F407VGT6 microcontroller as the control center of the cubic core, responsible for running attitude calculation and control algorithms, processing sensor data, executing communication protocols, and outputting control commands. It is the information processing and decision-making core of the system.

[0041] The three-axis rotary table 2 includes an inner ring support 3, an inner ring 4, a middle ring 5, a base 6, a connector 7, an outer ring 8, a fixing component 9, and a fixing connector 10. The specific installation method is as follows: A ring-shaped fixing component 9 is vertically installed above the base 6. The outer ring 8, middle ring 5, and inner ring 4 are sequentially arranged inside the fixing component 9, forming a three-layer orthogonal frame. The inner ring 4 is a cubic frame, and the cubic robot 1 is embedded inside the inner ring 4. The inner ring 4 is rotatably connected to the middle ring 5 via the inner ring support 3. The middle ring 5 is installed inside the outer ring 8 via the connector 7 and bearings. Axial interference occurs between the inner ring 4 and the middle ring 5, and between the middle ring 5 and the outer ring 8. The inner ring 4 rotates around the X-axis to achieve roll motion, the middle ring 5 rotates around the Y-axis to achieve pitch motion, and the outer ring 8 rotates around the Z-axis to achieve yaw motion, enabling the cubic robot 1 to rotate freely around the X, Y, and Z axes, thereby simulating the three-dimensional attitude motion of a satellite in a weightless environment. During the free rotation of the cube robot 1 around the X, Y, and Z axes, axial interference will generate frictional torque. The frictional torque will counteract the eccentric torque caused by the shift of the center of gravity, thus achieving interference suppression.

[0042] The three-axis rotary table 2 consists of a four-layer frame: an outer ring 8, a middle ring 5, an inner ring 4, and a fixing component 9. The first three layers correspond to the rotation of the yaw axis (Z-axis), pitch axis (Y-axis), and roll axis (X-axis), respectively. The fixing component 9, outer ring 8, and middle ring 5 are connected by a connecting component 7 and a bearing to achieve rotation, while the inner ring 4 and middle ring 5 are connected by an inner ring bracket 3 and a bearing to achieve rotation.

[0043] like Figure 4As shown, the corner connector 12 is an orthogonal polyhedral structure, and each corner connector 12 is fixed to the three outer shells 14 with screws. A momentum wheel 19 and a motor 18 form a group, and the three groups are respectively installed inside the three mutually orthogonal outer shells 14 of the cubic robot 1. The main board 16, camera board 17 and power supply system 15 are installed in the other three faces respectively. The IMU board 11 and the analog star sensor 13 are both installed on the outside of the outer shell 14 corresponding to the main board 16, ensuring that the IMU board 11 and the analog star sensor 13 are on the same plane to facilitate subsequent coordinate system alignment.

[0044] This invention uses a three-axis rotary stage 2 to replace the traditional air-bearing platform. It forms a three-layer orthogonal frame with an outer, middle, and inner ring. This three-layer orthogonal frame, along with bearings, allows for low-friction free rotation around the X, Y, and Z axes, thus simulating three-dimensional posture motion in a microgravity environment. By generating additional frictional torque through axial interference of the three-axis rotary stage 2 to counteract eccentric torque, and by using 3M adhesive to attach or magnetically attach counterweights, the center of gravity can be flexibly adjusted to bring the center of gravity of the entire demonstration system as close as possible to its geometric center, thereby avoiding additional oscillations caused by center of gravity shifts during posture adjustments.

[0045] The innermost layer of the three-axis rotary table 2 is equipped with a cubic frame structure (inner ring 4), which serves as the intermediate carrier connecting the cubic robot 1 and the three-axis rotary table 2. The cubic robot 1 is embedded and installed inside the inner ring 4, and is fitted with the middle ring 5 through the inner ring supports 3 on both sides. The outer side of the middle ring 5 is assembled with bearings through connectors 7 and forms axial interference with the outer ring 8, thereby realizing the fixation and rotation of the cubic robot on the three-axis support table.

[0046] To solve the problem of unbalanced torque caused by the misalignment of the center of gravity and the geometric center, this invention adopts two counterweight adjustment schemes: (1) Overfitting assembly balancing scheme: The four-layer ring structure of the three-axis rotary table is overfitted with the bearing through 7 connectors or 3 inner ring brackets to form axial interference. While the bearing is fitted on the side, it also forms axial interference with the middle frame. The overfitting loading on the front uses the additional friction torque generated therefrom to effectively offset the eccentric torque caused by the center of gravity shift, thereby achieving interference suppression at the structural level. (2) Counterweight adjustment scheme: 3M adhesive is used to attach counterweights or magnetic counterweights. The position and mass of the counterweights can be flexibly adjusted according to the actual center of gravity shift, so as to achieve quick and convenient adjustment of the center of gravity. The counterweights can be directly attached to the surface of the cube module or the four-layer ring structure. The two schemes can be used alone or in combination according to actual needs.

[0047] The working process of the three-axis rotary table 2 is as follows: When the cube robot 1 needs to adjust its posture under the action of the control torque, the inner ring 4 rotates around the X-axis to achieve roll motion, the middle ring 5 rotates around the Y-axis to achieve pitch motion, and the outer ring 8 rotates around the Z-axis to achieve yaw motion. The cube robot 1 is embedded inside the inner ring 4 and is connected to the middle ring 5 through the inner ring brackets 3 on both sides and bearings. The middle ring 5 is connected to the outer ring 8 through the connecting piece 7 and bearings. The outer ring 8 is also connected to the fixed piece 9 through the connecting piece 7 and bearings, realizing free rotation of the three axes. The counterweight adjustment device adjusts the center of gravity position through the above two schemes, effectively reducing the unbalanced torque and reducing the burden on the control system, thereby simulating the free rotation conditions in a microgravity environment.

[0048] like Figure 4-6 As shown, the cube robot 1 is shaped like a cube. An attitude sensing system is fixed to the upper surface of the cube, and a main board 16 is fixedly installed inside the cube. A main controller is mounted on the main board 16, and a control execution system is installed on the inner wall of the cube. The main controller processes the attitude data measured by the attitude sensing system and generates control commands. The control execution system then performs actions based on these control commands to achieve satellite attitude adjustment.

[0049] According to such Figure 6 The module wiring is completed as shown. Figure 6 The solid lines represent wired connections, while the dashed lines represent wireless transmission. The computer uses host computer software to wirelessly communicate with the STM32 development board via its built-in WiFi module, enabling functions such as target attitude control, current attitude acquisition, and work data collection. Simultaneously, the motherboard 16 has a built-in WiFi / Bluetooth module, an internal WiFi module, an IMU board 11, and motors 18, all directly connected to the development board for signal transmission. A lithium battery powers these components via the motherboard 16. The analog star sensor 13 and camera board are powered by separate 5V batteries, and their attitude data is transmitted through a stable connection between the analog star sensor 13 and the built-in Bluetooth module on the motherboard 16.

[0050] like Figure 4 and Figure 5 As shown, the cube robot 1 has a two-layer structure. The outer layer consists of corner connectors 12, shell 14, and IMU board 11 and simulated star sensor 13 fixed on its outer side. The inner layer consists of power supply system 15, main board 16, camera board 17, motor 18 and momentum wheel 19 fixed on the inner side of shell 14. All functional components are integrated on the cube to form cube robot 1.

[0051] All functional modules, including three momentum wheels, IMU, controller, and battery, are integrated into a single cube. Each module is fixed to the cube frame via its own designed sheet metal parts, forming an independent, detachable cube robot1. The internal module layout of the cube is compact, and each sheet metal part uses standard interfaces to connect to the cube frame, facilitating disassembly and maintenance.

[0052] like Figure 4 and Figure 6 As shown, the attitude perception system includes an IMU board 11 and an analog star sensor 13 (RA8D1-VisionBoard). The IMU board 11 integrates an inertial measurement unit (MPU6050, integrating an accelerometer and gyroscope). The IMU board 11 and the analog star sensor 13 are on the same plane. The inertial measurement unit is used to measure the raw three-axis angular velocity data in the satellite model's body coordinate system in real time, which is used as the IMU angular velocity data. The analog star sensor 13 is used to observe visual attitude data. The analog star sensor 13 is equipped with an analog star sensor controller. The analog star sensor controller acquires the current visual attitude data observed by the analog star sensor 13, calculates the current visual attitude data, and sends the calculated current visual attitude data to the main controller through the built-in Bluetooth module in the communication system. The inertial measurement unit (IMU) outputs angular velocity and acceleration data at a sampling frequency of 200Hz. The analog star sensor 13 acquires star images and calculates absolute attitude through the OV7725 image sensor at a frequency of 30Hz. The two are fused through an error state Kalman filter (ESKF) to output high-precision, interference-resistant three-axis attitude information.

[0053] To improve attitude measurement accuracy and overcome the heading angle drift problem of a single IMU, this invention introduces a simulated star sensor 13, which integrates a six-axis IMU (MPU6050) with the simulated star sensor 13 (RA8D1 Vision Board). The data fusion of inertial navigation and visual guidance is achieved through an error state Kalman filter (ESKF), enabling the system to combine the advantages of the IMU's high dynamic response (200Hz sampling rate) and the star sensor's absolute heading reference (30Hz update rate), thereby simulating high-precision integrated navigation attitude determination of satellites under ground conditions.

[0054] The attitude perception system is a multi-sensor fusion attitude reference system. Its core lies in fusing high-frequency short-term attitude prediction from the inertial measurement unit (IMU) with low-frequency absolute attitude observation from the simulated star sensor 13. The IMU (based on a gyroscope) provides high-bandwidth attitude changes through integration, but suffers from drift. The simulated star sensor (based on a camera and vision algorithm) provides drift-free absolute attitude by recognizing known beacons, but has a low update rate and is susceptible to transient interference. The system employs an Error-State Kalman Filter (ESKF) as the fusion framework, using the IMU as the prediction agent and visual attitude as the observation correction, ultimately outputting an optimal attitude estimate that combines high dynamic response and long-term stability.

[0055] like Figure 5 As shown, the control and execution system includes three motors 18 and three momentum wheels 19. Each motor 18 and momentum wheel 19 forms a set of execution mechanisms, and the three sets of execution mechanisms are respectively installed inside the three mutually orthogonal surfaces of the cubic robot 1. This invention uses three sets of orthogonally installed momentum wheels 19 as the execution mechanisms of the demonstration system. Each set includes a brushless DC motor and a flywheel. The motor drive circuit receives speed commands, changes angular momentum to generate a reaction torque, and achieves attitude adjustment of the satellite model. The battery pack powers each module, ensuring stable operation of the system under conditions such as momentum wheel acceleration and vision module operation.

[0056] This invention employs 20 sets of three orthogonal momentum wheels as actuators to control the torque output along the roll, pitch, and yaw axes, respectively. Each momentum wheel set includes:

[0057] a) Brushless DC motor: provides rotational torque and controls speed via an electronic speed controller;

[0058] b) Flywheel: Installed on the motor output shaft, it stores angular momentum through rotational inertia;

[0059] c) Motor drive circuit: Receives speed commands sent by the main controller and controls the motor to reach the target speed.

[0060] Three momentum wheels are orthogonally mounted inside the satellite model's inner frame, corresponding to the X, Y, and Z axes respectively. They possess braking, jumping, and balance stabilization capabilities. Under suspension, the system exhibits pure rotational motion.

[0061] like Figure 5 and Figure 6 As shown, a power supply system 15 is fixedly installed inside the cube robot 1. The power supply system includes a camera board battery and a motherboard battery. The camera board battery is used to power the analog star sensor 13, and the motherboard battery is used to power the motherboard 16.

[0062] like Figure 6As shown, the motherboard 16 houses a communication system, which includes a built-in Bluetooth module and a built-in Wi-Fi module. The built-in Bluetooth module is used to input the current attitude data observed by the simulated star sensor 13 into the attitude calculation and fusion program; the built-in Wi-Fi module wirelessly connects to an external host computer system. In this embodiment, the built-in Bluetooth module uses an HC-05 Bluetooth module to realize wireless data transmission between the satellite device and the host computer, supporting status parameter feedback and control command issuance, facilitating experimental monitoring and parameter debugging.

[0063] like Figure 6 As shown, the main controller collects angular velocity data measured by the inertial measurement unit (IMU) and current rotational speed values ​​fed back by the three momentum wheel motor drivers. The main controller also receives the calculated current visual attitude data from the analog star sensor controller. The main controller has a built-in attitude calculation and fusion program. After calculating the IMU angular velocity data, the calculated IMU angular velocity data and the calculated current visual attitude data are input to an error state Kalman filter for data fusion to obtain the optimal estimated unit quaternion. Based on the optimal estimated unit quaternion, the real-time estimate of the optimal three-axis attitude angle of the satellite model at the current moment is obtained. The attitude calculation and fusion program compares the optimal estimated unit quaternion with the preset target attitude quaternion to obtain the error quaternion. Simultaneously, it calculates the Kalman gain using the process noise covariance combined with the error state discrete dynamics equation. The attitude error is then obtained using the Kalman gain and the error quaternion.

[0064] like Figure 7 As shown, the specific content of the attitude calculation and fusion program is as follows:

[0065] S1, IMU attitude calculation, details are as follows:

[0066] The IMU, as the core inertial sensor of the system, provides high-frequency attitude prediction. Its calculation process is as follows:

[0067] S1.1 Acquisition of Raw Data

[0068] The main controller periodically reads the three-axis gyroscope data output by the MPU6050 sensor via the I2C bus, performs zero-bias correction and low-pass filtering on the raw data, and eliminates the effects of sensor noise and temperature drift.

[0069] S1.2 Quaternion Pose Update

[0070] Attitude is described using quaternions, and the quaternions are updated through gyroscope integration. The quaternion differential equation is:

[0071] ;

[0072] in, It is a quaternion. It is the angular velocity vector. This represents quaternion multiplication. Numerical integration using the first-order Runge-Kutta method yields the estimated quaternion value at the current time step.

[0073] S2. Simulated star sensor vision-based attitude calculation, as detailed below:

[0074] The simulated star sensor observes multiple point light sources ("star points") with a known spatial distribution through a camera, and calculates the absolute attitude of the carrier relative to a preset inertial coordinate system.

[0075] S2.1, Vector Observation of Star Points

[0076] After the camera captures an image, image processing (such as thresholding and speckle analysis) is used to extract the centroid pixel coordinates (u, v) of each point light source. The camera intrinsic parameter matrix is ​​then used... By inverse transformation of the perspective projection model, the unit direction observation vector of the point in the camera coordinate system is obtained. (Normalization in homogeneous coordinates):

[0077]

[0078] Observation vector This indicates the direction from the camera's optical center to the first... The direction of each "star point".

[0079] S2.2 Star point matching and attitude calculation

[0080] The system pre-stores a star map database, which contains the unit direction vector of each "star point" in the inertial coordinate system and its theoretical projection position in the image coordinate system. The core of attitude determination is solving for a rotation (represented by a rotation matrix R or a quaternion q) such that a set of observation vectors { The vector {ri} is optimally aligned with the corresponding reference vector {ri} in a least-squares sense. This is known as the Wahba problem.

[0081] The Davenport's Q-method used in this invention is a classic algorithm for solving the above problem. It does not explicitly solve for R, but directly solves for the optimal quaternion. .

[0082] ;

[0083] ;

[0084] The optimal solution to the Wahba problem is the unit eigenvector corresponding to the largest eigenvalue of matrix K. This eigenvector is the optimal pose quaternion we are looking for. This solution provides an absolute attitude observation relative to the inertial frame, without cumulative drift.

[0085] S3, IMU and star sensor data fusion

[0086] For high-frequency prediction of IMU Low-frequency absolute observations with star sensors This invention employs an error-state Kalman filter (ESKF). The specific steps are as follows:

[0087] (1) Coordinate system alignment

[0088] The quaternion obtained from the simulated star sensor represents the rotation from the inertial frame to the camera coordinate system. Using a pre-calibrated mounting matrix, the attitude is transformed to the carrier coordinate system (gyroscope coordinate system) aligned with the IMU using quaternion multiplication.

[0089] (2) Time synchronization

[0090] The system obtains timestamps and calculates the time difference dt between adjacent fusion cycles, which is used as the step size for the ESKF prediction step. IMU data is integrated within the dt interval, and star sensor data is asynchronously triggered to update upon arrival, achieving temporal alignment.

[0091] (3) ESKF fusion algorithm

[0092] ESKF uses IMU data as the nominal state prediction input and star sensor attitude observations as the observation update input.

[0093] It maintains two states:

[0094] The nominal state includes the attitude quaternion q and the gyroscope zero bias bg, and is directly driven by IMU data for integration.

[0095] The error state δx includes attitude error (usually represented as a 3D rotation vector) and zero bias error, among others. The error state is assumed to be a discrete, small quantity and is optimally estimated by a Kalman filter near zero.

[0096] The specific process of the ESKF fusion algorithm is as follows:

[0097] The attitude calculation and fusion program obtains the nominal state by performing quaternion integration on the IMU angular velocity measurements. After the attitude data observed by the simulated star sensor arrives, the state error between the nominal and observed attitudes is calculated. Then, the Kalman gain is obtained by combining the process noise covariance with the error state discrete dynamic equation. The error state δx of the optimal estimate is calculated, and then the nominal state is corrected by feedback.

[0098] State prediction (IMU driven):

[0099] This step is divided into two parts: nominal state prediction and error state covariance prediction.

[0100] The nominal state prediction uses IMU angular velocity measurements to compensate for the zero bias of the current estimate. Then, integrate the nominal attitude quaternion, referring to the IMU attitude calculation steps mentioned above.

[0101] When predicting the error state covariance, the discrete-time dynamic equation of the error state is used to predict the error covariance matrix. :

[0102] ;

[0103] in, The discrete error state transition matrix is... This is the discrete process noise covariance matrix. This step is performed at a high frequency (200Hz) using the IMU data rate.

[0104] Observation update (triggered by star sensor):

[0105] a) When the camera attitude observation quaternion data is received, calculate the error between the nominal attitude and the observed attitude, expressed as a rotation vector of relative rotation. .

[0106] b) Construct the observation matrix It is approximated that the relationship between the error state and the observation residual is linear, and the Kalman gain is calculated. and through and Update the error state estimate and the error covariance matrix :

[0107]

[0108]

[0109] c) Feedback the error state to correct the nominal attitude:

[0110] ;

[0111] The error state δx is then reset to zero. This step is triggered only when visual data arrives (10Hz).

[0112] (4) Fusion output

[0113] The fused pose data includes the optimally estimated unit quaternion. To meet the needs of higher-level applications such as control and human-computer interaction, this quaternion was converted into a more intuitive Euler angle representation.

[0114] a) Pitch angle: The angle of rotation about the Z-axis (vertical axis) of the carrier, indicating the orientation.

[0115] b) Roll angle: The angle of rotation about the Y-axis (starboard axis) of the carrier, indicating whether the vehicle is pitching up or down.

[0116] c) Yaw angle: The rotation angle about the X-axis (forward axis) of the carrier, indicating left and right tilt.

[0117] Even in areas without star sensor observation, the system can still provide high-frequency attitude angle output based on the IMU, ensuring the system's real-time performance. Once star sensor data arrives and triggers an update, the output value will immediately reflect this correction.

[0118] Through the aforementioned fusion mechanism, the pitch, roll, and yaw angles ultimately output by the system possess both the high dynamic response characteristics of the IMU and the absolute accuracy and long-term stability of the star sensor, thereby achieving high-precision and high-reliability real-time measurement of the carrier's three-axis attitude.

[0119] like Figure 6 and Figure 8 As shown, the main controller has a built-in momentum output calculation and control program. In the momentum output calculation and control program, the disturbance state observer estimates the lumped disturbance in real time and inputs the real-time estimate, attitude and angular velocity error together to the saturated sliding mode controller. The saturated sliding mode controller calculates the three-axis control torque vector required to make the system state converge to the sliding surface. Through the coordinate transfer matrix determined by the orthogonal installation geometry, the three-axis control torque vector is converted into the target speed command of the three momentum wheels.

[0120] like Figure 8 As shown, the specific contents of the momentum output calculation and control program are as follows:

[0121] Studies of the cube physical model show that the system has the following characteristics: frictional torque is often difficult to model with an accurate model, and even if a reasonable model is established, its parameters are difficult to accurately determine through experiments; parameters such as moment of inertia and gravitational lever arm need to be calibrated, and errors will inevitably be introduced during the measurement process; the measurement error of angular velocity will produce complex interference through coupling terms.

[0122] These characteristics require the control law to possess good robustness and the ability to handle nonlinear problems. Adaptive sliding mode control combined with feedback linearization becomes a superior choice. This invention uses a saturated sliding mode controller as the core control algorithm. Sliding mode control has strong robustness and is an effective method for handling nonlinear control problems. Simultaneously, a disturbance state observer is introduced to suppress complex disturbances in the system, ultimately verifying the feasibility of the simulation test system. The specific design is as follows:

[0123] (1) Design of the disturbance state observer:

[0124] Based on the conservation of total angular momentum, the dynamic equations of the cubic robot (1) are established as follows:

[0125]

[0126] in, This is the three-axis control torque vector; Here is the rotational inertia matrix; To control the target angular velocity;

[0127] These are known nonlinear terms in the dynamic equations; For total disturbance; total disturbance As the quantity to be estimated, a perturbation state observer is designed by treating the total perturbation as an "extended state":

[0128]

[0129] in, This is the three-axis control torque vector; This is an estimate of the angular velocity of the cubic robot; This is the estimated total disturbance. This represents the angular velocity estimation error.

[0130] The nonlinear function is defined as follows: , .

[0131] Theoretical and practical verification has shown that the estimation error of such observers can converge within a finite time.

[0132] (2) Design of saturated sliding mode controller:

[0133] This invention presents a saturated sliding mode controller based on quaternion attitude error. This controller combines feedforward compensation and robust feedback to effectively handle the system's nonlinear dynamics, model uncertainties, and external disturbances, ensuring global stability and good dynamic performance.

[0134] The control objective is to design a control law. This allows the actual attitude quaternion q and angular velocity ω of the carrier to asymptotically and stably track any given desired target attitude quaternion. and angular velocity (In the problem of postural calming, it is usually assumed that...) =0).

[0135] To achieve a calm posture for the target, we first define the error between the current posture quaternion and the target quaternion. For the target quaternion... and the current quaternion There exists a continuous rotation make Multiply both sides of the equation achievable .

[0136] Under the same polarity, define the angular velocity error (when the desired angular velocity is 0):

[0137] Sliding mode control requires selecting a linear sliding surface and constructing a control law to drive the system state to reach and remain on the sliding surface within a finite time, thereby achieving invariance to matched disturbances and parameter perturbations.

[0138]

[0139] The sliding surface s=0 defines an ideal error dynamic.

[0140]

[0141] This relationship guarantees the attitude error. It will converge to zero according to an exponential law.

[0142] The control input consists of two parts: equivalent control and robust control.

[0143]

[0144] (a) Equivalent control

[0145] Design based on nominal model:

[0146]

[0147] Equivalent control is used to counteract the nominal nonlinear dynamics of the system and known lumped disturbances. To achieve the ideal sliding mode.

[0148] (b) Robust control

[0149] A continuous robust term of the saturation function is used to suppress chattering caused by the traditional sign function:

[0150]

[0151] in, Here is the rotational inertia matrix. The robust gain matrix; Let be the boundary layer thickness vector, where |s| ≤ Inside the boundary layer, the control law is a continuous linear state feedback, which effectively eliminates chattering; outside the boundary layer, its behavior is similar to traditional variable structure control, providing strong robustness. Robust control is used to overcome model uncertainties, estimation errors, and uncompensated disturbances, ensuring that the system state can still reach the sliding surface even in the presence of these uncertainties.

[0152] Based on the above design, the complete saturated sliding mode control principle is obtained, and the calculation formula for the three-axis control torque vector is as follows:

[0153] ;

[0154] in, This is the three-axis control torque vector; These are known nonlinear terms in the dynamic equations; For lumped interference; Here is the rotational inertia matrix; The robust gain matrix; This is the boundary layer thickness vector.

[0155] By appropriately selecting the gain matrix K and boundary layer Based on Lyapunov stability theory, it can be proven that the control law can guarantee that all signals of the closed-loop system are bounded and that the attitude error quaternion is minimized. and angular velocity error The system asymptotically converges to a neighborhood of zero. Ultimately, the system achieves high-precision and robust attitude stabilization control.

[0156] (3) Control torque distribution

[0157] The three-axis control torque is distributed to the three momentum wheels through coordinate transformation. A transition matrix is ​​established between the IMU coordinate system and the 19. motor coordinate system. This matrix is ​​determined based on the geometric relationship of the triaxial orthogonal mounting. The control torque distribution formula is:

[0158] ;

[0159] in, The target rotational speed vectors of the three momentum wheels; This is the three-axis control torque vector.

[0160] The control execution flow of the main controller in the demonstration system of this invention is as follows:

[0161] Step 1, Data Acquisition: The main controller reads data from two types of sensors in parallel at a fixed frequency of 200Hz: first, the three-axis angular velocity data in the satellite model's body coordinate system measured in real time by the six-axis inertial measurement unit (IMU); second, the current rotational speed values ​​fed back by the three momentum wheel motor drivers. These two types of data have strict time synchronization, providing a unified time base for subsequent accurate calculations.

[0162] Step 2, Attitude Calculation: This step receives IMU angular velocity data from Step 1 and asynchronously receives visual attitude data from the simulated star sensor (camera). The angular velocity data is integrated using quaternions to obtain the angular velocity quaternion, while the simulated star sensor directly obtains the current observed attitude quaternion. These two types of data, with different characteristics and noise levels, are input into an Error State Kalman Filter (ESKF) for data fusion. The ESKF effectively combines the high dynamic response characteristics of the IMU with the absolute accuracy advantage of visual observation to obtain real-time estimates of the satellite model's optimal three-axis attitude angles (pitch, roll, yaw) at the current moment, providing a reliable state basis for control decisions.

[0163] Step 3, Error Calculation: After obtaining the accurate current attitude state, the attitude calculation and fusion program compares the optimal estimated unit quaternion with the preset target attitude quaternion to obtain the error quaternion. At the same time, it uses the process noise covariance combined with the error state discrete dynamic equation to calculate the Kalman gain, and uses the Kalman gain and the error quaternion to obtain the attitude error.

[0164] Step 4, Control Law Calculation: Combine the real-time estimated optimal three-axis attitude angles obtained in Step 2, the attitude error calculated in Step 3, the angular velocity measured by the inertial measurement unit, and the lumped disturbance estimated in real-time by the disturbance state observer. The inputs are fed into the saturated sliding mode controller. Based on the control law designed in Section 4.2, the controller calculates the three-axis control torque vector required to converge the system state to the sliding surface. .

[0165] Step 5, Torque Distribution: This is achieved through a coordinate transition matrix determined by the orthogonal installation geometry of the momentum wheel. The three-axis control torque vector is converted into target speed command vectors for the three momentum wheels. This transforms abstract control quantities into specific speed commands that the motor can execute.

[0166] Step 6, Command Transmission: The final step in the process is to convert the digital commands into physical actions. The target speed command vector generated in Step 5 is sent to the electronic speed controllers of the brushless DC motors corresponding to the three momentum wheels via the motor drive circuit. The electronic speed controllers drive the motors to accelerate or decelerate until the specified speed is reached. The change in the speed of the momentum wheels will generate the required reaction torque, which acts directly on the satellite model body, thereby achieving precise, closed-loop adjustment of the model's attitude and completing the execution of the entire control cycle.

[0167] The demonstration system of this invention has the following workflow:

[0168] The complete workflow of the system of this invention is a closed-loop control system consisting of "perception-decision-execution", the core of which is based on Figure 5 The system flow diagram shown tightly integrates the attitude sensing subsystem and the control execution subsystem. The entire process begins with system power-on initialization, followed by a stable real-time control loop. The specific steps are as follows:

[0169] Step 1: System Initialization

[0170] After the system powers on, it first performs a series of self-tests and initialization operations to lay the foundation for subsequent real-time control. The main controller sequentially detects and calibrates the hardware interfaces and sensors, loads preset control parameters, and simultaneously starts and resets the momentum wheel drive module. At the software level, the core algorithm modules—the error state Kalman filter for attitude fusion and the disturbance state observer for disturbance estimation—complete the initialization of their internal state variables, ensuring that all hardware and software modules are in a ready state.

[0171] Step 2: Posture-Aware Loop

[0172] After initialization, the system enters a high-frequency data acquisition and fusion loop running at a fixed frequency of 200Hz. During this loop, the attitude perception subsystem operates continuously: the IMU provides raw three-axis angular velocity data of the satellite model at a frequency of 200Hz, driving the attitude fusion algorithm to execute prediction steps and achieve high-frequency attitude recursion; simultaneously, the simulated star sensor provides drift-free absolute attitude observation data asynchronously at a lower frequency, triggering the algorithm's update step to correct for integral drift. This loop ultimately outputs high-precision, high-dynamic-response optimal estimates of the three-axis attitude angles and angular velocities.

[0173] Step 3: Controlling the calculation loop

[0174] Synchronized with the attitude sensing loop, the core control program in the control execution subsystem runs at the same frequency. Upon receiving the latest attitude and angular velocity estimates, the program immediately calculates the error between the current attitude and the target attitude. Subsequently, the saturated sliding mode control algorithm, combined with the total disturbance estimate provided in real-time by the disturbance state observer, calculates the real-time three-axis control torque. Finally, through the control torque allocation algorithm, the control torque vector is converted into target speed commands for each of the three momentum wheels, completing the decision-making process from state information to execution commands.

[0175] Step 4: Posture Adjustment Execution

[0176] This step translates digital control commands into physical actions, achieving closed-loop control. The target rotational speed command generated by the control calculation cycle is sent in real time to three orthogonally mounted momentum wheel actuators. Each momentum wheel accelerates or decelerates according to the command, generating the required reaction control torque by changing its own angular momentum. This torque acts on the entire satellite model through the cubic frame, driving it to rotate around the corresponding axis in the three-axis support platform, thereby achieving precise and robust adjustment of the satellite model's attitude. Simultaneously, the system transmits attitude data to a host computer via Wi-Fi, and the host computer interface is shown below. Figure 9 As shown.

[0177] Step 5: Counterweight Adjustment (Debugging Phase)

[0178] Before the system is put into high-precision control operation, debugging steps are required to optimize performance and suppress unbalanced torque interference caused by the misalignment of the center of gravity and geometric center. The aforementioned adjustment scheme is adopted.

[0179] This invention can simulate the weightlessness of a satellite, measure its attitude data in real time and display it on a host computer, and control its attitude to overcome external disturbances and maintain a horizontal position or adjust it to a preset angle. Compared with other similar inventions, its physical structure is simpler and more direct, making it suitable as a teaching demonstration device.

[0180] This invention constructs a teaching simulation platform for students to experiment with satellite control. The operation of each component involves fundamental knowledge that undergraduate students in related majors should master, and it fully embodies the basic principles of satellite navigation. As an innovative teaching demonstration platform, this platform can be used to develop and verify different control algorithms and strategies for various space missions, stimulating students' interest in designing simulated satellites and encouraging them to actively engage with related aerospace projects. Further development can be carried out on this device to incorporate other experiments, such as solar panel deployment experiments, radar simulation experiments with cameras, astronomical navigation simulation experiments, and so on.

Claims

1. A satellite attitude control demonstration system simulating weightlessness, characterized in that: Including a cubic robot (1) and a three-axis rotary table (2); The three-axis rotary table (2) includes a base (6) and an annular fixing member (9) vertically installed above the base (6). The fixing member (9) is provided with an outer ring (8), a middle ring (5) and an inner ring (4) in sequence. The inner circle (4) is a cubic frame, and the cubic robot (1) is embedded inside the inner circle (4); The inner ring (4) is rotatably connected to the middle ring (5) through the inner ring bracket (3). The middle ring (5) is installed inside the outer ring (8) through the connector (7) and bearing. Axial interference will occur between the inner ring (4) and the middle ring (5) and between the middle ring (5) and the outer ring (8). The inner ring (4) rotates around the X-axis to achieve rolling motion, the middle ring (5) rotates around the Y-axis to achieve pitch motion, and the outer ring (8) rotates around the Z-axis to achieve yaw motion, thereby realizing the free rotation of the cube robot (1) around the X, Y, and Z axes, and thus simulating the three-dimensional attitude motion of the satellite in a weightless environment. During the free rotation of the cubic robot (1) around the X, Y, and Z axes, axial interference will generate frictional torque. The frictional torque will counteract the eccentric torque caused by the shift of the center of gravity, thereby achieving interference suppression.

2. The satellite attitude control demonstration system under simulated weightlessness as described in claim 1, characterized in that: The cube robot (1) is in the shape of a cube. The upper surface of the cube is fixed with an attitude perception system. The inside of the cube is fixed with a motherboard (16). The motherboard (16) is equipped with a main controller. The inner wall of the cube is equipped with a control execution system. The main controller is used to process the attitude data measured by the attitude sensing system and generate control commands. The control execution system then performs actions based on these control commands to achieve satellite attitude adjustment.

3. The satellite attitude control demonstration system under simulated weightlessness as described in claim 2, characterized in that: The attitude sensing system includes an IMU board (11) and an analog star sensor (13), wherein the IMU board (11) integrates an inertial measurement unit; The IMU board (11) and the analog star sensor (13) are on the same plane; The inertial measurement unit is used to measure the raw data of the three-axis angular velocity in the coordinate system of the satellite model in real time, as IMU angular velocity data; the simulated star sensor (13) is used to observe visual attitude data; the simulated star sensor (13) is equipped with a simulated star sensor controller, the simulated star sensor controller acquires the current visual attitude data observed by the simulated star sensor (13), and performs calculation on the current visual attitude data, and sends the calculated current visual attitude data to the main controller.

4. The satellite attitude control demonstration system under simulated weightlessness as described in claim 3, characterized in that: The main controller acquires the IMU angular velocity data measured by the inertial measurement unit and the current rotational speed values ​​fed back by the three momentum wheel motor drivers. The main controller also receives the current visual attitude data after being solved by the analog star sensor controller. The main controller has a built-in attitude calculation and fusion program. After the attitude calculation and fusion program calculates the IMU angular velocity data, the calculated IMU angular velocity data and the calculated current visual attitude data are input to the error state Kalman filter for data fusion to obtain the optimal estimated unit quaternion. Based on the optimal estimated unit quaternion, the real-time estimated value of the optimal three-axis attitude angle of the satellite model at the current moment is obtained. The attitude calculation and fusion program compares the optimal estimated unit quaternion with the preset target attitude quaternion to obtain the error quaternion. At the same time, it uses the process noise covariance combined with the error state discrete dynamic equation to calculate the Kalman gain, and uses the Kalman gain and the error quaternion to obtain the attitude error.

5. The satellite attitude control demonstration system under simulated weightlessness environment according to claim 2, characterized in that: The main controller has a built-in momentum output calculation and control program. In the momentum output calculation and control program, the disturbance state observer estimates the lumped disturbance in real time and inputs the real-time estimated values ​​of the three-axis attitude angles, attitude error and IMU angular velocity data measured by the inertial measurement unit into the saturated sliding mode controller. The saturated sliding mode controller calculates the three-axis control torque vector required to make the satellite attitude control demonstration system converge to the sliding surface. Through the coordinate transfer matrix determined by the orthogonal installation geometry, the three-axis control torque vector is converted into the target rotation speed command of the three momentum wheels.

6. The satellite attitude control demonstration system under simulated weightlessness as described in claim 5, characterized in that: The perturbation state observer is designed as follows: Based on the conservation of total angular momentum, the dynamic equations of the cubic robot (1) are established as follows: ； in, This is the three-axis control torque vector; Here is the rotational inertia matrix; To control the target angular velocity; These are known nonlinear terms in the dynamic equations; For total disturbance; total disturbance As the quantity to be estimated, a perturbation state observer is designed by treating the total perturbation as an extended state: ； in, This is the three-axis control torque vector; This is an estimate of the angular velocity of the cubic robot; This is the estimated total disturbance. This represents the angular velocity estimation error. The nonlinear function is defined as follows: , .

7. The satellite attitude control demonstration system under simulated weightlessness as described in claim 5, characterized in that: The formula for calculating the three-axis control torque vector is as follows: ； in, This is the three-axis control torque vector; These are known nonlinear terms in the dynamic equations; For lumped interference; Here is the rotational inertia matrix; The robust gain matrix; This is the boundary layer thickness vector.

8. The satellite attitude control demonstration system under simulated weightlessness environment according to claim 2, characterized in that: The control execution system includes three motors (18) and three momentum wheels (19). One motor (18) and one momentum wheel (19) constitute a set of execution mechanisms. The three sets of execution mechanisms are respectively installed inside the three mutually orthogonal surfaces of the cubic robot (1).

9. The satellite attitude control demonstration system under simulated weightlessness as described in claim 1, characterized in that: The cube robot (1) is equipped with a fixed power supply system (15), which includes a camera board battery and a motherboard battery. The camera board battery is used to power the analog star sensor (13), and the motherboard battery is used to power the motherboard (16).

10. The satellite attitude control demonstration system under simulated weightlessness environment according to claim 2, characterized in that: The motherboard (16) is equipped with a communication system, which includes a built-in Bluetooth module and a built-in WIFI module; The built-in Bluetooth module is used to input the current attitude data observed by the simulated star sensor (13) into the attitude calculation and fusion program; the built-in WIFI module is wirelessly connected to the external host computer system.

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