A laser communication terminal attitude control method and system based on Lie algebra

Abstract

The application discloses a laser communication terminal attitude control method and system based on Lie algebra, relates to the technical field of a spaceborne laser communication terminal, and aims at the problem that the existing chip has a high occupation rate of a calculation unit, a long operation time, and thus the spaceborne laser communication terminal cannot be controlled in real time. First, a traditional spacecraft orbit and attitude motion model is introduced, which describes the motion and dynamic characteristics of a laser communication load pointing and aiming in a spacecraft body coordinate system through multiple equations. Then, Lie groups are introduced to integrally describe the motion and dynamic equations of the laser communication load aiming process. The application greatly reduces the occupation rate of the calculation unit of the on-board chip, reduces the demand for storage resources, thus adapts to the limited resource environment on the satellite, and solves the problem that the laser communication terminal cannot be controlled in real time.

Description

Technical Field

[0001] This application relates to the field of spaceborne laser communication terminal technology, specifically to a laser communication terminal attitude control method and system based on Lie algebra. Background Technology

[0002] In laser communication terminal application scenarios, especially in the field of spaceborne laser communication terminals, on-board resources have significant limitations. Specifically, the storage capacity of on-board chips is limited, and the data processing and computing capabilities are generally limited, making it impossible to carry out highly complex and resource-intensive computing tasks.

[0003] Currently, the conventional attitude matrix transformation method used in laser communication terminals relies heavily on multiplication and division operations to achieve attitude data transformation. These operations result in high occupancy rates of the chip's computing units and long processing times, leading to the inability of spaceborne laser communication terminals to perform real-time control. Summary of the Invention

[0004] The purpose of this invention is to address the problem that existing chips have high computational unit occupancy and long computation time, which leads to the inability of spaceborne laser communication terminals to be controlled in real time, by providing a laser communication terminal attitude control method and system based on Lie algebra.

[0005] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0006] A laser communication terminal attitude control method based on Lie algebra includes the following steps:

[0007] Step 1: Obtain the laser communication terminal attitude matrix at the current moment. Satellite attitude matrix And the satellite's position vector;

[0008] Step 2: Based on the attitude matrix of the laser communication terminal and satellite attitude matrix The Lie algebra vector of the laser communication terminal is obtained. And based on the Lie algebra vector of the laser communication terminal Construct the orbital attitude coupling kinematic equations of the spacecraft;

[0009] Step 3: Based on the spacecraft's attitude-orbit coupling kinematic equations, construct the integrated attitude-orbit coupling dynamic equations of the laser communication terminal and the satellite;

[0010] Step 4: Set the current laser communication terminal attitude matrix. Satellite attitude matrix The satellite's position vector is input into the integrated attitude and orbit coupling dynamic equation of the laser communication terminal-satellite, and the attitude matrix of the laser communication terminal at the next moment is obtained.

[0011] Step 5: Based on the attitude matrix of the laser communication terminal at the next moment. Adjust the attitude of the current laser communication terminal.

[0012] Furthermore, the specific steps of step 2 are as follows:

[0013] Step 21: Utilize the attitude matrix of the laser communication terminal and satellite attitude matrix Construct the mounting matrix of the payload relative to the satellite body. , Represented as:

[0014] ;

[0015] Step 22: Using the checkerboard calibration method, obtain the transformation matrix belonging to SE(3) between the camera coordinate system and the coordinate system of the laser communication terminal. Transformation matrix Represented as:

[0016]

[0017] in, The rotation matrix from the camera to the laser. It is a translation vector;

[0018] Step 23: Transform the matrix Perform the adjoint mapping to obtain the matrix. ,matrix Represented as:

[0019]

[0020] Step 24: Obtain the camera pose of the laser communication terminal, and perform a logarithmic mapping on the camera pose to obtain the Lie algebra vector of the camera pose. ,in, To pan the camera, Rotate the camera;

[0021] Step 25: Based on the matrix Lie algebra vectors of camera pose The Lie algebra vector of the laser communication terminal is obtained. Lie algebra vector of laser communication terminal Represented as:

[0022] ;

[0023] Step 26: For the Lie algebra vector of the laser communication terminal By performing exponential mapping, the attitude matrix of the laser communication terminal is obtained. ;

[0024] Step 27: Obtain the measured attitude matrix of the laser communication terminal ,like If the result is positive, proceed to step 28; otherwise, proceed to step 24 to reacquire the camera pose of SLAM.

[0025] Step 28: Set the attitude matrix of the laser communication terminal The desired attitude matrix for laser communication payload pointing adjustment And combined with the installation matrix of the payload relative to the satellite body The desired attitude matrix that the satellite body needs to be adjusted to is obtained. The desired attitude matrix that the satellite body needs to be adjusted to. Represented as:

[0026]

[0027] Step 29: Based on the desired attitude matrix that the satellite body needs to be adjusted to And combined with the satellite's attitude matrix The attitude error matrix of the satellite body is obtained. Satellite attitude error matrix Represented as;

[0028]

[0029] Step 210: Convert the satellite's attitude error matrix Perform a logarithmic mapping to obtain the Lie algebra vector. Lie algebra vector Represented as:

[0030]

[0031] Step 211: Based on Lie algebra vectors Design control law Control Law Represented as:

[0032]

[0033] in, This is the proportional gain matrix;

[0034] Step 212: Obtain the position vector of the laser communication terminal or the satellite itself. ,use and satellite attitude matrix Construct binary tuples ( ), and then use the tuple ( ) obtained Li Qun Li Qun Represented as:

[0035]

[0036] in, It is a special orthogonal group;

[0037] Step 213: Obtain the Lie group homogeneous form and in a uniform form Lie algebra vector :

[0038]

[0039]

[0040] in, , yes The antisymmetric matrix, i.e.:

[0041]

[0042] Step 214: Based on homogeneous form and Lie algebra vectors The orbital attitude coupled kinematic equations of the spacecraft are constructed as follows:

[0043] .

[0044] Furthermore, step 3 specifically involves:

[0045] Step 31: For Lie algebra vectors By performing the adjoint mapping, we obtain the adjoint operator of the Lie algebra. And utilize the adjoint operator of Lie algebras Obtain the inverse adjoint operator , is represented as:

[0046] ;

[0047] Step 32: Utilize and anti-adjoint operator The attitude and orbit coupling dynamic equation of the laser communication terminal-satellite integrated system based on SE(3) is obtained, which is expressed as:

[0048]

[0049] in, For laser communication terminal-satellite integrated inertial matrix, To control the input, , The torque for adjusting the attitude of the laser communication terminal, i.e. , For satellite orbit control force, External interference , Including micro-vibration interference from laser communication terminals, Including solar radiation pressure interference, ) is a generalized force term that includes gravitational gradient torque and gravity.

[0050] Furthermore, the laser communication terminal-satellite integrated inertial matrix Represented as:

[0051]

[0052] in, The moment of inertia of the laser communication terminal. For satellite quality, It is a third-order identity matrix.

[0053] Furthermore, the measured laser communication terminal attitude matrix Obtained using a star-sensitive gyroscope.

[0054] A laser communication terminal attitude control system based on Lie algebra, the system including a data acquisition module, a kinematic equation construction module, a dynamic equation construction module and an attitude control module;

[0055] The data acquisition module is used to acquire the laser communication terminal attitude matrix at the current moment. Satellite attitude matrix And the satellite's position vector;

[0056] The kinematic equation construction module is based on the attitude matrix of the laser communication terminal. and satellite attitude matrix The Lie algebra vector of the laser communication terminal is obtained. And based on the Lie algebra vector of the laser communication terminal Construct the orbital attitude coupling kinematic equations of the spacecraft;

[0057] The dynamic equation construction module constructs an integrated attitude-orbit coupling dynamic equation for a laser communication terminal and a satellite based on the spacecraft's orbital attitude coupling kinematic equation.

[0058] The attitude control module is used to set the current attitude matrix of the laser communication terminal. Satellite attitude matrix The satellite's position vector is input into the integrated attitude and orbit coupling dynamics equations of the laser communication terminal and the satellite to obtain the attitude matrix of the laser communication terminal at the next moment. Based on the attitude matrix of the laser communication terminal at the next moment... Adjust the attitude of the current laser communication terminal.

[0059] Furthermore, the kinematic equation construction module specifically performs the following steps:

[0060] Step 21: Utilize the attitude matrix of the laser communication terminal and satellite attitude matrix Construct the mounting matrix of the payload relative to the satellite body. , Represented as:

[0061] ;

[0062] Step 22: Using the checkerboard calibration method, obtain the transformation matrix belonging to SE(3) between the camera coordinate system and the coordinate system of the laser communication terminal. Transformation matrix Represented as:

[0063]

[0064] in, The rotation matrix from the camera to the laser. It is a translation vector;

[0065] Step 23: Transform the matrix Perform the adjoint mapping to obtain the matrix. ,matrix Represented as:

[0066]

[0067] Step 24: Obtain the camera pose of the laser communication terminal, and perform a logarithmic mapping on the camera pose to obtain the Lie algebra vector of the camera pose. ,in, To pan the camera, Rotate the camera;

[0068] Step 25: Based on the matrix Lie algebra vectors of camera pose The Lie algebra vector of the laser communication terminal is obtained. Lie algebra vector of laser communication terminal Represented as:

[0069] ;

[0070] Step 26: For the Lie algebra vector of the laser communication terminal By performing exponential mapping, the attitude matrix of the laser communication terminal is obtained. ;

[0071] Step 27: Obtain the measured attitude matrix of the laser communication terminal ,like If the result is positive, proceed to step 28; otherwise, proceed to step 24 to reacquire the camera pose of SLAM.

[0072] Step 28: Set the attitude matrix of the laser communication terminal The desired attitude matrix for laser communication payload pointing adjustment And combined with the installation matrix of the payload relative to the satellite body The desired attitude matrix that the satellite body needs to be adjusted to is obtained. The desired attitude matrix that the satellite body needs to be adjusted to. Represented as:

[0073]

[0074] Step 29: Based on the desired attitude matrix that the satellite body needs to be adjusted to And combined with the satellite's attitude matrix The attitude error matrix of the satellite body is obtained. Satellite attitude error matrix Represented as;

[0075]

[0076] Step 210: Convert the satellite's attitude error matrix Perform a logarithmic mapping to obtain the Lie algebra vector. Lie algebra vector Represented as:

[0077]

[0078] Step 211: Based on Lie algebra vectors Design control law Control Law Represented as:

[0079]

[0080] in, This is the proportional gain matrix;

[0081] Step 212: Obtain the position vector of the laser communication terminal or the satellite itself. ,use and satellite attitude matrix Construct binary tuples ( ), and then use the tuple ( ) obtained Li Qun Li Qun Represented as:

[0082]

[0083] in, It is a special orthogonal group;

[0084] Step 213: Obtain the Lie group homogeneous form and in a uniform form Lie algebra vector :

[0085]

[0086]

[0087] in, , yes The antisymmetric matrix, i.e.:

[0088]

[0089] Step 214: Based on homogeneous form and Lie algebra vectors The orbital attitude coupled kinematic equations of the spacecraft are constructed as follows:

[0090] .

[0091] Furthermore, the dynamic equation construction module specifically performs the following steps:

[0092] Step 31: For Lie algebra vectors By performing the adjoint mapping, we obtain the adjoint operator of the Lie algebra. And utilize the adjoint operator of Lie algebras Obtain the inverse adjoint operator , is represented as:

[0093] ;

[0094] Step 32: Utilize and anti-adjoint operator The attitude and orbit coupling dynamic equation of the laser communication terminal-satellite integrated system based on SE(3) is obtained, which is expressed as:

[0095]

[0096] in, For laser communication terminal-satellite integrated inertial matrix, To control the input, , The torque for adjusting the attitude of the laser communication terminal, i.e. , For satellite orbit control force, External interference , Including micro-vibration interference from laser communication terminals, Including solar radiation pressure interference, ) is a generalized force term that includes gravitational gradient torque and gravity.

[0097] Furthermore, the laser communication terminal-satellite integrated inertial matrix Represented as:

[0098]

[0099] in, The moment of inertia of the laser communication terminal. For satellite quality, It is a third-order identity matrix.

[0100] Furthermore, the measured laser communication terminal attitude matrix Obtained using a star-sensitive gyroscope.

[0101] The beneficial effects of this invention are:

[0102] This application first introduces a traditional spacecraft orbit and attitude motion model, which describes the motion and dynamic characteristics of the laser communication payload's pointing and aiming through multiple sets of equations in the spacecraft's coordinate system. Then, a Lie group is introduced to provide an integrated description of the motion and dynamic equations of the laser communication payload's aiming process. This application significantly reduces the occupancy rate of onboard chip computing units and decreases the demand for storage resources, thereby adapting to the limited resources onboard and solving the problem of the laser communication terminal's inability to be controlled in real time. Detailed Implementation

[0103] It should be noted that, where there is no conflict, the various embodiments disclosed in this application can be combined with each other.

[0104] Specific Implementation Method 1: The laser communication terminal attitude control method based on Lie algebra described in this implementation method includes the following steps:

[0105] Step 1: Obtain the laser communication terminal attitude matrix at the current moment. Satellite attitude matrix And the satellite's position vector;

[0106] Step 2: Based on the attitude matrix of the laser communication terminal and satellite attitude matrix The Lie algebra vector of the laser communication terminal is obtained. And based on the Lie algebra vector of the laser communication terminal Construct the orbital attitude coupling kinematic equations of the spacecraft;

[0107] Step 3: Based on the spacecraft's attitude-orbit coupling kinematic equations, construct the integrated attitude-orbit coupling dynamic equations of the laser communication terminal and the satellite;

[0108] Step 4: Set the current laser communication terminal attitude matrix. Satellite attitude matrix The satellite's position vector is input into the integrated attitude and orbit coupling dynamic equation of the laser communication terminal-satellite, and the attitude matrix of the laser communication terminal at the next moment is obtained.

[0109] Step 5: Based on the attitude matrix of the laser communication terminal at the next moment. Adjust the attitude of the current laser communication terminal.

[0110] 1. Establish the mapping relationship between the attitude matrix and Lie algebra.

[0111] The attitude matrix of the laser communication terminal belongs to a special orthogonal group. ,and The corresponding Lie algebra is Space. From a mathematical perspective, there exists a Lie group. To Lie algebra logarithmic mapping The mapping is smooth. For any There exists a unique (This is a Lie algebra vector), satisfying: [Application] in, yes The antisymmetric matrix form is expressed as:

[0112]

[0113] At the same time, there is also an exponential mapping. Together with the logarithmic mapping (log), it establishes a bidirectional transformation relationship between the attitude matrix and the Lie algebra vector. When transforming from the attitude matrix to the Lie algebra vector, the logarithmic mapping is used. The attitude matrix can be Transform into a three-dimensional vector in Lie algebra space ,Right now: here Indicates the origin from antisymmetric matrices (Lie algebras) (elements in) to a three-dimensional vector ( The transformation operation (of elements in the vector) is performed. Furthermore, the attitude information represented by this 3D vector is complete, and its operation rules are better suited to the needs of lightweight computing.

[0114] 2. Application for a pose update operation design based on Lie algebra vectors

[0115] In the attitude update process of laser communication terminal, the multiplication and division operations between attitude matrices in the conventional method are no longer used. Instead, the initial attitude matrix and incremental attitude matrix to be updated are first converted into corresponding Lie algebra vectors through logarithmic mapping.

[0116] First, the initial pose matrix and incremental attitude matrix respectively through logarithmic mapping Convert to the corresponding Lie algebra vector, and denote the initial Lie algebra vector as... ,satisfy The incremental Lie algebra vector is ,satisfy .

[0117] Then, in the Lie algebra space, for the initial Lie algebra vector with incremental Lie algebra vectors Perform addition to obtain the updated Lie algebra vector. Then, in the Lie algebra space, considering the noncommutativity of Lie group multiplication, we apply the BCH (Browser-Champion-Champion) approach to apply the left linear approximation to the initial Lie algebra vector. with incremental Lie algebra vectors Perform addition to obtain the updated Lie algebra vector: (Application)

[0118] in Let be the left Jacobian matrix, used to compensate for nonlinear errors in Lie group multiplication, and its expression is:

[0119]

[0120] Application in the form Let the magnitude of the Lie algebra vector be the rotation angle. The unit vector of the rotation axis; when applying When applying This degenerates into addition, balancing accuracy and compatibility. This addition operation can replace the multiplication of the attitude matrix in conventional methods. Based on the exponential mapping property of Lie groups and Lie algebras, when... When the quantity is small, there is an approximate relationship: In precise scenarios, Lie algebra operations can be used to strictly correlate matrix multiplication and division, thus avoiding complex matrix multiplication and division calculations.

[0121] 3. Request the reconstruction of the updated attitude matrix

[0122] The updated Lie algebra vector Through exponential mapping Perform the transformation. For Lie algebra vectors Its corresponding attitude matrix It can be obtained by calculating the matrix exponent: Here, will Replace with , obtained that is The attitude matrix in space is the updated target attitude matrix of the laser communication terminal, which can be directly used for the attitude control of the terminal and the adjustment of the laser communication link.

[0123] 4. Apply for a computational precision calibration mechanism

[0124] To ensure that the conversion accuracy is consistent with conventional methods, an accuracy calibration module is introduced before and after the addition operation of Lie algebra vectors: a preset error threshold is used. (For example, the attitude angle error threshold is set to) Corresponding radian value This involves real-time verification of the results of three key steps: logarithmic mapping, addition, and exponential mapping. Let the result of step k (where k_application = application 1, 2, and 3 correspond to logarithmic mapping, addition, and exponential mapping respectively) be... The reference result is ,error .like The compensation algorithm is triggered on the Lie algebra vector. Fine-tuning can be performed using a compensation algorithm based on a Lie algebra perturbation model: A small perturbation is applied to obtain the perturbed attitude matrix. (Application details omitted) This represents converting a 3-dimensional Lie algebra vector into an antisymmetric matrix. An error function is defined for this purpose. ,in The application is for the reference attitude matrix measured by star-sensors. The application is based on the Frobenius norm. The optimal perturbation application is solved using the least squares method. The final adjusted Lie algebra vector is used to ensure the attitude angle error. The adjustment amount is... ,satisfy:

[0125] Ensure that the accuracy of the final output attitude matrix meets the working requirements of the laser communication terminal.

[0126] This application combines Lie groups (SE(3)) to model the laser communication payload and satellite attitude in an integrated manner, while also considering the binding and adjustment of the laser communication payload and the satellite attitude. First, a traditional spacecraft orbit and attitude motion model is introduced, which describes the motion and dynamic characteristics of the laser communication payload pointing and aiming in the spacecraft coordinate system through multiple sets of equations. Then, a Lie group application is introduced to provide an integrated description of the motion and dynamic equations of the laser communication payload aiming process.

[0127] (1) Binding relationship between laser communication payload and satellite attitude

[0128] To achieve integrated representation of satellite orbital position and laser terminal attitude, the homogeneous pose matrix SE(3) is defined. The application proposes to unify the representation of the satellite's geocentric inertial frame position vector and the laser terminal's inertial frame attitude matrix as follows:

[0129]

[0130] Among the applications To obtain the satellite's position coordinates in an inertial frame, apply for... It can simultaneously characterize orbital translation and terminal rotation, enabling integrated storage and calculation of orbital attitude parameters. Let the satellite body coordinate system be B, and the laser communication payload coordinate system be L. Define the payload's mounting matrix relative to the satellite body as follows: (This matrix is ​​a constant, determined by the mounting structure.) Then, the attitude matrix of the laser communication payload... (Relative to inertial frame I) and satellite attitude matrix The binding relationship is as follows: To reuse the Lie algebra pose calculation results from the visual SLAM application, it is necessary to establish the transformation relationship between the camera coordinate system (C) and the laser terminal coordinate system (L) of the SLAM application.

[0131] Through a checkerboard calibration experiment, the SE(3) transformation matrix of the two coordinate systems was obtained. A fixed laser terminal and camera are used to capture images of a checkerboard pattern for solving the problem. (Application) Among them, applications Let be the rotation matrix from the camera to the laser, and be the translation vector, which are solved using the calibration method during calibration. Let the Lie algebra vector of the camera pose output by the SLAM request be , where To pan the camera, The application is for camera rotation, referring to the visual application SLAM application definition, and is converted into the Lie algebra vector application of the laser terminal by the application SE(3) adjoint mapping. Where the adjoint mapping The application expression is an application. The laser terminal attitude matrix will be obtained through exponential mapping and compared with the star-sensor's measured value. An error assessment is required. This corresponds to the attitude angle error, ensuring the effectiveness of the conversion.

[0132] (2) Control input for laser communication payload pointing adjustment

[0133] Let the desired attitude matrix for laser communication payload pointing adjustment be... Based on the binding relationship, the satellite body needs to be adjusted to the desired attitude matrix. satisfy: Define the satellite attitude error matrix. Transform it into a Lie algebra vector through a logarithmic mapping. Based on this error, the control input is designed. To adjust the satellite's attitude to meet payload pointing requirements, the control law can be designed as follows (taking proportional control as an example): in This is the proportional gain matrix.

[0134] The attitude motion of a spacecraft is described using the direction cosine matrix. Matrices satisfying the condition and form a Lie group, namely:

[0135]

[0136] Spacecraft configuration is determined by a binary representation of the position vector and the body attitude matrix (application). The description, and thus the definition of a Lie group application, are then used. for:

[0137]

[0138] Based on the application The homogeneous form of the spacecraft's pose configuration is represented, and the corresponding Lie algebra and its homogeneous form are defined:

[0139]

[0140]

[0141] Among the applications yes The antisymmetric matrix, i.e.:

[0142]

[0143] This leads to the derivation based on The spacecraft's orbital attitude coupling kinematic equations:

[0144]

[0145] At the same time, define Lie group applications The adjoint mapping and the adjoint operator and antiadjoint operator of Lie algebras:

[0146]

[0147] This leads to the spacecraft attitude-orbit coupling dynamics equations based on application SE(3):

[0148]

[0149] in, Application for an integrated laser terminal-satellite inertial matrix The moment of inertia of the laser terminal (determined by the terminal's structural parameters). The application is for satellite quality;

[0150] , where is a 6-dimensional velocity vector, represents the angular velocity of the laser terminal around the inertial frame, and represents the linear velocity of the satellite body;

[0151] The application is for control input. The application is for the attitude adjustment torque of the laser terminal, which is the satellite orbit control force;

[0152] External interference The application includes laser terminal micro-vibration interference. The application includes solar radiation pressure interference. ( (where m is the spacecraft's moment of inertia matrix and m is the spacecraft's mass). () represents a generalized force term that includes gravitational gradient torque and gravity, etc. For control input (including attitude adjustment control) wait), This represents the total external interference.

[0153] Significantly reduced resource consumption: This application updates the multiplication and division operations in the conventional attitude conversion method to addition and subtraction operations. Through actual testing, on the same on-board chip (such as a certain type of on-board FPGA chip), the computing unit occupancy rate during the operation is reduced from 65%-75% in the conventional method to 20%-25%, and the storage resource occupancy is reduced from 40KB-50KB in the conventional method to 8KB-12KB. This greatly reduces the demand on the limited chip resources on the satellite and reserves sufficient resources for other core functions of the laser communication terminal.

[0154] Stable accuracy is maintained: Through Lie algebra mapping relationship optimization and accuracy calibration mechanism, the accuracy of the attitude matrix output by this application is completely consistent with that of conventional methods, and the attitude angle calculation error is controlled within 0.1° of the application, which meets the stringent requirements of the spaceborne laser communication terminal for attitude control accuracy and avoids the impact of accuracy loss on the stability of the laser communication link.

[0155] Improved real-time performance: Addition and subtraction operations are much faster than multiplication and division operations. In scenarios where the computing power of onboard chips is generally limited, the attitude matrix transformation time of this application is reduced from 80ms-100ms to 15ms-20ms, which is a conventional method. This significantly improves the real-time performance of attitude updates, ensuring that the laser communication terminal can quickly respond to attitude adjustment requirements and adapt to dynamic communication scenarios in the spaceborne environment.

[0156] High compatibility and reliability: The method in this application only optimizes the operation logic of attitude matrix transformation, without changing the original attitude data input / output interface and overall control flow of the laser communication terminal. It can be directly integrated into the existing spaceborne laser communication terminal system without large-scale modification of the terminal hardware, thus reducing application costs. At the same time, the simplified operation logic reduces the number of operation failure points, improves the reliability of the attitude transformation process, and reduces the risk of operation interruption of the on-board system.

[0157] Example:

[0158] Step 1: Perform satellite orbit attitude matrix data and payload data acquisition and input.

[0159] The attitude data acquisition module of the spaceborne laser communication terminal acquires two sets of attitude matrix data in real time: initial attitude matrix R0, representing the terminal's current attitude, acquired at t0=0ms; and incremental attitude matrix ΔR, representing the terminal's attitude change within 100ms, acquired at t1=100ms. R0 and ΔR are input to the attitude matrix input unit of the computation control module via the SPI interface.

[0160] Step 2: Perform logarithmic mapping from the attitude matrix to Lie algebra vectors, Lie algebra vector addition, and exponential mapping from Lie algebra vectors to the attitude matrix. The exponential mapping module calls the preset Taylor expansion. Perform exponential mapping to reconstruct the target pose matrix. The attitude matrix output unit will The attitude control unit of the spaceborne laser communication terminal sends the request through the SPI interface to adjust the laser emission direction of the terminal, and finally outputs the delay and overall attitude conversion cycle.

[0161] Step 3: Calculate the load aiming angle using the Lie algebra method.

[0162] Based on the updated Lie algebra vector or attitude matrix The following steps are used to calculate the load aiming angle (in terms of pitch angle). Yaw angle Roll angle For example, the coordinate system must be consistent with the satellite payload system: Let... Its mold length Unit direction vector ( (Time). The three components of the load aiming angle can be calculated using the following formula:

[0163] .

[0164] Extract the attitude error of application SE(3) and define the expected pose of the laser terminal application SE(3).

[0165] in Given the desired aiming attitude and the desired orbital position, calculate the error pose as applied. The logarithmic mapping will transform the application into an error vector application of se(3). in For attitude error, apply For position error. Calculate the load aiming angle including error compensation, SE(3) error compensation term is: Application in the form By applying for GEO-LEO application link simulation calibration, To ensure that the accuracy of the aiming angle is controllably affected by the attitude error, the magnitude of the attitude error is set. Starting from this point, we obtain the Euler angles through matrix decomposition: The final result This is the load aiming angle, used for subsequent two-dimensional application AzEl application conversion.

[0166] Step 4: Perform a two-dimensional Az, El transformation of the load aiming angle.

[0167] Az (azimuth) is the angle projected onto the target from north in a clockwise direction on the horizontal plane, and El (elevation) is the angle between the target and the horizontal plane. The conversion steps are as follows:

[0168] Horizontal coordinate system: North (N), East (E), Sky (U). Let the satellite position vector be... (From Earth's center to the satellite), the unit vector pointing the payload in the satellite's body coordinate system is: (e.g., when applying along the z-axis of the body) ).

[0169] Inertial frame pointing vector: (Changed to) Inertial frame pointing vector: Application Among the applications This indicates the extraction of the homogeneous matrix SE(3) from the application. The upper left rotation portion of the application, i.e., the laser terminal attitude matrix, is the application. For the laser terminal body coordinate system, the pointing unit vector is such that when applying along the body's Z axis, the pointing vector of the inertial system is directly derived from the applied SE (3) orbit and attitude integrated parameters.

[0170] Horizon pointing vector: the transformation matrix from the inertial frame to the horizon frame. ,get .

[0171] The elevation angle is calculated by applying the angle between the pointing vector and the ground plane.

[0172] The azimuth angle Az is calculated as the angle between the north direction and the projection of the pointing vector onto the ground plane.

[0173]

[0174] make sure Values ​​in between.

[0175] It should be noted that the specific embodiments are merely explanations and illustrations of the technical solution of the present invention and should not be used to limit the scope of protection. Any modifications made in accordance with the claims and specification of the present invention that are only partial should still fall within the protection scope of the present invention.

Claims

1. A laser communication terminal attitude control method based on Lie algebra, characterized in that... Includes the following steps: Step 1: Obtain the laser communication terminal attitude matrix at the current moment. Satellite attitude matrix And the satellite's position vector; Step 2: Based on the attitude matrix of the laser communication terminal and satellite attitude matrix The Lie algebra vector of the laser communication terminal is obtained. And based on the Lie algebra vector of the laser communication terminal Construct the orbital attitude coupling kinematic equations of the spacecraft; Step 3: Based on the spacecraft's attitude-orbit coupling kinematic equations, construct the integrated attitude-orbit coupling dynamic equations of the laser communication terminal and satellite; Step 4: Set the current laser communication terminal attitude matrix. Satellite attitude matrix The satellite's position vector is input into the integrated attitude and orbit coupling dynamic equation of the laser communication terminal-satellite, and the attitude matrix of the laser communication terminal at the next moment is obtained. Step 5: Based on the attitude matrix of the laser communication terminal at the next moment. Adjust the attitude of the current laser communication terminal.

2. The attitude control method for a laser communication terminal based on Lie algebra according to claim 1, characterized in that... The specific steps of step 2 are as follows: Step 21: Utilize the attitude matrix of the laser communication terminal and satellite attitude matrix Construct the mounting matrix of the payload relative to the satellite body. , Represented as: ； Step 22: Using the checkerboard calibration method, obtain the transformation matrix belonging to SE(3) between the camera coordinate system and the coordinate system of the laser communication terminal. Transformation matrix Represented as: in, The rotation matrix from the camera to the laser. It is a translation vector; Step 23: Transform the matrix Perform the adjoint mapping to obtain the matrix. ,matrix Represented as: Step 24: Obtain the camera pose of the laser communication terminal, and perform a logarithmic mapping on the camera pose to obtain the Lie algebra vector of the camera pose. ,in, To pan the camera, Rotate the camera; Step 25: Based on the matrix Lie algebra vectors of camera pose The Lie algebra vector of the laser communication terminal is obtained. Lie algebra vector of laser communication terminal Represented as: ； Step 26: For the Lie algebra vector of the laser communication terminal By performing exponential mapping, the attitude matrix of the laser communication terminal is obtained. ; Step 27: Obtain the measured attitude matrix of the laser communication terminal ,like If the result is positive, proceed to step 28; otherwise, proceed to step 24 to reacquire the camera pose of SLAM. Step 28: Set the attitude matrix of the laser communication terminal The desired attitude matrix for laser communication payload pointing adjustment And combined with the installation matrix of the payload relative to the satellite body The desired attitude matrix that the satellite body needs to be adjusted to is obtained. The desired attitude matrix that the satellite body needs to be adjusted to. Represented as: Step 29: Based on the desired attitude matrix that the satellite body needs to be adjusted to And combined with the satellite's attitude matrix The satellite attitude error matrix is ​​obtained. Satellite attitude error matrix Represented as; Step 210: Convert the satellite's attitude error matrix Perform a logarithmic mapping to obtain the Lie algebra vector. Lie algebra vector Represented as: Step 211: Based on Lie algebra vectors Design control law Control Law Represented as: in, This is the proportional gain matrix; Step 212: Obtain the position vector of the laser communication terminal or the satellite itself. ,use and satellite attitude matrix Construct binary tuples ( ), and then use the tuple ( ) obtained Li Qun Li Qun Represented as: in, It is a special orthogonal group; Step 213: Obtain the Lie group homogeneous form and in a uniform form Lie algebra vector : in, , yes The antisymmetric matrix, i.e.: Step 214: Based on homogeneous form and Lie algebra vectors The orbital attitude coupled kinematic equations of the spacecraft are constructed as follows: 。 3. The attitude control method for a laser communication terminal based on Lie algebra according to claim 2, characterized in that... Step 3 specifically involves: Step 31: For Lie algebra vectors By performing the adjoint mapping, we obtain the adjoint operator of the Lie algebra. And utilize the adjoint operator of Lie algebras Obtain the inverse adjoint operator , represented as: ； Step 32: Utilize and anti-adjoint operator The attitude and orbit coupling dynamic equation of the laser communication terminal-satellite integrated system based on SE(3) is obtained, which is expressed as: in, For laser communication terminal-satellite integrated inertial matrix, To control the input, , The torque for adjusting the attitude of the laser communication terminal, i.e. , For satellite orbit control force, External interference , Including micro-vibration interference from laser communication terminals, Including solar radiation pressure interference, ) is a generalized force term that includes gravitational gradient torque and gravity.

4. The attitude control method for a laser communication terminal based on Lie algebra according to claim 3, characterized in that... The laser communication terminal-satellite integrated inertial matrix Represented as: in, The moment of inertia of the laser communication terminal. For satellite quality, It is a third-order identity matrix.

5. The attitude control method for a laser communication terminal based on Lie algebra according to claim 4, characterized in that... The measured attitude matrix of the laser communication terminal Obtained using a star-sensitive gyroscope.

6. A laser communication terminal attitude control system based on Lie algebra, characterized in that... The system includes a data acquisition module, a kinematic equation construction module, a dynamic equation construction module, and an attitude control module; The data acquisition module is used to acquire the laser communication terminal attitude matrix at the current moment. Satellite attitude matrix And the satellite's position vector; The kinematic equation construction module is based on the attitude matrix of the laser communication terminal. and satellite attitude matrix The Lie algebra vector of the laser communication terminal is obtained. And based on the Lie algebra vector of the laser communication terminal Construct the orbital attitude coupling kinematic equations of the spacecraft; The dynamic equation construction module constructs an integrated attitude-orbit coupling dynamic equation for a laser communication terminal and a satellite based on the spacecraft's orbital attitude coupling kinematic equation. The attitude control module is used to set the current attitude matrix of the laser communication terminal. Satellite attitude matrix The satellite's position vector is input into the integrated attitude and orbit coupling dynamics equations of the laser communication terminal and the satellite to obtain the attitude matrix of the laser communication terminal at the next moment. Based on the attitude matrix of the laser communication terminal at the next moment... Adjust the attitude of the current laser communication terminal.

7. The attitude control system for a laser communication terminal based on Lie algebra according to claim 6, characterized in that... The kinematic equation construction module specifically performs the following steps: Step 21: Utilize the attitude matrix of the laser communication terminal and satellite attitude matrix Construct the mounting matrix of the payload relative to the satellite body. , Represented as: ； Step 22: Using the checkerboard calibration method, obtain the transformation matrix belonging to SE(3) between the camera coordinate system and the coordinate system of the laser communication terminal. Transformation matrix Represented as: in, The rotation matrix from the camera to the laser. It is a translation vector; Step 23: Transform the matrix Perform the adjoint mapping to obtain the matrix. ,matrix Represented as: Step 24: Obtain the camera pose of the laser communication terminal, and perform a logarithmic mapping on the camera pose to obtain the Lie algebra vector of the camera pose. ,in, To pan the camera, Rotate the camera; Step 25: Based on the matrix Lie algebra vectors of camera pose The Lie algebra vector of the laser communication terminal is obtained. Lie algebra vector of laser communication terminal Represented as: ； Step 26: For the Lie algebra vector of the laser communication terminal By performing exponential mapping, the attitude matrix of the laser communication terminal is obtained. ; Step 27: Obtain the measured attitude matrix of the laser communication terminal ,like If the result is positive, proceed to step 28; otherwise, proceed to step 24 to reacquire the camera pose of SLAM. Step 28: Set the attitude matrix of the laser communication terminal The desired attitude matrix for laser communication payload pointing adjustment And combined with the installation matrix of the payload relative to the satellite body The desired attitude matrix that the satellite body needs to be adjusted to is obtained. The desired attitude matrix that the satellite body needs to be adjusted to. Represented as: Step 29: Based on the desired attitude matrix that the satellite body needs to be adjusted to And combined with the satellite's attitude matrix The satellite attitude error matrix is ​​obtained. Satellite attitude error matrix Represented as; Step 210: Convert the satellite's attitude error matrix Perform a logarithmic mapping to obtain the Lie algebra vector. Lie algebra vector Represented as: Step 211: Based on Lie algebra vectors Design control law Control Law Represented as: in, This is the proportional gain matrix; Step 212: Obtain the position vector of the laser communication terminal or the satellite itself. ,use and satellite attitude matrix Construct binary tuples ( ), and then use the tuple ( ) obtained Li Qun Li Qun Represented as: in, It is a special orthogonal group; Step 213: Obtain the Lie group homogeneous form and in a uniform form Lie algebra vector : in, , yes The antisymmetric matrix, i.e.: Step 214: Based on homogeneous form and Lie algebra vectors The orbital attitude coupled kinematic equations of the spacecraft are constructed as follows: 。 8. The attitude control system for a laser communication terminal based on Lie algebra according to claim 7, characterized in that... The dynamic equation construction module specifically performs the following steps: Step 31: For Lie algebra vectors By performing the adjoint mapping, we obtain the adjoint operator of the Lie algebra. And utilize the adjoint operator of Lie algebras Obtain the inverse adjoint operator , is represented as: ； Step 32: Utilize and anti-adjoint operator The attitude and orbit coupling dynamic equation of the laser communication terminal-satellite integrated system based on SE(3) is obtained, which is expressed as: in, For laser communication terminal-satellite integrated inertial matrix, To control the input, , The torque for adjusting the attitude of the laser communication terminal, i.e. , For satellite orbit control force, External interference , Including micro-vibration interference from laser communication terminals, Including solar radiation pressure interference, ) is a generalized force term that includes gravitational gradient torque and gravity.

9. The attitude control system for a laser communication terminal based on Lie algebra according to claim 8, characterized in that... The laser communication terminal-satellite integrated inertial matrix Represented as: in, The moment of inertia of the laser communication terminal. For satellite quality, It is a third-order identity matrix.

10. The attitude control system for a laser communication terminal based on Lie algebra according to claim 9, characterized in that... The measured attitude matrix of the laser communication terminal Obtained using a star-sensitive gyroscope.

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