A two-stage cooperative pointing control system and method based on a Stewart platform

Abstract

The application relates to a two-stage cooperative pointing control system and method based on a Stewart platform. The two-stage cooperative pointing control system is suitable for the field of airborne optical sensitive loads and the like with high-precision and high-stability pointing requirements. The two-stage cooperative pointing control system is composed of a Stewart platform subsystem and a steering head subsystem, wherein the steering head subsystem realizes large-range pointing, and the Stewart platform subsystem realizes high-precision and high-stability pointing. The two-stage cooperative pointing control method comprises the following steps: (1) structure design of the two-stage cooperative pointing platform; (2) dynamic model establishment and decoupling analysis of the Stewart platform; and (3) control module design of the two-stage cooperative pointing system. On the basis of realizing large-range pointing by the steering head, the Stewart platform is introduced to compensate for external disturbance, so that high-precision and high-stability pointing of the airborne optical sensitive load is realized.

Description

Technical Field

[0001] This invention belongs to the field of mechanical structure design and control, specifically relating to a two-level cooperative pointing control system and method based on the Stewart platform. Background Technology

[0002] With the rapid development of aerospace technologies such as high-resolution imaging, high-precision space exploration, and space laser communication, precision pointing control technology for spacecraft and other launch platforms has become a key technology in future optical applications. For precision imaging systems carried by spacecraft and other launch platforms, vibrations generated during spacecraft operation will cause optical axis wobbling, severely affecting the imaging quality and thus impacting important performance aspects such as system stability and pointing accuracy. To obtain high-quality target information, it is necessary to suppress disturbances while maintaining stable optical axis pointing of the imaging system, achieving high-precision target pointing control. The Stewart platform is a parallel mechanism with six degrees of freedom, possessing characteristics such as high precision, high load-bearing capacity, and good dynamic characteristics. A two-stage cooperative pointing system based on the Stewart platform can meet the dual requirements of vibration suppression and high-precision pointing control.

[0003] The prior art (Guo Sheng, Qu Haibo, Fang Yuefa. A three-degree-of-freedom parallel mechanism for attitude adjustment, CN101653944.[P].2010-02-24.) proposes a three-degree-of-freedom parallel mechanism with attitude adjustment capability. This mechanism can achieve rapid feed, but compared with the six-degree-of-freedom parallel mechanism Stewart platform, the three-degree-of-freedom parallel mechanism has a small workspace and low dimension, and its attitude adjustment capability is easily limited.

[0004] The existing technology (Wu Han, Jin Lei. A flexible satellite pointing and tracking control method with a six-degree-of-freedom vibration isolation platform, CN202010736828.9.[P].2020-07-28) proposes a flexible satellite pointing and tracking control method based on a six-degree-of-freedom vibration isolation platform, which can effectively attenuate the high-frequency vibration of the actuator and suppress the flexible vibration of the sail, but the attitude adjustment range of the vibration isolation platform is limited. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a two-level cooperative pointing control system and method based on the Stewart platform to reduce the impact of various disturbances on the pointing accuracy and stability of airborne optical sensitive loads.

[0006] To achieve the above objectives, the technical solution of the present invention is: a two-level cooperative pointing control system based on the Stewart platform, including a Stewart platform subsystem and a servo gimbal subsystem, wherein the servo gimbal subsystem achieves wide-range pointing and the Stewart platform subsystem achieves high-precision and high-stability pointing.

[0007] In one embodiment of the present invention, the servo gimbal subsystem includes a servo gimbal, an airborne optical sensing payload mounted on the upper bracket of the servo gimbal, and a CCD camera mounted on the upper bracket of the servo gimbal; the Stewart platform subsystem includes a Stewart platform and an accelerometer. The Stewart platform includes an upper plate, a lower plate, an actuator, and a ball joint. The actuator is connected to the upper plate and the lower plate respectively through the ball joint. The accelerometer is mounted on the upper plate, and the servo gimbal base is fixedly connected to the upper plate.

[0008] In one embodiment of the present invention, the actuating rod includes a force transmission rod, a voice coil motor actuator, and a displacement sensor. The voice coil motor actuator is used to generate micro-vibration at the upper end of the actuating rod, and the displacement sensor is used to measure the axial displacement of the force transmission rod.

[0009] In one embodiment of the present invention, the Stewart platform adopts a cubic configuration with mutually orthogonal actuators, and the center of mass of the upper plate coincides with the center of the cubic configuration formed by the actuators.

[0010] In one embodiment of the present invention, there are six actuators and six acceleration sensors. The positions of the actuators and the installation positions of the acceleration sensors correspond one-to-one. The acceleration sensors are used to measure the motion acceleration of the actuators.

[0011] In one embodiment of the present invention, the servo gimbal includes two servos to drive the airborne optical sensitive load to move around the longitudinal axis and the yaw axis respectively; the azimuth deflection angle and pitch deflection angle of the airborne optical sensitive load reflect the change in the center of the CCD camera target surface, the position information of the target imaging point is collected by the CCD camera, and the azimuth deflection angle and pitch deflection angle are calculated using the offset pixel number of the target imaging point on the CCD camera target surface.

[0012] This invention also provides a two-level cooperative pointing control method based on the Stewart platform, comprising the following steps:

[0013] (1) The structural design of the two-level cooperative pointing control system as described above is adopted;

[0014] (2) Establishment and decoupling analysis of the dynamic model of the Stewart platform;

[0015] (3) Design of the control module of the two-level cooperative pointing system.

[0016] In one embodiment of the present invention, the specific process of the dynamic modeling method and decoupling analysis of the Stewart platform in step (2) is as follows:

[0017] The force F exerted by the i-th actuator of the Stewart platform on the upper plate i Represented as:

[0018]

[0019] Among them, F ci Indicates the magnitude of the output force of the i-th actuator; k i c represents the stiffness of the i-th actuating rod; i The damping of the i-th actuating rod is indicated by l; i and Let represent the axial displacement and axial velocity of the i-th actuator, respectively;

[0020] The force vector F exerted by the six actuators on the upper plate is expressed as:

[0021]

[0022] Among them, F c This represents the output force vector of the six actuators; K = kE 6×6 and C = cE 6×6 E represents the stiffness matrix and damping matrix of the six actuators, respectively. 6×6 Let represent a 6×6 identity matrix, k represent the stiffness coefficient of the actuator, and c represent the damping coefficient of the actuator; l and These represent the axial displacement vector and axial velocity vector of the six actuators, respectively;

[0023] According to the Newton-Euler method, the dynamic model of the upper plate is expressed as:

[0024]

[0025] Where M = diag(mE, I) 6×6 Let m represent the mass / inertia matrix of the upper plate, and I = diag(I x ,I y ,I z Let I represent the mass and moment of inertia matrices of the upper plate, respectively. x I y and I z Let F represent the moments of inertia of the upper plate about the x-axis, y-axis, and z-axis, respectively, and let E be a 3×3 identity matrix; F d G represents the external disturbance force vector acting on the upper plate; G represents the gravitational force vector acting on the upper plate. This represents the acceleration vector of the center of mass of the upper plate. and Let x, y, and z represent the accelerations of the upper plate along the x-axis, y-axis, and z-axis, respectively. and These represent the angular accelerations of the upper plate rotating about the x-axis, y-axis, and z-axis, respectively; J represents the Jacobian variation matrix relating the motion of the six actuators and the motion of the upper plate. T Let J be the transpose of the Jacobian transformation matrix J;

[0026] The expression for the acceleration of the plate's center of mass and the axial acceleration of the actuator on the Stewart platform is:

[0027]

[0028] in, This represents the axial acceleration vector of the six actuators;

[0029] The dynamic model expression for the Stewart platform is then:

[0030]

[0031] Among them, J -1 Let J be the inverse of the Jacobian transformation matrix; perform decoupling analysis on the Stewart platform dynamics model; based on the Stewart dynamics model, define the input variable u and the output variable y, with the following expressions:

[0032] u=J T F c

[0033] y = J -1 l

[0034] During high-precision pointing, the Stewart platform actuator has a small displacement range, J -1 Neglecting other factors, the Stewart platform dynamics decoupling model expression from input u to output y is as follows:

[0035]

[0036] in, This represents the first derivative of the output variable y; This represents the second derivative of the output variable y.

[0037] In one embodiment of the present invention, during the establishment and decoupling analysis of the dynamic model of the Stewart platform, the Stewart platform adopts a cubic configuration with mutually orthogonal actuators, and the center of mass of the upper plate coincides with the center of the cubic configuration formed by the actuators. The mass / inertia matrices M and J of the upper plate... TJ are all diagonal matrices, and decoupling is achieved through the dynamic model expression from input variable u to output variable y, greatly reducing the coupling between actuators on the Stewart platform.

[0038] In one embodiment of the present invention, after completing the decoupling analysis of the dynamic model of the Stewart platform, the coupling between the actuators of the Stewart platform is greatly reduced. The axial acceleration response of the other five actuators caused by a single actuator is less than its own axial acceleration response. When compensating for external disturbances, the six actuators of the Stewart platform are controlled individually.

[0039] In one embodiment of the present invention, the specific process of designing the control module of the secondary cooperative pointing system in step (3) is as follows:

[0040] When pointing at a target object, the position information of the target object's imaging point is acquired by a CCD camera. The acquired position information is converted into the angle required to rotate the target imaging point to the center of the field of view of the airborne optical sensor. When this angle is greater than the set angle deviation threshold between the target and the center of the airborne optical sensor's field of view, it is fed back to the servo gimbal subsystem to achieve a wide-range pointing function through the servo motor; otherwise, it is fed back to the Stewart platform subsystem to achieve a precise pointing function.

[0041] The acquired position information is converted into the rotation angle required to position the target imaging point at the center of the optically sensitive payload's field of view. This rotation angle is calculated from the offset pixel count of the target imaging point on the CCD camera's target surface.

[0042]

[0043] Where θ represents the angle of rotation required to position the target imaging point at the center of the field of view of the optically sensitive load; ε represents the number of pixels; η represents the pixel size; d represents the focal length of the camera lens; and δ represents the angle between the azimuth axis and the camera optical axis.

[0044] After receiving the feedback angle information, the servo gimbal subsystem obtains the control voltage based on the kernel filter x-LMS algorithm and sends the control voltage to the servo gimbal. The servo gimbal then drives the onboard optical sensitive payload to move, achieving a wide-range pointing function.

[0045] After receiving the feedback angle information, the Stewart platform subsystem decouples the angle into the displacement of the actuator rod, and obtains the corresponding control voltage based on the kernel filter x-LMS algorithm. The control voltage is then sent to the voice coil motor actuator of the actuator rod to generate micro-vibration at the upper end of the actuator rod, thereby changing the position and attitude of the plate on the Stewart platform and realizing the precise pointing function.

[0046] When the target imaging point is located at the center of the field of view of the airborne optical sensitive payload, the accelerometer collects the axial acceleration at the upper end of the actuator and feeds the acceleration signal back to the Stewart platform subsystem. The control voltage is obtained based on the kernel filter x-LMS algorithm and sent to the voice coil motor actuator to generate micro-vibration at the upper end of the actuator, thereby compensating for external disturbances.

[0047] In one embodiment of the present invention, the kernel filter x-LMS algorithm utilizes a kernel adaptive filter to map the original input data to a high-dimensional feature space and applies a gradient descent search method to obtain the optimal solution, as detailed below:

[0048] The control voltage signal u(n) output by the kernel adaptive filter is expressed as:

[0049]

[0050] Where w(n) = [w1(n), w2(n), ..., w L [(n)] represents the weight vector of the kernel adaptive filter in the nth iteration, L represents the order of the kernel adaptive filter, and w T (n) represents the transpose matrix of the weight vector w(n) of the kernel adaptive filter; x(n) = [x(n), x(n-1), ..., (n-N+1)] represents the reference angle of the kernel adaptive filter in the nth iteration, N represents the length of the reference angle, and x(n) represents the reference angle signal input to the kernel adaptive filter in the nth iteration; Represents the mapping relationship in a high-dimensional feature space;

[0051] The angle error signal e(n) acquired and converted by the CCD camera is represented as:

[0052] e(n) = θ(n) - s(n) * u(n)

[0053] Where θ(n) represents the angular deviation signal of the airborne optical sensor relative to the target object; * represents the convolution operation; and s(n) represents the impulse response of the controller output voltage u(n) to the deflection angle of the airborne optical sensor via the secondary cooperative pointing control platform and the transfer function S(z).

[0054]

[0055] Where M represents the order of the transfer function S(z); Represents the impulse response coefficient;

[0056] The expression for the error signal e(n) is:

[0057]

[0058] Based on the least mean square criterion, the cost function of the kernel filter x-LMS algorithm is:

[0059] ξ=E[e 2 (n)]

[0060] Where E[·] represents the expected value; the weight vector update expression of the kernel adaptive filter obtained by the gradient descent method is:

[0061]

[0062] in, This represents the instantaneous gradient estimate of the cost function ξ with respect to the weight vector w(n):

[0063]

[0064] The weight vector of the kernel adaptive filter is then updated as follows:

[0065]

[0066] Where μ represents the convergence factor, which is used to control the convergence speed of the algorithm; Let N represent the filtered reference angle in the original space during the nth iteration, and let N represent the length of the filtered reference angle. The filtered reference angle signal for the nth iteration is:

[0067]

[0068] in, Represents the transfer function The order of Represents the transfer function The impulse response coefficient, The estimated model for the transfer function S(z) of the controller output voltage u(n) through the two-stage cooperative pointing control platform to the deflection angle of the airborne optical sensitive load is as follows:

[0069]

[0070] The weight vector update formula for the kernel adaptive filter is:

[0071]

[0072] Where the initial weight vector w(0) is 0, then the control voltage signal u(n) is:

[0073]

[0074] Where K(x,y) is the Gaussian kernel function, K(x,y) = exp(-η||xy|| 2), where η represents the kernel parameter.

[0075] Compared to existing technologies, this invention offers the following advantages: Targeting airborne optically sensitive payloads, this invention employs a Stewart platform and a servo gimbal to form a two-stage cooperative pointing control system, achieving high-precision and high-stability pointing over a wide range. The Stewart platform can, to a certain extent, isolate internal disturbances caused by the airframe structure and external disturbances during flight, improving the pointing accuracy and stability of the two-stage cooperative pointing system. The kernel-filtered x-LMS algorithm is used as the system's control algorithm. This algorithm introduces a Gaussian kernel function based on the x-LMS algorithm, mapping the original input data to a high-dimensional feature space and applying a gradient descent search method to obtain the optimal solution, achieving faster convergence speed and better pointing performance. Attached Figure Description

[0076] Figure 1 This is a flowchart of the present invention;

[0077] Figure 2 This is a schematic diagram of the two-level collaborative platform structure;

[0078] Figure 3 This is a block diagram of a two-level collaborative pointing control strategy;

[0079] Figure 4 This is a control principle diagram based on the kernel filter x-LMS algorithm;

[0080] Figure 2 In the middle, 1-Airborne optical sensitive payload; 2-Servo gimbal; 3-Acceleration sensor; 4-Spherical hinge; 5-Force transmission rod; 6-Voice coil motor actuator; 7-Stewart platform underplate; 8-Stewart platform; 9-Actuator rod; 10-Displacement sensor; 11-Stewart platform underplate; 12-CCD camera. Detailed Implementation

[0081] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0082] This invention provides a two-level cooperative pointing control system based on the Stewart platform, including a Stewart platform subsystem and a servo gimbal subsystem. The servo gimbal subsystem achieves wide-range pointing, while the Stewart platform subsystem achieves high-precision and high-stability pointing.

[0083] The structural diagram of the two-level collaborative pointing control platform is as follows: Figure 2As shown, the names of each component are: 1-Airborne optical sensor payload; 2-Servo gimbal; 3-Acceleration sensor; 4-Spherical hinge; 5-Force transmission rod; 6-Voice coil motor actuator; 7-Stewart platform lower plate; 8-Stewart platform; 9-Actuator rod; 10-Displacement sensor; 11-Stewart platform upper plate; 12-CCD camera. The servo gimbal 2 is mounted on the upper plate 11 of the Stewart platform 8, and the upper plate 11 is bolted to the base of the servo gimbal 2. The airborne optical sensor payload 1 is mounted on the upper bracket of the servo gimbal 2. The servo gimbal subsystem provides a wide-range pointing function, while the Stewart platform subsystem provides a high-precision and high-stability pointing function.

[0084] This invention also provides a two-level cooperative pointing control method based on the Stewart platform, such as... Figure 1 As shown, it includes the following steps:

[0085] (1) The structural design adopts a two-level cooperative pointing control system, such as Figure 2 As shown;

[0086] (2) Establishment and decoupling analysis of the dynamic model of the Stewart platform;

[0087] (3) Design of the control module of the two-level cooperative pointing system.

[0088] In the dynamic modeling method and decoupling analysis of the Stewart platform described in this invention, the force F exerted by the i-th actuating rod 9 on the upper plate 11 is... i Represented as:

[0089]

[0090] Among them, F ci Indicates the magnitude of the output force of the i-th actuator; k i c represents the stiffness of the i-th actuating rod; i The damping of the i-th actuating rod is indicated by l; i and Let represent the axial displacement and axial velocity of the i-th actuator, respectively.

[0091] The force vector F exerted by the six actuators on the upper plate 11 is expressed as:

[0092]

[0093] Among them, F c This represents the output force vector of the six actuators; K = kE 6×6 and C = cE 6×6Let E represent the stiffness matrix and damping matrix of the six actuators, respectively; k represents the stiffness coefficient of the actuator, and c represents the damping coefficient of the actuator; 6×6 Represents a 6×6 identity matrix; l and These represent the axial displacement vector and axial velocity vector of the six actuators, respectively.

[0094] According to the Newton-Euler method, the dynamic model of the upper plate 11 is expressed as:

[0095]

[0096] Where M = diag(mE, I) 6×6 Let m and I represent the mass / inertia matrix of the upper plate 11, respectively, and I = diag(I x ,I y ,I z Let I represent the mass and moment of inertia matrices of the upper plate 11, respectively. x I y and I z Let F represent the moments of inertia of the upper plate 11 about the x-axis, y-axis, and z-axis, respectively, and let E be a 3×3 identity matrix; d G represents the external disturbance force vector acting on the upper plate 11; G represents the gravity vector. This represents the acceleration vector of the center of mass of the upper plate 11. and These represent the accelerations of the upper plate 11 along the x-axis, y-axis, and z-axis, respectively. and These represent the angular accelerations of the upper plate 11 rotating about the x-axis, y-axis, and z-axis, respectively; J represents the Jacobian variation matrix relating the motion of the six actuators 9 and the motion of the upper plate 11. T Let J be the transpose of the Jacobian transformation matrix J.

[0097] The expression for the acceleration of the center of mass of the plate 11 on the Stewart platform and the acceleration of the actuator 9 is as follows:

[0098]

[0099] in, This represents the axial acceleration vector of the six actuators 9.

[0100] The dynamic model expression for Stewart platform 8 is:

[0101]

[0102] Among them, J -1This represents the inverse of the Jacobian transformation matrix J. A decoupling analysis is performed on the Stewart platform 8 dynamic model.

[0103] Based on the Stewart platform dynamics model, new input variables u and output variables y are defined, with the following expressions:

[0104] u=J T F c

[0105] y = J -1 l

[0106] During high-precision pointing, the displacement range of Stewart platform actuator 9 is relatively small. -1 Neglecting this, the Stewart platform dynamics decoupling model expression based on input u and output y is:

[0107]

[0108] in, This represents the first derivative of the output variable y; This represents the second derivative of the output variable y.

[0109] The control strategy block diagram of the two-level cooperative pointing system of this invention is as follows: Figure 3 As shown, the CCD camera 12 collects the position information of the target object's imaging point, converts the collected position information into the angle required to rotate the target imaging point to the center of the field of view of the optical sensitive load 1, and then feeds back the angle to the servo gimbal controller or Stewart platform controller.

[0110] After receiving the feedback angle information, the servo gimbal controller obtains the control voltage based on the kernel filter x-LMS algorithm and sends the control voltage to the servo gimbal 2. The servo gimbal 2 drives the optical sensitive load 1 to move, realizing a wide-range pointing function.

[0111] After receiving the feedback angle information, the Stewart platform controller decouples the angle deviation value into the displacement of the six actuators 9 according to the Jacobian transformation matrix of the Stewart platform 8, and obtains the corresponding control voltage based on the kernel filter x-LMS algorithm. The control voltage is then sent to the voice coil motor driver to change the position and attitude of the plate 11 on the Stewart platform, thereby achieving precise pointing function.

[0112] When the target imaging point is located at the center of the field of view of the optical sensitive load 1, the accelerometer 3 collects the axial acceleration at the upper end of the actuator 9 and feeds the acceleration signal back to the Stewart platform controller. The controller obtains the control voltage based on the kernel filter x-LMS algorithm and sends the control voltage to the voice coil motor 6 to generate micro-vibration at the upper end of the actuator 9, thereby compensating for external disturbances.

[0113] The Stewart platform subsystem of this invention includes an upper plate 11, a lower plate 7, and six actuators 9, each actuator being connected to the upper and lower plates via a flexible hinge 4.

[0114] Six acceleration sensors 3 are installed on the upper surface of the upper plate 11. The installation positions of the six acceleration sensors 3 correspond one-to-one with the positions of the six actuators 9. They are used to measure the motion acceleration of the actuators 9 and feed the acceleration back to the control system to compensate for external disturbances.

[0115] The six actuators 9 have the same structure, including force transmission rods 5, voice coil motor actuators 6, displacement sensors 10, etc.

[0116] The displacement sensor 10 is installed at the upper end of the actuator 9 to measure axial displacement and feed the axial displacement back to the control system, thereby achieving precise pointing of the Stewart platform 8.

[0117] The servo gimbal subsystem of the present invention includes two servos 2 and one CCD camera 12. The two servos 2 drive the optical sensitive load 1 to move around the longitudinal axis and the yaw axis, respectively. The azimuth deflection angle and pitch deflection angle of the optical sensitive load 1 are reflected in the change of the center of the target surface of the CCD camera 12. The position information of the target imaging point is collected by the CCD camera 12. The azimuth deflection angle and pitch deflection angle are calculated using the number of offset pixels of the target imaging point on the target surface of the CCD camera 12.

[0118] In the decoupling analysis of the dynamic model of this invention, the Stewart platform 8 adopts a cubic configuration with mutually orthogonal actuators 9, and the center of mass of the upper plate 11 coincides with the center of the cubic configuration formed by the actuators 9. The mass / inertia matrices M and J of the upper plate 11 are... T J are all diagonal matrices. The dynamic model expression from input variable u to output variable y will achieve decoupling, and the coupling between the six actuators 9 of the Stewart platform will be greatly reduced.

[0119] The coupling between the six actuators 9 of the Stewart platform is greatly reduced in this invention. The axial acceleration response of the other five actuators caused by a single actuator is less than its own axial acceleration response. When compensating for external disturbances, the six actuators 9 of the Stewart platform are controlled individually.

[0120] This invention converts the acquired position information into the rotation angle required to position the target imaging point at the center of the optically sensitive payload's field of view. This rotation angle is calculated from the offset pixel count of the target imaging point on the CCD camera's target surface.

[0121]

[0122] Where θ represents the angle of rotation required to position the target imaging point at the center of the field of view of the optically sensitive load; ε represents the number of pixels; η represents the pixel size; d represents the focal length of the camera lens; and δ represents the angle between the azimuth axis and the camera optical axis.

[0123] The specific process of this invention, which judges the angle deviation value and feeds it back to the servo controller or Stewart platform controller, includes the following steps: when the angle deviation value is greater than a set target point deviation threshold, it is fed back to the servo controller, enabling wide-range pointing via the servo. Conversely, it is fed back to the Stewart platform controller for precise pointing.

[0124] The kernel filter x-LMS algorithm of this invention uses a kernel adaptive filter to map the original input data to a high-dimensional feature space and applies a gradient descent search method to obtain the optimal solution.

[0125] The control voltage signal u(n) output by the kernel adaptive filter is expressed as:

[0126]

[0127] Where w(n) = [w1(n), w2(n), ..., w L [(n)] represents the weight vector of the kernel adaptive filter in the nth iteration, L represents the order of the kernel adaptive filter, and w T (n) represents the transpose matrix of the weight vector w(n) of the kernel adaptive filter; x(n) = [x(n), x(n-1), ..., (n-N+1)] represents the reference angle of the kernel adaptive filter in the nth iteration, N represents the length of the reference angle, and x(n) represents the reference angle signal input to the kernel adaptive filter in the nth iteration; It represents the mapping relationship in the high-dimensional feature space.

[0128] The angle error signal e(n) acquired and converted by the CCD camera 12 is represented as:

[0129] e(n) = θ(n) - s(n) * u(n)

[0130] Where θ(n) represents the angle signal of the optically sensitive load 1 relative to the target object; * represents the convolution operation; and s(n) represents the impulse response of the controller output voltage u(n) through the secondary cooperative pointing platform to the transfer function S(z) of the optically sensitive load deflection angle.

[0131]

[0132] Where M represents the order of the transfer function S(z); This represents the impulse response coefficient.

[0133] The expression for the error signal e(n) is:

[0134]

[0135] Based on the least mean square criterion, the cost function of the kernel filter x-LMS algorithm is:

[0136] ξ=E[e 2 (n)]

[0137] Where E[·] represents the expected value. The weight vector update expression for the kernel adaptive filter, obtained using the gradient descent method, is:

[0138]

[0139] in, This represents the instantaneous gradient estimate of the cost function ξ with respect to the weight vector w(n):

[0140]

[0141] The weight vector of the kernel adaptive filter is then updated as follows:

[0142]

[0143] Where μ represents the convergence factor, which is used to control the convergence speed of the algorithm; Let N represent the filtered reference angle in the original space during the nth iteration, and let N represent the length of the filtered reference angle. The filtered reference angle signal for the nth iteration is:

[0144]

[0145] in, Represents the transfer function The order of Represents the transfer function The impulse response coefficient, The estimated model for the transfer function S(z) of the controller output voltage u(n) through the secondary cooperative pointing platform to the deflection angle of the optically sensitive load is as follows:

[0146]

[0147] The weight vector update formula for the kernel adaptive filter is then expressed as:

[0148]

[0149] Where the initial weight vector w(0) is 0, the control voltage signal u(n) is obtained:

[0150]

[0151] Where K(x,y) is the Gaussian kernel function, K(x,y) = exp(-η||xy|| 2 ), where η represents the kernel parameter.

[0152] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A two-level cooperative pointing control system based on the Stewart platform, characterized in that, The system comprises a Stewart platform subsystem and a servo gimbal subsystem. The servo gimbal subsystem enables wide-range pointing, while the Stewart platform subsystem enables high-precision and high-stability pointing. The servo gimbal subsystem includes a servo gimbal, an onboard optical sensor mounted on the upper bracket of the servo gimbal, and a CCD camera mounted on the upper bracket of the servo gimbal. The Stewart platform subsystem includes a Stewart platform and an accelerometer. The Stewart platform includes an upper plate, a lower plate, an actuator, and a ball joint. The actuator is connected to the upper and lower plates via the ball joint. The accelerometer is mounted on the upper plate, and the servo gimbal base is fixedly connected to the upper plate. The actuator includes a force transmission rod, a voice coil motor actuator, and a displacement sensor. The voice coil motor actuator is used to move the actuator. The upper end generates micro-vibrations, and the displacement sensor is used to measure the axial displacement of the force transmission rod. The Stewart platform adopts a cubic configuration with mutually orthogonal actuator rods, and the center of mass of the upper plate coincides with the center of the cubic configuration formed by the actuator rods. There are six actuator rods and six acceleration sensors, and the positions of the actuator rods and the installation positions of the acceleration sensors correspond one-to-one. The acceleration sensors are used to measure the motion acceleration of the actuator rods. The servo gimbal includes two servos to drive the airborne optical sensitive load to move around the longitudinal axis and the yaw axis, respectively. The azimuth deflection angle and pitch deflection angle of the airborne optical sensitive load reflect the change in the center position of the CCD camera target surface. The position information of the target imaging point is collected by the CCD camera, and the azimuth deflection angle and pitch deflection angle are calculated using the offset pixel number of the target imaging point on the CCD camera target surface.

2. A two-level cooperative pointing control method based on the Stewart platform, characterized in that, Includes the following steps: (1) The structural design of the two-level cooperative pointing control system as described in claim 1 is adopted; (2) Establishment and decoupling analysis of the dynamic model of the Stewart platform; (3) Design of the control module of the two-level collaborative pointing system.

3. The two-level cooperative pointing control method based on the Stewart platform according to claim 2, characterized in that, In step (2), the specific process of the dynamic modeling method and decoupling analysis of the Stewart platform is as follows: The Stewart platform's... The force exerted by the actuator on the upper plate Represented as: in, Indicates the first The magnitude of the output force of the actuator rod; Indicates the first The stiffness of the actuator rod; Indicates the first Damping of the actuator rod; and They represent the first Axial displacement and axial velocity of the actuator rod; The force vector of the six actuators on the upper plate Represented as: in, This represents the output force vector of the six actuators; and Let represent the stiffness matrix and damping matrix of the six actuators, respectively. Indicates size is The identity matrix, This represents the stiffness coefficient of the actuator. This indicates the damping coefficient of the actuator; and These represent the axial displacement vector and axial velocity vector of the six actuators, respectively. According to the Newton-Euler method, the dynamic model of the upper plate is expressed as: in, This represents the mass / inertia matrix of the upper plate. and Let these represent the mass and moment of inertia matrices of the upper plate, respectively. , and They represent the upper flat plate winding Axial direction, Axial direction and Moment of inertia in the axial direction, It is a 3×3 identity matrix; This represents the external disturbance force vector acting on the upper plate. This represents the vector of gravity acting on the upper plate. This represents the acceleration vector of the center of mass of the upper plate. , and They represent the upper plate edge Axial direction, Axial direction and Acceleration in the axial direction, , and They represent the upper flat plate winding Axial direction, Axial direction and Angular acceleration of rotation in the axial direction; This represents the Jacobian transformation matrix relating the motion of the six actuators to the motion of the upper plate. Representing the Jacobian transformation matrix The transpose of the matrix; The expression for the acceleration of the plate's center of mass and the axial acceleration of the actuator on the Stewart platform is: in, This represents the axial acceleration vector of the six actuators; The dynamic model expression for the Stewart platform is then: in, Representing the Jacobian transformation matrix The inverse matrix; decoupling analysis of the Stewart platform dynamics model; defining input variables based on the Stewart dynamics model. and output variables The expression is: During high-precision pointing, the Stewart platform actuator has a relatively small displacement range. If ignored, then the input... To output The expression for the Stewart platform dynamic decoupling model is as follows: in, Indicates output variable The first derivative; Indicates output variable The second derivative of .

4. The two-level cooperative pointing control method based on the Stewart platform according to claim 2, characterized in that, In step (3), the specific process of designing the control module of the secondary cooperative pointing system is as follows: When pointing at a target object, the position information of the target object's imaging point is collected by the CCD camera. The collected position information is converted into the angle required to rotate the target imaging point to the center of the airborne optical sensitive payload's field of view. When this angle is greater than the set angular deviation threshold between the target and the center of the airborne optical sensitive payload's field of view, it is fed back to the servo gimbal subsystem, and the servo motor realizes a wide-range pointing function. Conversely, the feedback is sent to the Stewart platform subsystem to achieve precise pointing functionality; After receiving the feedback angle information, the servo gimbal subsystem obtains the control voltage based on the kernel filter x-LMS algorithm and sends the control voltage to the servo gimbal. The servo gimbal then drives the onboard optical sensitive payload to move, achieving a wide-range pointing function. After receiving the feedback angle information, the Stewart platform subsystem decouples the angle into the displacement of the actuator rod, and obtains the corresponding control voltage based on the kernel filter x-LMS algorithm. The control voltage is then sent to the voice coil motor actuator of the actuator rod to generate micro-vibration at the upper end of the actuator rod, thereby changing the position and attitude of the plate on the Stewart platform and realizing the precise pointing function. When the target imaging point is located at the center of the field of view of the airborne optical sensitive payload, the accelerometer collects the axial acceleration at the upper end of the actuator and feeds the acceleration signal back to the Stewart platform subsystem. The control voltage is obtained based on the kernel filter x-LMS algorithm and sent to the voice coil motor actuator to generate micro-vibration at the upper end of the actuator, thereby compensating for external disturbances.

5. The two-level cooperative pointing control method based on the Stewart platform according to claim 4, characterized in that, The kernel filter x-LMS algorithm utilizes a kernel adaptive filter to map the original input data to a high-dimensional feature space and applies a gradient descent search method to obtain the optimal solution, as detailed below: The control voltage signal output by the kernel adaptive filter Represented as: in, Indicates the first The weight vector of the kernel adaptive filter at the next iteration. This indicates the order of the kernel adaptive filter. Represents the weight vector of the kernel adaptive filter. The transpose of the matrix; Indicates the first The reference angle of the kernel adaptive filter in the next iteration. Indicates the length of the reference angle. Indicates the first The reference angle signal input to the kernel adaptive filter in the next iteration; Represents the mapping relationship in a high-dimensional feature space; Angle error signal acquired and converted by CCD camera Represented as: in, This indicates the angular deviation signal of the airborne optical sensing payload relative to the target object; This represents the convolution operation. Indicates the controller output voltage The transfer function from the secondary cooperative pointing control platform to the deflection angle of the airborne optical sensitive payload Impulse response: in, This indicates the transfer function The order of; Represents the impulse response coefficient; Then the error signal The expression is: Based on the least mean square criterion, the cost function of the kernel filter x-LMS algorithm is: in, This represents the expected value; the weight vector update expression for the kernel adaptive filter obtained by gradient descent is: in, Represents the cost function Relative to the weight vector Instantaneous gradient estimation: The weight vector of the kernel adaptive filter is then updated as follows: in, This represents the convergence factor, used to control the convergence speed of the algorithm; Indicates the first The filtered reference angle in the original space of the next iteration. This represents the length of the filtered reference angle. Indicates the first The filtered reference angle signal for the next iteration: in, Represents the transfer function The order of Represents the transfer function The impulse response coefficient, Indicates the controller output voltage The transfer function from the secondary cooperative pointing control platform to the deflection angle of the airborne optical sensitive payload Estimation model: The weight vector update formula for the kernel adaptive filter is: Wherein, the initial weight vector If it is 0, then the control voltage signal : in, For Gaussian kernel function, , Indicates kernel parameters.

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