A Two-DOF Turntable Visual Servo Control Method Based on Model Predictive Control

Abstract

This invention discloses a two-degree-of-freedom turntable visual servo control method based on model predictive control, belonging to the field of turntable motion control technology. The invention addresses the problem that existing turntable servo control methods cannot simultaneously handle multiple constraints, affecting tracking performance. The method includes: establishing a turntable attitude dynamics model based on the pitch and yaw angles, and setting actuator saturation constraints; establishing a visual servo model based on the pitch and yaw angles, and setting visual visibility constraints; discretizing to obtain discretized state-space equations and a discrete-form visual servo model; designing an optimization cost function for visual servo control and defining a control optimization problem for visual servo control, solving for the optimal angular velocity command; designing a tracking cost function based on the optimal angular velocity command, and defining an angular velocity control optimization problem according to the discretized state-space equations, solving for the turntable torque control command that satisfies the saturation constraints. This invention can improve the control efficiency and target tracking accuracy of the servo turntable.

Description

Technical Field

[0001] This invention relates to a two-degree-of-freedom turntable vision servo control method based on model predictive control, belonging to the field of turntable motion control technology. Background Technology

[0002] With the rapid development of fields such as space observation, industrial manufacturing, and laser communication, high-precision turntables have attracted widespread attention, especially the demand for high-performance control technology for two-degree-of-freedom turntables, which continues to grow. Turntable control involves adjusting the platform's attitude to track or aim at a target area. To accomplish pointing control tasks, autonomous sensing technology is often required to obtain real-time feedback from the target or environment.

[0003] Optical cameras are increasingly used in turntable systems due to their advantages such as small size, high precision, and comprehensive detection algorithms. A servo system that includes an optical camera and a turntable works by acquiring a target image through optical equipment, extracting target features using image processing algorithms, and then generating control signals to drive the actuator, achieving precise pointing and manipulation of the target.

[0004] Visual servoing technology is generally divided into two main categories: position-based visual servoing and image-based visual servoing. Position-based servoing requires camera intrinsic and extrinsic parameter calibration and 3D information reconstruction; therefore, its accuracy and performance heavily depend on the accuracy of parameter calibration and environmental information modeling. In contrast, image-based visual servoing methods directly utilize image errors to guide the attitude control of the turntable, offering a more intuitive physical meaning and greater robustness to errors in parameter calibration and position reconstruction.

[0005] Despite the extensive research and numerous successful applications of image-based visual servoing technology, practical deployments still face challenges due to limitations in sensor and actuator performance. Specifically, the limited field of view of optical cameras (commonly found in airborne cameras, often not exceeding 120°) imposes significant visual visibility constraints on camera-based turntable servo systems. Furthermore, motors, crucial actuators within the turntable, often exhibit severe saturation characteristics, meaning their input voltage is limited. Therefore, the impact of actuator constraints must be considered during the control design of turntable servo systems.

[0006] Model predictive control (MMC) is an advanced control method capable of simultaneously achieving constraint tuning and performance optimization, and it has been researched and applied in industry in recent years. There are some deployment cases of this method in turntable vision servo systems; however, existing results often only consider performance optimization control or the handling of visual visibility constraints, and have not yet formed a design paradigm for handling multiple constraints simultaneously. Therefore, how to design a servo method based on MMC to achieve high-precision servo pointing performance under conditions of multiple constraints (visual visibility, actuator saturation constraints) remains a pressing problem to be solved. Summary of the Invention

[0007] To address the problem that existing turntable servo control cannot handle multiple constraints simultaneously, thus affecting tracking performance, this invention provides a two-degree-of-freedom turntable visual servo control method based on model predictive control.

[0008] The present invention provides a two-degree-of-freedom turntable vision servo control method based on model predictive control, comprising:

[0009] An attitude dynamics model of the turntable is established based on its pitch and yaw angles, and actuator saturation constraints are set.

[0010] A visual servo model is then established based on the pitch and yaw angles of the turntable, and visual visibility constraints are set.

[0011] The continuous state-space equation of the turntable is obtained from the attitude dynamics model of the turntable, and then discretized by the zero-order hold method to obtain the discretized state-space equation; at the same time, the visual servoing model is discretized to obtain the discrete form of the visual servoing model.

[0012] Design an optimization cost function for visual servo control, and define the control optimization problem of visual servo based on the discrete form visual servo model and the optimization cost function of visual servo control, and solve it to obtain the optimal angular velocity command.

[0013] The tracking cost function is designed based on the optimal angular velocity command, and the angular velocity control optimization problem is defined according to the discretized state space equation. The turntable torque control command that satisfies the saturation limit is obtained by solving the problem.

[0014] According to the model predictive control-based visual servo control method for a two-degree-of-freedom turntable, the attitude dynamics model of the turntable is as follows:

[0015] ,

[0016] In the formula For the moment of inertia of the pitch channel, The moment of inertia of the yaw channel. The pitch angle, Yaw angle The viscosity-friction coefficient of the pitch channel. The viscous friction coefficient of the yaw channel. To restore the torque coefficient, This is the torque control command for the pitch channel turntable. This is the torque control command for the yaw channel turntable;

[0017] Set the actuator saturation constraint as follows:

[0018] ,

[0019] In the formula To minimize the torque control value of the pitch channel turntable, This is the maximum torque control value for the pitch channel turntable. This is the minimum torque control value for the yaw channel turntable. This represents the maximum torque control value for the yaw channel turntable.

[0020] Representing actuator saturation constraints in set form:

[0021] ,

[0022] In the formula For the actuator saturation constraint set, This is a torque control command for the turntable. , To control the minimum torque of the turntable, This is the maximum value for turntable torque control. It is the set of real numbers.

[0023] According to the model predictive control-based visual servo control method for a two-degree-of-freedom turntable, the method for establishing the visual servo model includes:

[0024] The target feature points captured by the optical camera are represented as... In the formula The X-axis coordinate in the camera coordinate system. The Y-axis coordinate in the camera coordinate system Z-axis coordinates in the camera coordinate system; target feature points At the projection point position in the pixel coordinate system In the formula The horizontal pixel coordinates are Vertical pixel coordinates;

[0025] Based on the principle of pinhole cameras, the relationship between three-dimensional coordinates and two-dimensional projection is expressed as follows:

[0026] ,

[0027] In the formula For the focal length of an optical camera, Scale the target horizontally. Scaling the target vertically. The x-coordinate of the center point in the pixel coordinate system. The ordinate of the center point in the pixel coordinate system;

[0028] Differentiating the above equation, we get:

[0029] ,

[0030] In the formula To normalize camera parameters laterally, To normalize camera parameters longitudinally, , ;

[0031] This leads to the visual servoing model:

[0032] ;

[0033] In the formula For visual servo Jacobian matrix.

[0034] According to the model predictive control-based two-degree-of-freedom turntable visual servo control method of the present invention, the visual servo model is represented in vector form:

[0035] ,

[0036] In the formula For time, It is the angular velocity vector. ;

[0037] Set the visual visibility constraint as follows:

[0038] ,

[0039] In the formula The minimum value of the horizontal pixel coordinate. This represents the maximum value of the horizontal pixel coordinate. The minimum value of the vertical pixel coordinate. The maximum value of the vertical pixel coordinate;

[0040] Representing visual visibility constraints in set form:

[0041] ,

[0042] In the formula For the set of visual visibility constraints, The minimum pixel coordinate. This represents the maximum pixel coordinate.

[0043] According to the model predictive control-based two-degree-of-freedom turntable visual servo control method of the present invention, the continuous state-space equations of the turntable are obtained from the attitude dynamics model of the turntable:

[0044] ,

[0045] In the formula For state variables, , The state transition matrix is ​​in continuous form. Input matrix in continuous form:

[0046] ;

[0047] Discretize the continuous state-space equations of the turntable to obtain the discretized state-space equations:

[0048] ,

[0049] In the formula Representing discrete time, The state transition matrix is ​​in discrete form. Input matrix in discrete form:

[0050] , ,

[0051] In the formula Sampling time, for Integral variables within the interval.

[0052] According to the model predictive control-based two-degree-of-freedom turntable visual servo control method of the present invention, the visual servo model is discretized to obtain the discrete form visual servo model as follows:

[0053] .

[0054] According to the model predictive control-based two-degree-of-freedom turntable visual servo control method of the present invention, the optimization cost function of visual servo control is expressed as follows: :

[0055] ,

[0056] In the formula To predict the time domain, The expected value of the projection point position. In order to be in Time prediction Position of the projection point at any given time. This is the servo error weight matrix. In order to be in Time prediction angular velocity vector at time, Input the weight matrix for angular velocity.

[0057] According to the model predictive control-based two-degree-of-freedom turntable visual servoing control method of the present invention, the control optimization problem of visual servoing is defined as follows:

[0058] ,

[0059] In the formula The obtained sequence of angular velocity vectors:

[0060] ;

[0061] The constraints are:

[0062] ,

[0063] ;

[0064] Select angular velocity vector sequence The first value As the optimal angular velocity command .

[0065] According to the model predictive control-based two-degree-of-freedom turntable visual servo control method of the present invention, the tracking cost function is expressed as follows: :

[0066] ,

[0067] In the formula For the inner loop, predict the state in the time domain. The inner loop quadratic error weight matrix is... The input weight matrix is ​​the inner loop quadratic form.

[0068] According to the model predictive control-based two-degree-of-freedom turntable visual servo control method of the present invention, the angular velocity control optimization problem is defined as follows:

[0069] ,

[0070] In the formula To obtain the turntable torque control command sequence that satisfies the saturation limit:

[0071] ;

[0072] The constraints are:

[0073] ,

[0074] ,

[0075] ;

[0076] Select the turntable torque control command sequence The first value As the optimal turntable torque control command that satisfies the saturation limit .

[0077] The beneficial effects of this invention are as follows: Based on servo errors in the image plane, this invention designs a dual-loop servo control method based on model predictive control. This method first establishes the attitude dynamics model of the two-degree-of-freedom turntable and the camera servo model, and then discretizes the continuous dynamics model. An outer-loop visual servo controller and an inner-loop angular velocity tracking controller based on model predictive control are designed respectively. These controllers can explicitly handle camera visibility constraints and actuator saturation constraints. Deploying this invention onto a two-degree-of-freedom turntable servo control system, based on camera image data, can generate control torque commands that satisfy multi-source constraints, thus completing the adjustment of the turntable's attitude. This invention solves the problem of camera-based target tracking for turntables, improving the control efficiency and target tracking accuracy of servo turntables.

[0078] This invention enables a two-degree-of-freedom turntable to track and control a moving target using only an optical camera and inertial measurement. The method explicitly addresses visual visibility constraints and actuator saturation constraints. Based on the established turntable attitude dynamics and visual servo dynamics models, an online optimized servo controller under multiple constraints is designed, forming a comprehensive servo framework that can simultaneously achieve performance optimization and constraint tuning. This invention considers the common multi-constraint problems in practice, and the designed servo method is more adaptable and has better tracking performance. It can comprehensively improve the overall control performance of the autonomous perception-based turntable servo system, meeting the requirements of the turntable system for high-precision servo tracking of targets.

[0079] Compared with existing methods, the method of this invention considers more comprehensive constraints, has a wider range of applicable turntables, and is more adaptable. Furthermore, the control performance of the model predictive control method can be guaranteed, laying a solid foundation for visual servoing and turntable-based visual pointing tasks. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of a servo control system for implementing the model predictive control-based two-degree-of-freedom turntable visual servo control method described in this invention.

[0081] Figure 2 This is a flowchart of the two-degree-of-freedom turntable visual servo control method based on model predictive control as described in this invention;

[0082] Figure 3This is a schematic diagram of the visual perception of an optical camera;

[0083] Figure 4 The method of this invention is used to... Figure 1 The diagram shows the control block diagram for the system. Detailed Implementation

[0084] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0085] Specific Implementation Method 1: Combination Figures 1 to 4 As shown, this invention provides a two-degree-of-freedom turntable visual servo control method based on model predictive control, comprising:

[0086] An attitude dynamics model of the turntable is established based on its pitch and yaw angles, and actuator saturation constraints are set.

[0087] A visual servo model is then established based on the pitch and yaw angles of the turntable, and visual visibility constraints are set.

[0088] The continuous state-space equation of the turntable is obtained from the attitude dynamics model of the turntable, and then discretized by the zero-order hold method to obtain the discretized state-space equation; at the same time, the visual servoing model is discretized to obtain the discrete form of the visual servoing model.

[0089] Design an optimization cost function for visual servo control, and define the control optimization problem of visual servo based on the discrete form visual servo model and the optimization cost function of visual servo control, and solve it to obtain the optimal angular velocity command.

[0090] The tracking cost function is designed based on the optimal angular velocity command, and the angular velocity control optimization problem is defined according to the discretized state space equation. The turntable torque control command that satisfies the saturation limit is obtained by solving the problem.

[0091] This implementation method can be used for... Figure 1 The system shown performs servo control. The system includes a two-degree-of-freedom turntable, on which an encoder and attitude measurement gyroscope are mounted to acquire the system's angle and angular velocity in real time. An optical camera is installed to detect the target position in real time. The visual servo error is calculated using the results obtained from the YOLO image detection algorithm.

[0092] Figure 1The system also includes a laser pointer. A two-degree-of-freedom turntable is the motion foundation of the entire servo system, driving the propellers to rotate and generate pitch and yaw moments, enabling the system to perform two-degree-of-freedom pointing tasks. Other sensors and pointers are mounted on this turntable. An encoder and attitude measurement gyroscope measure the pitch and yaw angles and angular velocities, while an optical camera performs target detection, providing real-time feedback on the target's servo error in the image plane. The laser pointer emits a laser beam to demonstrate the current direction vector, explicitly characterizing the system's servo tracking performance.

[0093] Figure 1 The execution logic of the turntable servo control system shown is as follows:

[0094] The first step is to calibrate the optical camera and initialize the parameters of the servo controller and the target servo reference coordinates.

[0095] The second step involves activating the optical camera module, which captures real-time images of the target. The image detection algorithm within the servo system then extracts the target's features. Specifically, this module employs the YOLO deep learning image detection algorithm. This algorithm is first trained on a target object feature dataset to obtain a trained target detection network. When the algorithm is started online, the system matches the target's feature regions according to the detection network and returns a bounding box for the detected target object. The geometric center of this bounding box is the centroid of the target object.

[0096] The third step involves activating the visual servo control algorithm. This algorithm calculates the difference between the target object's position fed back by the optical camera and the desired servo coordinates. Based on this image servo error, it controls the turntable's input torque in real time, ensuring that the target feature position coincides with the desired servo coordinates. This means the target image coordinates have reached the center point of the camera plane, and the turntable is now servo-pointing towards the target object. Using the control method described in this embodiment, the servo system can accurately track and aim at the target without violating target visibility constraints and actuator saturation constraints. Specifically, the target remains within the field of view, and the torque signal remains within the actuator's saturation input range.

[0097] The fourth step involves projecting a focused laser beam through a laser pointer to demonstrate the current servo pointing effect in real time.

[0098] The visual servo control method described in this embodiment can solve the problems of visual visibility constraints and actuator saturation constraints in servo systems.

[0099] In this embodiment, the attitude dynamics model of the turntable is as follows:

[0100] ,

[0101] In the formula For the moment of inertia of the pitch channel, The moment of inertia of the yaw channel. ; The pitch angle, Yaw angle The viscosity-friction coefficient of the pitch channel. The viscous friction coefficient of the yaw channel. ; To restore the torque coefficient, This is the torque control command for the pitch channel turntable. This is the torque control command for the yaw channel turntable;

[0102] Considering the saturation characteristics of the actuator, the actuator saturation constraint is set as follows:

[0103] ,

[0104] In the formula To minimize the torque control value of the pitch channel turntable, This is the maximum torque control value for the pitch channel turntable. This is the minimum torque control value for the yaw channel turntable. This represents the maximum torque control value for the yaw channel turntable.

[0105] Representing actuator saturation constraints in set form:

[0106] ,

[0107] In the formula For the actuator saturation constraint set, This is a torque control command for the turntable. , To control the minimum torque of the turntable, This is the maximum value for turntable torque control. It is the set of real numbers.

[0108] Methods for building visual servoing models include:

[0109] according to Figure 3 A schematic diagram of camera visual perception in the figure. Indicates the camera coordinate system. This is a pixel coordinate system.

[0110] The target feature points captured by the optical camera are represented as... In the formula The X-axis coordinate in the camera coordinate system. The Y-axis coordinate in the camera coordinate system Z-axis coordinates in the camera coordinate system; target feature points At the projection point position in the pixel coordinate system In the formula The horizontal pixel coordinates are Vertical pixel coordinates;

[0111] Based on the principle of pinhole cameras, the relationship between three-dimensional coordinates and two-dimensional projection is expressed as follows:

[0112] ,

[0113] In the formula For the focal length of an optical camera, Scale the target horizontally. Scaling the target vertically. The x-coordinate of the center point in the pixel coordinate system. These are the ordinates of the center point in the pixel coordinate system; these parameters are essentially intrinsic parameters of the camera model.

[0114] Differentiating the above equation, we get:

[0115] ,

[0116] In the formula To normalize camera parameters laterally, To normalize camera parameters longitudinally, , ;

[0117] This leads to the visual servoing model:

[0118] ;

[0119] In the formula For visual servo Jacobian matrix.

[0120] The visual servoing model is represented in vector form:

[0121] ,

[0122] In the formula For time, It is the angular velocity vector. ;

[0123] Since the field of view of an airborne camera is finite, a target is only visible if the feature points corresponding to the target lie within a bounded image plane. The visual visibility constraint is set as follows:

[0124] ,

[0125] In the formula The minimum value of the horizontal pixel coordinate. This represents the maximum value of the horizontal pixel coordinate. The minimum value of the vertical pixel coordinate. The maximum value of the vertical pixel coordinate;

[0126] Representing visual visibility constraints in set form:

[0127] ,

[0128] In the formula For the set of visual visibility constraints, The minimum pixel coordinate. This represents the maximum pixel coordinate.

[0129] The visual visibility constraint corresponds to all feasible feature coordinates that keep the target within the camera's field of view.

[0130] Furthermore, the continuous state-space equations of the turntable are obtained from the attitude dynamics model of the turntable:

[0131] ,

[0132] In the formula For state variables, , The state transition matrix is ​​in continuous form. Input matrix in continuous form:

[0133] ;

[0134] Discretize the continuous state-space equations of the turntable to obtain the discretized state-space equations:

[0135] ,

[0136] In the formula Representing discrete time, The state transition matrix is ​​in discrete form. The input matrices, in discrete form, are all obtained by discretization using the zero-order preservation method:

[0137] , ,

[0138] In the formula Sampling time, for Integral variables within the interval.

[0139] To design a visual servo controller, the visual servo model is discretized to obtain a discrete visual servo model as follows:

[0140] .

[0141] Furthermore, the task of the model predictive control-based visual servo controller is to generate a suitable angular velocity reference signal under two-dimensional visibility constraints, so that the features of the target in the visual coordinate system converge to the camera center point. The optimization cost function of visual servo control is expressed in quadratic form. :

[0142] ,

[0143] In the formula To predict the time domain, The expected value of the projection point position. In order to be in Time prediction Position of the projection point at any given time. This is the servo error weight matrix. In order to be in Time prediction angular velocity vector at time, Input the weight matrix for angular velocity. This represents the Euclidean space norm.

[0144] Define the control optimization problem for visual servoing:

[0145] ,

[0146] In the formula The obtained sequence of angular velocity vectors:

[0147] ;

[0148] The constraints are:

[0149] ,

[0150] ;

[0151] Select angular velocity vector sequence The first value As the optimal angular velocity command , .

[0152] in As an image visibility constraint, the control input based on the above optimization problem can be explicitly satisfied. Constraints ensure that the target remains within the image's field of view at all times.

[0153] Solving the constrained optimization problem described above, we can obtain the sequence of angular velocity vectors that minimizes the cost function. .

[0154] The goal of inner-loop angular velocity control is to track the angular velocity commands generated by the outer-loop servo controller. However, inner-loop angular velocity control is often limited by actuator saturation characteristics, so the input constraint problem needs to be addressed when designing the controller. To enable the inner-loop angular velocity to track the outer-loop servo commands, the following optimized cost function is designed.

[0155] The tracking cost function is expressed as :

[0156] ,

[0157] In the formula For the inner loop, predict the state in the time domain. The inner loop quadratic error weight matrix is... The input weight matrix is ​​the inner loop quadratic form.

[0158] Based on the above cost function, in order to satisfy the actuator saturation constraint, the following model predictive control optimization problem is designed:

[0159] Define the angular velocity control optimization problem:

[0160] ,

[0161] In the formula To obtain the turntable torque control command sequence that satisfies the saturation limit:

[0162] ;

[0163] The constraints are:

[0164] ,

[0165] ,

[0166] ;

[0167] The above constraints are designed to address the control input constraints caused by actuator saturation. Solving the optimization problem described above yields a turntable torque control command sequence that satisfies the saturation limit. .

[0168] Select the turntable torque control command sequence The first value As the optimal turntable torque control command that satisfies the saturation limit .

[0169] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A two-degree-of-freedom turntable visual servo control method based on model predictive control, characterized in that, include: An attitude dynamics model of the turntable is established based on its pitch and yaw angles, and actuator saturation constraints are set. A visual servo model is then established based on the pitch and yaw angles of the turntable, and visual visibility constraints are set. The continuous state-space equation of the turntable is obtained from the attitude dynamics model of the turntable, and then discretized by the zero-order hold method to obtain the discretized state-space equation; at the same time, the visual servoing model is discretized to obtain the discrete form of the visual servoing model. Design an optimization cost function for visual servo control, and define the control optimization problem of visual servo based on the discrete form visual servo model and the optimization cost function of visual servo control, and solve it to obtain the optimal angular velocity command. The tracking cost function is designed based on the optimal angular velocity command, and the angular velocity control optimization problem is defined according to the discretized state space equation. The turntable torque control command that satisfies the saturation limit is obtained by solving the problem.

2. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 1, characterized in that, The attitude dynamics model of the turntable is as follows: ， In the formula For the moment of inertia of the pitch channel, The moment of inertia of the yaw channel. The pitch angle, Yaw angle The viscosity-friction coefficient of the pitch channel. The viscous friction coefficient of the yaw channel. To restore the torque coefficient, This is the torque control command for the pitch channel turntable. This is the torque control command for the yaw channel turntable; Set the actuator saturation constraint as follows: ， In the formula To minimize the torque control value of the pitch channel turntable, This is the maximum torque control value for the pitch channel turntable. This is the minimum torque control value for the yaw channel turntable. This represents the maximum torque control value for the yaw channel turntable. Representing actuator saturation constraints in set form: ， In the formula For the actuator saturation constraint set, This is a torque control command for the turntable. , To control the minimum torque of the turntable, This is the maximum value for turntable torque control. It is the set of real numbers.

3. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 2, characterized in that, Methods for building visual servoing models include: The target feature points captured by the optical camera are represented as... In the formula The X-axis coordinate in the camera coordinate system. The Y-axis coordinate in the camera coordinate system Z-axis coordinates in the camera coordinate system; target feature points At the projection point position in the pixel coordinate system In the formula The horizontal pixel coordinates are Vertical pixel coordinates; Based on the principle of pinhole cameras, the relationship between three-dimensional coordinates and two-dimensional projection is expressed as follows: ， In the formula For the focal length of an optical camera, Scale the target horizontally. Scaling the target vertically. The x-coordinate of the center point in the pixel coordinate system. The ordinate of the center point in the pixel coordinate system; Differentiating the above equation, we get: ， In the formula To normalize camera parameters laterally, To normalize camera parameters longitudinally, , ; This leads to the visual servoing model: ； In the formula For visual servo Jacobian matrix.

4. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 3, characterized in that, The visual servoing model is represented in vector form: ， In the formula For time, It is the angular velocity vector. ; Set the visual visibility constraint as follows: ， In the formula The minimum value of the horizontal pixel coordinate. This represents the maximum value of the horizontal pixel coordinate. The minimum value of the vertical pixel coordinate. The maximum value of the vertical pixel coordinate; Representing visual visibility constraints in set form: ， In the formula For the set of visual visibility constraints, The minimum pixel coordinate. This represents the maximum pixel coordinate.

5. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 4, characterized in that, The continuous state-space equations of the turntable are obtained from the attitude dynamics model of the turntable: ， In the formula For state variables, , The state transition matrix is ​​in continuous form. Input matrix in continuous form: ； Discretize the continuous state-space equations of the turntable to obtain the discretized state-space equations: ， In the formula Representing discrete time, The state transition matrix is ​​in discrete form. Input matrix in discrete form: ， ， In the formula Sampling time, for Integral variables within the interval.

6. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 5, characterized in that, Discretizing the visual servoing model yields the discrete form of the visual servoing model as follows: 。 7. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 6, characterized in that, The optimization cost function of visual servo control is expressed as: : ， In the formula To predict the time domain, The expected value of the projection point position. In order to be in Time prediction Position of the projection point at any given time. This is the servo error weight matrix. In order to be in Time prediction angular velocity vector at time, Input the weight matrix for angular velocity.

8. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 7, characterized in that, Define the control optimization problem for visual servoing: ， In the formula The obtained sequence of angular velocity vectors: ； The constraints are: ， ； Select angular velocity vector sequence The first value As the optimal angular velocity command .

9. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 8, characterized in that, The tracking cost function is expressed as : ， In the formula For the inner loop, predict the state in the time domain. The inner loop quadratic error weight matrix is... The input weight matrix is ​​the inner loop quadratic form.

10. The two-degree-of-freedom turntable visual servo control method based on model predictive control according to claim 9, characterized in that, Define the angular velocity control optimization problem: ， In the formula To obtain the turntable torque control command sequence that satisfies the saturation limit: ； The constraints are: ， ， ； Select the turntable torque control command sequence The first value As the optimal turntable torque control command that satisfies the saturation limit .

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