An adaptive robust constraint-following control method for a photographic unmanned aerial vehicle stabilizing holder

Abstract

The application discloses a kind of photographic unmanned aerial vehicle stabilizing gimbals adaptive robust constraint following control method, belong to unmanned aerial vehicle control technical field, comprising: first based on establishing gimbals system kinematics model, through Lagrange equation construction includes all working condition dynamics model with uncertainty and disturbance;Photographic lens desired trajectory is converted into second-order constraint equation, and a constraint tracking error index is constructed;Design includes nominal control item and adaptive robust compensation item Compound controller, solve servo constraint force, while embedding fixed threshold anti-shake strategy;Unknown uncertainty of system is estimated in real time by adaptive law with leakage term, and control compensation strength is updated;Finally, the system stability is verified by Lyapunov theory, and simulation and physical testing are completed.The application improves the gimbals trajectory tracking accuracy and motion stability, solves the problem of weak control buffeting, weak anti-interference ability and parameter drift in the prior art, and has strong engineering practicability.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) control technology, and in particular to an adaptive robust constraint following control method for a stabilized gimbal of a photography UAV. Background Technology

[0002] With the rapid development of aerial photography, film and television production, and geographic surveying, photographic drones have become core equipment for acquiring aerial visual information due to their advantages such as maneuverability, low operating costs, and rich shooting perspectives. As the core payload of photographic drones, the stabilizing gimbal's core function is to counteract the image shake caused by fuselage vibrations and attitude changes during drone flight, while precisely controlling the camera lens to track a preset motion trajectory. Its control performance directly determines the clarity, stability, and shooting effect of the aerial footage.

[0003] Currently, high-end application scenarios such as professional film and television aerial photography, dynamic target tracking, and multi-drone collaborative shooting place extremely high demands on gimbal control performance. Not only does the gimbal need to achieve precise linkage control of the two degrees of freedom of yaw and pitch to ensure the lens's sub-millimeter-level tracking accuracy of the desired trajectory, but the control process also needs to be extremely smooth to avoid the "jelly effect" in the footage caused by control jitter. At the same time, the complex airflow disturbances, body vibration transmission, load parameter changes caused by lens replacement, and parameter drift caused by component wear faced by drones during high-altitude operations all require the gimbal control system to have extremely strong robustness and adaptability.

[0004] Existing gimbal control solutions suffer from several insurmountable drawbacks: PID control, due to its simple structure and ease of implementation, is widely used in consumer-grade gimbals, but it suffers from large trajectory tracking errors when faced with the strong nonlinearity, strong coupling characteristics, and complex external disturbances of the gimbal system, failing to meet the high-precision requirements of professional photography; Model predictive control, while capable of balancing multiple constraints and dynamic response performance, has extremely high computational complexity, placing stringent demands on the computing power and real-time performance of embedded controllers, making it difficult to implement on the limited hardware resources of small drones; Sliding mode control possesses excellent disturbance rejection performance, but its inherent control jitter problem directly leads to a rolling shutter effect in the captured image, completely failing to meet the smoothness requirements of professional photography; Traditional constraint-following control methods, based on precise system model design, are prone to constraint violations when the system has parameter uncertainties and unknown external disturbances, resulting in a significant decrease in trajectory tracking accuracy, and cannot solve the problems of slow error convergence and large overshoot caused by incompatible initial conditions.

[0005] Furthermore, existing control schemes are mostly optimized for single working conditions and cannot dynamically balance control accuracy, response speed, robustness, and smoothness in different scenarios such as static fixed-position shooting, dynamic trajectory tracking, and operation in highly disturbed environments. They are also unable to simultaneously solve the five core technical pain points of gimbal systems: nonlinear coupling, parameter uncertainty, unknown external disturbances, insufficient trajectory tracking accuracy, and control jitter. This severely limits the promotion and application of photography drones in high-end film and television aerial photography, precision surveying and mapping, and other fields. Summary of the Invention

[0006] The purpose of this invention is to propose an adaptive robust constraint-following control method for a stabilized gimbal of a photography drone. This method overcomes the shortcomings of existing technologies, such as low gimbal control accuracy, weak anti-disturbance capability, easy control jitter, and easy parameter drift. It deeply integrates constraint-following theory with adaptive robust control, effectively suppressing control jitter while ensuring the trajectory tracking accuracy of the gimbal system. It also adaptively compensates for unknown uncertainties and external disturbances in the system, achieving high-precision and high-stability tracking of the desired trajectory by the camera lens under complex working conditions.

[0007] To achieve the above objectives, this invention provides an adaptive robust constraint following control method for a stabilized gimbal of a photography drone, comprising the following steps: Step S1: Establish a kinematic model of the stabilized gimbal system of the photography drone based on the Denavit-Hartenberg parametric method, and obtain the mapping relationship between the motion of the gimbal joints and the pose of the end of the camera lens; Step S2: Construct an unconstrained dynamic model of the gimbal system based on the Lagrange equation, introduce system uncertainties and external disturbance terms, and obtain a full-condition dynamic model with disturbances. Step S3: Transform the desired motion trajectory of the camera lens into constraint equations that fit the second-order characteristics of the dynamic model, and construct a quantitative index for constraint tracking error. Step S4: Design a composite controller that includes a nominal control term and an adaptive robust compensation term. Solve the servo constraint force of the nominal control term based on the Udwadia-Kalaba equation. At the same time, embed a fixed threshold anti-jitter strategy in the adaptive robust compensation term. Verify the uniform boundedness and uniform final boundedness of the controlled gimbal system based on Lyapunov stability theory. Step S5: Design an adaptive law with leakage terms, estimate the upper bound parameters of the unknown uncertainty of the system in real time online, and update the adaptive robust compensation terms of the composite controller synchronously. Step S6: Build a modular simulation model in the MATLAB Simulink environment, set the gimbal physical parameters, simulation conditions and initial conditions, and output and analyze the performance indicators of joint control torque, trajectory tracking error and adaptive parameter convergence curve.

[0008] Preferably, in step S1, the specific steps are as follows: the stabilizing gimbal system is equivalent to a two-degree-of-freedom robotic arm system including a yaw joint and a pitch joint; a base coordinate system, a yaw joint coordinate system, and a pitch joint coordinate system are established; the link parameters are defined by the Denavit-Hartenberg parametric method; the homogeneous transformation matrix between adjacent coordinate systems is derived; and the position mapping relationship of the end of the camera lens in the base coordinate system is obtained, thus completing the kinematic model construction. The homogeneous transformation matrix is ​​the transformation matrix from the base coordinate system to the pitch joint coordinate system. The expression is: ; in, The joint angle of the lateral joint. The joint angle of the pitch joint. Let be the transformation matrix from the base coordinate system to the yaw joint coordinate system. This is the transformation matrix from the yaw joint coordinate system to the pitch joint coordinate system; Combine the coordinates of the camera lens tip in the pitch coordinate system Derive its position mapping relationship in the base coordinate system: .

[0009] Preferably, in step S2, the specific steps are as follows: based on the Lagrange function Construct an unconstrained dynamic model of the gimbal system, in which The total kinetic energy of the gimbal system, The total potential energy of the gimbal system; the expression for the unconstrained dynamic model is: ; In the formula, Let be the inertial matrix of the gimbal system, which is a symmetric positive definite matrix; Joint angle vector, The joint angular velocity vector. This is the joint angular acceleration vector; It is a generalized force matrix that integrates the centrifugal force, Coriolis force, and gravitational effect of the system; Introducing joint control input torque With the total system disturbance term The dynamic model with disturbances under all operating conditions is obtained: ; in, , The control torque for the yaw joint, The control torque is input to the pitch joint; This is the total system disturbance term, which includes parameter uncertainties and external environmental disturbances.

[0010] Preferably, step S3 includes the following specific steps: Step S31: Define the desired motion trajectory of the end of the camera lens according to the requirements of the photography operation, and combine the kinematic model of step S1 to transform the desired trajectory into an equation constraint for the motion of the gimbal joint. The formula for the expected trajectory is: ; In the formula, , The desired position at the end of the lens, with a trajectory radius of 0.06m and a center point... ; The trajectory constraint formula is: ; Step S32: Take the first derivative of the equality constraints with respect to time, and construct the first-order constraint equations: ; in, For the constraint matrix, It is a first-order constraint vector that includes position error feedback; Step S33: Differentiate the first-order constraint equations with respect to time again, and rearrange to obtain the second-order constraint equations that fit the second-order characteristics of the dynamic model: ; ; in, The time derivative of the constraint matrix. The time derivative of the first-order constraint vector; Step S34: Define the constraint tracking error It is used to quantify the tracking deviation of the gimbal system on the desired trajectory.

[0011] Preferably, in step S4, the control input torque of the composite controller is the superposition of the nominal control term, the deviation compensation term, and the uncertainty suppression term, and its overall expression is: ; in, For nominal control items, This is the deviation compensation item. To embed the uncertainty suppression term of the fixed threshold anti-jitter strategy, These are adaptive estimation parameters for the upper bound of the unknown uncertainty of the system.

[0012] Preferred, nominal control items Designed based on the Udwadia-Kalaba equation, the expression is: ; in, For Moore-Penrose generalized inverse, , This is the nominal parameter matrix of the gimbal system dynamics model. It is a second-order constraint vector.

[0013] Preferred deviation compensation item The expression used to eliminate constraint deviations caused by incompatible initial conditions is: ; in, For bias feedback gain, It is a positive definite weighted matrix. To constrain tracking error.

[0014] Preferred uncertainty suppression term The expression is: ; in, , ; Fixed threshold anti-jitter strategy uses piecewise function-based anti-jitter gain. The implementation is achieved through the following expression: ; in, To control intermediate variables, This is a preset fixed anti-jitter threshold used to suppress jitter in the control input.

[0015] Preferably, in step S4, to verify the uniform boundedness and uniform final boundedness of the gimbal system under the designed controller, a Lyapunov function is constructed and the boundedness of its derivative is analyzed. The proof is completed by combining the final boundedness criterion. The boundedness of the derivative is analyzed by inequality scaling. Combined with the Lyapunov stability criterion, the uniform boundedness and uniform final boundedness of the controlled gimbal system are verified, ensuring that the tracking error can converge to the preset bounded neighborhood under the condition of unknown uncertainty and external disturbance. Select to constrain tracking deviation Lyapunov functions with the core as the core: ; right Regarding the time derivative, as shown in the following formula, the controlled system satisfies uniform boundedness. ; in, Used to adjust the convergence rate; Parameters related to system uncertainty; For the system's bounded disturbance term; To analyze the uniform eventual boundedness, we first define a threshold function. : ; in, , ; The controlled system has the following uniform eventual boundedness: .

[0016] Preferably, in step S5, the expression for the adaptive law with leakage terms is: ; in, To adaptively estimate the update rate of parameters, For adaptive growth rate coefficient, Let be the leakage coefficient; the adaptive law satisfies the following constraints: For all Established, among which To control the start time; leakage items It is used to suppress the excessive growth and drift of adaptive estimation parameters, and to achieve a bounded estimate of the upper bound of the unknown uncertainty of the system.

[0017] Therefore, the adaptive robust constraint following control method for a stabilized gimbal of a photography drone described above has the following advantages: (1) This invention deeply integrates Udwadia-Kalaba constraint following theory with adaptive robust control. By transforming the desired trajectory into a second-order constraint equation, the servo constraint force for achieving optimal constraint following can be directly solved without the need for complex Lagrange multiplier calculations, which greatly improves the trajectory tracking accuracy of the gimbal system. (2) The present invention designs an adaptive law with leakage term, which can estimate the upper bound of the unknown uncertainty of the system in real time online. At the same time, the leakage term effectively suppresses the excessive growth and drift problem of parameters of the traditional adaptive law, so that the controller can adaptively adjust the compensation intensity according to the changes in the system operating conditions, which greatly improves the system's adaptability to multiple uncertainties such as load changes, component wear, and airflow disturbance, and significantly enhances its robustness. (3) The present invention embeds a fixed threshold anti-shaking strategy in the adaptive robust compensation term. The anti-shaking gain in the form of a piecewise function replaces the sign function in the traditional sliding mode control, thereby eliminating the control jitter problem from the root, ensuring the smoothness of the joint control torque, completely avoiding the jelly effect of aerial images, and greatly improving the quality of photographic imaging. (4) The composite controller designed in this invention ensures the constraint following performance under ideal working conditions through the nominal control term, accelerates the convergence speed of the initial error through the deviation compensation term, and compensates for system disturbances and uncertainties through the uncertainty suppression term. The three work together to dynamically balance control accuracy, response speed, robustness and smoothness under different working conditions, solving the pain point that multiple performance indicators are difficult to balance in the prior art. (5) This invention rigorously proves the uniform boundedness and uniform final boundedness of the controlled system through Lyapunov stability theory, ensuring the stability and convergence of the system under all operating conditions. At the same time, the control algorithm has a small computational load and can run in real time on a small embedded controller, which has strong engineering practicality and promotion value.

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0019] Figure 1 This is an overall flowchart of an adaptive robust constraint following control method for a camera drone gimbal in an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure and DH coordinate system of the two-degree-of-freedom gimbal system in an embodiment of the present invention; Figure 3 This is a structural block diagram of the composite controller in an embodiment of the present invention; Figure 4 This is a comparison diagram of the actual tracking trajectory and the expected trajectory at the end of the lens during simulation testing in an embodiment of the present invention; Figure 5 This is a curve showing the variation of constraint tracking error during simulation testing in this embodiment of the invention; Figure 6 This is the update convergence curve of the adaptive estimation parameters in the simulation test of this embodiment of the invention; Figure 7 This is a composite diagram showing the control torque, joint angle, and position error of the gimbal joint during simulation testing in this embodiment of the invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0021] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0022] Example like Figure 1-7 As shown in the figure, this embodiment proposes an adaptive robust constraint following control method for a stabilized gimbal of a photography drone. The specific steps are as follows: Step S1: Establish the kinematic model of the gimbal system based on the Denavit-Hartenberg (DH) parametric method: The two-degree-of-freedom stabilized gimbal is equivalent to a serial robotic arm system, and a kinematic model is established as follows: Figure 2 The DH coordinate system shown: base coordinate system Horizontal joint coordinate system Pitch joint coordinate system The axes of the two rotational joints are perpendicular to each other and intersect, and the origins of the three coordinate systems are coincident and fixed at the center of the pitch joint; The axis is in the same direction as the yaw joint axis. The axis is in the same direction as the pitch joint axis. , , The axes are all pointing towards the camera lens. , , The axis is determined by the right-hand rule.

[0023] set up At the end of the camera lens, For line segments length, For line segments Angle with the lens axis. The link parameters are defined using the Denavit-Hartenberg (DH) method, and the coordinate transformation matrix is ​​derived: ; in, For the lateral joint angle, This refers to the pitch joint angle.

[0024] Combine the coordinates of the end of the lens in the pitch coordinate system Derive its position mapping relationship in the base coordinate system: ; By taking the derivative with respect to time, the velocity mapping relationship is obtained, and the kinematic model is completed.

[0025] Step S2: Construct a full-condition dynamic model with disturbances based on the Lagrange equations: Based on Lagrange function ,in For the total power of the gimbal, Given the total potential energy, the unconstrained dynamic model is derived as follows: ; in, , , , , ; Among them, for the inertia matrix ,remember , , , , ; ; ; in: , These are the masses of the yaw and pitch components, respectively. , Let the coordinates of the centroid of the yaw component be . , , The coordinates of the center of mass of the pitch component; Let be the moment of inertia of the yaw component about its rotation axis. , The moment of inertia of the pitch component about its own coordinate axis; For the generalized force matrix It integrates centrifugal force and gravitational effects. The gravitational acceleration is taken as... .

[0026] ; ; Considering the parameter uncertainties (such as mass and moment of inertia drift) and external disturbances (such as airflow interference and vibration) in actual operation, and combining the control input torque, the unconstrained dynamic equations are rewritten as follows: ; in, The input torque is used to control the yaw and pitch joints. This is the total disturbance term.

[0027] Step S3: Transform the desired trajectory into a second-order constraint equation and construct the constraint tracking error: The desired trajectory is defined according to the requirements of the photography scene. By constructing constraint equations and transforming derivatives, the requirement for tracking the trajectory at the end of the lens is transformed into a second-order constraint on the motion of the gimbal joint, providing a basis for the controller design.

[0028] Step S31: Define the desired motion trajectory. The desired trajectory at the end of the camera lens is... The equation of a planar circular locus is: ; In the formula, , The desired position at the end of the lens, with a trajectory radius of 0.06m and a center point... ; The trajectory constraints are: .

[0029] Step S32: Construct first-order constraint equations. Combining the mapping relationship between the actual position of the lens end and the gimbal joint angle in the kinematic model of Step S1, and ensuring the actual velocity tracks the desired velocity, construct the first-order constraint equations: ; Wherein, the constraint matrix First-order constraint vector Based on kinematic relationships, the expression is derived as follows: ; in, For position error feedback gain, , This refers to the actual position at the end of the lens. , This represents the desired speed at the end of the lens.

[0030] Step S33: Transform into second-order constraint equations. To adapt to the second-order characteristics of the dynamic model, differentiate the first-order constraint equations with respect to time, and rearrange to obtain the second-order constraint equations: ; Among them, the second-order constraint vector , , These are the time derivatives of the constraint matrix and the first-order constraint vector, respectively, derived according to the rules of differentiation. Step S34: Define the first-order constraint tracking error It is used to quantify trajectory following deviation, providing a basis for subsequent controller error correction.

[0031] Step S4: Design a composite adaptive robust controller: For dynamic models with disturbances and second-order constraint equations, an adaptive robust controller is designed. The controller consists of a nominal control term, a deviation compensation term, and an uncertainty suppression term. The control input torque is the superposition of the sub-terms. All control term formulas, parameter values, and generalized inverse solution methods are designed according to control theory specifications.

[0032] The overall form of the controller is as follows: ; in, For nominal control items, For deviation compensation items, This is an uncertainty suppression term; For nominal control items Designed based on the Udwadia-Kalaba equations, and adapted to the nominal dynamic model and second-order constraint equations, it achieves perfect constraint following under ideal, undisturbed operating conditions. The calculation formula is as follows: ; in, This is the nominal part of the dynamic model. For Moore-Penrose generalized inverse; For deviation compensation items This is used to resolve the incompatibility between initial conditions and constraint equations, and to accelerate the convergence of constraint tracking errors. The calculation formula is as follows: ; in, For feedback gain, It is a 2-order identity matrix. To constrain tracking error; For uncertainty suppression term Used to compensate for the total disturbance term To address parameter uncertainties and avoid controlling chattering, the calculation formula is as follows: ; in, , , The piecewise function form of the jitter reduction gain is shown in the following equation. To prevent jitter threshold, These are adaptively estimated parameters.

[0033] .

[0034] To verify the uniformly bounded and uniformly eventually bounded nature of the system under the designed controller, a Lyapunov function was constructed and the boundedness of its derivative was analyzed. The proof was then completed using the eventually boundedness criterion. The boundedness of the derivative was analyzed through inequality scaling, and combined with the Lyapunov stability criterion, the uniformly bounded and uniformly eventually bounded nature of the controlled gimbal system was verified. This ensures that under conditions of unknown uncertainties and external disturbances, the tracking error can converge to a preset bounded neighborhood. Select to constrain tracking deviation Lyapunov functions with the core as the core: ; right Differentiation with respect to time is as follows. Therefore, the controlled system satisfies uniform boundedness.

[0035] ; In the formula, Used to adjust the convergence rate; Parameters related to system uncertainty; This is a bounded disturbance term for the system.

[0036] To analyze the eventual boundedness, we first define a threshold function. : ; in, , .

[0037] Therefore, the controlled system also possesses the following consistent eventual boundedness: .

[0038] Step S5: Design an adaptive law with leakage terms: To estimate the upper bound of uncertainty in real time and avoid the excessive parameter growth problem of traditional adaptive laws, an adaptive law with a leakage term is designed to achieve adaptive parameter estimation. The online updates, formula forms, parameter values, and initial conditions are designed according to adaptive control theory.

[0039] The core formula of the adaptive law is: ; in, For adaptive growth rate, Leakage coefficient; The constraint is to ensure that the adaptive estimation parameter is always positive, i.e. For all Established, Leaked Item It effectively suppresses excessive parameter growth and solves the parameter drift problem.

[0040] Step S6: System performance simulation test: A modular simulation model was built in the MATLAB Simulink environment, including kinematics, dynamics, desired trajectory generation, constraint equations, adaptive robust controller, adaptive law with leakage term, and disturbance and uncertainty modules. The physical parameters of the gimbal, simulation time, solution step size, parameter uncertainty and external disturbance intensity, and system initial conditions were set. The simulation outputs the yaw / pitch joint control torque curve, joint angle / angular velocity curve, constraint tracking error curve, and adaptive estimation parameter convergence curve to verify the performance of the control method.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An adaptive robust constraint following control method for a stabilized gimbal of a photography drone, characterized in that, Includes the following steps: Step S1: Establish a kinematic model of the stabilized gimbal system of the photography drone based on the Denavit-Hartenberg parametric method, and obtain the mapping relationship between the motion of the gimbal joints and the pose of the end of the camera lens; Step S2: Construct an unconstrained dynamic model of the gimbal system based on the Lagrange equation, introduce system uncertainties and external disturbance terms, and obtain a full-condition dynamic model with disturbances. Step S3: Transform the desired motion trajectory of the camera lens into constraint equations that fit the second-order characteristics of the dynamic model, and construct a quantitative index for constraint tracking error. Step S4: Design a composite controller that includes a nominal control term and an adaptive robust compensation term. Solve the servo constraint force of the nominal control term based on the Udwadia-Kalaba equation, and embed a fixed threshold anti-jitter strategy in the adaptive robust compensation term. Verify the uniform boundedness and uniform final boundedness of the controlled gimbal system based on Lyapunov stability theory; Step S5: Design an adaptive law with leakage terms, estimate the upper bound parameters of the unknown uncertainty of the system in real time online, and update the adaptive robust compensation terms of the composite controller synchronously. Step S6: Build a modular simulation model in the MATLAB Simulink environment, set the gimbal physical parameters, simulation conditions and initial conditions, and output and analyze the performance indicators of joint control torque, trajectory tracking error and adaptive parameter convergence curve.

2. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 1, characterized in that: In step S1, the specific steps are as follows: the stabilized gimbal system is equivalent to a two-degree-of-freedom robotic arm system including a yaw joint and a pitch joint. The base coordinate system, the yaw joint coordinate system and the pitch joint coordinate system are established. The link parameters are defined by the Denavit-Hartenberg parametric method. The homogeneous transformation matrix between adjacent coordinate systems is derived. Then the position mapping relationship of the end of the camera lens in the base coordinate system is obtained, and the kinematic model is completed. The homogeneous transformation matrix is ​​the transformation matrix from the base coordinate system to the pitch joint coordinate system. The expression is: ； in, The joint angle of the lateral joint. The joint angle of the pitch joint. Let be the transformation matrix from the base coordinate system to the yaw joint coordinate system. This is the transformation matrix from the yaw joint coordinate system to the pitch joint coordinate system; Combine the coordinates of the camera lens tip in the pitch coordinate system Derive its position mapping relationship in the base coordinate system: 。 3. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 2, characterized in that: In step S2, the specific steps are as follows: based on the Lagrange function Construct an unconstrained dynamic model of the gimbal system, in which The total kinetic energy of the gimbal system, The total potential energy of the gimbal system; the expression for the unconstrained dynamic model is: ； In the formula, Let be the inertial matrix of the gimbal system, which is a symmetric positive definite matrix; Joint angle vector, The joint angular velocity vector. This is the joint angular acceleration vector; It is a generalized force matrix that integrates the centrifugal force, Coriolis force, and gravitational effect of the system; Introducing joint control input torque With the total system disturbance term The dynamic model with disturbances under all operating conditions is obtained: ； in, , The control torque for the yaw joint, The control torque is input to the pitch joint; This is the total system disturbance term, which includes parameter uncertainties and external environmental disturbances.

4. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 3, characterized in that: Step S3 includes the following specific steps: Step S31: Define the desired motion trajectory of the end of the camera lens according to the requirements of the photography operation, and combine the kinematic model of step S1 to transform the desired trajectory into an equation constraint for the motion of the gimbal joint. The formula for the expected trajectory is: ； In the formula, , The desired position at the end of the lens, with a trajectory radius of 0.06m and a center point... ; The trajectory constraint formula is: ； Step S32: Take the first derivative of the equality constraints with respect to time, and construct the first-order constraint equations: ； in, For the constraint matrix, It is a first-order constraint vector that includes position error feedback; Step S33: Differentiate the first-order constraint equations with respect to time again, and rearrange to obtain the second-order constraint equations that fit the second-order characteristics of the dynamic model: ； ； in, The time derivative of the constraint matrix, The time derivative of the first-order constraint vector; Step S34: Define the constraint tracking error It is used to quantify the tracking deviation of the gimbal system on the desired trajectory.

5. The adaptive robust constraint following control method for a camera drone gimbal according to claim 4, characterized in that: In step S4, the control input torque of the composite controller is the superposition of the nominal control term, the deviation compensation term, and the uncertainty suppression term, and its overall expression is: ； in, For nominal control items, This is the deviation compensation item. To embed the uncertainty suppression term of the fixed threshold anti-jitter strategy, These are adaptive estimation parameters for the upper bound of the unknown uncertainty of the system.

6. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 5, characterized in that: Nominal control items Designed based on the Udwadia-Kalaba equation, the expression is: ； in, For Moore-Penrose generalized inverse, , This is the nominal parameter matrix of the gimbal system dynamics model. It is a second-order constraint vector.

7. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 6, characterized in that: Deviation Compensation Item The expression used to eliminate constraint deviations caused by incompatible initial conditions is: ； in, For bias feedback gain, It is a positive definite weighted matrix. To constrain tracking error.

8. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 7, characterized in that: Uncertainty suppression term The expression is: ； in, , ; Fixed threshold anti-jitter strategy uses piecewise function-based anti-jitter gain. The implementation is achieved through the following expression: ； in, To control intermediate variables, This is a preset fixed anti-jitter threshold used to suppress jitter in the control input.

9. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 8, characterized in that: In step S4, to verify the uniform boundedness and uniform eventual boundedness of the designed controller-controlled gimbal system, a Lyapunov function is constructed and the boundedness of its derivative is analyzed. The proof is completed by combining the eventual boundedness criterion. The boundedness of the derivative is analyzed by inequality scaling. Combined with the Lyapunov stability criterion, the uniform boundedness and uniform eventual boundedness of the controlled gimbal system are verified, ensuring that the tracking error can converge to the preset bounded neighborhood under the condition of unknown uncertainty and external disturbance. Select to constrain tracking deviation Lyapunov functions with the core as the core: ； right Regarding the time derivative, as shown in the following formula, the controlled system satisfies uniform boundedness. ； in, Used to adjust the convergence rate; Parameters related to system uncertainty; For the system's bounded disturbance term; To analyze the uniform eventual boundedness, we first define a threshold function. : ； in, , ; The controlled system has the following uniform eventual boundedness: 。 10. The adaptive robust constraint following control method for a stabilized gimbal of a photography drone according to claim 9, characterized in that: In step S5, the expression for the adaptive law with leakage terms is: ； in, To adaptively estimate the update rate of parameters, For adaptive growth rate coefficient, Let be the leakage coefficient; the adaptive law satisfies the following constraints: For all Established, among which To control the start time; leakage items It is used to suppress the excessive growth and drift of adaptive estimation parameters, and to achieve a bounded estimate of the upper bound of the unknown uncertainty of the system.

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