A quadrotor unmanned aerial vehicle fixed-time attitude tracking control method

Abstract

The application provides a quad-rotor unmanned aerial vehicle fixed-time attitude tracking control method, constructs a quad-rotor unmanned aerial vehicle attitude dynamics model based on a quaternion, obtains tracking errors of attitude angles and angular velocities according to the attitude dynamics model, and determines an attitude tracking control target; a hyperbolic tangent function is introduced to approximate a saturation term, so that the problem of actuator saturation is solved; a preset performance function with fixed-time convergence is constructed based on the relationship between the tracking errors and transient performance constraints, so that overshoot and steady-state accuracy of the tracking errors are constrained; equivalent coordinate conversion is used to convert the constrained problem into an unconstrained problem; a fixed-time controller is constructed according to a backstepping method and a fuzzy approximation theory, and fixed-time attitude tracking control of the quad-rotor unmanned aerial vehicle is completed. The application can ensure that the control quantity meets the saturation constraint, and at the same time, ensure that the tracking error is always within the preset performance index range during the attitude adjustment process.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent control of aircraft, in particular to a fixed-time attitude tracking control method for quadrotor unmanned aerial vehicles considering actuator saturation and preset performance. BACKGROUND

[0002] Quadrotor unmanned aerial vehicles are widely used in aerospace, logistics transportation, fire fighting and disaster relief due to their light structure, low cost and high flexibility. In order to meet a series of tasks of quadrotor unmanned aerial vehicles, high-precision attitude control is essential, and it is also the premise of position control. However, actuator saturation is inevitable in the process of attitude control, and if this problem is not addressed, it will affect the system performance and even cause system instability. On the other hand, if the transient performance (overshoot, steady-state error) is not constrained, the unmanned aerial vehicle is prone to collision during task execution. Although the patent (CN111324138B: A quadrotor attitude specified time performance output feedback control method) considers the impact of performance constraints on unmanned aerial vehicle attitude control, it does not consider the impact of actuator saturation on system performance, and the specified time control requires a large control input, which is often difficult to meet in practice. The patent (CN113419565B: A quadrotor aircraft preset performance trajectory tracking backstepping control method and system) also considers preset performance constraints, but it does not consider actuator saturation and fixed-time control. Therefore, it is important and meaningful to consider the fixed-time attitude tracking control of quadrotor unmanned aerial vehicles considering actuator saturation and preset performance. SUMMARY

[0003] The present application relates to the field of intelligent control of aircraft, in particular to a fixed-time attitude tracking control method for quadrotor unmanned aerial vehicles considering actuator saturation and preset performance.

[0004] The technical solution for achieving the purpose of the present application is as follows: A fixed-time attitude tracking control method for quadrotor unmanned aerial vehicles, comprising the following steps:

[0005] Step 1: Construct a quadrotor unmanned aerial vehicle attitude dynamics model based on quaternions, and determine the attitude tracking control target according to the tracking error of attitude angle and angular velocity.

[0006] Step 2: Introduce a hyperbolic tangent function to approximate the saturation term to solve the actuator saturation problem.

[0007] Step 3: Based on the relationship between the tracking error and the transient performance constraint, construct a fixed-time convergent preset performance function to constrain the overshoot and steady-state accuracy of the tracking error, and use equivalent coordinate transformation to convert the constrained problem into an unconstrained problem.

[0008] Step 4, Construct the fixed-time controller according to the inverse method and fuzzy approximation theory, complete the fixed-time attitude tracking control of quadrotor unmanned aerial vehicle.

[0009] Further, step 1, construct the attitude dynamics model of quadrotor unmanned aerial vehicle based on quaternion, and then get the tracking error of attitude angle and angular velocity, determine the attitude tracking control target, the specific method is:

[0010] Step 1, construct the attitude dynamics model of quadrotor unmanned aerial vehicle based on quaternion, the specific form is as follows:

[0011]

[0012] Where q0 and represent the scalar part and vector part of unit quaternion , and satisfy represents the angular velocity in the body coordinate system, I 3×3 represents the 3 × 3 unit matrix, S(q v ) is the Coriolis force term, and its expression is as follows:

[0013]

[0014] Where q v is the vector part of unit quaternion, and q v1 , q v2 , q v3 are three components of the vector part of unit quaternion;

[0015] The attitude tracking control target is to track the error still converges to the bound within the fixed time range, where the tracking error of attitude angle is defined as Its expression is as follows:

[0016]

[0017] Where, and are the scalar component and vector component of the desired quaternion q r , represents the i-th component of the vector component, and the desired tracking signal is defined as q0 and q v1 , q v2 , q v3 are the scalar component and vector component of unit quaternion q, q vi represents the i-th component of the vector component;

[0018] The attitude angular velocity tracking error is defined as represents the desired attitude angular velocity relative to the body coordinate system, and satisfies ω b represents the attitude angular velocity, and its expression is as follows:

[0019]

[0020] wherein represents the moment of inertia matrix of the unmanned aerial vehicle, is the control moment of the three attitudes, represents unknown disturbance variables, and S(ω b ) is the Coriolis force term, and its expression is as follows:

[0021]

[0022] According to formulas (1)-(5), the mathematical model of the attitude angular error and the angular velocity error of the quad-rotor unmanned aerial vehicle is obtained, and is expressed in the following form:

[0023]

[0024] From this, the control problem is converted into designing τ b so that the tracking error can converge to a small bound within a fixed time.

[0025] Further, in step 2, the hyperbolic tangent function is introduced to approximate the saturation term to solve the actuator saturation problem, and the specific method is as follows:

[0026] The actuator saturation problem is expressed as follows:

[0027] τ b =sat(u) (7) wherein is the control quantity to be designed, and the size is limited by the following saturation function:

[0028]

[0029] wherein, is the saturation upper limit of the i-th control quantity;

[0030] The hyperbolic tangent function is introduced, and the actuator saturation is approximately expressed as:

[0031] sat(u) = q(u) + ε(u) (9) wherein, and

[0032]

[0033] represents the approximation error, and the maximum upper bound of ε i (u i ) is represented as

[0034] According to the Mean Value Theorem:

[0035]

[0036] in, To control the initial value, For ease of use, let The above expression can then be represented in the following form:

[0037]

[0038] in,

[0039] Substituting equations (9) and (12) into equation (7), we get:

[0040] τ b =gu+ε(u) (13)

[0041] in, and

[0042] Furthermore, substituting equation (13) into equation (6), we have:

[0043]

[0044] Where D = J -1 ε(u)+J -1 d τ , because d τ Since both ε(u) and ε are bounded, D is also bounded. Therefore, assume there exists an unknown upper bound d. m , satisfying ||D||≤d m ;

[0045] Therefore, the control objective is transformed into designing a controller u for the error system (14) that minimizes the attitude tracking error e, while considering actuator saturation. q and e ω It converges to a small bound within a fixed time period, meaning that q can keep up with the reference signal q within a fixed time range. r .

[0046] Furthermore, in step 3, based on the relationship between tracking error and transient performance constraints, a pre-defined performance function with fixed-time convergence is constructed to constrain the overshoot and steady-state accuracy of the tracking error. Using equivalent coordinate transformation, the constrained problem is transformed into an unconstrained problem. The specific method is as follows:

[0047] The following constraints are imposed on the tracking error:

[0048]

[0049] Among them, e qi (t) represents the i-th component of the tracking error. σ i and The preset performance parameters to be designed, and the initial values ​​satisfy... A performance function is preset for a fixed time period, and its form is as follows:

[0050]

[0051] in, T is a preset time constant;

[0052] By introducing an equivalent coordinate transformation, the constrained problem is transformed into an unconstrained optimization problem, as follows:

[0053]

[0054] Where, ζ i (t) represents the conversion error. It is a strictly increasing, smooth, and invertible function, with the following form:

[0055]

[0056] According to s(ζ) i The definition of (t) and the error transformation relationship (17) are as follows:

[0057]

[0058] Its derivative is:

[0059]

[0060] in

[0061]

[0062] Therefore, the converted error is expressed as:

[0063]

[0064] Based on the above process, the control problem with preset performance constraints is transformed into an unconstrained control problem, and the subsequent controller design can be based on the transformed attitude error signal. Instead of using the original system's attitude error signal e qi .

[0065] Furthermore, in step 4, a fixed-time controller is constructed based on the backstepping method and fuzzy approximation theory to complete the fixed-time attitude tracking control of the quadcopter UAV. The specific method is as follows:

[0066] Two new error variables, z1 and z2, are introduced and defined as follows:

[0067]

[0068] Where α1 is the virtual control variable;

[0069] Differentiating with respect to the z1 subsystem, we have:

[0070]

[0071] in

[0072]

[0073]

[0074] The Lyapunov functions of the z1 subsystem are defined as follows:

[0075]

[0076] Its derivative is:

[0077]

[0078] The virtual control variables are constructed as follows:

[0079]

[0080] in

[0081]

[0082] Differentiating the z2 subsystem, we have:

[0083]

[0084] in, The fuzzy logic system is used to approximate unknown nonlinear terms, as follows:

[0085]

[0086] Where χ is the weight coefficient of the fuzzy system. For fuzzy basis functions, To approximate the error;

[0087] For the z2 system, the following Lyapunov function is defined:

[0088]

[0089] in This represents the estimation error of the adaptive parameters;

[0090] The derivative of V2 is:

[0091]

[0092] Where k1, k2, and λ1 are all constants greater than 0;

[0093] According to Yang's inequality:

[0094]

[0095] in, θ b d m All are constants greater than 0;

[0096] Substituting equation (32) into equation (31), we get:

[0097]

[0098] Let ‖χ‖ 2 =θ, then we have

[0099]

[0100] Build the following controller:

[0101]

[0102] Where k3 and k4 are both constants greater than 0;

[0103]

[0104] Where δ is a constant greater than 0;

[0105] Substituting (35) into (34), we get:

[0106]

[0107] The parameter adaptation rate is:

[0108]

[0109] From this point on, under the action of the controller (35) and the adaptive regulation rate (37), the actual attitude of the quadcopter drone can keep up with the desired attitude, and the transient performance will not exceed the preset performance function, and the input of the controller will not exceed the saturation limit.

[0110] A fixed-time attitude tracking control method for a quadrotor unmanned aerial vehicle (UAV) is provided, which realizes fixed-time attitude tracking control of the quadrotor UAV considering actuator saturation and preset performance.

[0111] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements fixed-time attitude tracking control of a quadcopter UAV, taking into account actuator saturation and preset performance, based on the aforementioned fixed-time attitude tracking control method for quadcopter UAVs.

[0112] A computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements fixed-time attitude tracking control of a quadcopter UAV, taking into account actuator saturation and preset performance, based on the aforementioned fixed-time attitude tracking control method for quadcopter UAVs.

[0113] Compared with the prior art, the present invention has the following significant advantages: (1) On the basis of ensuring that the control quantity meets the saturation constraint, it also ensures that the tracking error is always within the preset performance index range during the attitude adjustment process; (2) The introduction of fuzzy approximation theory enables the designed control method to handle the unknown nonlinear function in the modeling process; (3) The design of fixed-time control, compared with asymptotic tracking control, not only enables the tracking error to achieve the control purpose within a finite time, but also increases the anti-interference capability of the controller. Attached Figure Description

[0114] Figure 1 This is a schematic diagram of the structure of a quadcopter drone.

[0115] Figure 2 This is a flowchart of the controller design method proposed in this invention.

[0116] Figure 3 It shows the roll angle tracking trajectory and tracking error diagram under the action of different controllers.

[0117] Figure 4 It shows the pitch angle tracking trajectory and tracking error under the action of different controllers.

[0118] Figure 5 It shows the yaw angle tracking trajectory and tracking error diagram under the action of different controllers.

[0119] Figure 6 This is the output diagram of the controller designed in this invention. Detailed Implementation

[0120] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0121] This invention proposes a fixed-time attitude tracking control method for a quadrotor UAV that considers actuator saturation and preset performance. First, a quaternion-based attitude dynamics model of the quadrotor UAV is established. Second, a hyperbolic tangent function is introduced to address actuator saturation. Then, by analyzing the relationship between tracking error and transient performance constraints, a preset performance function with fixed-time convergence is designed to constrain overshoot and steady-state accuracy of the tracking error. Finally, the fixed-time attitude tracking controller is designed using the backstepping method and fuzzy approximation theory. The effectiveness of the control method is verified through Lyapunov stability theory and implementation examples. The flowchart of the method is shown below. Figure 2 As shown, the specific steps are as follows:

[0122] Step 1: Establish an attitude dynamics model of a quadrotor UAV based on quaternions. The specific form is as follows:

[0123]

[0124] Where q0 and Representing unit quaternions The scalar and vector parts, and satisfying I represents the angular velocity in the body coordinate system. 3×3 S(q) represents a 3×3 identity matrix. v The term ) represents the Coriolis force, and its expression is as follows:

[0125]

[0126] Where q v The vector part of the unit quaternion, and q v1 ,q v2 ,q v3 The three components of the unit quaternion vector part.

[0127] The purpose of this invention is to design a controller that, considering actuator saturation and preset performance constraints, allows the tracking error to converge to a small bound within a fixed time range.

[0128] The desired tracking signal is defined as The tracking error of the attitude angle is defined as Its expression is as follows:

[0129]

[0130] in, and For the expected quaternion q r scalar components and vector components, Representing the i-th quantity of the vector component, q0 and q v1 ,q v2 ,qv3 Let q be the scalar and vector components of the unit quaternion q. vi This represents the i-th quantity of the vector component.

[0131] The attitude angle tracking error and attitude angular velocity error are expressed in a more compact form. The attitude angular velocity tracking error is defined as... This represents the desired attitude angular velocity relative to the body coordinate system, and satisfies... In addition, the tracking errors of attitude angle and attitude angular velocity satisfy The expression for attitude angular velocity is as follows:

[0132]

[0133] in The matrix representing the rotational inertia of the drone. For the control torque of three attitudes, S(ω) represents an unknown perturbation variable. b The term ) represents the Coriolis force, and its expression is as follows:

[0134]

[0135] According to equations (1)-(5), the mathematical models of attitude angle error and angular velocity error of the quadcopter UAV can be expressed as follows:

[0136]

[0137] From this point on, the control problem is transformed into designing τ. b This allows the tracking error to converge to a small bound within a fixed time.

[0138] Step 2: Introduce a hyperbolic tangent function to approximate the saturation term and address the actuator saturation problem. In practical applications, due to energy and safety constraints, the control input cannot be infinitely large. Based on this, this invention considers common actuator saturation problems, the mathematical representation of which is as follows:

[0139] τ b =sat(u) (7)

[0140] in The control variable to be designed is subject to the following saturation function:

[0141]

[0142] in, This represents the saturation upper limit of the i-th control variable.

[0143] To address the actuator saturation problem, this invention introduces a hyperbolic tangent function for processing, and actuator saturation can be approximated as:

[0144] sat(u)=q(u)+ε(u) (9)where, and

[0145]

[0146] This represents the approximation error, and ε i (u i The maximum upper bound of ) can be expressed as

[0147] Furthermore, according to the Mean Value Theorem, we have:

[0148]

[0149] in, To control the initial value, For ease of use, let And choose the appropriate q i (u i If ), then the above formula can be expressed in the following form:

[0150]

[0151] in,

[0152] Substituting equations (9) and (12) into equation (7) yields:

[0153] τ b =gu+ε(u) (13)

[0154] in, and

[0155] Furthermore, substituting equation (13) into equation (6) yields:

[0156]

[0157] Where D = J -1 ε(u)+J -1 d τ Because d τ Since both ε(u) and ε are bounded, we know that D is also bounded. Therefore, we can assume that there exists an unknown upper bound d. m , satisfying ||D||≤d m .

[0158] Therefore, the control objective is transformed into designing a controller u for the error system (14) that minimizes the attitude tracking error e, while considering actuator saturation. q and e ω By converging to a small bound within a fixed time period, the achievement of the control objective of this invention means that q can keep up with the reference signal q within a fixed time range. r .

[0159] Step 3: Design a preset performance function and use equivalent coordinate transformation to transform the constrained problem into an unconstrained problem. In practical applications, traditional control algorithms only consider the steady-state performance of the tracking error signal, neglecting transient performance. This can easily lead to large fluctuations in the tracking error during convergence, affecting system performance. For example, excessive overshoot can cause a collision between the UAV and obstacles when traversing a narrow passage. Therefore, this invention imposes the following constraints on the tracking error:

[0160]

[0161] Among them, e qi (t) represents the i-th component of the tracking error, σ i and The preset performance parameters to be designed, and the initial values ​​satisfy... A performance function is preset for a fixed time period, and its form is as follows:

[0162]

[0163] in, T is a preset time constant;

[0164] Since directly handling control problems with performance constraints is quite difficult, this invention transforms the constrained problem into an unconstrained optimization problem by introducing an equivalent coordinate transformation, as follows:

[0165]

[0166] Where, ζ i (t) represents the conversion error. It is a strictly increasing, smooth, and invertible function, with the following form:

[0167]

[0168] According to s(ζ) i The definition of (t) and the error transformation relationship (16) are as follows:

[0169]

[0170] Its derivative is:

[0171]

[0172] in

[0173]

[0174] Therefore, the converted error can be expressed as:

[0175]

[0176] Based on the above process, the control problem with preset performance constraints is transformed into an unconstrained control problem, and the subsequent controller design can be based on the transformed attitude error signal. Instead of using the original system's attitude error signal e qi .

[0177] Step 4: Design a fixed-time controller based on the backstepping method and fuzzy approximation theory. Traditional UAV attitude control only converges the tracking error to zero or a small bound when time t approaches infinity. However, this is unreasonable in practical applications. Therefore, this invention considers the fixed-time control problem, enabling the tracking error to converge within a fixed time range. Specifically, to obtain a fixed-time attitude controller, the backstepping method is used to design the controller. First, two new error variables, z1 and z2, are introduced and defined as follows:

[0178]

[0179] Where α1 is the virtual control variable. Taking the derivative with respect to the z1 subsystem, we have:

[0180]

[0181] in

[0182]

[0183]

[0184] The Lyapunov functions of the z1 subsystem are defined as follows:

[0185]

[0186] Its derivative is:

[0187]

[0188] The virtual control quantity is designed as follows:

[0189]

[0190] in

[0191]

[0192] Differentiating the z2 subsystem, we have:

[0193]

[0194] in, Because a quadcopter drone is a highly nonlinear and strongly coupled nonlinear system, its system model is often difficult to obtain accurately. Therefore, this invention uses a fuzzy logic system to approximate unknown nonlinear terms, specifically as follows:

[0195]

[0196] Where χ is the weight coefficient of the fuzzy system. For fuzzy basis functions, This is the approximation error.

[0197] For the z2 system, the following Lyapunov function is defined:

[0198]

[0199] in This represents the estimation error of the adaptive parameters.

[0200] The derivative of V2 is:

[0201]

[0202] Where k1, k2, and λ1 are all constants greater than 0.

[0203] According to Yang's inequality:

[0204]

[0205] in, θ b d m All are constants greater than 0.

[0206] Substituting equation (32) into equation (31), we get:

[0207]

[0208] Let ‖χ‖ 2 =θ, then we have

[0209]

[0210] Design the following controller:

[0211]

[0212] Where k3 and k4 are both constants greater than 0.

[0213]

[0214] Where δ is a constant greater than 0.

[0215] Substituting (35) into (34) yields:

[0216]

[0217] The design parameter adaptability rate is:

[0218]

[0219] From this point on, under the action of the controller (35) and the adaptive regulation rate (37), the actual attitude of the quadcopter drone can keep up with the desired attitude, and the transient performance will not exceed the preset performance function, and the input of the controller will not exceed the saturation limit.

[0220] Step 5: Prove the stability of the designed algorithm based on Lyapunov theory.

[0221] Substituting (37) into (36), we have

[0222]

[0223] because We have

[0224]

[0225] Substituting (39) into (38), we get:

[0226]

[0227] According to commonly used mathematical inequalities:

[0228]

[0229] Substituting equation (41) into equation (40) yields:

[0230]

[0231] in,

[0232] According to the form of the Lyapunov function of the system designed in (42) and the stability theory of nonlinear systems, the designed controller is stable.

[0233] Example

[0234] To verify the effectiveness of the present invention, the following experiment was conducted.

[0235] The method proposed in this invention is compared with traditional PID algorithms and fixed-time attitude controllers. Figures 3-5 It can be seen that the attitude tracking controller with preset performance has better convergence performance, and the tracking error remains within the preset performance constraint range throughout the convergence process. Figure 6 It can be seen that even if the control quantity is limited by the saturation function, the controller designed in this invention can still achieve the control objective.

[0236] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0237] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A fixed-time attitude tracking and control method for a quadcopter unmanned aerial vehicle, characterized in that, Includes the following steps: Step 1: Construct a quadrotor UAV attitude dynamics model based on quaternions, thereby obtaining the tracking errors of attitude angles and angular velocities and determining the attitude tracking control target. Step 2: Introduce a hyperbolic tangent function to approximate the saturation term in order to solve the actuator saturation problem; Step 3: Based on the relationship between tracking error and transient performance constraints, construct a preset performance function with fixed-time convergence to constrain the overshoot and steady-state accuracy of tracking error. Then, use equivalent coordinate transformation to transform the constrained problem into an unconstrained problem. Step 4: Construct a fixed-time controller based on the backstepping method and fuzzy approximation theory to complete the fixed-time attitude tracking control of the quadcopter UAV.

2. The fixed-time attitude tracking and control method for a quadcopter UAV according to claim 1, characterized in that, Step 1: Construct a quadrotor UAV attitude dynamics model based on quaternions, thereby obtaining the tracking errors of attitude angles and angular velocities, and determining the attitude tracking control target. The specific method is as follows: Step 1: Construct a quadrotor UAV attitude dynamics model based on quaternions, in the following form: Where q0 and Representing unit quaternions The scalar and vector parts, and satisfying I represents the angular velocity in the body coordinate system. 3×3 S(q) represents a 3×3 identity matrix. v The term ) represents the Coriolis force, and its expression is as follows: Where, q v The vector part of the unit quaternion, and q v1 ,q v2 ,q v3 The three components of the unit quaternion vector part; The objective of attitude tracking control is to reduce the tracking error while considering actuator saturation and preset performance constraints. It can still converge to within the bounds within a fixed time range, where the tracking error of the attitude angle is defined as... Its expression is as follows: in, and For the expected quaternion q r scalar and vector components, The i-th quantity representing the vector component, the desired tracking signal is defined as follows: q0 and q v1 ,q v2 ,q v3 Let q be the scalar and vector components of the unit quaternion q. vi This represents the i-th quantity of the vector component; Attitude angular velocity tracking error is defined as This represents the desired attitude angular velocity relative to the body coordinate system, and satisfies... ω b This represents the attitude angular velocity, and its expression is as follows: in The matrix representing the rotational inertia of the drone. The control torque for the three attitudes, S(ω) represents an unknown perturbation variable. b The term ) represents the Coriolis force, and its expression is as follows: Based on equations (1)-(5), the mathematical models for the attitude angle error and angular velocity error of the quadcopter UAV are obtained, and are expressed in the following form: From this point on, the control problem is transformed into designing τ. b This allows the tracking error to converge to a small bound within a fixed time.

3. The fixed-time attitude tracking and control method for a quadcopter UAV according to claim 2, characterized in that, Step 2: Introduce a hyperbolic tangent function to approximate the saturation term in order to solve the actuator saturation problem. The specific method is as follows: The actuator saturation problem can be represented as follows: τ b =sat(u)(7) where The control variable to be designed is subject to the following saturation function: Among them, u Mi This represents the upper limit of saturation for the i-th control variable; Introducing the hyperbolic tangent function, actuator saturation can be approximated as: sat(u)=q(u)+ε(u) (9) in, and This represents the approximation error, and ε i (u i The maximum upper bound of ) is represented as |ε i (u i )|=|sign(u i )-q i (u i )|≤u Mi (1-tanh(1)); According to the Mean Value Theorem: in, To control the initial value, For ease of use, let The above expression can then be represented in the following form: in, Substituting equations (9) and (12) into equation (7), we get: t b =gu+ε(u) (13) in, and Furthermore, substituting equation (13) into equation (6), we have: Where D = J -1 ε(u)+J -1 d τ , because d τ Since both ε(u) and ε are bounded, D is also bounded. Therefore, assume there exists an unknown upper bound d. m , satisfying ||D||≤d m ; Therefore, the control objective is transformed into designing an error system controller u based on formula (14) that minimizes the attitude tracking error e, while considering actuator saturation. q and e ω It converges to a small bound within a fixed time period, meaning that q can keep up with the reference signal q within a fixed time range. r .

4. The fixed-time attitude tracking and control method for a quadcopter UAV according to claim 3, characterized in that, Step 3: Based on the relationship between tracking error and transient performance constraints, a pre-defined performance function with fixed-time convergence is constructed to constrain the overshoot and steady-state accuracy of the tracking error. Using equivalent coordinate transformation, the constrained problem is transformed into an unconstrained problem. The specific method is as follows: The following constraints are imposed on the tracking error: Among them, e qi (t) represents the i-th component of the tracking error. and The preset performance parameters to be designed, and the initial values ​​satisfy... A performance function is preset for a fixed time period, and its form is as follows: in, T is a preset time constant; By introducing an equivalent coordinate transformation, the constrained problem is transformed into an unconstrained optimization problem, as follows: Where, ζ i (t) represents the conversion error. It is a strictly increasing, smooth, and invertible function, with the following form: According to s(ζ) i The definition of (t) and the error transformation relationship (17) are as follows: Its derivative is: in Therefore, the converted error is expressed as: Based on the above process, the control problem with preset performance constraints is transformed into an unconstrained control problem, and the subsequent controller design can be based on the transformed attitude error signal. Instead of using the original system's attitude error signal e qi .

5. The fixed-time attitude tracking and control method for a quadcopter UAV according to claim 1, characterized in that, Step 4: Construct a fixed-time controller based on the backstepping method and fuzzy approximation theory to complete the fixed-time attitude tracking control of the quadcopter UAV. The specific method is as follows: Two new error variables, z1 and z2, are introduced and defined as follows: Where α1 is the virtual control variable; Differentiating with respect to the z1 subsystem, we have: in The Lyapunov functions of the z1 subsystem are defined as follows: Its derivative is: The virtual control variables are constructed as follows: in Differentiating the z2 subsystem, we have: in, The fuzzy logic system is used to approximate unknown nonlinear terms, as follows: Where χ is the weight coefficient of the fuzzy system. For fuzzy basis functions, To approximate the error; For the z2 system, the following Lyapunov function is defined: in This represents the estimation error of the adaptive parameters; The derivative of V2 is: Where k1, k2, and λ1 are all constants greater than 0; According to Yang's inequality: in, d m All are constants greater than 0; Substituting equation (32) into equation (31), we get: Let ‖χ‖ 2 =θ, then we have Build the following controller: Where k3 and k4 are both constants greater than 0; Where δ is a constant greater than 0; Substituting (35) into (34), we get: The adaptive adjustment rate of the constructed parameters is: From this point on, under the action of the controller designed according to formula (35) and the adaptive adjustment rate designed according to formula (37), the actual attitude of the quadcopter UAV can keep up with the desired attitude, and the transient performance will not exceed the preset performance function, and the input of the controller will not exceed the saturation limit.

6. A fixed-time attitude tracking and control method for a quadcopter unmanned aerial vehicle, characterized in that, Based on the fixed-time attitude tracking control method for quadrotor UAVs according to any one of claims 1-5, fixed-time attitude tracking control of quadrotor UAVs considering actuator saturation and preset performance is realized.

7. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements fixed-time attitude tracking control of a quadcopter UAV considering actuator saturation and preset performance based on the fixed-time attitude tracking control method for a quadcopter UAV according to any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements fixed-time attitude tracking control of a quadcopter UAV, taking into account actuator saturation and preset performance, based on the fixed-time attitude tracking control method for a quadcopter UAV according to any one of claims 1-5.

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