A UAV predefined time trajectory tracking method based on observer perturbation compensation

Abstract

This invention discloses a predefined time trajectory tracking method for unmanned aerial vehicles (UAVs) based on observer disturbance compensation. First, a quadrotor position and attitude dynamics model incorporating external forces and torque disturbances is established. A predefined time-stability function with linear terms and piecewise auxiliary functions are constructed, obtaining a preset upper bound for convergence time unaffected by initial conditions and avoiding singularity issues caused by negative fractional powers. Then, predefined time sliding mode observers are designed in the position and attitude loops respectively to estimate various lumped disturbances. Based on the observation results, control laws, attitude sliding surfaces, and corresponding control terms are designed, and rotor speed commands are output through an X-configuration control allocation matrix. This method enables disturbance estimation errors to converge to a bounded neighborhood within a preset time, and attitude tracking errors to converge within a time limit, ensuring smooth trajectory tracking, effectively resisting interference from wind disturbances and load changes, reducing chattering, and optimizing control input smoothness. It is suitable for high-dynamic trajectory tracking and high-precision attitude control of UAVs.

Description

Technical Field

[0001] This invention relates to the field of quadcopter unmanned aerial vehicle (UAV) control technology, and in particular to a method for tracking a predefined time trajectory of a UAV based on observer disturbance compensation. Background Technology

[0002] Quadcopter drones possess advantages such as vertical takeoff and landing, excellent hovering performance, high maneuverability, and compact overall structure, leading to their widespread adoption and application in numerous fields including equipment inspection, terrain mapping, disaster monitoring, logistics transportation, and swarm collaborative operations. On the other hand, quadcopter drones are typical underactuated, strongly coupled, and nonlinear flight devices, making their position and attitude highly susceptible to interference from multiple factors such as aerodynamic disturbances, system parameter perturbations, changes in onboard loads, and external wind fields. Under conditions of performing high-dynamic trajectory tracking tasks, these disturbances can further exacerbate problems such as increased transient deviations in flight trajectory, intensified body attitude fluctuations, and abrupt changes in control input commands, severely impacting the drone's flight stability and control accuracy.

[0003] Currently, sliding mode control is commonly used in the field of quadcopter drone control. This method has a certain degree of robustness and can resist external disturbances and system uncertainties to a certain extent, as shown in the patent application with publication number CN120335485A. However, existing sliding mode control schemes still have several obvious technical shortcomings and cannot fully adapt to the high dynamic trajectory tracking requirements of quadcopter drones:

[0004] First, traditional finite-time and fixed-time sliding mode control methods make it difficult for designers to explicitly set the upper bound of the system convergence time, which cannot adapt to the time constraints of flight missions and is not conducive to the design of flight control systems oriented towards mission timeliness requirements.

[0005] Secondly, negative fractional power terms are often introduced into existing sliding surfaces or reaching laws. Such structures are prone to singularity problems in the neighborhood of the origin, which can lead to a sudden surge in control commands and threaten flight safety.

[0006] Third, when drones encounter strong unknown disturbances, existing technologies generally improve their anti-disturbance capabilities by increasing the switching gain. This method will cause significant jitter in the control system and degrade flight quality.

[0007] Fourth, currently, disturbance observers and controllers are mostly designed separately, and the two are not coordinated for optimization within the same predefined time frame. This results in a mismatch between the dynamic time scales of the disturbance estimation process and the trajectory tracking adjustment process, thus limiting the overall control effect. Summary of the Invention

[0008] The purpose of this invention is to solve the problems of existing quadrotor UAV trajectory tracking control convergence time being difficult to explicitly set, singularity easily occurring in the origin neighborhood, significant control jitter under strong disturbance conditions, and insufficient coordination between the observer and the controller. It provides a UAV predefined time trajectory tracking method based on observer disturbance compensation, which improves the trajectory tracking accuracy, attitude stability, and control input smoothness of quadrotor UAVs under complex external disturbances and parameter changes.

[0009] To solve the above problems, the present invention adopts the following technical solution:

[0010] A method for tracking a predefined time trajectory of a UAV based on observer perturbation compensation, the method comprising the following steps:

[0011] S1. Establish a dynamic model of the position and attitude of a quadrotor UAV with external disturbances, using the position state, Euler angle state, angular velocity state of the machine system, total lift input, attitude torque input, external disturbance force and external disturbance torque in the inertial coordinate system as the modeling variables of the controlled object.

[0012] S2. Construct a predefined time-stability function containing linear terms and a piecewise auxiliary function. Use the function to make the sliding surface and the observer correction term avoid negative fractional power singularity in the neighborhood of the origin, and provide a predefined time stability analysis basis for attitude loop control and disturbance observation.

[0013] S3. Design a predefined time sliding mode observer for the position loop to monitor the position state. , , The external disturbance forces of the three channels are estimated online to obtain the estimated external disturbance forces.

[0014] S4. Design a predefined time sliding mode observer for the attitude loop to estimate the angular error derivatives and lumped disturbances of the roll, pitch and yaw channels online, and obtain the estimated values ​​of the first derivative of the attitude error and the estimated values ​​of the lumped disturbances of the attitude channels.

[0015] S5. Based on the position loop disturbance estimation results, construct a composite nonlinear dynamic inverse control law, obtain the three-axis virtual acceleration, and further obtain the desired roll angle. Desired pitch angle and total lift ;

[0016] S6. Based on the attitude loop observation results, construct a predefined time sliding surface, equivalent control term and switching control term to obtain the attitude control torque. Then, obtain the rotation speed command of the four rotors through the X configuration control allocation matrix to complete the predefined time trajectory tracking control of the quadcopter UAV.

[0017] Furthermore, the position and attitude dynamics model of the quadcopter UAV in step S1 is as follows:

[0018]

[0019] in, This is the attitude angle vector; It is the angular velocity vector; This is the attitude control torque vector; The external disturbance torque vector; For quality; It is the acceleration due to gravity; This is the translational damping coefficient; The inertia matrix; External disturbance force; attitude transformation matrix The expression is:

[0020]

[0021] in, The pitch angle; This is the roll angle.

[0022] Furthermore, the predefined time-stable function in step S2 The expression is:

[0023]

[0024] in, For predefined time parameters; α, β As preset design parameters, α and β satisfy 0 < α < β. It is a positive constant and satisfies ; symbolic power function , These are general scalar variables used to construct predefined time-stable functions; This is a piecewise auxiliary function used to avoid the singularity caused by traditional negative fractional power terms in the neighborhood of the origin.

[0025] Furthermore, the piecewise auxiliary function for:

[0026]

[0027] in, The threshold for switching between the origin and neighborhood; .

[0028] Furthermore, in step S3, for any position channel The structure of the predefined time sliding mode observer for the position loop is as follows:

[0029]

[0030] in, This corresponds to the position status; For the corresponding virtual acceleration input; For position loop observation gain; This is an estimate of the external disturbance force of the location channel; This is the translational damping coefficient;

[0031] The observer correction term is:

[0032]

[0033] in, These are all predefined time parameters in the predefined time sliding mode observer of the position loop, corresponding to the upper bounds of the convergence time of the first-level and second-level correction terms of the observer, respectively, and satisfying the following conditions: .

[0034] Furthermore, the expression for the attitude loop error dynamics in step S4 is:

[0035]

[0036] in, ; For attitude angle tracking error, , , ; , , , The inertia matrix; Let i be the control torque component of the i-th attitude channel; and define... and , is represented as:

[0037]

[0038]

[0039] in, Represents the vector of the first item; This is the attitude transformation matrix; The external disturbance torque vector; In anticipation; For attitude loop lumped disturbance; For the i-th attitude channel perturbation; It is the angular velocity vector; For the i-th attitude channel, there is a known nonlinear term;

[0040] Therefore, the attitude change predefined time sliding mode observer is:

[0041]

[0042] in, This is the estimated value of the perturbation for the i-th attitude channel; For attitude loop observation gain;

[0043] The observer correction term satisfies:

[0044]

[0045] in, and Let be the predefined time parameters for the attitude loop observer, corresponding to the upper bounds of the convergence times of the first-level and second-level correction terms, respectively, and satisfying . .

[0046] Furthermore, the expression for the position loop composite nonlinear dynamic inverse control law in step S5 is:

[0047]

[0048] in, ; , For the desired trajectory; and The position loop control gain;

[0049] The desired roll angle in the desired attitude angle is then obtained based on the virtual acceleration. Desired pitch angle Total lift :

[0050]

[0051]

[0052]

[0053] in, For total lift input; The desired yaw angle given for the mission; , , This is virtual acceleration.

[0054] Furthermore, the expression for the attitude slip surface in step S6 is:

[0055]

[0056] in, For attitude angle tracking error, , , ; This is an estimate of the first derivative of the attitude error; These are predefined time parameters for the attitude sliding phase.

[0057] Furthermore, the attitude loop control torque satisfies:

[0058]

[0059] Among them, equivalent control items and switching control items They are respectively:

[0060]

[0061]

[0062] in, This is the estimated attitude error value; Represents the partial derivative operator; Represents a predefined time-steady function To address attitude error The partial derivative of , this term is used to compensate for nonlinear functions in the sliding surface. The time derivative;

[0063] To suppress chattering, the switching control option has been replaced with a smooth mode:

[0064]

[0065] in, These are predefined time parameters for the attitude approach phase; To switch the gain; The smoothing factor is used; when the switching control term adopts the form of a sign function, the attitude loop error converges within the predefined time range; when the switching control term adopts the form of hyperbolic tangent smoothing, the attitude loop error and sliding mode variable enter the adjustable bounded small neighborhood within the predefined time range.

[0066] Furthermore, the X-configuration control allocation matrix in the attitude loop control and control allocation steps satisfies:

[0067]

[0068] in, The lift coefficient; It is the inverse torque coefficient; This is the distance from the fuselage's center of mass to the rotor mounting point. , , and These are the angular velocities of the four rotors;

[0069] And from this we can conclude:

[0070]

[0071] in, Assign a matrix to the control.

[0072] The beneficial effects of this invention are as follows:

[0073] By constructing a predefined time-stable function containing linear terms, the upper bound of the convergence time, which is difficult to set directly in traditional sliding mode control, is transformed into an explicit adjustable parameter. This allows the approach process of the attitude loop sliding mode variables and the attitude error adjustment process to be pre-configured according to the time requirements of the task, and enables the disturbance observation error to enter a bounded small neighborhood within a predefined time frame.

[0074] By introducing predefined time sliding mode observers into the position loop and attitude loop respectively, the coordinated estimation of external disturbance force, attitude error derivative and attitude lumped disturbance is realized, which effectively reduces the dependence of attitude loop sliding mode control on large switching gain, while enabling the position loop to maintain smooth tracking under bounded disturbance compensation conditions, thereby enhancing the anti-disturbance capability under complex wind disturbance, load change and other conditions.

[0075] By introducing a piecewise auxiliary function into the predefined time-stabilized function and adopting a hyperbolic tangent smoothing form in the attitude loop switching control term, singularity in the origin neighborhood can be avoided and control chattering can be reduced. At the same time, by combining position loop composite nonlinear dynamic inverse control and X-configuration control allocation, the smoothness of control input and the high dynamic trajectory tracking accuracy of quadcopter UAVs can be improved. Attached Figure Description

[0076] Figure 1 This is a flowchart of the method in Example 1;

[0077] Figure 2 This is a schematic diagram of the quadcopter drone structure in Example 1;

[0078] Figure 3 This is the overall control block diagram for Example 1;

[0079] Figure 4 This is a schematic diagram of the position loop estimation perturbation of the observer in Example 1;

[0080] Figure 5 This is a schematic diagram of the attitude loop estimation perturbation of the observer in Example 1;

[0081] Figure 6 This is a schematic diagram of trajectory tracking verification in Example 1;

[0082] Figure 7 This is a schematic diagram of the error in trajectory tracking in Example 1. Detailed Implementation

[0083] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0084] Example 1:

[0085] like Figures 1-7 As shown, this embodiment takes the trajectory tracking task of a quadcopter UAV under complex wind disturbance and load variation conditions as the object, and provides a UAV predefined time trajectory tracking method based on observer disturbance compensation, including the following steps:

[0086] S1. Establish a dynamic model of the position and attitude of a quadrotor UAV with external disturbances, using the position state, Euler angle state, angular velocity state of the machine system, total lift input, attitude torque input, external disturbance force and external disturbance torque in the inertial coordinate system as the modeling variables of the controlled object.

[0087] S2. Construct a predefined time-stable function containing linear terms. and piecewise auxiliary functions This enables the sliding surface and observer correction terms to avoid negative fractional power singularity in the neighborhood of the origin, and provides a predefined time stability analysis basis for attitude loop control and disturbance observation.

[0088] S3. Design a predefined time sliding mode observer for the position loop to monitor the position state. , , The external disturbance forces of the three channels are estimated online to obtain the external disturbance force estimates. , and ;

[0089] S4. Design a predefined time sliding mode observer for the attitude loop to estimate the angular error derivatives and lumped disturbances of the roll, pitch, and yaw channels online. and ,in 1, 2, and 3 correspond to the roll, pitch, and yaw channels, respectively;

[0090] S5. Construct a composite nonlinear dynamic inverse control law based on the position loop disturbance estimation results, and obtain the virtual acceleration. , , And further calculate the desired roll angle. Desired pitch angle and total lift ;

[0091] S6. Based on the attitude loop observation results, construct a predefined time sliding surface, equivalent control term, and switching control term to obtain the attitude control torque. Then, the rotation speed commands of the four rotors are obtained through the X-configuration control allocation matrix to achieve trajectory tracking control of the quadcopter UAV.

[0092] In step S1, establishing a position and attitude dynamics model of the quadrotor UAV with external disturbances first requires establishing translational and rotational dynamics models of the quadrotor UAV, where the position state is... The attitude angle state is Angular velocity state is Total lift input is The attitude torque input is External disturbance force is The external disturbance torque is The trajectory tracking problem of a quadcopter UAV can be decomposed into a position loop control problem and an attitude loop control problem using the aforementioned state variables.

[0093] In this embodiment, to maintain consistency with the translational damping parameters in the position error dynamics and the position loop CNDI control law, the triaxial translational damping is uniformly denoted as... The position dynamics of the quadcopter UAV are as follows:

[0094]

[0095] Attitude dynamics are presented in the following compact form:

[0096]

[0097] in, This is the attitude angle vector; It is the angular velocity vector; This is the attitude control torque vector; The external disturbance torque vector; For quality; It is the acceleration due to gravity; This is the translational damping coefficient; The inertia matrix; This is the attitude transformation matrix.

[0098] In step S2, based on the model established in S1, the coupled dynamic characteristics of the quadcopter UAV under the combined effects of wind disturbance, model uncertainty, and load changes can be incorporated into a unified analysis framework.

[0099] To construct a predefined time-stable mechanism, a predefined time-stable function is defined:

[0100]

[0101] in, Predefined time parameter; sign power function , It is a general scalar variable used to construct a predefined time-stable function, which can represent observation error, attitude error, or sliding mode variable, etc. The sign function is defined as follows: sgn(z) = 1 when z > 0, sgn(z) = -1 when z < 0, and sgn(z) = 0 when z = 0. α, β, ϑ1, ϑ2, and ϑ3 are preset design parameters, where α and β satisfy 0 < α < β, and ϑ1, ϑ2, and ϑ3 are positive constants satisfying 4ϑ1ϑ3 ≥ ϑ2². Under these constraints, these preset design parameters can be selected based on the desired convergence speed and control smoothness. A predefined upper bound for time convergence can be established using the Lyapunov derivative inequality with linear terms, thus introducing the convergence time as a designable parameter into the trajectory tracking system.

[0102] To avoid singularities caused by traditional negative fractional power terms in the neighborhood of the origin, a piecewise auxiliary function is defined. , is represented as:

[0103]

[0104] Where α and β are preset design parameters, satisfying 0 < α < β; ; The threshold is set as the switching threshold. When the error is far from the origin, the auxiliary function retains the fractional power acceleration convergence characteristic; when the error enters the neighborhood of the origin, the auxiliary function automatically switches to a cubic polynomial form, thereby preventing the control command from growing unbounded near the origin.

[0105] It should be noted that, for the convenience of subsequent dual-loop controller design, this embodiment further defines position error and attitude error. Position error is written as... ,in For the corresponding position status, For the desired trajectory, Attitude error is written as ,in As desired, ,in It is calculated from the position loop control law in the subsequent step S5. The desired yaw angle is given for the mission. The above error definition can simultaneously characterize translational trajectory deviation and attitude adjustment deviation, providing a unified error state for position loop disturbance compensation and attitude loop predefined time sliding mode control.

[0106] In step S3, the position loop uses a predefined time sliding mode observer to estimate the external disturbance force. The design of the predefined time sliding mode observer first assumes that the external disturbance force is differentiable with respect to time and its derivative is bounded, for any position channel... Construct an observer, represented as:

[0107]

[0108] in, This corresponds to the position status; Input the virtual acceleration along the corresponding axis direction; For position loop observation gain; This is an estimate of the external disturbance force of the location channel; The translational damping coefficient; correction term satisfy:

[0109]

[0110] in, For the corresponding virtual acceleration input, , These are all predefined time parameters in the predefined time sliding mode observer of the position loop, corresponding to the upper bounds of the convergence time of the first-level and second-level correction terms of the observer, respectively. Through the above design, estimation results of external disturbance forces can be obtained within a predetermined time range, thereby compensating for unknown wind disturbances and model perturbations in translational trajectory tracking.

[0111] In step S5, based on the position loop disturbance estimation results, a composite nonlinear dynamic inverse control law is designed:

[0112]

[0113] in, and The position loop control gain; , For the desired trajectory;

[0114] This yields the three-axis virtual acceleration. , and Furthermore, the desired attitude angle and total lift are obtained:

[0115]

[0116]

[0117]

[0118] in, For total lift input; The desired yaw angle is given for the mission; through the above steps, the position tracking error and disturbance estimate can be directly mapped into the attitude expectation command and the total lift command.

[0119] The attitude loop in step S4 is first established under the condition that the attitude lumped perturbation is differentiable with respect to time and its derivative is bounded, and the attitude error dynamics are written in a unified second-order form:

[0120]

[0121] in, These correspond to the roll, pitch, and yaw channels, respectively. , , Corresponding attitude error ;and , , , The inertia matrix; Let i be the control torque component of the i-th attitude channel; and define the lumped disturbance of the attitude loop. for:

[0122]

[0123] in, This is the attitude transformation matrix; The external disturbance torque vector; In anticipation; Represent the lumped perturbation component of the i-th attitude channel; and define... for:

[0124]

[0125] in, The known nonlinear term for the i-th attitude channel is obtained by combining the gyroscope coupling term, attitude transformation matrix change term, and control input coupling term in attitude dynamics. Represents the vector of the first item; This is the attitude transformation matrix; The external disturbance torque vector; In anticipation; Let be the angular velocity vector. Further design a predefined time sliding mode observer for the attitude loop:

[0126]

[0127] in, This is the estimated value of the perturbation for the i-th attitude channel. ; For attitude loop observation gain;

[0128]

[0129] in, and These are predefined time parameters for the attitude loop observer, corresponding to the upper bounds of the convergence times of the first-level and second-level correction terms, respectively, and are predefined by the designer and satisfy [the specified conditions]. This allows for a faster convergence timescale in the lumped disturbance estimation stage. Consequently, estimates of the attitude error derivative and the attitude lumped disturbance can be obtained simultaneously.

[0130] In step S6, a predefined time sliding surface is designed based on the attitude loop observation results:

[0131]

[0132] in, This is an estimate of the first derivative of the attitude error; Define predefined time parameters in the time sliding surface of the attitude loop to set the upper bound of the convergence time of the attitude error during the sliding phase;

[0133] Based on this, the attitude loop control law is constructed:

[0134]

[0135]

[0136]

[0137] in, This is the estimated attitude error value; Represents the partial derivative operator; Represents a predefined time-steady function To address attitude error The partial derivative of , this term is used to compensate for nonlinear functions in the sliding surface. The time derivative.

[0138] The equivalent control term is used to compensate for the known nonlinear term and the disturbance estimation term, and the switching control term is used to ensure that the sliding mode variable approaches the sliding surface within a predefined time frame.

[0139] To further reduce chattering, this embodiment replaces the attitude loop switching control term with a smoothing method:

[0140]

[0141] in, The attitude of a UAV includes two phases: sliding and approaching. Therefore, the predefined time parameters for the attitude approaching phase are... and Together they determine the predefined upper bound of the attitude loop control; To switch the gain; This is a smoothing factor. Through the above substitution, control chattering caused by high-frequency switching can be reduced while maintaining a predefined time stability framework, thereby improving the smoothness of rotor speed commands and the feasibility of actuators.

[0142] To convert total lift and attitude control torque into rotor speed commands, an X-configuration control distribution matrix is ​​used. , is represented as:

[0143]

[0144] in, The lift coefficient; It is the inverse torque coefficient; This is the distance from the fuselage's center of mass to the rotor mounting point. , , and These are the angular velocities of the four rotors;

[0145] Thus obtain

[0146]

[0147] in, The control allocation matrix is ​​then applied. This control allocation process converts the dual-loop controller output into directly executable rotor speed commands.

[0148] Through the above-mentioned position loop disturbance observation, position loop composite nonlinear dynamic inverse control, attitude loop disturbance observation, attitude loop predefined time sliding mode control, and control allocation design, this embodiment can achieve smooth tracking of position trajectory, predefined time convergence or smooth bounded adjustment of attitude adjustment error, and reasonable allocation of control input under the dual-loop cooperative framework.

[0149] To verify the effectiveness of the above method, this example also uses the MATLAB / Simulink environment to simulate and verify the proposed method, with a fixed step size set to... The physical parameters of the quadcopter drone are set as follows: mass arm length Gravitational acceleration Moment of inertia , Lift coefficient Anti-torque coefficient Translational damping coefficient .

[0150] In this embodiment, the initial state of the system is set to rad, rad / s. The predefined time-steady function parameters are set to... The gain parameter in the CNDI control law of the position loop is taken as... , , Position loop observation gain Location loop observation time parameters are taken Attitude loop switching gain parameters Corresponding to , , The attitude loop total control time parameter is taken as follows and the sliding phase time Approaching phase time Designed to meet Attitude loop observation gain Attitude loop observation time parameters are taken .

[0151] To verify the perturbation estimation performance, a time-varying external perturbation force was injected into the position loop:

[0152]

[0153] Simultaneously, a torque disturbance is injected into the attitude loop:

[0154]

[0155] Simulation results show that the position loop observer can estimate external disturbance forces relatively quickly, among which... The estimated value is approximately Converging to a small neighborhood; the attitude loop observer's estimate of the lumped disturbance in the yaw channel is approximately... The convergence to a small neighborhood indicates that the dual-loop observer has high perturbation estimation efficiency within a predefined time frame.

[0156] To verify the trajectory tracking performance, this embodiment has the quadcopter drone track the following reference trajectory:

[0157]

[0158] The trajectory has rapidly changing curvature and velocity, which can simultaneously test the coordinated control capability of the position loop and attitude loop under high dynamic maneuvering conditions.

[0159] Under the reference trajectory and perturbation conditions, simulations were performed using the method of this invention. The results show that the method can closely track the target trajectory, and the overall position tracking error remains within a small range, with the maximum position error being approximately [missing value]. Further statistical analysis of the root mean square error of attitude tracking yields the following root mean square errors for the roll, pitch, and yaw channels: approximately [missing information]. The values ​​of 0.4021 rad and 0.0004 rad indicate that the method of the present invention balances both position tracking accuracy and attitude adjustment accuracy.

[0160] Because this invention employs a smoothly switching control term in the attitude loop, the total variation of the control input during simulation is approximately [missing information]. This indicates that the proposed method can effectively suppress high-frequency chattering in traditional sliding mode control while enhancing the anti-disturbance performance, making the rotor speed command change smoother and facilitating engineering implementation.

[0161] The simulation results of this embodiment demonstrate that by unifying the position loop and attitude loop observers into a predefined time frame, and combining the position loop composite nonlinear dynamic inverse control with the attitude loop predefined time sliding mode control, this invention can achieve the following under complex disturbance conditions: the disturbance estimation error enters a bounded small neighborhood within a predefined time frame; the position trajectory is smoothly tracked; the attitude error is rapidly adjusted; and the control input is reasonably allocated. This invention has good engineering application value.

[0162] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and detail without departing from the principles and structure of the present invention; however, these modifications and changes based on the spirit of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for tracking a predefined time trajectory of a UAV based on observer perturbation compensation, characterized in that, The method includes the following steps: S1. Establish a dynamic model of the position and attitude of a quadrotor UAV with external disturbances, using the position state, Euler angle state, angular velocity state of the machine system, total lift input, attitude torque input, external disturbance force and external disturbance torque in the inertial coordinate system as the modeling variables of the controlled object. S2. Construct a predefined time-stability function containing linear terms and a piecewise auxiliary function. Use the function to make the sliding surface and the observer correction term avoid negative fractional power singularity in the neighborhood of the origin, and provide a predefined time stability analysis basis for attitude loop control and disturbance observation. S3. Design a predefined time sliding mode observer for the position loop to monitor the position state. , , The external disturbance forces of the three channels are estimated online to obtain the estimated external disturbance forces. S4. Design a predefined time sliding mode observer for the attitude loop to estimate the angular error derivatives and lumped disturbances of the roll, pitch and yaw channels online, and obtain the estimated values ​​of the first derivative of the attitude error and the estimated values ​​of the lumped disturbances of the attitude channels. S5. Based on the position loop disturbance estimation results, construct a composite nonlinear dynamic inverse control law, obtain the three-axis virtual acceleration, and further obtain the desired roll angle. Desired pitch angle and total lift ; S6. Based on the attitude loop observation results, construct a predefined time sliding surface, equivalent control term and switching control term to obtain the attitude control torque. Then, obtain the rotation speed command of the four rotors through the X configuration control allocation matrix to complete the predefined time trajectory tracking control of the quadcopter UAV.

2. The tracking method according to claim 1, characterized in that, The position and attitude dynamics model of the quadcopter UAV in step S1 is as follows: in, This is the attitude angle vector; It is the angular velocity vector; This is the attitude control torque vector; The external disturbance torque vector; For quality; It is the acceleration due to gravity; This is the translational damping coefficient; The inertia matrix; External disturbance force; attitude transformation matrix The expression is: in, The pitch angle; This is the roll angle.

3. The tracking method according to claim 2, characterized in that, The predefined time-stable function in step S2 The expression is: in, For predefined time parameters; α, β As preset design parameters, α and β satisfy 0 < α < β. It is a positive constant and satisfies ; symbolic power function , These are general scalar variables used to construct predefined time-stable functions; This is a piecewise auxiliary function used to avoid the singularity caused by traditional negative fractional power terms in the neighborhood of the origin.

4. The tracking method according to claim 3, characterized in that, The piecewise auxiliary function for: in, The threshold for switching between the origin and neighborhood; .

5. The tracking method according to claim 4, characterized in that, In step S3, for any location channel The structure of the predefined time sliding mode observer for the position loop is as follows: in, This corresponds to the position status; For the corresponding virtual acceleration input; For position loop observation gain; This is an estimate of the external disturbance force of the location channel; This is the translational damping coefficient; The observer correction term is: in, These are all predefined time parameters in the predefined time sliding mode observer of the position loop, corresponding to the upper bounds of the convergence time of the first-level and second-level correction terms of the observer, respectively, and satisfying the following conditions: .

6. The tracking method according to claim 5, characterized in that, The expression for the attitude loop error dynamics in step S4 is as follows: in, ; For attitude angle tracking error, , , ; , , , The inertia matrix; Let i be the control torque component of the i-th attitude channel; and define... and , is represented as: in, Represents the vector of the first item; This is the attitude transformation matrix; The external disturbance torque vector; In anticipation; For attitude loop lumped disturbance; For the i-th attitude channel perturbation; It is the angular velocity vector; For the i-th attitude channel, there is a known nonlinear term; Therefore, the attitude change predefined time sliding mode observer is: in, This is the estimated value of the perturbation for the i-th attitude channel; For attitude loop observation gain; The observer correction term satisfies: in, and Let be the predefined time parameters for the attitude loop observer, corresponding to the upper bounds of the convergence times of the first-level and second-level correction terms, respectively, and satisfying . .

7. The tracking method according to claim 6, characterized in that, The expression for the position loop composite nonlinear dynamic inverse control law in step S5 is: in, ; , For the desired trajectory; and The position loop control gain; The desired roll angle in the desired attitude angle is then obtained based on the virtual acceleration. Desired pitch angle Total lift : in, For total lift input; The desired yaw angle given for the mission; , , This is virtual acceleration.

8. The tracking method according to claim 7, characterized in that, The expression for the attitude slip surface in step S6 is: in, For attitude angle tracking error, , , ; This is an estimate of the first derivative of the attitude error; These are predefined time parameters for the attitude sliding phase.

9. The tracking method according to claim 8, characterized in that, The attitude loop control torque satisfies: Among them, equivalent control items and switching control items They are respectively: in, This is the estimated attitude error value; Represents the partial derivative operator; Represents a predefined time-steady function To address attitude error The partial derivative of , this term is used to compensate for nonlinear functions in the sliding surface. The time derivative; To suppress chattering, the switching control option has been replaced with a smooth mode: in, These are predefined time parameters for the attitude approach phase; To switch the gain; The smoothing factor is used; when the switching control term adopts the form of a sign function, the attitude loop error converges within the predefined time range; when the switching control term adopts the form of hyperbolic tangent smoothing, the attitude loop error and sliding mode variable enter the adjustable bounded small neighborhood within the predefined time range.

10. The tracking method according to claim 9, characterized in that, The X-configuration control allocation matrix in the attitude loop control and control allocation steps satisfies: in, The lift coefficient; It is the inverse torque coefficient; This is the distance from the fuselage's center of mass to the rotor mounting point. , , and These are the angular velocities of the four rotors; And from this we can conclude: in, Assign a matrix to the control.

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