Four-rotor unmanned aerial vehicle robust trajectory tracking method based on sliding mode control-improved extended state observer

Abstract

The invention relates to the technical field of aircraft control, in particular to a four-rotor unmanned aerial vehicle robust trajectory control method based on a sliding mode control-improved extended state observer. The method comprises the following steps: firstly, establishing a nonlinear dynamic model of the quad-rotor unmanned aerial vehicle, and decomposing the system into a hierarchical control structure of a position outer ring and an attitude inner ring; secondly, a third-order extended state observer (ESO) is designed to estimate composite disturbance of each channel in real time, an improved sliding mode control law with observation error compensation is provided, and the vibration bearing phenomenon is effectively restrained; and finally, proving the asymptotic stability of the closed-loop system through the Lyapunov stability theory. The method is used for solving the problems of low trajectory tracking precision and control signal buffeting caused by underactuation, strong coupling nonlinear characteristics and external disturbance of the four-rotor unmanned aerial vehicle. High-precision trajectory tracking under complex disturbance can be realized, and control signal buffeting can be suppressed at the same time.

Description

Technical Field

[0001] This invention relates to the field of aircraft control technology, and in particular to a robust trajectory control method for a quadrotor unmanned aerial vehicle based on sliding mode control and an improved extended state observer. Background Technology

[0002] Quadcopter drones, with their advantages of simple structure, low cost, and good vertical takeoff and landing and hovering stability, have been widely used in military reconnaissance, civilian aerial photography, agricultural plant protection, environmental monitoring, emergency rescue, and logistics distribution. However, quadcopter drones are essentially underactuated, strongly coupled nonlinear dynamic systems with six degrees of freedom (three translational degrees of freedom and three rotational degrees of freedom) and only four control inputs (four rotor thrusts), making horizontal position control difficult. Moreover, in actual flight, they are easily affected by uncertainties such as atmospheric turbulence, gusts, load changes, and model parameter perturbations, which severely restricts trajectory tracking accuracy.

[0003] Existing control methods have significant shortcomings: while PID control is easy to implement, its ability to suppress model uncertainties and external disturbances is limited, making it difficult to meet high-precision requirements; adaptive control can adapt to parameter changes, but its convergence speed is slow, and its performance degrades significantly when parameters change rapidly; traditional sliding mode control is robust, but the sign function can cause severe control signal chattering, affecting control accuracy and system stability; Active disturbance rejection control (ADRC) estimates and compensates for the "total disturbance" through an extended state observer (ESO), but its observation accuracy is limited by bandwidth and suffers from phase lag. Therefore, there is an urgent need for a quadrotor UAV control method that can balance robustness, tracking accuracy, and chattering suppression. Summary of the Invention

[0004] The purpose of this invention is to provide a robust trajectory tracking method for quadrotor UAVs based on sliding mode control and an improved extended state observer, which can achieve high-precision trajectory tracking under complex disturbances while suppressing control signal jitter.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A robust trajectory tracking method for a quadrotor UAV based on sliding mode control and an improved extended state observer, characterized by comprising the following steps: S1. Establish a dynamic model of the quadcopter UAV in the inertial coordinate system F_I and the body coordinate system F_B, and clarify the mathematical relationship between position, velocity, attitude, angular velocity and control input and disturbance. S2. Design third-order improved extended state observers (ESOs) with observation error compensation terms for the vertical channel, horizontal channel and attitude channel respectively, establish the observation error dynamic equation, and determine the stable gain range of the observer based on the Routh-Hurwitz criterion; S3. Construct a hierarchical control structure with an outer position loop and an inner attitude loop. The outer position loop generates the desired attitude command through improved active disturbance rejection sliding mode control. The inner attitude loop achieves accurate attitude tracking based on IESO and sliding mode control. An observation error compensation term is introduced to reduce the sliding mode gain. S4. Select the Lyapunov function and prove that the closed-loop system is asymptotically stable, ensuring that the tracking error exponent converges to zero.

[0006] The above steps complete the implementation of a robust trajectory tracking method for quadrotor UAVs based on sliding mode control and an improved extended state observer.

[0007] In the preferred embodiment, the dynamic model of the quadcopter UAV in step S1 is as follows: (1) In the formula: Indicates speed, Represents translational inertial force. Indicates the rate of change of attitude. Represents the rate of change of angular momentum; where, Position in inertial coordinate system y represents the x-axis component in the inertial coordinate system, z represents the y-axis component in the inertial coordinate system, and z represents the z-axis component in the inertial coordinate system. For speed, where, Represents velocity in inertial coordinate system Components in the axial direction, Represents velocity in inertial coordinate system Components in the axial direction, Represents velocity in inertial coordinate system The component along the axis, where T represents the transpose operation; For Euler angles, where, Indicates the roll angle. Indicates pitch angle, Indicates the yaw angle; Let q be the angular velocity of the aircraft, where q represents the pitch angular velocity, r represents the yaw angular velocity, and m is the mass. Let be the rotational inertia matrix, where Represents the moment of inertia along the x-axis. Indicates the moment of inertia along the y-axis. Represents the moment of inertia along the z-axis; It is the acceleration due to gravity. Let be a rotation matrix. Let be the total thrust vector, where Indicates the magnitude of the total thrust; For translational disturbances, among which, This indicates the translational disturbance in the inertial coordinate system. Components in the axial direction, This indicates the translational disturbance in the inertial coordinate system. Components in the axial direction, This indicates the translational disturbance in the inertial coordinate system. Components along the axial direction; The control torque for the body coordinate system, where, Indicates the roll control torque. Indicates pitch control torque. Indicates the yaw control torque; For rotational disturbance, where, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft; This is the transformation matrix between Euler angles and angular velocity.

[0008] In the preferred embodiment, step S2 involves designing a third-order improved extended state observer with an observation error compensation term, which includes the following sub-steps: The designs of S21 and ESO are as follows: (2) In the formula: These are the estimated values ​​for the observed altitude, velocity, and disturbance, respectively. ESO observer gain; Indicates the actual height; Indicates the roll angle. Indicates the pitch angle.

[0009] S22, Observation Error Vector The dynamic equation is: (3) Among them, the definition , , To compensate for observation errors, the stability condition is: In the formula: Indicates altitude observation error. This indicates the error in the observation of yaw rate. This represents the z-axis perturbation observation error. Represents the derivative of the observation error. Represents the observer gain matrix. Indicates observation error. This represents the observer output gain matrix. This represents the z-axis perturbation derivative.

[0010] In the preferred embodiment, step S3, where the outer position loop generates the desired attitude command through improved active disturbance rejection sliding mode control, includes the following sub-steps: S31, The improved active disturbance rejection sliding mode control law for the vertical channel is: (4) In the formula: Indicates the magnitude of the total thrust. This represents the z-axis perturbation. This represents the derivative of the z-axis observation error. Let gravitational acceleration be 1; where 1 is the acceleration due to gravity. For the synovial surface, For high tracking poor, and These are the sliding mode parameters (specifically 2-0.5) and the gain. This is the disturbance estimate. This represents the position observation error.

[0011] S32, Horizontal channel via virtual control law , Convert to desired attitude angle , The transformation relationship is as follows: (5) In the formula: Indicates the expected roll angle. Indicates the desired pitch angle. Indicates the yaw angle. It is the acceleration due to gravity. They are respectively Directional virtual control input.

[0012] S33, the improved active disturbance rejection sliding mode control law for the inner loop of attitude is: (6) In the formula: , , For attitude sliding surface; , , This refers to attitude tracking error; This is an estimate of the composite disturbance; For sliding mode gain; These are the observation error compensation coefficients (specifically 30000, 30000, 30000). This indicates the sliding mode parameter for the roll angle (specifically 10). This represents the pitch angle sliding mode parameter (specifically 10). This represents the yaw angle sliding mode parameter (specifically 10). This represents the derivative of the roll angle tracking error. This represents the reciprocal of the pitch tracking error. This represents the derivative of the yaw angle tracking error. This indicates the error in the roll angle observation. This indicates the pitch angle observation error. This indicates the error in the yaw angle observation.

[0013] In the preferred scheme, step S4 proves that the closed-loop system is asymptotically stable, and the Lyapunov function is selected: (7) In the formula: Represents the square of the whole. Represents the sliding mode function for roll angle. Represents the pitch angle sliding mode function. Represents the yaw angle sliding mode function; where, when , , hour, Strictly decreasing, the attitude tracking error will converge exponentially to zero; This represents the derivative of the expected value of the roll angle. This represents the derivative of the expected value of the pitch angle. This represents the derivative of the expected value of the yaw angle.

[0014] The beneficial effects of this invention are as follows: The IESO (Improved Extended State Observer) with the introduction of an observation error compensation term can accurately estimate the system state and internal and external disturbances, reduce sliding mode gain, effectively suppress control signal chattering, and improve system practicality. The hierarchical control structure (outer position loop + inner attitude loop) utilizes the system's multi-timescale characteristics to simplify controller design, achieve decoupling of position and attitude, and improve control accuracy and dynamic response speed. Simulation verification shows that under three-dimensional spiral trajectories and periodic disturbances, the position tracking RMSE reaches the centimeter level, the maximum attitude tracking error is small, and the disturbance rejection performance and robustness are significantly better than PID, traditional sliding mode control, and other methods, making it suitable for high-precision flight requirements in multiple scenarios. Attached Figure Description

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 The coordinate transformation diagram of the quadcopter is shown for this invention.

[0016] Figure 2 This invention presents a block diagram of the control structure for a quadcopter unmanned aerial vehicle.

[0017] Figure 3 This is a three-dimensional trajectory diagram of the quadcopter of the present invention, demonstrating the overall control performance of the quadcopter.

[0018] Figure 4 This invention presents a position tracking diagram of a quadcopter.

[0019] Figure 5 The diagram shows the attitude tracking results of the quadcopter.

[0020] Figure 6 This invention demonstrates the IESO estimation map for position loop perturbation.

[0021] Figure 7 This invention demonstrates the IESO estimation map for attitude loop perturbation.

[0022] Figure 8 This invention presents a performance diagram of IESO state estimation.

[0023] Figure 9 This invention illustrates the quadcopter control - control input and performance diagram.

[0024] Figure 10 This invention presents an estimation accuracy versus gyroscope effect diagram. Detailed Implementation

[0025] like Figures 1-10 As shown, a robust trajectory tracking method for a quadrotor UAV based on sliding mode control and an improved extended state observer includes the following steps: S1. Establish a dynamic model of the quadcopter UAV in the inertial coordinate system F_I and the body coordinate system F_B, and clarify the mathematical relationship between position, velocity, attitude, angular velocity and control input and disturbance. S2. Design third-order improved extended state observers (ESOs) with observation error compensation terms for the vertical channel, horizontal channel and attitude channel respectively, establish the observation error dynamic equation, and determine the stable gain range of the observer based on the Routh-Hurwitz criterion; S3. Construct a hierarchical control structure with an outer position loop and an inner attitude loop. The outer position loop generates the desired attitude command through improved active disturbance rejection sliding mode control. The inner attitude loop achieves accurate attitude tracking based on IESO and sliding mode control. An observation error compensation term is introduced to reduce the sliding mode gain. S4. Select the Lyapunov function and prove that the closed-loop system is asymptotically stable, ensuring that the tracking error exponent converges to zero.

[0026] The above steps complete the implementation of a robust trajectory tracking method for quadrotor UAVs based on sliding mode control and an improved extended state observer.

[0027] This method addresses the disturbance observation error problem of traditional ESOs by designing an improved sliding mode control law with observation error compensation. By introducing a position observation error feedback term and utilizing the intrinsic relationship between observation error and disturbance estimation error, the disturbance suppression error is reduced, thereby lowering the required sliding mode gain and effectively suppressing control signal chattering. A hierarchical control structure design scheme is proposed, fully utilizing the time-scale separation characteristics of the quadrotor system to decompose the complex six-degree-of-freedom trajectory tracking problem into cascade control of the outer position loop and the inner attitude loop, simplifying the controller design and improving system performance. A complete stability analysis framework is established, and the closed-loop asymptotic stability of the proposed control method is rigorously proved based on Lyapunov stability theory, providing theoretical support for engineering applications.

[0028] In the preferred embodiment, the dynamic model of the quadcopter UAV is as follows: (1) Wherein: Indicates speed, Represents translational inertial force. Indicates the rate of change of attitude. Represents the rate of change of angular momentum; where, Position in inertial coordinate system y represents the x-axis component in the inertial coordinate system, z represents the y-axis component in the inertial coordinate system, and z represents the z-axis component in the inertial coordinate system. For speed, where, Represents velocity in inertial coordinate system Components in the axial direction, Represents velocity in inertial coordinate system Components in the axial direction, Represents velocity in inertial coordinate system The component along the axis, where T represents the transpose operation; For Euler angles, where, Indicates the roll angle. Indicates pitch angle, Indicates the yaw angle; Let q be the angular velocity of the aircraft, where q represents the pitch angular velocity, r represents the yaw angular velocity, and m is the mass. Let be the rotational inertia matrix, where Represents the moment of inertia along the x-axis. Indicates the moment of inertia along the y-axis. Represents the moment of inertia along the z-axis; It is the acceleration due to gravity. Let be a rotation matrix. Let be the total thrust vector, where Indicates the magnitude of the total thrust; For translational disturbances, among which, This indicates the translational disturbance in the inertial coordinate system. Components in the axial direction, This indicates the translational disturbance in the inertial coordinate system. Components in the axial direction, This indicates the translational disturbance in the inertial coordinate system. Components along the axial direction; The control torque for the body coordinate system, where, Indicates the roll control torque. Indicates pitch control torque. Indicates the yaw control torque; For rotational disturbance, where, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft; This is the transformation matrix between Euler angles and angular velocity; Position in inertial coordinate system For speed, For Euler angle orientation, Let m be the angular velocity of the body and m be the mass. Here is the rotational inertia matrix. It is the acceleration due to gravity. Let be a rotation matrix. This is the total thrust vector. For translational disturbances, For the control torque of the body coordinate system, For rotational disturbance, This is the transformation matrix between Euler angles and angular velocity.

[0029] Expanding equation (1), we can obtain the state-space expression of the system: (8) In the formula: Represents the velocity component in the x-direction. Represents the y-axis velocity component. Represents the z-axis velocity component. Indicates acceleration in the x-direction. This represents acceleration in the y-axis direction. This represents acceleration in the z-axis direction. This represents the derivative of the roll angle. Represents the derivative of the pitch angle. This represents the reciprocal of the yaw angle. Indicates roll acceleration. Represents pitch acceleration. Indicates yaw acceleration. Represents the x-axis velocity component. Represents the y-axis velocity component. This represents the z-axis velocity component.

[0030] In the preferred embodiment, the design of the improved extended state observer includes the following sub-steps: S21. The vertical direction of the quadcopter is affected by the coupling effect of the resultant force of the main rotor, gravity, and external disturbances (such as airflow and load changes). Its dynamic model is expressed as follows: (9) ESO is designed as follows: (2) In the formula: These are the estimated values ​​for the observed altitude, velocity, and disturbance, respectively. ESO observer gain; Indicates the actual height; Indicates the roll angle. Indicates the pitch angle.

[0031] Combining equations (2) and (9), the dynamic equation for the observation error corresponding to ESO can be expressed as: (10) In the formula: This represents the derivative of the z-axis observation error. This represents the derivative of the z-axis velocity observation error. This represents the derivative of the z-axis perturbation observation error. This indicates the error in the z-axis velocity observation. This represents the z-axis perturbation observation error. Indicates the z-axis observation error. This represents the derivative of the z-axis perturbation component. This indicates that the observer gain is 1. This indicates that the observer gain is 2. This indicates the observer gain is 3; it can be observed that... Includes ,and It can be obtained directly, therefore it can be obtained through To reduce disturbance estimation errors, this paper proposes an improved active disturbance rejection sliding mode control law: (11) In the formula: Indicates sliding mode input. This represents the z-axis perturbation estimate.

[0032] S22, Observation Error Vector The dynamic equation is: (3) In the formula: Represents the derivative of the observation error. Represents the observer gain matrix. This represents the observer output gain matrix. This represents the derivative of the z-axis perturbation component.

[0033] Among them, the definition , , To compensate for observation errors, the stability condition is: .

[0034] In the preferred embodiment, constructing a hierarchical improved active disturbance rejection sliding mode controller includes the following sub-steps: S31. Choosing a quadratic Lyapunov function: (12) In the formula: Represents the Lyapunov function along the z-axis. This represents the sliding mode function along the z-axis.

[0035] Differentiating equation (12) and substituting equation (9) into the definition of sliding surface, we get: (13) In the formula: This represents the derivative of the Lyapunov function along the z-axis. This represents the z-axis error gain.

[0036] Substituting the improved active disturbance rejection sliding mode control law (11) into the above equation: (4) In the formula: Indicates the magnitude of the total thrust. This represents the z-axis perturbation. This represents the derivative of the z-axis observation error. Let gravitational acceleration be 1; where 1 is the acceleration due to gravity. For the synovial surface, For high tracking poor, and These are the sliding mode parameters (specifically 2-0.5) and the gain. This is the disturbance estimate. This represents the position observation error.

[0037] S32. The dynamic equation of the quadcopter in the horizontal direction can be extracted from equation (8): (14) Input virtual control and The relationship with the actual control input is established, and it can be seen from equation (14): (15) Horizontal channel via virtual control law , Convert to desired attitude angle , The transformation relationship is as follows: (5) In the formula: Indicates the expected roll angle. Indicates the desired pitch angle. Indicates the yaw angle. It is the acceleration due to gravity. They are respectively Directional virtual control input.

[0038] S33, the improved active disturbance rejection sliding mode control law for the inner loop of attitude is: (6) In the formula: , , For attitude sliding surface; , , This refers to attitude tracking error; This is an estimate of the composite disturbance; For sliding mode gain; These are the observation error compensation coefficients (specifically 30000, 30000, 30000). This indicates the sliding mode parameter for the roll angle (specifically 10). This represents the pitch angle sliding mode parameter (specifically 10). This represents the yaw angle sliding mode parameter (specifically 10). This represents the derivative of the roll angle tracking error. This represents the reciprocal of the pitch tracking error. This represents the derivative of the yaw angle tracking error. This indicates the error in the roll angle observation. This indicates the pitch angle observation error. This indicates the error in the yaw angle observation.

[0039] In the preferred scheme, the Lyapunov function is selected for closed-loop system stability verification: (7) In the formula: Represents the square of the whole. Represents the sliding mode function for roll angle. Represents the pitch angle sliding mode function. This represents the yaw angle sliding mode function.

[0040] right Differentiate, combine attitude to simplify dynamics and control law (6). We have: (16) In the formula: Represents the attitude angle function. Indicates the sliding mode gain of the roll angle. This represents the roll angle constant (10) that is greater than zero. Represents the pitch angle constant that is greater than zero (10); The yaw angle constant is greater than zero (10). Represents the sliding mode function for roll angle. This represents the sliding mode function for yaw angle. Indicates the pitch angle sliding mode gain. Indicates the yaw angle sliding mode gain. This represents the yaw angle sliding mode function.

[0041] Among them, when , , hour, Strictly decreasing, the attitude tracking error will converge exponentially to zero; This represents the derivative of the expected value of the roll angle. This represents the derivative of the expected value of the pitch angle. This represents the expected guidance number for the yaw angle.

Claims

1. A robust trajectory tracking method for a quadrotor UAV based on sliding mode control and an improved extended state observer, characterized in that... Includes the following steps: S1. Establish a dynamic model of the quadcopter UAV in the inertial coordinate system F_I and the body coordinate system F_B, and clarify the mathematical relationship between position, velocity, attitude, angular velocity and control input and disturbance. S2. Design third-order improved extended state observers with observation error compensation terms for the vertical channel, horizontal channel and attitude channel respectively, establish the observation error dynamic equation, and determine the stable gain range of the observer based on the Routh-Hurwitz criterion. S3. Construct a hierarchical control structure with an outer position loop and an inner attitude loop. The outer position loop generates the desired attitude command through improved active disturbance rejection sliding mode control. The inner attitude loop achieves accurate attitude tracking based on IESO and sliding mode control. An observation error compensation term is introduced to reduce the sliding mode gain. S4. Select the Lyapunov function and prove that the closed-loop system is asymptotically stable, ensuring that the tracking error exponent converges to zero.

2. The robust trajectory tracking method for a quadrotor UAV based on sliding mode control and an improved extended state observer as described in claim 1, characterized in that... In step S1, the dynamic model of the quadcopter UAV is as follows: (1) In the formula: Indicates speed, Represents translational inertial force. Indicates the rate of change of attitude. Represents the rate of change of angular momentum; where, Position in inertial coordinate system y represents the x-axis component in the inertial coordinate system, z represents the y-axis component in the inertial coordinate system, and z represents the z-axis component in the inertial coordinate system. For speed, where, Represents velocity in inertial coordinate system Components in the axial direction, Represents velocity in inertial coordinate system Components in the axial direction, Represents velocity in inertial coordinate system The component along the axis, where T represents the transpose operation; For Euler angles, where, Indicates the roll angle. Indicates pitch angle, Indicates the yaw angle; Let q be the angular velocity of the aircraft, where q represents the pitch angular velocity, r represents the yaw angular velocity, and m is the mass. Let be the rotational inertia matrix, where Represents the moment of inertia along the x-axis. Indicates the moment of inertia along the y-axis. Represents the moment of inertia along the z-axis; It is the acceleration due to gravity. Let be a rotation matrix. Let be the total thrust vector, where Indicates the magnitude of the total thrust; For translational disturbances, among which, This indicates the translational disturbance in the inertial coordinate system. Components in the axial direction, This indicates the translational disturbance in the inertial coordinate system. Components in the axial direction, This indicates the translational disturbance in the inertial coordinate system. Components along the axial direction; The control torque for the body coordinate system, where, Indicates the roll control torque. Indicates pitch control torque. Indicates the yaw control torque; For rotational disturbance, where, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft, Indicates the rotational disturbance around the body coordinate system Torque components of the shaft; This is the transformation matrix between Euler angles and angular velocity.

3. The robust trajectory tracking method for a quadrotor UAV based on sliding mode control and an improved extended state observer as described in claim 1, characterized in that... In step S2, a third-order improved extended state observer with observation error compensation terms is designed, including the following sub-steps: The designs of S21 and ESO are as follows: (2) In the formula: These are the estimated values ​​for the observed altitude, velocity, and disturbance, respectively. ESO observer gain; Indicates the actual height; Indicates the roll angle. Indicates the pitch angle; S22, Observation Error Vector The dynamic equation is: (3) Among them, the definition , , To compensate for observation errors, the stability condition is: In the formula: Indicates altitude observation error. This indicates the error in the observation of yaw rate. This represents the z-axis perturbation observation error. Represents the derivative of the observation error. Represents the observer gain matrix. Indicates observation error. This represents the observer output gain matrix. This represents the z-axis perturbation derivative.

4. A robust trajectory tracking method for a quadrotor UAV based on sliding mode control and an improved extended state observer as described in claim 1, characterized in that... In step S3, the outer position loop generates the desired attitude command through improved active disturbance rejection sliding mode control, including the following sub-steps: S31, The improved active disturbance rejection sliding mode control law for the vertical channel is: , (4) In the formula: Indicates the magnitude of the total thrust. This represents the z-axis perturbation. This represents the derivative of the z-axis observation error. Let gravitational acceleration be 1; where 1 is the acceleration due to gravity. For the synovial surface, For high tracking poor, and These are the sliding mode parameters (specifically 2-0.5) and the gain. This is the disturbance estimate. This refers to the position observation error; S32, Horizontal channel via virtual control law , Convert to desired attitude angle , The transformation relationship is as follows: (5) In the formula: Indicates the expected roll angle. Indicates the desired pitch angle. Indicates the yaw angle. It is the acceleration due to gravity. They are respectively Directional virtual control input; S33, the improved active disturbance rejection sliding mode control law for the inner loop of attitude is: (6) In the formula: , , For attitude sliding surface; , , This refers to attitude tracking error; This is an estimate of the composite disturbance; For sliding mode gain; This is the observation error compensation coefficient; Indicates the sliding mode parameters of the roll angle. This represents the sliding mode parameter for the pitch angle. This represents the sliding mode parameter for the yaw angle. This represents the derivative of the roll angle tracking error. This represents the reciprocal of the pitch tracking error. This represents the derivative of the yaw angle tracking error. This indicates the error in the roll angle observation. This indicates the pitch angle observation error. This indicates the error in the yaw angle observation.

5. A robust trajectory tracking method for a quadrotor UAV based on sliding mode control and an improved extended state observer as described in claim 1, characterized in that... In step S4, it is proven that the closed-loop system is asymptotically stable, and the Lyapunov function is chosen: , (7) In the formula: Represents the square of the whole. Represents the sliding mode function for roll angle. Represents the pitch angle sliding mode function. Represents the yaw angle sliding mode function; where, when , , hour, Strictly decreasing, the attitude tracking error will converge exponentially to zero; This represents the derivative of the expected value of the roll angle. This represents the derivative of the expected value of the pitch angle. This represents the derivative of the expected value of the yaw angle.

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