Four-rotor nonsingular terminal sliding mode attitude control method, device, equipment and medium

Abstract

The invention provides a quadrotor nonsingular terminal sliding mode attitude control method, device and equipment and a medium, and relates to the technical field of quadrotor unmanned aerial vehicles. According to the method, coupling interference and external unknown interference in unmanned aerial vehicle attitude control are efficiently estimated by adopting a finite time sliding mode observer; the problem of insufficient control precision caused by interference in a traditional method is effectively solved; according to the invention, by combining the rapid nonsingular terminal sliding mode control technology, rapid and accurate tracking of the preset attitude is realized, the anti-interference capability of the system in the face of complex and changeable disturbance is greatly enhanced, the output buffeting of the controller is effectively inhibited, and the flight smoothness is guaranteed. The objective of the invention is to improve attitude control precision, response speed and anti-interference capability of the quad-rotor unmanned aerial vehicle in a complex environment.

Description

Technical Field

[0001] The present invention relates to the technical field of quadrotor unmanned aerial vehicles, and particularly to a non-singular terminal sliding mode attitude control method, device, equipment and medium for quadrotors. Background Art

[0002] With the rapid development of unmanned aerial vehicle technology, quadrotor unmanned aerial vehicles have been widely used in many fields such as military, civilian and scientific research due to their advantages of simple structure, strong maneuverability and easy control. However, the attitude control of quadrotor unmanned aerial vehicles faces many challenges. Due to its multi-input multi-output, strong coupling and non-linear characteristics, as well as external disturbances (such as wind speed changes, airflow disturbances, etc.) and internal parameter changes (such as battery power changes, load changes, etc.) during flight, traditional control methods often struggle to meet the requirements for attitude control accuracy and response speed.

[0003] In the field of attitude control of quadrotor unmanned aerial vehicles, sliding mode control methods have received extensive attention due to their robustness against system uncertainties and external disturbances. However, traditional sliding mode control methods have some problems, such as the "singularity" phenomenon and the problem of control output chattering. The singularity phenomenon can lead to the failure of the control law, while the control output chattering will reduce the control accuracy and reliability of the system. To solve these problems, researchers have proposed various improved sliding mode control methods, such as fast terminal sliding mode control and non-singular terminal sliding mode control. These methods have improved the control performance of the system to a certain extent, but still have problems such as insufficient response speed and robustness when facing complex and variable disturbances.

[0004] In addition, to improve the anti-interference ability of the attitude control system of quadrotor unmanned aerial vehicles, researchers have also proposed observer-based control methods. By designing an observer to estimate the system state and external disturbances and feeding the estimated values back into the control law, the robustness of the system can be effectively improved. However, most of the existing observer designs are based on infinite-time convergence, which will result in a slow system response speed in practical applications and cannot meet the requirements of rapid attitude adjustment of quadrotor unmanned aerial vehicles.

[0005] In summary, the existing attitude control methods for quadrotor unmanned aerial vehicles still have problems such as slow response speed, insufficient robustness and control output chattering when facing complex and variable disturbances, and it is difficult to meet the requirements for stable flight of quadrotor unmanned aerial vehicles in complex environments. Therefore, there is an urgent need for a new attitude control method that can converge quickly in a finite time, effectively suppress chattering, and improve the anti-interference ability of the system.

[0006] In view of this, this application is proposed. Summary of the Invention

[0007] The present invention provides a non-singular terminal sliding mode attitude control method, device, equipment and medium for a quadrotor, which can at least partially improve the above problems.

[0008] To achieve the above object, the present invention adopts the following technical solutions: A non-singular terminal sliding mode attitude control method for a quadrotor, which includes: According to the attitude data of the quadrotor UAV to be controlled, establish a ground coordinate system and a body coordinate system, and based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation, obtain the rotational dynamics model of the UAV; Based on a preset non-linear system and the rotational dynamics model of the UAV, design a finite-time sliding mode disturbance observer and an extended state observer, wherein the extended state observer is used to track the attitude of the quadrotor UAV; According to the rotational dynamics model of the UAV, design a global fast non-singular terminal sliding mode controller, and adjust the global fast non-singular terminal sliding mode controller based on the resultant moment received by the UAV; Use the finite-time sliding mode disturbance observer and the extended state observer to estimate the total disturbance of the quadrotor UAV, obtain the total disturbance estimation value, and use the global fast non-singular terminal sliding mode controller to supplement the total disturbance estimation value to obtain the UAV tracking control result.

[0009] The present invention also provides a non-singular terminal sliding mode attitude control device for a quadrotor, which includes: A model establishment unit, configured to establish a ground coordinate system and a body coordinate system according to the attitude data of the quadrotor UAV to be controlled, and based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation, obtain the rotational dynamics model of the UAV; An observer unit, configured to design a finite-time sliding mode disturbance observer and an extended state observer based on a preset non-linear system and the rotational dynamics model of the UAV, wherein the extended state observer is used to track the attitude of the quadrotor UAV; A controller unit, configured to design a global fast non-singular terminal sliding mode controller according to the rotational dynamics model of the UAV, and adjust the global fast non-singular terminal sliding mode controller based on the resultant moment received by the UAV; A control unit, configured to use the finite-time sliding mode disturbance observer and the extended state observer to estimate the total disturbance of the quadrotor UAV, obtain the total disturbance estimation value, and input the total disturbance estimation value into the global fast non-singular terminal sliding mode controller to compensate the total disturbance estimation value to obtain the UAV tracking control result.

[0010] The present invention also provides a quadrotor non-singular terminal sliding mode attitude control device, which includes: a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, the quadrotor non-singular terminal sliding mode attitude control method described in any one of the above is implemented.

[0011] The present invention also provides a readable storage medium, which includes: a computer program stored therein, and the computer program can be executed by the processor of the device where the storage medium is located to implement the quadrotor non-singular terminal sliding mode attitude control method described in any one of the above.

[0012] In summary, the quadrotor non-singular terminal sliding mode attitude control method aims to significantly improve its flight stability, response speed and anti-interference ability in complex environments. This method accurately estimates the coupling interference and external unknown interference in attitude control through a finite-time sliding mode observer, effectively overcoming the chattering and singularity problems existing in traditional sliding mode control methods; and combining with the fast non-singular terminal sliding mode control technology, it realizes the efficient tracking of the preset attitude, while enhancing the adaptability of the system under complex and variable disturbances. At the same time, it can prove the efficiency of this method through theoretical analysis and simulation experiments, its ability to complete attitude adjustment within a finite time, as well as its faster convergence speed and higher robustness compared with the existing technology, providing a strong guarantee for the reliable flight of quadrotor UAVs in diverse application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a schematic flowchart of the quadrotor non-singular terminal sliding mode attitude control method provided by the first embodiment of the present invention; Figure 2 is a schematic diagram of the quadrotor UAV coordinate system provided by the embodiment of the present invention; Figure 3 is a schematic diagram of the attitude angle tracking curve provided by the embodiment of the present invention; Figure 4 is a schematic diagram of the attitude angle tracking error curve provided by the embodiment of the present invention; Figure 5 is a schematic diagram of the controller output comparison curve provided by the embodiment of the present invention; Figure 6 is a schematic diagram of the disturbance estimation curve provided by the embodiment of the present invention; Figure 7 is a schematic diagram of the attitude angular velocity curve provided by the embodiment of the present invention; Figure 8 is a schematic diagram of the controller output curve provided by the embodiment of the present invention; Figure 9 is a schematic diagram of the modules of the quadrotor non-singular terminal sliding mode attitude control device provided by the second embodiment of the present invention. Detailed implementation manners

[0014] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0015] Refer to Figure 1 As shown, the first embodiment of the present invention discloses a four-rotor non-singular terminal sliding mode attitude control method, which can be executed by a four-rotor non-singular terminal sliding mode attitude control device (hereinafter referred to as the control device), and particularly, by one or more processors in the control device to implement the following method: Please refer to Figure 2 , S1. According to the attitude data of the four-rotor unmanned aerial vehicle to be controlled, establish a ground coordinate system and a body coordinate system, and based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation, obtain the rotational dynamics model of the unmanned aerial vehicle; Specifically, step S1 includes: obtaining the attitude data of the four-rotor unmanned aerial vehicle to be controlled, and establishing a ground coordinate system and a body coordinate system based on the attitude data, wherein the positive direction of the axis of the ground coordinate system is due north, and the positive direction of the axis of the body coordinate system is the forward direction of the four-rotor unmanned aerial vehicle; Calculate the resultant moment M received by the four-rotor unmanned aerial vehicle according to the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation , , , , , , where is the angular acceleration of the four-rotor unmanned aerial vehicle, , , are respectively the angle components of the unmanned aerial vehicle rotating around the three axes, , , are respectively the components of the moment of inertia of the unmanned aerial vehicle on the three axes of the body coordinate system, , , are respectively the resultant moment components of the four-rotor unmanned aerial vehicle on the three axes of the body coordinate system, , , are all angular velocity components, is the driving moment, is the gyroscopic moment, is the drag moment, is the lift coefficient of the rotor, is the square of each rotor speed, is the propeller lift coefficient, is the distance from the center of the rotor to the center of the drone, is the inertia constant of the rotor, are the air resistance coefficients of each channel, is the combined speed of the four rotors; The combined torque acting on the quad-rotor UAV is simplified to obtain the mathematical expression of the UAV rotational dynamics model: , ,in, , , They are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, , , are the angular velocity components, is the square of each rotor speed, is the propeller lift coefficient, is the distance from the center of the rotor to the center of the drone, is the inertia constant of the rotor, are the air resistance coefficients of each channel, is the total rotation speed of the four rotors, , , They are the control inputs of the three attitude channels respectively. , , They are all unknown disturbances of the attitude channel.

[0016] In this embodiment, an "X"-shaped frame drone is used. It is assumed that the drone is a rigid body with a completely symmetrical structure and the center of gravity overlaps with the geometric center. The gravity is constant when the drone is flying, and aerodynamic parameters such as air density remain constant. The attitude data of the four-rotor drone to be controlled are obtained through sensors and other equipment. These data include key information such as the orientation and angle of the drone. Based on these attitude data, a ground coordinate system and a body coordinate system are established, wherein the positive direction of the ground coordinate system axis is set to the north direction, and the positive direction of the body coordinate system axis is the forward direction of the four-rotor drone. This way of setting the coordinate system can clearly reflect the orientation of the drone relative to the ground and its own motion posture, providing an accurate reference framework for subsequent dynamic analysis.

[0017] Subsequently, based on the established ground coordinate system, body coordinate system, and Newton-Euler dynamics equations, the calculation of the resultant moment acting on the quadrotor UAV begins. During the calculation process, the comprehensive consideration of multiple parameters and variables is involved. Specifically, parameters such as the moment of inertia of the quadrotor UAV, angular momentum vector, and angular components of rotation about the three axes are key factors in calculating the resultant moment; it can be obtained that . At the same time, since the UAV is a completely symmetric rigid body, the products of inertia for non-parallel axes are 0, so . The components of the moment of inertia of the UAV on the three axes of the body coordinate system, the components of the resultant moment on the three axes of the body coordinate system, angular velocity components, etc. also need to be included in the calculation scope, and we get , are the components of the resultant moment for the three attitude channels, , , are respectively the components of the moment of inertia of the UAV on the three axes of the body coordinate system, , , are all angular velocity components.

[0018] In addition, driving moments , gyroscopic moments , drag moments and other different types of moments, as well as the lift coefficient of the rotor , the square of the rotational speed of each rotor , the lift coefficient of the propeller , the distance from the center of the rotor to the center of the UAV , the inertial constant of the rotor , the air resistance coefficients of each channel and the combined rotational speed of the four rotors etc. These parameters jointly determine the magnitude and direction of the resultant moment. By accurately calculating these complex factors, the force conditions of the quadrotor UAV in different flight states can be comprehensively grasped, and the resultant moment formula is .

[0019] After calculating the resultant moment, the resultant moment acting on the quadrotor UAV is jointly simplified. This process requires in-depth analysis and mathematical derivation of the relationships among the numerous parameters and variables mentioned above to simplify the calculation process and highlight the key factors. After joint simplification, the mathematical expression of the UAV's rotational dynamics model is finally obtained. This expression takes the output of the UAV as the key variable and introduces the unknown total disturbances in the attitude channels. These unknown total disturbances cover the coupling effects among the attitude channels and external unknown interferences, which are the key factors affecting the attitude control accuracy and stability of the UAV. By incorporating these disturbances into the dynamics model, the complex situations faced by the UAV during actual flight can be more comprehensively reflected, providing an accurate model basis for the subsequent design of control strategies. Through the above steps, the rotational dynamics model of the quadrotor UAV is successfully established. This model not only accurately describes the motion characteristics of the UAV but also provides an important theoretical basis for the subsequent design of control strategies. Based on this model, advanced control methods that can effectively cope with unknown disturbances and quickly respond to control commands can be further designed, thereby significantly improving the flight stability and attitude control accuracy of the quadrotor UAV in complex environments.

[0020] S2. Based on the preset nonlinear system and the UAV rotational dynamics model, design a finite-time sliding mode disturbance observer and an extended state observer, where the extended state observer is used to track the attitude of the quadrotor UAV. Specifically, step S2 includes: Based on the preset nonlinear system , where is the state variable of the system, is the state equation of the system, is a function of time , is the function the initial state of, adjust the mathematical expression of the UAV rotational dynamics model to , is the input of the system, is the initial value of, where the system state variable , , , are respectively the angular components of the UAV's rotation around the three axes, the system state variable , , , are all angular velocity components, is the unknown disturbance in the three attitude channels, , are respectively the control outputs of the three attitude channels, , , , are the components of the inertia moment of the UAV on the three axes of the body coordinate system, is the quadrotor , is the inertia constant of the rotor, are the air resistance coefficients of each channel respectively, is the combined rotational speed of the four rotors, thus designing a finite-time sliding mode disturbance observer , where , where the estimation error is and the error derivative is , the adjustable parameter satisfies the conditions: , , , and , is the estimated value of the system state variable , is 's estimated value.

[0021] In this embodiment, first, according to the preset nonlinear system, the mathematical expression of the UAV rotational dynamics model is adjusted to make it adapt to the design requirements of the finite-time sliding mode disturbance observer. In the adjusted model, the variables and parameters involved include system state, control input, system initial state, and time, etc. Through this adjustment, the actual motion characteristics of the UAV can be more effectively combined with the preset nonlinear system, providing a solid theoretical basis for the subsequent observer design.

[0022] In the process of designing the finite-time sliding mode disturbance observer, a series of key parameters are introduced, such as the estimated value of the system state, etc. The introduction of these parameters enables the observer to quickly and accurately estimate various disturbances suffered by the UAV during flight. This fast response ability is difficult to achieve by traditional observers, and it greatly improves the adaptability and stability of the UAV in complex environments. Through the finite-time sliding mode disturbance observer, we can estimate the disturbance within a finite time and timely feedback these estimated values into the control law, thereby realizing effective compensation for the disturbance. This process not only improves the accuracy of UAV attitude control but also significantly enhances its robustness in the face of external disturbances.

[0023] The final expression of the finite-time sliding mode disturbance observer is: , where , , , are the components of the inertia moment of the UAV on the three axes of the body coordinate system respectively, , are the control outputs of three attitude channels respectively, is for the quadrotor , system state , , , are all angular velocity components, is the inertial constant of the rotor, are the air resistance coefficients of each channel respectively, is the combined rotational speed of the four rotors, are the unknown disturbances of the three attitude channels, , where the estimation error is and the error derivative is , where the estimation error is and the error derivative is , adjustable parameter satisfies the conditions: , , , and , is the estimated value of the system state variable , is 's estimated value.

[0024] The discontinuity of the sign function may cause chattering problems. At this time, introducing continuous functions: sig function, hyperbolic tangent function and exponential function into this expression can effectively weaken chattering, and the denominator in the fraction is greater than zero, which will not cause singularity problems. Therefore, the finite-time sliding mode disturbance observer can effectively weaken chattering while avoiding singularity problems.

[0025] Preferably, the mathematical expression of the extended state observer is: , where, , , , , , , system state variable , , , are all angular velocity components, is 's estimated value, , are the unknown disturbances of the three attitude channels respectively, is 's estimated value, are the sliding mode surfaces of the three channels of the observer respectively, The control outputs of the three attitude channels respectively, is the inertia constant of the rotor, are the air resistance coefficients of each channel respectively, is the combined rotational speed of the four rotors, 、 、 are the components of the inertia moment of the UAV on the three axes of the body coordinate system respectively. , where the estimation error and the error derivative , the adjustable parameter satisfies , , , and , it should be noted that the in the observer does not represent an error, but represents the mathematical constant .

[0026] In this embodiment, the extended state observer is mainly used to track the attitude of the quadrotor UAV. This observer can monitor the attitude changes of the UAV in real time and feedback this information to the control system. Through the extended state observer, accurate tracking of the UAV's attitude can be achieved. Whether in steady flight or in complex maneuvers, the attitude of the UAV can always be kept within the preset range. This accurate tracking ability is the basis for realizing fast non-singular terminal sliding mode control, which enables the UAV to quickly adjust its attitude in a short time to adapt to different flight mission requirements.

[0027] According to the mathematical expression of the extended state observer, through the careful design of the sliding surface, the observer can quickly respond to the changes in the UAV's attitude and achieve accurate tracking of the attitude within a finite time; this design not only improves the adaptability of the UAV in complex environments, but also significantly enhances its anti-interference ability. By introducing the observer gain, the sensitivity of the observer to attitude changes can be effectively adjusted. During the actual flight process, the UAV may be affected by various external interferences, such as changes in airflows and sudden changes in wind speed; at this time, the extended state observer can quickly capture the impact of these interferences on the attitude and compensate for these interferences by adjusting the gain, thereby maintaining the stability of the UAV's attitude. This fast response and interference compensation ability are difficult to achieve by traditional observers, which greatly improves the flight stability of the UAV in complex environments.

[0028] In addition, through an optimally designed extended state observer, real-time monitoring and feedback control of the UAV's attitude can also be achieved. During flight, the observer can provide real-time attitude information of the UAV, and this information will be fed back into the control law to achieve precise adjustment of the UAV's attitude. This real-time feedback mechanism not only improves the accuracy of UAV attitude control but also significantly shortens the attitude adjustment time, enabling the UAV to quickly respond to control commands within a short time and complete complex flight tasks.

[0029] Specifically, in this embodiment, the stability of the finite-time sliding mode disturbance observer and the extended state observer is further analyzed. Assume the unknown disturbance and its first derivative are continuously bounded, then there exist positive constants satisfying , . According to Lemma 1, under the above conditions for the external disturbance of the system, the extended state observer ensures that the disturbance estimation error is actually finite-time stable, that is, the disturbance estimation error converges to an arbitrarily small neighborhood near zero within a finite time. Lemma 1 is for the nonlinear system , where is the state variable of the system, is the state equation of the system, is a function of time , is the initial state of the function , is the input of the system, is the initial value of, there exists a continuously positive definite Lyapunov function satisfying: , where the conditional parameter needs to satisfy the condition when the state trajectory of the system is finite-time stable, and the convergence time satisfies: , where the exponential parameter satisfies . When , the state trajectory of the system is finite-time stable, and the convergence time satisfies: . Further, for a nonlinear system, if the convergence time satisfies the condition , then the nonlinear system is finite-time stable.

[0030] Taking the roll angle channel as an example, according to Lemma 1, it can be proved , and substituting it into the of the extended state observer, we get​​​ , Construct the Lyapunov function , and take the derivative of it to obtain . Where is the estimation error of the roll angle channel observer, is the roll angular velocity, is the roll angular velocity estimation value of, is the roll angle channel observer's sliding mode surface, is the roll angle channel's unknown disturbance, is the unknown disturbance estimation value of, adjustable parameter satisfies: , , , and .

[0031] Furthermore, according to Lemma 2, we can obtain , where Lemma 2 is the assumption , is a non - negative real number, then , if and only if the equal sign holds. Also, according to the above assumption, there exists a positive constant satisfying , because , so ; because , so it can be obtained that . Where is the roll angle channel observer's sliding mode surface, is the roll angle channel's unknown disturbance, is the unknown disturbance estimation value of, adjustable parameter satisfies: , , , and . Immediately substitute the above formula into the derivative formula of the Lyapunov function to obtain , where , , , . Subsequently, according to Lemma 1, the constructed roll angle channel sliding mode surface is finite - time stable, Convergence domain is: , the convergence time satisfies , where is the Lyapunov function initial state, adjustable parameter satisfies: , , , and , , , . S3. According to the rotational dynamics model of the UAV, design a global fast non-singular terminal sliding mode controller and adjust the global fast non-singular terminal sliding mode controller based on the resultant moment acting on the UAV; Specifically, step S3 includes: Construct a global fast non-singular terminal sliding mode surface for the adjusted rotational dynamics model of the UAV. The mathematical expression is: , where the adjustable parameters respectively satisfy , , , , , are all positive odd numbers, and , , the tracking error , the system state variables , , , are respectively the angular components of the UAV's rotation around the three axes, and the desired control objective of the system , , , are all desired attitude angles; Design a global fast non-singular terminal sliding mode controller according to the global fast non-singular terminal sliding mode surface. The mathematical expression of the controller is: , , where is the sliding mode surface, is the tracking error, , the adjustable parameters respectively satisfy , , , , , are all positive odd numbers, and , , the gain parameters , All are positive real numbers, adjustable parameters Satisfy , , , , , Are respectively the components of the moment of inertia of the UAV on the three axes of the body coordinate system Is a quadrotor , system state variables , , , Are respectively the angular components of the UAV rotating around the three axes, and the desired control objective of the system , , , Are all desired attitude angles, system state variables , , , Are all angular velocity components; Let , , and substitute the modeled drag terms and internal coupling terms Into the global fast non-singular terminal sliding mode controller to obtain a new mathematical expression of the global fast non-singular terminal sliding mode controller: , where , Are respectively the tracking errors of the three attitude angles, adjustable parameters Respectively satisfy , , , , , Are all positive odd numbers, and , , gain parameters , Are all positive real numbers, adjustable parameters Satisfy , , , , Are all angular velocity components, Is the inertia constant of the rotor, Are respectively the air drag coefficients of each channel, Is the combined rotational speed of the four rotors, , , Are respectively the components of the moment of inertia of the UAV on the three axes of the body coordinate system , , are all desired attitude angles , , is an unknown disturbance and its estimated value is obtained by an extended state observer.

[0032] In this embodiment, for the adjusted rotational dynamics model of the UAV, a global fast non-singular terminal sliding mode surface is constructed. The selection of the parameters in its formula is crucial for the performance of the sliding mode surface, and they determine the convergence speed and stability of the sliding mode surface. By carefully designing these parameters, it can be ensured that the sliding mode surface quickly converges to the desired attitude angle within a finite time, thus achieving fast attitude adjustment. The formula is: . Wherein, is the sliding mode surface, is the tracking error, , the adjustable parameters respectively satisfy , , , , , are all positive odd numbers, and , .

[0033] Based on the above global fast non-singular terminal sliding mode surface, a global fast non-singular terminal sliding mode controller is further designed. This design not only ensures the fast response ability of the controller but also effectively avoids the singular problem existing in the traditional sliding mode controller. By introducing a non-singular term, it can be ensured that the controller can work normally under all working conditions, thus improving the reliability and stability of the system. In order to further improve the performance of the controller, the modeled drag term and internal coupling term are substituted into the global fast non-singular terminal sliding mode controller to obtain a new mathematical expression of the global fast non-singular terminal sliding mode controller. Among them, in the traditional global fast terminal sliding mode, there is ( , , are all positive odd numbers) terms, , when , , the controller has a singular problem, and the exponential term in the controller formula is ( , , are all positive odd numbers), the exponential term becomes ( , , Since they are all positive odd numbers, there is no singularity problem with the controller.

[0034] Specifically, in this embodiment, the stability of the controller is further analyzed. First, the proof that the tracking error reaches the sliding surface in finite time is carried out, taking the roll angle channel as an example to prove the stability. Substitute the controller formula into formula and the tracking error of the channel is where and are the rotation angle of the quadrotor roll angle and its expected value respectively. Therefore is the sliding surface of the channel controller, is the estimated disturbance of the unknown disturbance of the roll angle channel. The adjustable parameters respectively satisfy , , , , , , are all positive odd numbers, and , . The gain parameters , are all positive real numbers, , . The adjustable parameter satisfies , .

[0035] Substitute formula and , into to get , where is the sliding surface of the channel observer.

[0036] Construct Lyapunov and take its derivative. At the same time, substitute the simultaneous equations of formula , to get .

[0037] Furthermore, according to Lemma 2, we can get . Because , so . And because , so . Therefore . Let and substitute it into the above formula to get: , because , , are all positive odd numbers and satisfy , so . In this formula, , , , , . In summary, the derivative Lyapunov function can always satisfy Lemma 1, and the sliding mode surface is actually finite-time stable, and the convergence time satisfies , where represents the initial state of the Lyapunov function of this system.

[0038] Secondly, prove the finite-time convergence after the tracking error reaches the sliding mode surface. Assume that when the system is at , the system reaches the sliding mode surface, that is, . According to the formula of the global fast non-singular terminal sliding mode surface, the tracking error of the roll angle channel becomes: . Multiply both sides by to get: ; then integrate both sides to get , where , because , , , , , are all positive odd numbers, so .

[0039] According to the above formula, , and because , are all positive odd numbers and , so , so the function of t decreases monotonically as t increases, that is, decreases monotonically as t increases. When , the time satisfies , that is, the tracking error of the roll angle channel can converge to 0 in finite time.

[0040] S4. Use a finite-time sliding-mode disturbance observer and an extended state observer to estimate the total disturbance of the quadrotor UAV, obtain the total disturbance estimation value, and use a global fast non-singular terminal sliding-mode controller to supplement the total disturbance estimation value to obtain the UAV tracking control result.

[0041] Preferably, the total disturbance estimation value includes the coupling between attitude channels and unknown external disturbances.

[0042] Specifically, in this embodiment, first, use a finite-time sliding-mode disturbance observer and an extended state observer to estimate the total disturbance of the quadrotor UAV. The design of these two observers is based on the dynamic model of the UAV and actual flight data, and can monitor and estimate the coupling effect between attitude channels and unknown external disturbances in real time. These disturbances are the key factors affecting the attitude control accuracy of the UAV. By accurately estimating these disturbances, we can provide accurate data support for subsequent control strategies. During the estimation process, the finite-time sliding-mode disturbance observer can quickly respond and estimate the magnitude and direction of the disturbance, while the extended state observer can track the attitude changes of the UAV in real time. This combined use enables us to obtain a high-precision disturbance estimation value within a finite time. These estimation values not only include the coupling effect between attitude channels, but also cover unknown external disturbances in the external environment, such as airflow changes and sudden wind speed changes. Through this comprehensive estimation, we can more accurately grasp the complex situations faced by the UAV during actual flight.

[0043] Subsequently, input the obtained total disturbance estimation value into the global fast non-singular terminal sliding-mode controller. The design of this controller aims to effectively compensate for the estimated disturbance, thereby achieving rapid adjustment and precise control of the UAV attitude. By introducing the disturbance estimation value into the control law, we can adjust the control input in real time to offset the influence of the disturbance on the UAV attitude. This real-time compensation mechanism not only improves the accuracy of the UAV attitude control, but also significantly shortens the attitude adjustment time, enabling the UAV to quickly respond to control commands within a short time and complete complex flight tasks.

[0044] In addition, the design of the global fast non-singular terminal sliding-mode controller also has good robustness. When facing complex and variable external disturbances, this controller can maintain a stable working state and ensure the stability of the UAV attitude. This robustness is crucial for the reliable flight of the UAV in a complex environment, enabling the UAV to maintain good performance under different flight conditions.

[0045] In this embodiment, in order to verify the effectiveness of the proposed method (FTSESO-CFNTSMC) for the attitude control of quadrotor UAVs, a comparison is made with the global fast terminal sliding mode controller (GFTSMC). In the simulation experiment, the parameters of the quadrotor UAV are shown in Table 1, the parameters of the finite-time extended state observer are shown in Table 2, and the parameters of the fast non-singular terminal sliding mode controller are shown in Table 3.

[0046] Table 1 Parameters of quadrotor UAV

[0047] Table 2 Parameters of extended state observer

[0048] Table 3 Controller parameters

[0049] The sliding mode surface of the GFTSMC for comparison is designed as: , where is the tracking error of the state quantity, the adjustable parameter , satisfying , , and are all positive odd numbers. The GFTSMC control law is designed as , where the tracking error , is the state quantity of the system, is the desired system state quantity, is the sliding mode surface of the system, the gain adjustment parameter , , , , are the components of the moment of inertia of the UAV on the three axes of the body coordinate system respectively, is the quadrotor ; The desired attitude is . In order to prove the effectiveness of the finite-time extended state observer for unknown disturbances, the unknown disturbances in the channel are assumed in segments, as shown in Table 4.

[0050] Table 4 Unknown disturbances

[0051] According to the figure, Figure 3 , Figure 4The tracking curves and tracking error curves of two control methods for different tracking targets and different initial values in three attitude channels. No unknown disturbance was added in the first 0 - 5 s, a constant disturbance was added in the 5 - 10 s, and a sinusoidal disturbance was added in the 10 - 15 s. When no disturbance was added in the 0 - 5 s, both control methods could track sinusoidal signals and step signals with different periods well in the three attitude channels with different initial values, and could complete convergence within 0.5 s. However, from the tracking curves and error curves of the roll angle and yaw angle, it can be seen that the control method in this paper has a shorter convergence time compared with the GFTSMC control method; when a constant disturbance was added in the 5 - 10 s, both methods have a certain robustness to the constant disturbance. But from the tracking curves and error curves of the yaw angle, it can be seen that as the disturbance amplitude increases, the GFTSMC control method will have a certain tracking error, while the control method in this paper can still maintain good tracking. Therefore, the control method used in this paper has higher robustness compared with the GFTSMC control method. When a sinusoidal disturbance was added in the 10 - 15 s, from the tracking curves of the pitch angle and yaw angle, it can be seen that the tracking curve of the GFTSMC control method has obvious errors, while the control method in this paper can still track the preset curve well. To sum up, through Figure 3 and Figure 4 it can be proved that this method can control the attitude of the UAV well, and has a higher convergence speed and robustness compared with the GFTSMC control method.

[0052] Figure 7 This is the curve of the attitude angle change of the UAV controlled by this method. Since there is a large error between the initial values of the roll angle and pitch angle channels and the preset values at the beginning, the angular velocity curve has a large initial value within 0.2 s, indicating that the control system can quickly compensate for the initial value error at startup and make the system reach the preset value in a short time. From the angular velocity curve, it can be seen that after adding constant and sinusoidal disturbances with different amplitudes, the angular velocity curve still maintains its original change trend. For example, after the pitch angular velocity stabilizes, since the preset tracking curve is a fixed value, the angular velocity always remains zero, which can prove that the control method in this paper has a high anti-disturbance ability for complex and variable disturbances.

[0053] Figure 8 This is the curve output by the controller using this method. Figure 5 The comparative output curves of the two controllers. From Figure 4 it can be seen that when there is a large error between the initial value and the preset value at startup in the control method in this paper, the controller will have a large output, and then the control output tends to be stable output according to a certain rule. The stable output curve is mainly determined by the control target and disturbance compensation. From Figure 8It can be observed that the output curve of the controller of the control method in this paper has the same changing trend as that of the GFTSMC control method, and the output amplitude belongs to the same order of magnitude. However, there is chattering in the output of the GFTSMC control method, while the control method used in this paper can not only quickly compensate for the error but also greatly eliminate the chattering situation.

[0054] Figure 6 is the estimation of the disturbance by the finite-time extended observer. It can be seen that the observer can accurately estimate the disturbances with complex changes and different amplitudes, and apply the disturbance estimation to the controller to compensate for the disturbances, thereby improving the robustness and reliability of the system.

[0055] In summary, the non-singular terminal sliding mode attitude control method for quadrotors aims to significantly improve the flight stability, response speed and anti-interference ability of quadrotor UAVs in complex environments. Through an innovative control strategy, combining a finite-time sliding mode disturbance observer and an extended state observer, the total disturbances of the quadrotor UAV are accurately estimated, and a global fast non-singular terminal sliding mode controller is used to effectively compensate for these disturbances, so as to achieve fast and accurate control of the UAV attitude.

[0056] Specifically, first establish the ground coordinate system and the body coordinate system according to the attitude data of the quadrotor UAV, and obtain the rotational dynamics model of the UAV based on the Newton-Euler dynamics equation. This model provides a theoretical basis for the subsequent design of the control strategy. Subsequently, design a finite-time sliding mode disturbance observer and an extended state observer to estimate the coupling effect between the attitude channels of the UAV and the external unknown disturbances in real time. These observers can quickly respond within a finite time and provide high-precision disturbance estimation values, providing accurate data support for the implementation of the control strategy. Further, based on the rotational dynamics model of the UAV, design a global fast non-singular terminal sliding mode controller. By introducing the disturbance estimation value, the controller can adjust the control input in real time to offset the influence of the disturbance on the UAV attitude. This real-time compensation mechanism not only improves the accuracy of the UAV attitude control but also significantly shortens the attitude adjustment time, enabling the UAV to quickly respond to control commands within a short time and complete complex flight tasks. In addition, the design of this controller also has good robustness and can maintain a stable working state in the face of complex and changeable external disturbances, ensuring the stability of the UAV attitude.

[0057] By combining a finite-time sliding mode disturbance observer, an extended state observer, and a global fast nonsingular terminal sliding mode controller, the present invention not only improves the response speed and accuracy of the attitude control of a quadrotor UAV, but also significantly enhances the anti-interference ability of the system. This innovative control strategy provides strong technical support for the reliable flight of quadrotor UAVs in diverse application scenarios, significantly improving their performance in practical applications. Whether in steady flight or during complex maneuvers, the UAV can maintain good attitude stability and quickly adapt to different flight mission requirements, thus showing broad application prospects in multiple fields such as military, civilian, and scientific research.

[0058] Please refer to Figure 9 , the second embodiment of the present invention provides a quadrotor nonsingular terminal sliding mode attitude control device, which includes: A model establishment unit 101, configured to establish a ground coordinate system and a body coordinate system according to the attitude data of the quadrotor UAV to be controlled, and obtain the rotational dynamics model of the UAV based on the ground coordinate system, the body coordinate system, and the Newton-Euler dynamics equation; An observer unit 102, configured to design a finite-time sliding mode disturbance observer and an extended state observer based on a preset nonlinear system and the rotational dynamics model of the UAV, wherein the extended state observer is used to track the attitude of the quadrotor UAV; A controller unit 103, configured to design a global fast nonsingular terminal sliding mode controller according to the rotational dynamics model of the UAV, and adjust the global fast nonsingular terminal sliding mode controller based on the total moment acting on the UAV; A control unit 104, configured to estimate the total disturbance of the quadrotor UAV using the finite-time sliding mode disturbance observer and the extended state observer to obtain a total disturbance estimate value, and supplement the total disturbance estimate value using the global fast nonsingular terminal sliding mode controller to obtain the UAV tracking control result.

[0059] The third embodiment of the present invention provides a quadrotor nonsingular terminal sliding mode attitude control device, which includes: a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the quadrotor nonsingular terminal sliding mode attitude control method described in any one of the above.

[0060] The fourth embodiment of the present invention provides a readable storage medium, which includes: a computer program stored therein, and the computer program can be executed by the processor of the device where the storage medium is located to implement the quadrotor nonsingular terminal sliding mode attitude control method described in any one of the above.

[0061] The above are the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also regarded as the protection scope of the present invention.

Claims

1. A non-singular terminal sliding mode attitude control method for a quadrotor, characterized in that, Including: Based on the attitude data of the quadrotor UAV to be controlled, establish a ground coordinate system and a body coordinate system, and based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation, obtain the rotational dynamics model of the UAV; Based on a preset nonlinear system and the rotational dynamics model of the UAV, design a finite-time sliding mode disturbance observer and an extended state observer, where the extended state observer is used to track the attitude of the quadrotor UAV; According to the rotational dynamics model of the UAV, design a global fast non-singular terminal sliding mode controller, and adjust the global fast non-singular terminal sliding mode controller based on the resultant moment acting on the UAV; Use the finite-time sliding mode disturbance observer and the extended state observer to estimate the total disturbance of the quadrotor UAV, obtain the total disturbance estimation value, and use the global fast non-singular terminal sliding mode controller to supplement the total disturbance estimation value to obtain the UAV tracking control result.

2. The attitude control method of the quadrotor non-singular terminal sliding mode according to claim 1, characterized in that Based on the attitude data of the quadrotor UAV to be controlled, establish a ground coordinate system and a body coordinate system, and based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation, obtain the rotational dynamics model of the UAV, specifically: Obtain the attitude data of the quadrotor UAV to be controlled, and establish a ground coordinate system and a body coordinate system based on the attitude data. Among them, the positive direction of the axis of the ground coordinate system is due north, and the positive direction of the axis of the body coordinate system is the forward direction of the quadrotor UAV; Calculate the resultant moment acting on the quadrotor UAV according to the ground coordinate system, body coordinate system and Newton-Euler dynamics equations M , , , , , , , where is the angular acceleration of the quadrotor UAV, , , are the angular components of the UAV's rotation about the three axes respectively, , , are the components of the UAV's moment of inertia on the three axes of the body coordinate system respectively, , , are the resultant moment components of the quadrotor UAV on the three axes of the body coordinate system respectively, , , are all angular velocity components, is the driving moment, is the gyroscopic moment, is the drag moment, is the lift coefficient of the rotor, is the square of the rotational speed of each rotor, is the lift coefficient of the propeller, is the distance from the rotor center to the UAV center, is the inertia constant of the rotor, are the air drag coefficients of each channel respectively, is the combined rotational speed of the four rotors; By simultaneously simplifying the resultant moment acting on the quadrotor UAV, the mathematical expression of the rotational dynamics model of the UAV is obtained: , , where , , are the components of the moment of inertia of the UAV on the three axes of the body coordinate system respectively, , , are all angular velocity components, is the square of the rotational speed of each rotor, is the lift coefficient of the propeller, is the distance from the center of the rotor to the center of the UAV, is the inertial constant of the rotor, are the air resistance coefficients of each channel respectively, is the combined rotational speed of the four rotors, , , are the control inputs of the three attitude channels respectively, , , are all unknown disturbances of the attitude channels.

3. The attitude control method of the quadrotor non-singular terminal sliding mode according to claim 2, characterized in that Based on a preset nonlinear system and the rotational dynamics model of the UAV, design a finite-time sliding mode disturbance observer, specifically: Based on a preset non - linear system , where is the state variable of the system, is the state equation of the system, is a function of time , is the initial state of the function , is the input of the system, is the initial value of. Adjust the mathematical expression of the drone rotation dynamics model to , is the input of the system, is the initial value of, where the system state variable , , , are respectively the angular components of the drone's rotation around the three axes. The system state variable , , , are all angular velocity components, is the unknown disturbance of the three attitude channels, , are respectively the control outputs of the three attitude channels, , , , are respectively the components of the drone's moment of inertia on the three axes of the body coordinate system, is the quadrotor , is the inertia constant of the rotor, are respectively the air resistance coefficients of each channel, is the combined rotational speed of the four rotors. Thus, design a finite - time sliding - mode disturbance observer , where , where the estimation error is and the error derivative is . The adjustable parameter satisfies the conditions: , , , and , is the estimated value of the system state variable , is the estimated value of.

4. The attitude control method of the quadrotor non-singular terminal sliding mode according to claim 3, characterized in that The mathematical expression of the expansion state observer is as follows: , where , , , , , , the system state variables , , , are all angular velocity components, is 's estimated value, , are the unknown disturbances of the three attitude channels respectively, is 's estimated value, are the sliding mode surfaces of the three channels of the observer respectively, are the control outputs of the three attitude channels respectively, is the inertia constant of the rotor, are the air resistance coefficients of each channel respectively, is the combined rotational speed of the four rotors, , , are the components of the moment of inertia of the UAV on the three axes of the body coordinate system respectively; , where the estimation error and the error derivative , the adjustable parameter satisfies , , , and . It should be noted that in the observer does not represent an error, but represents the mathematical constant .

5. The attitude control method of the quadrotor non-singular terminal sliding mode according to claim 4, characterized in that According to the rotational dynamics model of the UAV, design a global fast non-singular terminal sliding mode controller, and adjust the global fast non-singular terminal sliding mode controller based on the resultant moment acting on the UAV, specifically: For the adjusted rotational dynamics model of the UAV, construct a global fast non-singular terminal sliding mode surface, and its mathematical expression is: , where the adjustable parameters respectively satisfy , , , , , are all positive odd numbers, and , , the tracking error , the system state variables , , , are respectively the angular components of the UAV's rotation around the three axes, and the desired control objectives of the system , , , are all desired attitude angles; A global fast non-singular terminal sliding mode controller is designed based on the global fast non-singular terminal sliding mode surface. The mathematical expression of the controller is as follows: , , where is the sliding mode surface of the channel controller, is the tracking error, , the adjustable parameters respectively satisfy , , , , , are all positive odd numbers, and , , the gain parameters , are all positive real numbers. The adjustable parameter satisfies , , , , , are the components of the inertia of the UAV on the three axes of the body coordinate system respectively, is the quadrotor , the system state variables , , , are the angular components of the UAV rotating around the three axes respectively. The desired control objective of the system , , , are all desired attitude angles. The system state variables , , , are all angular velocity components; Let , , and substitute the modeled drag terms and internal coupling terms into the global fast nonsingular terminal sliding mode controller to obtain a new mathematical expression of the global fast nonsingular terminal sliding mode controller: , where , are the tracking errors of the three attitude angles respectively, and the adjustable parameters respectively satisfy , , , , , are all positive odd numbers, and , , the gain parameters , are all positive real numbers, the adjustable parameter satisfies , , , , are the angular velocity components respectively, is the inertia constant of the rotor, are the air drag coefficients of each channel respectively, is the combined rotational speed of the four rotors, , , are the components of the drone's moment of inertia on the three axes of the body coordinate system respectively, , , are the desired attitude angles , , is the unknown disturbance is the estimated value, which is obtained by the extended state observer.

6. The attitude control method of the quadrotor non-singular terminal sliding mode according to claim 1, wherein The total disturbance estimation value includes the coupling between each attitude channel and the external unknown disturbance.

7. A four-rotor non-singular terminal sliding mode attitude control device, characterized in that Including: A model establishment unit for establishing a ground coordinate system and a body coordinate system based on the attitude data of the quadrotor UAV to be controlled, and obtaining the rotational dynamics model of the UAV based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation; An observer unit for designing a finite-time sliding mode disturbance observer and an extended state observer based on a preset nonlinear system and the rotational dynamics model of the UAV, where the extended state observer is used to track the attitude of the quadrotor UAV; A controller unit for designing a global fast non-singular terminal sliding mode controller according to the rotational dynamics model of the UAV, and adjusting the global fast non-singular terminal sliding mode controller based on the resultant moment acting on the UAV; A control unit for using the finite-time sliding mode disturbance observer and the extended state observer to estimate the total disturbance of the quadrotor UAV, obtaining the total disturbance estimation value, and using the global fast non-singular terminal sliding mode controller to supplement the total disturbance estimation value to obtain the UAV tracking control result.

8. A four-rotor non-singular terminal sliding mode attitude control device, characterized in that, Including a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the quadrotor non-singular terminal sliding mode attitude control method according to any one of claims 1 to 6.

9. A readable storage medium, characterized in that, Stored with a computer program, the computer program can be executed by the processor of the device where the storage medium is located to implement the quadrotor non-singular terminal sliding mode attitude control method according to any one of claims 1 to 6.

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