Quadrotor non-singular terminal sliding mode attitude control method, device, equipment and medium

Abstract

The present invention provides a method, device, equipment, and medium for non-singular terminal sliding mode attitude control of a quadrotor, relating to the technical field of quadrotor unmanned aerial vehicles (UAVs). This method uses a finite-time sliding mode observer to efficiently estimate coupled disturbances and external unknown disturbances in UAV attitude control, effectively resolving the problem of insufficient control accuracy due to disturbances in traditional methods. Combined with fast non-singular terminal sliding mode control technology, this method not only achieves rapid and accurate tracking of the preset attitude but also significantly enhances the system's anti-interference capability in the face of complex and variable disturbances. It also effectively suppresses controller output chatter, ensuring smooth flight. The goal is to improve the attitude control accuracy, response speed, and anti-interference capability of quadrotor UAVs in complex environments.

Description

Technical Field

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

[0002] With the rapid development of drone technology, quadrotors (UAVs) have gained widespread application in various fields, including military, civilian, and scientific research, due to their simple structure, strong maneuverability, and ease of control. However, attitude control of quadrotors faces numerous challenges. Due to their multi-input and multi-output (MIMO) characteristics, strong coupling, and nonlinearity, as well as the external disturbances (such as wind speed and airflow fluctuations) and internal parameter variations (such as battery charge and load changes) during flight, traditional control methods often struggle to meet the required attitude control accuracy and response speed.

[0003] In the field of attitude control for quadrotor drones, sliding mode control methods have attracted widespread attention due to their robustness to system uncertainties and external disturbances. However, traditional sliding mode control methods have some problems, such as "singularity" phenomena and control output chattering. Singularity phenomena can cause the control law to fail, while control output chattering can reduce the control accuracy and reliability of the system. To address these problems, researchers have proposed a variety of 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 they still suffer from problems such as insufficient response speed and insufficient robustness in the face of complex and variable disturbances.

[0004] Furthermore, to improve the interference resistance of quadrotor UAV attitude control systems, researchers have proposed observer-based control methods. By designing an observer to estimate the system state and external disturbances and feeding the estimated values ​​into the control law, the robustness of the system can be effectively improved. However, existing observer designs are mostly based on infinite time convergence, which results in slow system response in practical applications and cannot meet the requirements of quadrotor UAVs for rapid attitude adjustment.

[0005] In summary, existing quadrotor UAV attitude control methods still suffer from slow response, insufficient robustness, and control output chattering when faced with complex and variable disturbances, making them difficult to meet the requirements for stable flight in complex environments. Therefore, there is an urgent need for a new attitude control method that can converge quickly within a limited time, effectively suppress chattering, and improve the system's anti-interference ability.

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

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

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A non-singular terminal sliding mode attitude control method for a quadrotor, comprising:

[0010] According to the attitude data of the quadrotor drone to be controlled, the ground coordinate system and the body coordinate system are established, and the drone rotation dynamics model is obtained based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation;

[0011] Based on the preset nonlinear system and the UAV rotational dynamics model, a finite-time sliding mode disturbance observer and an extended state observer are designed. The extended state observer is used to track the attitude of the quadrotor UAV.

[0012] Based on the UAV rotational dynamics model, a global fast non-singular terminal sliding mode controller is designed and adjusted based on the total torque acting on the UAV.

[0013] The total disturbance of the quadrotor UAV is estimated using a finite-time sliding mode disturbance observer and an extended state observer to obtain a total disturbance estimate, which is then supplemented by a global fast non-singular terminal sliding mode controller to obtain the UAV tracking control result.

[0014] The present invention also provides a quadrotor non-singular terminal sliding mode attitude control device, which includes:

[0015] A model building unit is used to establish a ground coordinate system and a body coordinate system according to the attitude data of the quadrotor drone to be controlled, and obtain a rotational dynamics model of the drone based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation;

[0016] The observer unit is used to design a finite-time sliding mode disturbance observer and an extended state observer based on a preset nonlinear system and the UAV rotational dynamics model. The extended state observer is used to track the attitude of the quadrotor UAV.

[0017] A controller unit is used to design a global fast non-singular terminal sliding mode controller based on the UAV rotational dynamics model and adjust the global fast non-singular terminal sliding mode controller based on the total torque acting on the UAV;

[0018] The control unit is used to estimate the total disturbance of the quadrotor UAV using a finite-time sliding mode disturbance observer and an extended state observer to obtain a total disturbance estimation value, and input the total disturbance estimation value into a global fast non-singular terminal sliding mode controller to compensate for the total disturbance estimation value, thereby obtaining a UAV tracking control result.

[0019] 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, it implements the quadrotor non-singular terminal sliding mode attitude control method as described in any one of the above items.

[0020] The present invention also provides a readable storage medium, which includes: a computer program stored therein, wherein the computer program can be executed by a processor of a device where the storage medium is located to implement the quadrotor non-singular terminal sliding mode attitude control method as described in any one of the above items.

[0021] In summary, the non-singular terminal sliding mode attitude control method for quadrotors aims to significantly improve their flight stability, response speed, and anti-interference ability in complex environments. This method uses a finite-time sliding mode observer to accurately estimate the coupled interference and external unknown interference in attitude control, effectively overcoming the chattering and singularity problems existing in traditional sliding mode control methods. It also combines fast non-singular terminal sliding mode control technology to achieve efficient tracking of the preset attitude, while enhancing the system's adaptability under complex and variable disturbances. At the same time, the efficiency of this method can be demonstrated through theoretical analysis and simulation experiments. Its ability to complete attitude adjustment within a limited time, as well as its faster convergence speed and higher robustness compared to existing technologies, provide a strong guarantee for the reliable flight of quadrotors in a variety of application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 1 is a flow chart of a non-singular terminal sliding mode attitude control method for a quadrotor provided by the first embodiment of the present invention;

[0023] Figure 2 Schematic diagram of the coordinate system of the quadrotor drone provided by an embodiment of the present invention;

[0024] Figure 3 is a schematic diagram of an attitude angle tracking curve provided by an embodiment of the present invention;

[0025] Figure 4 is a schematic diagram of an attitude angle tracking error curve provided by an embodiment of the present invention;

[0026] Figure 5 1 is a schematic diagram of a controller output comparison curve provided by an embodiment of the present invention;

[0027] Figure 6 is a schematic diagram of a disturbance estimation curve provided by an embodiment of the present invention;

[0028] Figure 7 is a schematic diagram of an attitude angular velocity curve provided by an embodiment of the present invention;

[0029] Figure 8 is a schematic diagram of a controller output curve provided by an embodiment of the present invention;

[0030] Figure 9 It is a module schematic diagram of a quadrotor non-singular terminal sliding mode attitude control device provided by the second embodiment of the present invention. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0032] refer to Figure 1 As shown, the first embodiment of the present invention discloses a quadrotor non-singular terminal sliding mode attitude control method, which can be executed by a quadrotor non-singular terminal sliding mode attitude control device (hereinafter referred to as the control device), and in particular, executed by one or more processors in the control device to implement the following method:

[0033] See also Figure 2 ,S1, according to the attitude data of the quadrotor drone to be controlled, establish the ground coordinate system and the body coordinate system, and obtain the drone rotation dynamics model based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation;

[0034] Specifically, step S1 includes: obtaining the attitude data of the quadcopter to be controlled, establishing a ground coordinate system and a body coordinate system based on the attitude data, wherein the ground coordinate system The positive direction of the axis is due north, and the body coordinate system The positive direction of the axis is the forward direction of the quadrotor drone;

[0035] Calculate the resultant torque on the quadrotor drone based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation M , , , , , , ,in, is the angular acceleration of the quadrotor drone, 、 、 are the angular components of the UAV’s rotation around the three axes, 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, 、 、 are the resultant torque components of the quadrotor drone on the three axes of the body coordinate system, 、 、 are all angular velocity components, is the driving torque, is the gyroscopic torque, is the resistance torque, 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 total rotational speed of the four rotors;

[0036] By simplifying the resultant torque acting on the quadrotor drone, the mathematical expression of the drone's rotational dynamics model is obtained: , ,in, 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, 、 、 are all 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 rotational 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.

[0037] 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 its center of gravity overlaps with its geometric center. The gravity is constant during flight, and aerodynamic parameters such as air density remain constant. The attitude data of the quadcopter 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 due north, and the positive direction of the body coordinate system axis is the forward direction of the quadcopter. This way of setting the coordinate system can clearly reflect the orientation of the drone relative to the ground and its own motion attitude, providing an accurate reference framework for subsequent dynamic analysis.

[0038] Then, based on the established ground coordinate system, body coordinate system and Newton-Euler dynamic equation, the resultant torque of the quadcopter is calculated. In the calculation process, multiple parameters and variables are involved. Specifically, the parameters such as the quadcopter's moment of inertia, angular momentum vector, and the angular components of rotation around the three axes are all key factors in calculating the resultant torque; it can be obtained At the same time, since the drone is a completely symmetrical rigid body, the inertia product of non-parallel axes is 0, so , the components of the UAV's rotational inertia on the three axes of the body coordinate system, the components of the resultant torque on the three axes of the body coordinate system, the angular velocity components, etc., also need to be included in the calculation scope, and we can get , is the resultant torque component of the three attitude channels, 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, 、 、 are all angular velocity components.

[0039] In addition, the driving torque , gyroscopic torque , resistance torque Different types of torque, such as the lift coefficient of the rotor , the square of each rotor speed , propeller lift coefficient , the distance from the rotor center to the center of the drone , the inertia constant of the rotor , the air resistance coefficient of each channel and the total speed of the four rotors These parameters together determine the magnitude and direction of the resultant torque. By accurately calculating these complex factors, we can fully understand the force conditions of the quadcopter in different flight states. The formula for the resultant torque is: .

[0040] After calculating the resultant torque, the resultant torque acting on the quadrotor is simultaneously simplified. This process requires in-depth analysis and mathematical derivation of the relationships between the numerous parameters and variables mentioned above to simplify the calculation process and highlight key factors. After simultaneous simplification, the mathematical expression for the UAV's rotational dynamics model is ultimately derived. This expression uses the UAV's output as the key variable and also incorporates the unknown total disturbances in the attitude channel. These unknown total disturbances encompass the coupling effects between attitude channels and external unknown interference, and are key factors affecting the UAV's attitude control accuracy and stability. By incorporating these disturbances into the dynamics model, the complex conditions faced by the UAV in actual flight can be more comprehensively reflected, providing an accurate model foundation for subsequent control strategy design. Through the above steps, a rotational dynamics model for the quadrotor UAV is successfully established. This model not only accurately describes the UAV's motion characteristics but also provides an important theoretical basis for subsequent control strategy design. Based on this model, advanced control methods can be designed that can effectively cope with unknown disturbances and quickly respond to control commands, significantly improving the flight stability and attitude control accuracy of the quadrotor UAV in complex environments.

[0041] S2, based on the preset nonlinear system and the UAV rotational dynamics model, a finite-time sliding mode disturbance observer and an extended state observer are designed. The extended state observer is used to track the attitude of the quadrotor UAV.

[0042] Specifically, step S2 includes: based on the preset nonlinear system ,in, is the state variable of the system, is the state equation of the system, for About Time function, For function The mathematical expression of the UAV rotation dynamics model is adjusted to , is the input of the system, for The initial value of the system state variable , 、 、 They are the angle components of the UAV's rotation around the three axes, and the system state variables , 、 、 are all angular velocity components, is the unknown disturbance of the three attitude channels, , There are three attitude channel control outputs respectively. , 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, are the drag term and internal coupling term that can be modeled for the quadrotor, is the inertia constant of the rotor, are the air resistance coefficients of each channel, The total speed of the four rotors is used to design a finite-time sliding mode disturbance observer. ,in, , where the estimation error is And the error derivative is , adjustable parameters Requirements: , , , and , is the system state variable The estimated value of for estimated value.

[0043] In this example, the mathematical expression of the UAV's rotational dynamics model is first adjusted based on a predefined nonlinear system to accommodate the design requirements of a finite-time sliding-mode disturbance observer. The adjusted model includes variables and parameters such as system state, control input, initial system state, and time. This adjustment more effectively integrates the UAV's actual motion characteristics with the predefined nonlinear system, providing a solid theoretical foundation for subsequent observer design.

[0044] In the design of the finite-time sliding mode disturbance observer, a series of key parameters, such as the estimated value of the system state, were introduced. The introduction of these parameters enables the observer to quickly and accurately estimate the various disturbances to which the drone is subjected during flight. This rapid response capability, difficult to achieve with traditional observers, significantly improves the drone's adaptability and stability in complex environments. The finite-time sliding mode disturbance observer allows us to estimate disturbances within a finite timeframe and promptly feed these estimates into the control law, effectively compensating for the disturbances. This process not only improves the accuracy of the drone's attitude control but also significantly enhances its robustness to external disturbances.

[0045] The final expression of the finite-time sliding mode disturbance observer is: ,in, , 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, , There are three attitude channel control outputs respectively. For quadrotor , system status , 、 、 are all angular velocity components, is the inertia constant of the rotor, are the air resistance coefficients of each channel, is the total rotational speed of the four rotors, is the unknown disturbance 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 parameters Requirements: , , , and , is the system state variable The estimated value of for estimated value.

[0046] The discontinuity of the sign function may cause chattering. In this case, introducing continuous functions into the expression: sig function, hyperbolic tangent function, and exponential function can effectively reduce chattering. Moreover, the denominator in the fraction is greater than zero, which does not cause singularity problems. Therefore, the finite-time sliding mode disturbance observer can effectively reduce chattering while avoiding singularity problems.

[0047] Preferably, the mathematical expression of the extended state observer is: ,in, , , , , , , system state variables , 、 、 are all angular velocity components, for The estimated value of , are the unknown disturbances of the three attitude channels, for The estimated value of are the sliding surfaces of the three channels of the observer, There are three attitude channel control outputs respectively. is the inertia constant of the rotor, are the air resistance coefficients of each channel, is the total rotational speed of the four rotors, 、 、 They are the components of the UAV's moment of inertia on the three axes of the body coordinate system. , where the estimation error and error derivative , adjustable parameters satisfy , , , and , it should be noted that in the observer It does not represent an error, but a mathematical constant .

[0048] In this embodiment, an extended state observer (ESO) is primarily used to track the attitude of a quadrotor drone. This observer monitors the drone's attitude changes in real time and feeds this information back to the control system. This ESO enables precise tracking of the drone's attitude, ensuring it remains within a preset range, whether in steady flight or during complex maneuvers. This precise tracking capability is the foundation for fast, non-singular terminal sliding mode control, enabling the drone to rapidly adjust its attitude to suit different flight mission requirements.

[0049] The mathematical expression of the extended state observer (ESO) reveals that, through the careful design of the sliding surface, the observer can rapidly respond to changes in the drone's attitude and accurately track it within a limited time. This design not only improves the drone's adaptability in complex environments but also significantly enhances its anti-interference capability. By introducing an observer gain, the observer's sensitivity to attitude changes can be effectively adjusted. During actual flight, drones may be subject to various external disturbances, such as airflow variations and sudden changes in wind speed. The ESO can quickly detect the effects of these disturbances on the drone's attitude and compensate for them by adjusting the gain, thereby maintaining the drone's attitude stability. This rapid response and disturbance compensation capability, which is difficult to achieve with traditional observers, significantly improves the drone's flight stability in complex environments.

[0050] Furthermore, an optimized extended state observer enables real-time monitoring and feedback control of the drone's attitude. During flight, the observer provides real-time attitude information, which is fed back into the control law to precisely adjust the drone's attitude. This real-time feedback mechanism not only improves the accuracy of the drone's attitude control but also significantly reduces attitude adjustment time, enabling the drone to quickly respond to control commands and complete complex flight missions.

[0051] Specifically, in this embodiment, the stability of the finite-time sliding mode disturbance observer and the extended state observer is further analyzed. Assuming that the unknown disturbance and its first-order derivative is continuous and bounded, then there exists a positive constant ,satisfy , According to Lemma 1, when the external disturbance of the system satisfies the above conditions, the extended state observer ensures that the disturbance estimation error is practically finite-time stable, that is, the disturbance estimation error converges to an arbitrary small neighborhood near zero in a finite time. Lemma 1 is for nonlinear systems ,in, is the state variable of the system, is the state equation of the system, for About Time function, For function The initial state, is the input of the system, for For the initial value of satisfy: , where the conditional parameters , the conditions must be met When the state trajectory of the system is finite time stable, the convergence time satisfy: , where the exponential parameter satisfy .when When , the state trajectory of the system is finite time stable, and the convergence time satisfies: . Furthermore, for nonlinear systems, if the convergence time Meet the conditions , then the nonlinear system is finite-time stable.

[0052] Roll angle Channel as an example, according to Lemma 1, it can be proved that , and substitute it into the extended state observer Go in and get , . Construct Lyapunov function , and taking its derivative, we get .in is the estimated error of the roll angle channel observer, is the rolling angular velocity, is the rolling angular velocity The estimated value of Roll angle The sliding surface of the channel observer, Roll angle Unknown disturbances in the channel, For unknown disturbance The estimated value of , adjustable parameter satisfy: , , , and .

[0053] Further according to Lemma 2, we can get , where Lemma 2 assumes , is a non-negative real number, then , if and only if When the equality sign holds. According to the above assumptions, we know that there exists a positive constant satisfy ,because , so ;because , so Available .in Roll angle The sliding surface of the channel observer, Roll angle Unknown disturbances in the channel, For unknown disturbance The estimated value of , adjustable parameter satisfy: , , , and Then substitute the above formula into the derivative formula of Lyapunov function to obtain ,in, , , , .

[0054] Then according to Lemma 1, the constructed roll angle Channel sliding surface is finite-time stable, The convergence region of for: , the convergence time satisfies ,in is the Lyapunov function The initial state, adjustable parameters satisfy: , , , and , , , .

[0055] S3, based on the UAV rotational dynamics model, a global fast non-singular terminal sliding mode controller is designed and adjusted based on the resultant torque acting on the UAV;

[0056] Specifically, step S3 includes: constructing a global fast non-singular terminal sliding mode surface for the adjusted UAV rotation dynamics model, and the mathematical expression is: , where the adjustable parameters Satisfy respectively , , 、 、 、 are all positive odd numbers, and , , tracking error , system state variables , 、 、 They are the angle components of the UAV's rotation around the three axes, and the control objectives expected by the system are , 、 、 are all desired attitude angles;

[0057] 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: , ,in, is the sliding surface, is the tracking error, , adjustable parameters Satisfy respectively , , 、 、 、 are all positive odd numbers, and , , gain parameter 、 All are positive real numbers, adjustable parameters satisfy , , , 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, is the drag term and internal coupling term that can be modeled for the quadrotor, and the system state variable , 、 、 They are the angle components of the UAV's rotation around the three axes, and the control objectives expected by the system are , 、 、 are the desired attitude angles, and the system state variables , 、 、 are all angular velocity components;

[0058] make , , and the modeled resistance term and internal coupling term Substituting into the global fast non-singular terminal sliding mode controller, we get the new mathematical expression of the global fast non-singular terminal sliding mode controller: ,in, , They are the tracking errors of the three attitude angles, and the adjustable parameters are Satisfy respectively , , 、 、 、 are all positive odd numbers, and , , gain parameter 、 All are positive real numbers, adjustable parameters satisfy , , 、 、 are all angular velocity components, is the inertia constant of the rotor, are the air resistance coefficients of each channel, is the total rotational speed of the four rotors, 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, 、 、 Both are expected attitude angles 、 、 For unknown disturbance The estimated value of is obtained by the extended state observer.

[0059] In this example, a global fast non-singular terminal sliding surface is constructed for the adjusted UAV rotational dynamics model. The choice of parameters in this formula is crucial to the performance of the sliding surface, as they determine its convergence speed and stability. By carefully designing these parameters, it is possible to ensure that the sliding surface converges quickly to the desired attitude angle within a finite time, thereby achieving rapid attitude adjustment. The formula is: .in, is the sliding surface, is the tracking error, , adjustable parameters Satisfy respectively , , 、 、 、 are all positive odd numbers, and , .

[0060] 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 capability of the controller, but also effectively avoids the singularity problem existing in the traditional sliding mode controller. By introducing non-singular terms, it can ensure that the controller can work normally under all working conditions, thereby improving the reliability and stability of the system. In order to further improve the performance of the controller, the modeled resistance term and internal coupling term are combined Substituting into the global fast non-singular terminal sliding mode controller, a new mathematical expression of the global fast non-singular terminal sliding mode controller is obtained. Among them, in the traditional global fast terminal sliding mode, there is ( , 、 are all positive odd numbers), ,when , When , the controller has a singular problem, and the controller formula The exponential term is ( , 、 are all positive odd numbers), The exponential term becomes ( , 、 are all positive odd numbers), so there is no singularity problem in the controller.

[0061] Specifically, in this embodiment, the stability of the controller is further analyzed. First, it is proved that the tracking error reaches the sliding surface in a finite time. The stability is demonstrated by taking the channel as an example. Substituting the controller formula into the formula In, and Channel tracking error , are the rotation angle and expected value of the quadrotor roll angle respectively, so , .in for The sliding surface of the channel controller, Roll angle channel Unknown disturbance The estimated disturbance of Satisfy respectively , , 、 、 、 are all positive odd numbers, and , , gain parameter 、 are all positive real numbers, , , adjustable parameters satisfy , .

[0062] The formula and , Substitution In, get ,in for Sliding surface of the channel observer.

[0063] Constructing Lyapunov , and take its derivative, and at the same time , Combined substitution, .

[0064] Furthermore, according to Lemma 2, we can get ,because , so , and because , so ,therefore ;make , and combine the above formulas to get: ,because , 、 are all positive odd numbers and satisfy , so In this formula, , , , , In summary, the derived Lyapunov function can always satisfy Lemma 1, the sliding surface is practically finite-time stable, with a convergence time satisfy ,in Represents the system Lyapunov function The initial state.

[0065] Secondly, the convergence of the tracking error to the sliding surface is proved to be finite time. Assuming that the system When the system reaches the sliding surface , according to the formula of the global fast non-singular terminal sliding surface, the roll angle The tracking error of the channel becomes: Multiply both ends of the have to: ; Then integrate on both sides to get ,in, ,because , , 、 、 、 are all positive odd numbers, so .

[0066] According to the above formula, , and because 、 are all positive odd numbers and ,so , so the function of t It decreases monotonically with the increase of t, that is, It decreases monotonically with the increase of t. Time satisfy , that is, the roll angle The tracking error of the channel can converge to 0 in a finite time.

[0067] S4, uses the finite-time sliding mode disturbance observer and the extended state observer to estimate the total disturbance of the quadrotor UAV, obtains the total disturbance estimate, and uses the global fast non-singular terminal sliding mode controller to supplement the total disturbance estimate to obtain the UAV tracking control result.

[0068] Preferably, the total disturbance estimation value includes coupling between attitude channels and external unknown interference.

[0069] Specifically, in this embodiment, the total disturbance of the quadrotor UAV is first estimated using a finite-time sliding mode disturbance observer and an extended state observer. These two observers, designed based on the UAV's dynamic model and actual flight data, can monitor and estimate the coupling effects between attitude channels and external unknown disturbances in real time. These disturbances are key factors affecting the accuracy of the UAV's attitude control. 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 UAV's attitude changes in real time. This combined approach enables us to obtain highly accurate disturbance estimates within a finite timeframe. These estimates not only account for the coupling effects between attitude channels, but also for unknown disturbances in the external environment, such as airflow variations and sudden changes in wind speed. This comprehensive estimation enables a more accurate understanding of the complex conditions faced by the UAV during actual flight.

[0070] The resulting total disturbance estimate is then fed into a global fast nonsingular terminal sliding mode controller. This controller is designed to effectively compensate for the estimated disturbance, enabling rapid adjustment and precise control of the drone's attitude. By incorporating the disturbance estimate into the control law, we can adjust the control input in real time to offset the effect of the disturbance on the drone's attitude. This real-time compensation mechanism not only improves the accuracy of the drone's attitude control but also significantly reduces the time required for attitude adjustment, enabling the drone to quickly respond to control commands and complete complex flight missions.

[0071] Furthermore, the design of the global fast non-singular terminal sliding mode controller exhibits excellent robustness. It maintains stable operation in the face of complex and changing external disturbances, ensuring the stability of the drone's attitude. This robustness is crucial for reliable drone flight in complex environments, enabling the drone to maintain excellent performance under diverse flight conditions.

[0072] In this example, to verify the effectiveness of this method (FTSESO-CFNTSMC) for quadrotor attitude control, we compared it with a global fast terminal sliding mode controller (GFTSMC). In the simulation, the quadrotor parameters are shown in Table 1, the finite-time extended state observer parameters are shown in Table 2, and the fast nonsingular terminal sliding mode controller parameters are shown in Table 3.

[0073] Table 1 Quadrotor UAV parameters

[0074]

[0075] Table 2 Extended state observer parameters

[0076]

[0077] Table 3 Controller parameters

[0078]

[0079] The sliding surface design of GFTSMC for comparison is: ,in is the tracking error of the state quantity, and the adjustable parameter ,satisfy , ,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, is the synovial surface of the system, and the gain adjustment parameter , , 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, For quadrotor ;

[0080] The expected posture is In order to prove the effectiveness of the finite time extended state observer for unknown disturbances, The unknown disturbance of the channel is assumed to be segmented, as shown in Table 4.

[0081] Table 4 Unknown disturbance

[0082]

[0083] According to the figure, Figure 3 、 Figure 4The tracking curves and tracking error curves of the two control methods for different tracking targets and different initial values ​​in three attitude channels are shown. No unknown disturbance is added in the first 0-5 seconds, a constant disturbance is added in 5-10 seconds, and a sinusoidal disturbance is added in 10-15 seconds. When no disturbance is added in the 0-5 seconds, the two control methods track sinusoidal signals and step signals of different periods in the three attitude channels with different initial values. Both can track the set target well and converge within 0.5 seconds. However, the tracking curves and error curves of the roll angle and yaw angle show that the control method of this paper has a shorter convergence time than the GFTSMC control method. When a constant disturbance is added in the 5-10 seconds, both methods have a certain degree of robustness to the constant disturbance. However, the tracking curve and error curve of the yaw angle show that as the disturbance amplitude increases, the GFTSMC control method will have a certain tracking error, while the control method of this paper can still maintain good tracking. Therefore, the control method used in this paper has higher robustness than the GFTSMC control method. When a sinusoidal disturbance is added for 10 to 15 seconds, it can be seen from the tracking curves of the pitch angle and yaw angle that the GFTSMC control method has a relatively obvious tracking error, while the control method of this paper can still track the preset curve well. Figure 3 and Figure 4 It can be proved that this method can better control the attitude of the UAV, and has higher convergence speed and robustness compared with the GFTSMC control method.

[0084] Figure 7 This is the attitude angle change curve for the drone controlled by this method. Due to the large error between the initial values ​​of the roll and pitch angle channels and the preset values, the angular velocity curve has a large initial value within 0.2s. This shows that the control system can quickly compensate for the initial value error at startup, allowing the system to reach the preset value in a relatively short time. The angular velocity curve shows that after adding constant values ​​and sinusoidal disturbances of different amplitudes, the angular velocity curve still maintains its original change trend. For example, after the pitch angular velocity stabilizes, the angular velocity remains at zero due to the fixed value of the preset tracking curve. This proves that the control method proposed in this paper has a high interference resistance to complex and changing disturbances.

[0085] Figure 8 is the curve output by the controller using this method, Figure 5 Comparison of the output curves of the two controllers, from Figure 4 It can be seen that when the control method of this paper is started, if there is a large error between the initial value and the preset value, the controller will have a large output, and then the control output tends to a certain regular and stable output. The output curve after stabilization is mainly determined by the control target and disturbance compensation. Figure 8It can be observed that the output curve of the controller of the control method in this paper has the same change trend as the output curve of the GFTSMC control method, and the output amplitude amplitude is of the same order of magnitude, but there is chattering in the output of the GFTSMC control method. The control method used in this paper can not only quickly compensate for the error but also greatly eliminate the chattering.

[0086] Figure 6 The finite time expansion observer estimates the disturbance. It can be seen that the observer can accurately estimate disturbances with complex changes and different amplitudes, and apply the disturbance estimate to the controller to compensate for the disturbance, thereby improving the robustness and reliability of the system.

[0087] In summary, the nonsingular terminal sliding mode attitude control method for quadrotors aims to significantly improve the flight stability, responsiveness, and interference resistance of quadrotor drones in complex environments. This method uses an innovative control strategy, combined with a finite-time sliding mode disturbance observer and an extended state observer, to accurately estimate the total disturbances of the quadrotor drone. It then effectively compensates for these disturbances using a global fast nonsingular terminal sliding mode controller, thereby achieving rapid and precise control of the drone's attitude.

[0088] Specifically, a ground coordinate system and an aircraft coordinate system are established based on the quadrotor UAV's attitude data. The UAV's rotational dynamics model is derived based on the Newton-Euler dynamics equations. This model provides a theoretical foundation for the subsequent control strategy design. Subsequently, a finite-time sliding mode disturbance observer and an extended state observer are designed to estimate the coupling effects between the UAV's attitude channels and external unknown disturbances in real time. These observers are able to respond quickly and provide highly accurate disturbance estimates within a finite time, providing accurate data support for the implementation of the control strategy. Furthermore, a global fast non-singular terminal sliding mode controller is designed based on the UAV's rotational dynamics model. By incorporating disturbance estimates, this controller adjusts the control input in real time to offset the impact of disturbances on the UAV's attitude. This real-time compensation mechanism not only improves the accuracy of the UAV's attitude control but also significantly reduces the attitude adjustment time, enabling the UAV to quickly respond to control commands and complete complex flight missions. Furthermore, the controller design exhibits excellent robustness, maintaining stable operation in the face of complex and changing external disturbances, ensuring the stability of the UAV's attitude.

[0089] By combining a finite-time sliding mode disturbance observer, an extended state observer, and a global fast non-singular terminal sliding mode controller, the present invention not only improves the response speed and accuracy of the attitude control of the quadrotor drone, but also significantly enhances the system's anti-interference capability. This innovative control strategy provides strong technical support for the reliable flight of quadrotor drones in a variety of application scenarios, significantly improving their performance in practical applications. Whether in smooth flight or during complex maneuvers, the drone 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.

[0090] See also Figure 9 The second embodiment of the present invention provides a quadrotor non-singular terminal sliding mode attitude control device, which includes:

[0091] The model building unit 101 is used to establish a ground coordinate system and a body coordinate system according to the attitude data of the quadrotor drone to be controlled, and obtain a rotational dynamics model of the drone based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation;

[0092] The observer unit 102 is used to design a finite-time sliding mode disturbance observer and an extended state observer based on a preset nonlinear system and a UAV rotational dynamics model, wherein the extended state observer is used to track the attitude of the quadrotor UAV;

[0093] The controller unit 103 is configured to design a global fast non-singular terminal sliding mode controller based on the UAV rotational dynamics model and adjust the global fast non-singular terminal sliding mode controller based on the resultant torque acting on the UAV;

[0094] The control unit 104 is used to estimate the total disturbance of the quadrotor UAV using a finite-time sliding mode disturbance observer and an extended state observer to obtain a total disturbance estimate, and to supplement the total disturbance estimate using a global fast non-singular terminal sliding mode controller to obtain a UAV tracking control result.

[0095] The third embodiment of the present invention 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, it implements the quadrotor non-singular terminal sliding mode attitude control method as described in any one of the above items.

[0096] A fourth embodiment of the present invention provides a readable storage medium, which includes: a computer program stored therein, wherein the computer program can be executed by a processor of a device where the storage medium is located to implement a quadrotor non-singular terminal sliding mode attitude control method as described in any one of the above items.

[0097] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A non-singular terminal sliding mode attitude control method for a quadrotor, characterized in that: include: According to the attitude data of the quadrotor drone to be controlled, the ground coordinate system and the body coordinate system are established, and the drone rotation dynamics model is obtained based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation; Based on the preset nonlinear system and the UAV rotational dynamics model, a finite-time sliding mode disturbance observer and an extended state observer are designed. The extended state observer is used to track the attitude of the quadrotor UAV. Based on the UAV rotational dynamics model, a global fast non-singular terminal sliding mode controller is designed and adjusted based on the total torque acting on the UAV. The total disturbance of the quadrotor UAV is estimated using a finite-time sliding mode disturbance observer and an extended state observer to obtain a total disturbance estimate. This is then supplemented by a global fast non-singular terminal sliding mode controller to obtain the UAV tracking control result. Based on the preset nonlinear system and UAV rotation dynamics model, a finite-time sliding mode disturbance observer is designed, specifically: Based on preset nonlinear system ,in, is the state variable of the system, is the state equation of the system, for About Time function, For function The initial state, is the input of the system, for The initial value of , the mathematical expression of the UAV rotation dynamics model is adjusted to , where the system state variables , 、 、 They are the angle components of the UAV's rotation around the three axes, and the system state variables , 、 、 are all angular velocity components, is the unknown disturbance of the three attitude channels, , They are the control inputs of the three attitude channels respectively. , 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, are the drag term and internal coupling term that can be modeled for the quadrotor, is the inertia constant of the rotor, are the air resistance coefficients of each channel, The total speed of the four rotors is used to design a finite-time sliding mode disturbance observer. ,in, , where the estimation error is And the error derivative is , adjustable parameters Requirements: , , , and , is the system state variable The estimated value of for estimated value.

2. The quadrotor non-singular terminal sliding mode attitude control method according to claim 1, characterized in that: According to the attitude data of the quadrotor drone to be controlled, the ground coordinate system and the body coordinate system are established. Based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation, the drone rotation dynamics model is obtained, which is specifically: Obtain the attitude data of the quadcopter to be controlled, and establish the ground coordinate system and the body coordinate system based on the attitude data. The positive direction of the axis is due north, and the body coordinate system The positive direction of the axis is the forward direction of the quadrotor drone; Calculate the resultant torque on the quadrotor drone based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation M , , , , , , ,in, is the angular acceleration of the quadrotor drone, 、 、 are the resultant torque components of the quadrotor drone on the three axes of the body coordinate system, is the driving torque, is the gyroscopic torque, is the resistance torque, 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 total rotational speed of the four rotors; By simplifying the resultant torque acting on the quadrotor drone, the mathematical expression of the drone's rotational dynamics model is obtained: , .

3. The quadrotor non-singular terminal sliding mode attitude control method according to claim 2, characterized in that: The mathematical expression of the extended state observer is: ,in, , , , , , , for The estimated value of is obtained by observing the extended state observer. They are the sliding surfaces of the three channels of the observer, and the adjustable parameters are satisfy , , , and , mathematical constant .

4. The quadrotor non-singular terminal sliding mode attitude control method according to claim 3, characterized in that: According to the UAV rotational dynamics model, a global fast non-singular terminal sliding mode controller is designed. The global fast non-singular terminal sliding mode controller is adjusted based on the total torque acting on the UAV. Specifically, For the adjusted UAV rotation dynamics model, a global fast non-singular terminal sliding mode surface is constructed, and its mathematical expression is: , where the adjustable parameters Satisfy respectively , , 、 、 、 are all positive odd numbers, and , , tracking error , the desired control target 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: , ,in, is the controller sliding surface, is the tracking error, the gain parameter 、 All are positive real numbers , adjustable parameters satisfy , , ; make , , , and the modeled resistance term and internal coupling term Substituting into the global fast non-singular terminal sliding mode controller, we get the new mathematical expression of the global fast non-singular terminal sliding mode controller: .

5. The quadrotor non-singular terminal sliding mode attitude control method according to claim 1, characterized in that: The total disturbance estimation value includes the coupling between the attitude channels and the external unknown disturbance.

6. A quadrotor non-singular terminal sliding mode attitude control device, characterized in that: include: A model building unit is used to establish a ground coordinate system and a body coordinate system according to the attitude data of the quadrotor drone to be controlled, and obtain a rotational dynamics model of the drone based on the ground coordinate system, the body coordinate system and the Newton-Euler dynamics equation; The observer unit is used to design a finite-time sliding mode disturbance observer and an extended state observer based on a preset nonlinear system and the UAV rotational dynamics model. The extended state observer is used to track the attitude of the quadrotor UAV. A controller unit is used to design a global fast non-singular terminal sliding mode controller based on the UAV rotational dynamics model and adjust the global fast non-singular terminal sliding mode controller based on the total torque acting on the UAV; A control unit is used to estimate the total disturbance of the quadrotor UAV using a finite-time sliding mode disturbance observer and an extended state observer to obtain a total disturbance estimate, and to supplement the total disturbance estimate using a global fast non-singular terminal sliding mode controller to obtain a UAV tracking control result; Based on the preset nonlinear system and UAV rotation dynamics model, a finite-time sliding mode disturbance observer is designed, specifically: Based on preset nonlinear system ,in, is the state variable of the system, is the state equation of the system, for About Time function, For function The initial state, is the input of the system, for The initial value of , the mathematical expression of the UAV rotation dynamics model is adjusted to , is the input of the system, for The initial value of the system state variable , 、 、 They are the angle components of the UAV's rotation around the three axes, and the system state variables , 、 、 are all angular velocity components, is the unknown disturbance of the three attitude channels, , They are the control inputs of the three attitude channels respectively. , 、 、 are the components of the UAV’s moment of inertia on the three axes of the body coordinate system, are the drag term and internal coupling term that can be modeled for the quadrotor, is the inertia constant of the rotor, are the air resistance coefficients of each channel, The total speed of the four rotors is used to design a finite-time sliding mode disturbance observer. ,in, , where the estimation error is And the error derivative is , adjustable parameters Requirements: , , , and , is the system state variable The estimated value of for estimated value.

7. A quadrotor non-singular terminal sliding mode attitude control device, characterized in that: The invention comprises a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein when the processor executes the computer program, the quadrotor non-singular terminal sliding mode attitude control method according to any one of claims 1 to 5 is implemented.

8. A readable storage medium, characterized in that: A computer program is stored, and the computer program can be executed by a 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 5.

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