Non-singular sliding mode control method, device and equipment for quadrotor unmanned aerial vehicle and medium

Abstract

The invention provides a non-singular sliding mode control method, device and equipment for a quad-rotor unmanned aerial vehicle, and a medium, and relates to the technical field of unmanned aerial vehicle flight control. According to the method, a quadrotor unmanned aerial vehicle body coordinate system and an inertial coordinate system are established, and an attitude model of the quadrotor unmanned aerial vehicle is established by considering air resistance and external unknown disturbance conditions according to a rigid body motion law; introducing an auxiliary equation to construct a predefined time disturbance observer, and rapidly estimating external disturbance by adjusting predefined time in combination with a Lyapunov function; then designing a non-singular predefined time sliding mode controller; and controlling the quadrotor unmanned aerial vehicle to perform attitude tracking according to the nonsingular predefined time sliding mode controller, and controlling the attitude tracking error of the quadrotor unmanned aerial vehicle to converge within the predefined time by adjusting predefined time parameters. According to the method, the external disturbance can be quickly estimated within the preset time, and the convergence rate of the four-rotor unmanned aerial vehicle is flexibly controlled.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) flight control, and more particularly, to a nonsingular sliding mode control method, device, equipment and medium for a quadrotor UAV. Background Art

[0002] Quadrotor UAVs have been widely used in military and civilian fields due to their advantages such as good stability, simple operation, small size, and light weight. However, as a typical underactuated and strongly coupled system, quadrotor UAVs are highly sensitive to external environmental factors and are particularly vulnerable to unknown disturbances during flight, which increases the difficulty of their control. To address these challenges, researchers have proposed various control methods, such as adaptive control, neural network control, and observer-based anti-disturbance control. Although these methods have improved the anti-disturbance ability of the system to some extent, there are still certain limitations. For example, adaptive control and neural network control require complex parameter adjustment processes, while traditional finite-time or fixed-time disturbance observers can achieve fast convergence of the disturbance estimation error, but their convergence time is often limited by the initial state of the system and cannot be flexibly adjusted. In addition, although sliding mode control, as a commonly used non-linear control method, has strong robustness, it is prone to singularity problems in practical applications, which affects the stability and control accuracy of the system.

[0003] In the prior art, the design of disturbance observers and controllers for quadrotor UAVs mainly focuses on the research of finite-time and fixed-time control algorithms. For example, some finite-time disturbance observers and fixed-time disturbance observers have been proposed in the existing literature to estimate the state and external disturbances of quadrotor UAVs, so as to improve the anti-disturbance ability of the system. However, these methods usually can only ensure the convergence of the disturbance estimation error within a finite time or a fixed time, and the convergence time is closely related to the initial state, making it difficult to meet the application scenarios with strict requirements for the convergence time. At the same time, there is less research on the combination of existing predefined time control algorithms and observers, resulting in difficulties in achieving fast and accurate estimation of disturbances and efficient control of attitude tracking errors in practical applications.

[0004] In view of this, the present application is specifically proposed. Summary of the Invention

[0005] The present invention aims to provide a nonsingular sliding mode control method, device, equipment and medium for a quadrotor UAV to solve the technical problem that it is difficult to achieve fast convergence and high-precision attitude tracking in the existing attitude control methods for quadrotor UAVs in the presence of external unknown disturbances and model uncertainties.

[0006] To solve the above technical problems, the present invention is implemented through the following technical solutions: A nonsingular sliding mode control method for a quadrotor drone, comprising: S1. Establish the body coordinate system and the inertial coordinate system of the quadrotor drone, and assume that the body structure of the quadrotor drone is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coinciding with the geometric center of gravity, and its mass and moment of inertia do not change with time; S2. According to the rigid body motion law, considering the air resistance and external unknown disturbances, establish the attitude model of the quadrotor drone, and use the component torques of the quadrotor drone as the control input; S3. Introduce an auxiliary equation to construct a predefined-time disturbance observer, and combine the Lyapunov function to quickly estimate the external disturbance by adjusting the predefined time; S4. Based on the attitude model and the predefined-time disturbance observer, design a nonsingular predefined-time sliding mode controller; S5. Control the quadrotor drone to perform attitude tracking according to the nonsingular predefined-time sliding mode controller, and control the attitude tracking error of the quadrotor drone to converge within the predefined time by adjusting the predefined-time parameter.

[0007] Preferably, the quadrotor drone adopts an X-shaped layout. Specifically, establishing the attitude model of the quadrotor drone is as follows: Define the body coordinate system b as ; and the inertial coordinate system e as ; According to the rigid body motion law, establish the torque balance equation of the quadrotor drone attitude, and the expression is: ; where, is the moment of inertia of the quadrotor; is the angular momentum, , , , are the angular velocities of the quadrotor rotating around the , , three axes of the quadrotor drone respectively; is the first derivative of; T is the transpose symbol; is the total torque received by the quadrotor, and the three-axis components in the body coordinate system are expressed as: ; where, , , are the component torques received by the quadrotor around the , , three axes respectively; , , are the moments of inertia about the , , three axes respectively; , , are the first derivatives of , , respectively; Assuming that the four rotors of the UAV are symmetric, then the moment of inertia of the asymmetric part is 0, that is ; Assuming that the attitude of the quadrotor UAV changes slightly during flight, the relationship between the angular velocity and the angle is expressed as: ; where is the roll angle, is the pitch angle, is the yaw angle; , , are the corresponding first derivatives respectively; The component torques received by the quadrotor UAV about the , , three axes are used as control inputs respectively, and are expressed as: ; Combined with the air resistance and external unknown disturbances that the propellers will receive during the flight of the quadrotor, the attitude model of the quadrotor UAV is expressed as: ; ; ; where is the inertia constant of the propeller; , , are the component torques received by the quadrotor UAV about the , , three axes respectively; , , are the second derivatives of the roll angle, pitch angle, and yaw angle respectively; , , are the air resistance coefficients respectively, and the air resistance is expressed as: ; , , are three different external unknown disturbances respectively.

[0008] Preferably, the auxiliary equation is used to estimate the disturbance vector, and its expression is: ; where is the second derivative of the auxiliary equation state vector Z, , , are respectively the second derivatives of the auxiliary equation state quantities of the quadrotor UAV in the body coordinate system; is a normal constant vector in the body coordinate system; , is the moment of inertia reciprocal; , is the control input vector in the body coordinate system; is the coupling term and air resistance of the attitude model, expressed as: ; , , respectively represent corresponding to , , axis values in the body coordinate system; , is the attitude state quantity of the quadrotor UAV and the error vector of the auxiliary equation state quantity Z; , is the second derivative of the state vector of the quadrotor UAV; respectively represent corresponding to , , axis values of the three axes in the body coordinate system; respectively represent the components of the second derivatives of the state quantities of the quadrotor UAV corresponding to , , the three axes in the body coordinate system; Then, a predefined time disturbance observer is constructed according to the auxiliary equation, and its expression is: ; ; where is the estimated value of the disturbance vector; is the error state quantity, which is the estimated value of the error vector , is The second derivative of; is the error state variable The first derivative of; is the normal value control parameter of the disturbance observer, ; is the sign function; is the predefined time; , representing the disturbance error.

[0009] Preferably, the external disturbance is quickly estimated by adjusting the predefined time in combination with the Lyapunov function, specifically: Combining the Lyapunov function with the disturbance error Taking the time derivative, the disturbance error can converge within the predefined time The expression is: ; ; Among them, is the Lyapunov function, a scalar function for analyzing the stability of nonlinear systems; when is selected, then the class function is expressed as: ; The scalar function ; is the parameter variable of the scalar function; , when is the case, ; is the normal value parameter of the class function; When is the case, the following formula is obtained: ; ; represents the derivative of with respect to; The estimated error of the disturbance vector is obtained and satisfies the following formula: ; Among them, is the estimated error of the disturbance vector; is the external unknown disturbance vector; is the estimated value of the disturbance vector; is the attitude state variable of the quadrotor UAV in the body coordinate system; is The second derivative of is the error state variable; is the normal value in the body coordinate system; ; is the auxiliary equation state variable in the body coordinate system; Thus, when the disturbance error satisfies the predefined time to converge, the estimation error of the disturbance estimation vector also satisfies convergence within the predefined time, that is, by adjusting the predefined time the disturbance of the quadrotor UAV can be estimated quickly.

[0010] Preferably, the nonsingular predefined-time sliding mode controller realizes parameter adjustment of the convergence time of the quadrotor UAV in the sliding phase through a nonsingular predefined-time sliding mode surface; wherein, the expression of the nonsingular predefined-time sliding mode surface is: ; wherein, is the sliding mode surface, ; is the attitude tracking error, ; is the attitude state variable of the quadrotor UAV in the body coordinate system; is the tracking target of the quadrotor attitude angle, is the tracking target value of the quadrotor UAV attitude angle; is the tracking target value of the roll angle, is the tracking target value of the pitch angle, is the tracking target value of the yaw angle; The Lyapunov function is selected as ; is the nonsingular predefined-time control parameter; is the predefined time of the sliding mode surface; is the sign function; and ; Under the action of the nonsingular predefined-time sliding mode surface, the attitude tracking error converges within time; According to the nonsingular predefined-time sliding mode surface, the attitude model of the quadrotor UAV and the estimated value of the predefined-time disturbance observer, the nonsingular predefined-time sliding mode controller is obtained, and its expression is: ; ; wherein, The component torques of the quadrotor UAV in the body coordinate system, i.e., the control inputs; The coupling terms of the attitude model and the values of the air resistance in the body coordinate system, ; , is the non-singular predefined time control parameter; is the estimated value of the disturbance vector; is the predefined time in the reaching phase; represents the Lyapunov function selection ; Under the action of the non-singular predefined time sliding mode controller, the system state converges to the sliding mode surface within the predefined time , and within the predefined time , the attitude angles of the quadrotor can track the expected values.

[0011] The present invention also provides a non-singular sliding mode control device for a quadrotor UAV, including: A coordinate system establishment unit, configured to establish the body coordinate system and the inertial coordinate system of the quadrotor UAV, and assume that the body structure of the quadrotor UAV is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coinciding with the geometric center of gravity, and its mass and moment of inertia do not change with time; An attitude model establishment unit, configured to establish an attitude model of the quadrotor UAV according to the rigid body motion law, considering the air resistance and external unknown disturbance conditions, and use the component torques of the quadrotor UAV as control inputs; A disturbance observer establishment unit, configured to introduce an auxiliary equation to construct a predefined time disturbance observer, and quickly estimate the external disturbance by adjusting the predefined time in combination with the Lyapunov function; A sliding mode controller establishment unit, configured to design a non-singular predefined time sliding mode controller based on the attitude model and the predefined time disturbance observer; An attitude tracking control unit, configured to control the quadrotor UAV to perform attitude tracking according to the non-singular predefined time sliding mode controller, and control the attitude tracking error of the quadrotor UAV to converge within the predefined time by adjusting the predefined time parameter.

[0012] The present invention also provides a non-singular sliding mode control device for a quadrotor UAV, including a processor and a memory, where the memory stores a computer program that can be executed by the processor to implement a non-singular sliding mode control method for a quadrotor UAV as described above.

[0013] The present invention also provides a computer-readable storage medium, on which computer-readable instructions are stored. When the computer-readable instructions are executed by a processor of a device where the computer-readable storage medium is located, a non-singular sliding mode control method for a quadrotor UAV as described above is implemented.

[0014] In summary, compared with the prior art, the present invention has the following beneficial effects: By designing a new predefined-time disturbance observer, the present invention can quickly estimate external disturbances within a preset time and flexibly control the convergence rate of the quadrotor UAV by adjusting the predefined-time parameters, thereby effectively reducing the influence of disturbances on the attitude tracking of the quadrotor UAV. At the same time, in order to avoid the singularity problem in traditional sliding mode control, the present invention also designs a non-singular predefined-time sliding mode surface, enabling the attitude tracking error to converge within a predefined time and further improving the control performance of the system, specifically as follows: First, by adjusting the predefined-time parameters, the present invention can flexibly adjust the disturbance estimation and the convergence rate of attitude tracking, thereby meeting the requirements of different application scenarios.

[0015] Second, by designing the sliding mode surface, the present invention avoids the possible singularity problem in traditional sliding mode control and improves the control accuracy.

[0016] Third, by jointly designing the disturbance observer and the controller, the present invention significantly improves the robustness of the system, enabling it to have strong adaptability to external unknown disturbances and initial state changes.

[0017] Therefore, the present invention not only solves the problem that the convergence time of disturbance estimation and attitude tracking control in the prior art cannot be adjusted, but also overcomes the singularity defect in traditional sliding mode control, providing an innovative solution for the high-precision attitude control of quadrotor UAVs. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the embodiments. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other related drawings can be obtained based on these drawings without creative efforts.

[0019] Figure 1 A schematic diagram of a non-singular sliding mode control method for a quadrotor UAV provided for Embodiment 1.

[0020] Figure 2 A schematic diagram of a quadrotor UAV in an inertial coordinate system and a body coordinate system provided for Embodiment 1.

[0021] Figures 3(a), 3(b), and 3(c) are respectively the comparison diagrams of the attitude angle (roll angle / pitch angle / yaw angle) tracking curves of the method of the present invention (NPTSM) provided in the first embodiment, the existing predefined time sliding mode control method (PTSM), the existing fixed time sliding mode control method (FTSM), and the desired trajectory under the condition of changing the initial state.

[0022] Figures 4(a), 4(b), and 4(c) are respectively the comparison diagrams of the attitude angle (roll angle / pitch angle / yaw angle) tracking error curves of the method of the present invention (NPTSM) provided in the first embodiment, the existing predefined time sliding mode control method (PTSM), the existing fixed time sliding mode control method (FTSM), and the desired trajectory under the condition of changing the initial state.

[0023] Figures 5(a), 5(b), and 5(c) are respectively the comparison diagrams of the output curves of the controller (u1 / u2 / u3) of the method of the present invention (NPTSM) provided in the first embodiment, the existing predefined time sliding mode control method (PTSM), the existing fixed time sliding mode control method (FTSM), and the desired trajectory under the condition of changing the initial state.

[0024] Figure 6 It is a schematic diagram of a nonsingular sliding mode control device for a quadrotor UAV provided in the second embodiment.

[0025] The following further details the present invention in conjunction with the accompanying drawings and specific embodiments. Specific Embodiments

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of the present invention.

[0027] First Embodiment Embodiment 1 of the present invention provides a non-singular sliding mode control method for a quadrotor UAV, which can be implemented by a non-singular sliding mode control device for a quadrotor UAV (hereinafter referred to as the control device), and particularly, is executed by one or more processors in the control device.

[0028] In this embodiment, the control device may be an electronic device equipped with a processor, and the processor has a computer program of the non-singular sliding mode control method for the quadrotor UAV and the computer program can be executed, such as a computer, a smart phone, a smart tablet, a workstation, etc., which is not limited herein.

[0029] As Figure 1 shown, a non-singular sliding mode control method for a quadrotor UAV includes steps S1 to S5.

[0030] S1. Establish a body coordinate system and an inertial coordinate system for the quadrotor UAV, and assume that the body structure of the quadrotor UAV is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coinciding with the geometric center of gravity, and its mass and moment of inertia do not change with time.

[0031] As Figure 2 shown in the schematic diagram of the quadrotor UAV in the inertial coordinate system and the body coordinate system, the quadrotor UAV in this embodiment adopts an "X" layout, and the propellers f1 and f3 of the quadrotor UAV rotate clockwise, and the propellers f2 and f4 rotate counterclockwise.

[0032] To accurately describe the structure and motion principle of the UAV, define the body coordinate system b as , and the inertial coordinate system e as .

[0033] For better analysis, make the following assumptions before modeling the quadrotor UAV: Assumption 1: The body structure of the quadrotor UAV is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coinciding with the geometric center of gravity.

[0034] Assumption 2: The mass and moment of inertia of the quadrotor UAV do not change with time.

[0035] S2. According to the rigid body motion law, considering the air resistance and external unknown disturbance conditions, establish an attitude model of the quadrotor UAV, and use the component torque of the quadrotor UAV as the control input.

[0036] According to the rigid body motion law, establish the torque balance equation of the quadrotor UAV attitude, and the expression is: , formula (1) Among them, is the moment of inertia of the quadrotor; is the angular momentum, , 、 、 are the angular velocities of the four-rotor UAV rotating around the three axes respectively 、 、 ; is 's first derivative; T is the transpose symbol; is the total resultant moment acting on the four-rotor UAV, and its three-axis components in the body coordinate system are expressed as: , formula (2) where 、 、 are the component moments acting on the four-rotor UAV rotating around 、 、 the three axes respectively; 、 、 are the moments of inertia rotating around 、 、 the three axes respectively; 、 、 are 、 、 's first derivatives respectively; Assume that the four rotors of the UAV are symmetric, then the moment of inertia of the asymmetric part is 0, that is ; Assume that the attitude of the four-rotor UAV changes slightly during flight, then the relationship between the angular velocity and the angle is expressed as: ; where is the roll angle, is the pitch angle, is the yaw angle; 、 、 are the corresponding first derivatives respectively; The component moments acting on the four-rotor UAV rotating around 、 、 the three axes are used as control inputs respectively, and are expressed as: , formula (3) Combined with the air resistance and external unknown disturbances that the propellers will encounter during the flight of the four-rotor UAV, the attitude model of the four-rotor UAV is expressed as: , formula (4) wherein is the inertia constant of the propeller; , , are the component torques received by the quadrotor UAV around , , three axes; , , are the second-order derivatives of the roll angle, pitch angle, and yaw angle, respectively; , , are the air resistance coefficients, and the air resistance is expressed as: ; , , are three different external unknown disturbances, respectively.

[0037] S3. Introduce an auxiliary equation to construct a predefined-time disturbance observer, and combine the Lyapunov function to quickly estimate the external disturbance by adjusting the predefined time.

[0038] In this embodiment, the control objective of the present invention is to achieve accurate estimation of the external disturbance and attitude tracking control of the quadrotor UAV within a predefined time. The external disturbance is quickly and accurately estimated and compensated into the control law. Therefore, the present invention designs a disturbance observer and a controller based on the predefined-time stability theory. The following basic knowledge is required when designing the disturbance observer and the controller: Function definition: The scalar continuous function , if is strictly monotonically increasing, and ; when , , then belongs to The function is expressed as , is the parameter variable of the scalar function. The following examples illustrate several functions that satisfy functions.

[0039] , formula (5) , formula (6) , formula (7) Let be a differentiable function, and there exists is a continuously positive definite and radially unbounded function. If for any , such that the time derivative of the function satisfies the following equation: , Equation (8) where, is the control parameter, , , and is the state quantity of the nonlinear system , and the origin is the only equilibrium point of the system, then the trajectory of the nonlinear system corresponding to the function can achieve predefined-time stability, and the upper bound of the convergence time is , which is proved as follows: According to the above Equation (8), we can get: , Equation (9) From Equation (9), we know that decreases with time and finally . Integrating both sides of the equation with respect to time, we can get: , Equation (10) In Equation (10), is the initial value of . According to the definition of the class function, we know that , and from the range of the control parameter , we know that . Therefore, it can be rewritten as: ; Therefore, the time for to converge to zero is less than . From the definition of the class function, we know that when converges to zero, . It can be seen that is a continuously positive definite and radially unbounded function. When , we can get , then the system state quantity can be stable within the predefined time .

[0040] For the convenience of subsequent observer and controller design, the attitude model of the quadrotor UAV is simplified as: , Equation (11) In the formula, is the second-order derivative of the state vector of the quadrotor UAV; respectively represent the components of the second-order derivative of the state vector corresponding to the three axes of the quadrotor UAV in the body coordinate system; , , the second-order derivative of the state vector corresponding to the three axes of the quadrotor UAV in the body coordinate system; , is the moment of inertia reciprocal; is the disturbance vector; , is the control input vector in the body coordinate system; is the coupling term and air resistance of the attitude model, expressed as: ; , , respectively represent the values corresponding to , , the axes in the body coordinate system.

[0041] In this embodiment, an auxiliary equation is introduced to estimate the disturbance vector, and its expression is: , formula (12) where is the second-order derivative of the state vector Z of the auxiliary equation, , , respectively represent the second-order derivatives of the state variables of the auxiliary equation of the quadrotor UAV in the body coordinate system; is the normal constant vector in the body coordinate system; , is the attitude state variable of the quadrotor UAV and the error vector of the state variable Z of the auxiliary equation; respectively represent the values corresponding to , , the three axes in the body coordinate system.

[0042] Then, a predefined-time disturbance observer is constructed according to the auxiliary equation, and its expression is: , formula (13) , formula (14) where is the estimated value of the disturbance vector; is the error state variable, which is the estimated value of the error vector , is the second-order derivative; is the error state variable and the first derivative thereof; is the normal value control parameter of the disturbance observer, ; is the sign function; is the predefined time of the disturbance observer; , representing the disturbance error.

[0043] According to the expression of the disturbance observer at the predefined time, it is proved that the disturbance error can converge within the predefined time. Subtracting from both sides of Equation (14), the following equation can be obtained: , Equation (15) To analyze the convergence of , combined with the Lyapunov function, it is proved that the error of the disturbance observer can converge within the predefined time. The Lyapunov function is selected as follows: , Equation (16) Taking the time derivative of the Lyapunov function, we get: , Equation (17) According to the definition of the type function, when , and the type function is selected as: ; wherein, is the normal value parameter of the type function. When , it can be known that , then the formula for taking the time derivative of the Lyapunov function can be rewritten as: , Equation (18) From the above Equation (18), it can be seen that the error converges within the predefined time .

[0044] Through Equations (12), (13), and (14), the estimation error of the disturbance vector is obtained, and it satisfies the following equation: , Equation (19) wherein, is the estimation error of the disturbance vector; is the external unknown disturbance vector; is the estimated value of the disturbance vector; is the attitude state variable of the quadrotor UAV in the body coordinate system; is the second derivative of; is the error state variable; is the normal value in the body coordinate system; ; is the auxiliary equation state variable in the body coordinate system; is the second derivative of.

[0045] According to the above, when the perturbation error satisfies the predefined time to converge, the estimation error of the perturbation estimation vector also satisfies convergence within the predefined time, that is, by adjusting the predefined time the perturbation of the quadrotor UAV can be quickly estimated.

[0046] S4. Based on the attitude model and the predefined time perturbation observer, design a nonsingular predefined time sliding mode controller.

[0047] In this embodiment, in order to avoid the singular problem in the traditional predefined time sliding mode control, a nonsingular predefined time sliding mode controller is designed. The nonsingular predefined time sliding mode controller realizes parameter adjustment of the convergence time of the quadrotor UAV in the sliding stage through a nonsingular predefined time sliding mode surface; wherein, the expression of the nonsingular predefined time sliding mode surface is: , formula (20) wherein, is the sliding mode surface, ; is the attitude tracking error, ; is the attitude state variable of the quadrotor UAV in the body coordinate system; is the tracking target of the quadrotor attitude angle, is the tracking target value of the quadrotor UAV attitude angle; is the tracking target value of the roll angle, is the tracking target value of the pitch angle, is the tracking target value of the yaw angle; The Lyapunov function is selected as ; is the nonsingular predefined time control parameter; is the predefined time of the sliding mode surface; is the sign function; .

[0048] The designed sliding mode surface adjusts the parameter The constraints avoid the occurrence of singular phenomena and improve the performance of the subsequent designed controller.

[0049] Under the action of the non-singular predefined-time sliding mode surface, the attitude tracking error At time, it converges.

[0050] When , the formula (20) of the sliding mode surface can be evolved into: , formula (21) From 's operation relationship, the following formula can be obtained: , formula (22) Furthermore, from 's operation relationship, the following formula can be obtained: , formula (23) When choosing as the Lyapunov function and taking its derivative with respect to time, it is expressed as: ; When the class function is selected as , it can be known that , then: , formula (24) Therefore, according to this formula, it can be known that the design of the sliding mode surface makes the convergence time of the sliding stage satisfy within the preset time parameter .

[0051] Then, according to the non-singular predefined-time sliding mode surface, the attitude model of the quadrotor UAV and the estimated value of the predefined-time disturbance observer, design a non-singular predefined-time sliding mode controller (i.e., the control law), and its expression is: , formula (25) , formula (26) Among them, the component torque of the quadrotor UAV in the body coordinate system, that is, the control input; the coupling term of the attitude model and the value of air resistance in the body coordinate system, ; , is the non-singular predefined-time control parameter; is the estimated value of the disturbance vector; is the preset time of the approaching stage; represents the Lyapunov function selection ; Under the action of the nonsingular predefined-time sliding mode controller, the system state converges to the sliding mode surface within the predefined time and, within the predefined time , the attitude angles of the quadrotor can track the desired values.

[0052] When the parameter , the negative exponential term in is avoided, so that the designed controller avoids the singularity problem during the attitude control process.

[0053] Meanwhile, under the action of the nonsingular predefined-time sliding mode controller, the system state can reach the sliding mode surface within the predefined time .

[0054] Taking the time derivative of the sliding mode surface formula (20) gives: , formula (27) Combining with the nonsingular predefined-time sliding mode controller formula (25), we get: , formula (28) When choosing as the Lyapunov function and taking its time derivative, we can obtain: , formula (29) From the observer, when the time , . According to the formula, we know that . Scaling the above formula gives: , formula (30) When the type function is selected as , we can know that Then formula (30) can be rewritten as: , formula (31) Therefore, under the action of the control law, the system state converges to the sliding mode surface within the predefined time , and within the predefined time , the attitude angles of the quadrotor can track the desired values.

[0055] S5, controlling the quadrotor UAV for attitude tracking according to the nonsingular predefined-time sliding mode controller, and controlling the attitude tracking error of the quadrotor UAV to converge within the predefined time by adjusting the predefined-time parameter.

[0056] ​When performing attitude tracking, the attitude angles of the quadrotor UAV are made to track the desired trajectory, and then the attitude angle tracking trajectory curve and the attitude angle tracking error curve are analyzed to control the convergence of the attitude tracking error within a predefined time by adjusting the predefined time parameter to meet the different mission requirements of the UAV.

[0057] In another preferred embodiment, to verify the effectiveness of the control method proposed in this paper, the control method of the present invention is simulated using the matlab / simulink simulation platform. In the simulation experiment, the parameters of the quadrotor UAV control system are set as follows: The moment of inertia is set to , , the air resistance coefficient is expressed as , , the inertia constant of the rotor is set to . The parameters of the predefined time disturbance observer are set to , , . The parameters of the nonsingular predefined time sliding mode controller are set to . The external disturbance acting on the quadrotor UAV is set to , and the attitude angle tracking trajectory target is set to .

[0058] To verify the tracking performance of the controller and observer designed in the present invention, under the condition of changing the initial state, the tracking performance of the control system under different control schemes is discussed. In the simulation experiment, the control algorithm of the present invention (NPTSM) is compared with the predefined time sliding mode control method (PTSM) in the prior art and the fixed time sliding mode control method (FTSM) in the prior art. In the simulation experiment, the initial state of the quadrotor attitude is changed to , where the predefined time parameters of the present invention NPTSM and the prior art PTSM are both set to ( is the predefined time to converge to the sliding mode surface, is the predefined time to converge to the desired value), and the simulation results are shown in Figures 3(a), 3(b), 3(c), 4(a), 4(b), 4(c), 5(a), 5(b), and 5(c). In the simulation result figures, PT is used to represent the predefined convergence time of the observer or controller of the present invention, and Desired trajectory is the desired trajectory.

[0059] In this embodiment, the predefined-time sliding mode control method (PTSM): is an advanced variant of sliding mode control, aiming to solve the singularity problem existing in traditional sliding mode control and achieve the goal of completing the convergence of the control system within a predefined time. It adjusts the dynamic behavior of the system by introducing a specific time function, and realizes more flexible and smooth control performance while maintaining strong robustness. For example, in the attitude tracking control of a spacecraft, PTSM can preset the completion time of attitude adjustment according to mission requirements.

[0060] The fixed-time sliding mode control method FTSM: can ensure the convergence of the system within a finite time, but the upper bound of the convergence time is independent of the initial state of the system and only depends on the control parameters. This characteristic enables FTSM to ensure convergence even when the initial state cannot be accurately obtained, but it cannot directly preset a specific convergence time. It is applicable to scenarios where the initial state is unknown or difficult to accurately measure. For example, in the trajectory tracking of an omnidirectional mobile robot, it can achieve fast fixed-time convergence characteristics, improving the trajectory tracking accuracy and system robustness.

[0061] Figures 3(a), 3(b), 3(c), 4(a), 4(b) and 4(c) respectively show the simulation results of the tracking curves of the attitude angles (roll angle, pitch angle, yaw angle) of the quadrotor and the attitude angle tracking error curves under the action of different control schemes. Among them, Figures 3(a) and 4(a) are for the roll angle, Figures 3(b) and 4(b) are for the pitch angle, and Figures 3(c) and 4(c) are for the yaw angle. It can be seen that after changing the initial state, the attitude angle tracking curves and error curves of the quadrotor under the NPTSM algorithm of the present invention have completed convergence within 0.5 s, and the results prove that: Under the condition of changing the initial state of the system, the convergence time of the algorithm of the present invention still satisfies within the preset time. At the same time, it can be seen from Figures 3(a), 3(b), 3(c), 4(a), 4(b) and 4(c) that the convergence time of the attitude angles of the quadrotor under the PTSM algorithm is about 0.6 s, and the convergence time under the FTSM algorithm is as long as about 2.5 s. It can be seen from the simulation results that the control algorithm designed in this paper has a faster convergence rate compared with the PTSM algorithm and the FTSM algorithm, thus proving the superiority of this algorithm. It can be seen from Figures 5(a), 5(b) and 5(c) that there is a long-term chattering phenomenon in the control outputs of the PTSM algorithm and the FTSM algorithm.

[0062] In summary of the above simulation experiment results, the predefined-time disturbance observer and the nonsingular predefined-time sliding mode controller designed in the present invention can both complete the tracking of the expected value within the preset time, and the convergence rate of the quadrotor UAV can be improved by adjusting the preset time parameters of this control scheme.

[0063] In summary, compared with the prior art, the present invention has the following beneficial effects: Combined with the Lyapunov stability theory, the designed controller and observer of the present invention achieve convergence within a predefined time. By adjusting the time parameters of the controller and observer, the convergence rate of the system can be effectively improved. Through simulation experiments, it is verified that even if the initial state of the system changes, the convergence time can still be maintained within the predetermined upper limit, proving the insensitivity of the system of the present invention to changes in the initial state and avoiding the problem that the convergence time in traditional sliding mode control depends on the initial state. The observer combines with the Lyapunov function through an auxiliary equation and can accurately estimate external disturbances within a predefined time, improving the control robustness. The designed sliding mode surface controller eliminates control singularity and avoids the singularity problem caused by negative exponential terms in traditional sliding mode control. Compared with the existing traditional fixed-time control methods, the method of the present invention has an advantage in the convergence rate.

[0064] Embodiment 2 As Figure 6 shown, the second embodiment of the present invention further provides a non-singular sliding mode control device for a quadrotor UAV, including: A coordinate system establishment unit, configured to establish a body coordinate system and an inertial coordinate system of the quadrotor UAV, and assume that the body structure of the quadrotor UAV is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coinciding with the geometric center of gravity, and its mass and moment of inertia do not change with time; An attitude model establishment unit, configured to establish an attitude model of the quadrotor UAV according to the rigid body motion law, considering air resistance and external unknown disturbance conditions, and use the component torque of the quadrotor UAV as the control input; A disturbance observer establishment unit, configured to introduce an auxiliary equation to construct a predefined time disturbance observer, and quickly estimate external disturbances by adjusting the predefined time in combination with the Lyapunov function; A sliding mode controller establishment unit, configured to design a non-singular predefined time sliding mode controller based on the attitude model and the predefined time disturbance observer; An attitude tracking control unit, configured to control the quadrotor UAV to perform attitude tracking according to the non-singular predefined time sliding mode controller, and control the attitude tracking error of the quadrotor UAV to converge within a predefined time by adjusting the predefined time parameter.

[0065] Embodiment 3 The third embodiment of the present invention further provides a non-singular sliding mode control device for a quadrotor UAV, which includes a memory and a processor. The memory stores a computer program, and the computer program can be executed by the processor to implement the non-singular sliding mode control method for the quadrotor UAV as described above.

[0066] Embodiment 4 The fourth embodiment of the present invention also provides a computer-readable storage medium, on which computer-readable instructions are stored. When the computer-readable instructions are executed by a processor of the device where the computer-readable storage medium is located, the non-singular sliding mode control method of the quadrotor UAV as described above is implemented.

[0067] In several embodiments provided by the embodiments of the present invention, it should be understood that the disclosed devices and methods can also be implemented in other ways. The device and method embodiments described above are merely illustrative. For example, the flowcharts in the accompanying drawings show the possible architectures, functions, and operations of devices, methods, and computer program products according to multiple embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, a program segment, or a part of code, and the module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than marked in the accompanying drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in the reverse order, depending on the functions involved. It should also be noted that each block in the block diagram and / or flowchart, as well as the combination of blocks in the block diagram and / or flowchart, can be implemented by a dedicated hardware-based system for performing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0068] In addition, each functional module in various embodiments of the present invention may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.

[0069] When the above-mentioned functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, an electronic device, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs. It should be noted that in this article, the terms "include", "comprise", or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such a process, method, article, or device. Without further limitation, an element defined by the statement "including a..." does not exclude the existence of another identical element in the process, method, article, or device including the said element.

[0070] The terms used in the embodiments of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The singular forms "a", "the", and "said" used in the embodiments of the present invention and the appended claims are also intended to include the plural forms unless the context clearly dictates otherwise.

[0071] It should be understood that the term "and / or" used herein is only a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in this article generally represents an "or" relationship between the associated objects before and after.

[0072] Depending on the context, the word "if" as used herein can be interpreted as "when", "while", "in response to determining", or "in response to detecting". Similarly, depending on the context, the phrase "if determined" or "if detecting (stated condition or event)" can be interpreted as "when determined", "in response to determining", "when detecting (stated condition or event)", or "in response to detecting (stated condition or event)".

[0073] The "first / second" mentioned in the embodiments is only used to distinguish similar objects and does not represent a specific order for the objects. It can be understood that the "first / second" can be interchanged in a specific order or sequence when permitted. It should be understood that the objects distinguished by the "first / second" can be interchanged under appropriate circumstances so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0074] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A nonsingular sliding mode control method for a quadrotor UAV, characterized in that including: Establish the body coordinate system and inertial coordinate system of the quadrotor UAV, and assume that the body structure of the quadrotor UAV is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coincides with the geometric center of gravity, and its mass and moment of inertia do not change with time; According to the rigid body motion law, considering the air resistance and external unknown disturbance conditions, establish the attitude model of the quadrotor UAV, and use the component torque of the quadrotor UAV as the control input; Introduce an auxiliary equation to construct a predefined-time disturbance observer, and combine the Lyapunov function to quickly estimate the external disturbance by adjusting the predefined time; Based on the attitude model and the predefined-time disturbance observer, design a nonsingular predefined-time sliding mode controller; According to the nonsingular predefined-time sliding mode controller, control the quadrotor UAV to perform attitude tracking, and control the attitude tracking error of the quadrotor UAV to converge within the predefined time by adjusting the predefined time parameter.

2. The non-singular sliding mode control method for a quadrotor UAV according to claim 1, characterized in that The quadrotor UAV adopts an X-shaped layout. The specific process of establishing the attitude model of the quadrotor UAV is as follows: Define the body coordinate system b as ; and the inertial coordinate system e as ; According to the rigid body motion law, establish the moment balance equation of the quadrotor UAV attitude, and the expression is: ； Among them, is the moment of inertia of the quadrotor; is the angular momentum, , 、 、 are respectively the angular velocities of the quadrotor UAV rotating around the 、 、 three axes; is the first derivative; T is the transpose symbol; The resultant moment acting on the quadrotor, and its three-axis components in the body coordinate system are expressed as follows: ； Among them, 、 、 are the component torques acting on the quadrotor rotating around the 、 、 three axes respectively; 、 、 are the moments of inertia around the 、 、 three axes respectively; 、 、 are the first-order derivatives of 、 、 respectively. Assume that the quadrotor of the drone is symmetric, then the moment of inertia of the asymmetric part is 0, that is ; Assume that the attitude of the quadrotor UAV changes slightly during flight, then the relationship between the angular velocity and the angle is expressed as: ； Among them, is the roll angle, is the pitch angle, is the yaw angle; 、 、 are the corresponding first-order derivatives respectively; The components of the moment acting on a quadrotor UAV about , , the three axes are used as control inputs respectively, and are expressed as: ； Combined with the air resistance and external unknown disturbance conditions that the propellers of the quadrotor UAV will encounter during flight, the attitude model of the quadrotor UAV is expressed as: ； ； ； Among them, is the inertia constant of the propeller; , , are the component torques received by the quadrotor UAV around , , the three axes; , , are the second-order derivatives of the roll angle, pitch angle, and yaw angle respectively; , , are the air resistance coefficients respectively, and the air resistance is expressed as: ； , , are three different external unknown disturbances respectively.

3. A nonsingular sliding mode control method for a quadrotor UAV according to claim 2, characterized in that The auxiliary equation is used to estimate the disturbance vector, and its expression is: ； Among them, is the second derivative of the auxiliary equation state vector Z, , , are respectively the second derivatives of the auxiliary equation state variables of the quadrotor UAV in the body coordinate system; is a constant vector in the body coordinate system; , which is the moment of inertia reciprocal; , which is the control input vector in the body coordinate system; is the coupling term and air resistance of the attitude model, expressed as: ； , , respectively represent the values corresponding to the , , axes in the body coordinate system; , is the attitude state quantity of the quadrotor UAV and the error vector between the auxiliary equation state quantity Z; , is the second derivative of the state vector of the quadrotor UAV; respectively represent the corresponding values of the three axes in the body coordinate system , , the three-axis values; respectively represent the components of the second derivative of the state quantity of the three axes corresponding to the quadrotor UAV in the body coordinate system , , ; Then, construct a predefined-time disturbance observer according to the auxiliary equation, and its expression is: ； ； Among them, is the estimated value of the disturbance vector; is the error state quantity, and is the estimated value of the error vector ; is the second derivative of; is the error state variable the first derivative of; is the normal value control parameter of the disturbance observer, ; is the sign function; is the predefined time of the disturbance observer , representing the disturbance error.

4. A nonsingular sliding mode control method for a quadrotor UAV according to claim 3, characterized in that Combined with the Lyapunov function, quickly estimate the external disturbance by adjusting the predefined time. Specifically: Taking the time derivative of the perturbation error in combination with the Lyapunov function yields the perturbation error that can converge within a predefined time with the expression:[[]]END]] ； ； Among them, is a Lyapunov function, a scalar function used to analyze the stability of a nonlinear system; when is selected, then the class function is expressed as: ； Scalar function ; is the parameter variable of the scalar function; , when , ; is the normal value parameter of the class function; When the following formula is obtained: ； ； represent of derivative; Obtain the estimation error of the perturbation vector , and satisfy the following formula: ； Among them, is the estimation error of the disturbance vector; is the external unknown disturbance vector; is the estimated value of the disturbance vector; is the attitude state quantity of the quadrotor UAV in the body coordinate system; is the second derivative of; is the error state quantity; is the normal value in the body coordinate system; ; is the auxiliary equation state quantity in the body coordinate system; Thus, it can be obtained that when the disturbance error satisfies the predefined time to converge, the estimation error of the disturbance estimation vector also satisfies to converge within the predefined time, that is, by adjusting the predefined time the disturbance of the quadrotor UAV can be estimated quickly.

5. A nonsingular sliding mode control method for a quadrotor UAV according to claim 4, characterized in that The nonsingular predefined-time sliding mode controller realizes parameter adjustment of the convergence time of the quadrotor UAV in the sliding phase through the nonsingular predefined-time sliding mode surface; Among them, the expression of the nonsingular predefined-time sliding mode surface is: ； Among them, is the sliding mode surface, ; is the attitude tracking error, ; is the attitude state quantity of the quadrotor UAV in the body coordinate system; is the tracking target of the quadrotor attitude angle, is the tracking target value of the quadrotor UAV attitude angle; is the tracking target value of the roll angle, is the tracking target value of the pitch angle, is the tracking target value of the yaw angle; Lyapunov function is selected ; is a non-singular predefined time control parameter; is the predefined time of the sliding mode surface; is the sign function; and ; Under the action of the non-singular predefined time sliding mode surface, the attitude tracking error converges within the time; According to the nonsingular predefined-time sliding mode surface, the attitude model of the quadrotor UAV, and the estimated value of the predefined-time disturbance observer, obtain the nonsingular predefined-time sliding mode controller, and its expression is: ； ； Among them, The component moments of the quadrotor UAV in the body coordinate system, i.e., the control inputs; The values of the coupling terms of the attitude model and the air resistance in the body coordinate system, ; , is the non-singular predefined time control parameter; is the estimated value of the disturbance vector; is the preset time in the approaching phase; represents the Lyapunov function selection ; Under the action of the nonsingular predefined-time sliding mode controller, the system state converges to the sliding mode surface within the predefined time and within the predefined time the attitude angles of the quadrotor can track the desired values.

6. A non-singular sliding mode control device for a quadrotor UAV, which is used to implement the non-singular sliding mode control method for a quadrotor UAV according to any one of claims 1-5, characterized in that including: A coordinate system establishment unit, which is used to establish the body coordinate system and inertial coordinate system of the quadrotor UAV, and assume that the body structure of the quadrotor UAV is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coincides with the geometric center of gravity, and its mass and moment of inertia do not change with time; An attitude model establishment unit, which is used to establish the attitude model of the quadrotor UAV according to the rigid body motion law, considering the air resistance and external unknown disturbance conditions, and use the component torque of the quadrotor UAV as the control input; A disturbance observer establishment unit, which is used to introduce an auxiliary equation to construct a predefined-time disturbance observer, and combine the Lyapunov function to quickly estimate the external disturbance by adjusting the predefined time; A sliding mode controller establishment unit, which is used to design a nonsingular predefined-time sliding mode controller based on the attitude model and the predefined-time disturbance observer; An attitude tracking control unit is configured to control a quadrotor UAV to perform attitude tracking according to the non-singular predefined-time sliding mode controller, and control the attitude tracking error of the quadrotor UAV to converge within a predefined time by adjusting the predefined-time parameter.

7. A non-singular sliding mode control device for a quadrotor UAV, characterized in that, It includes a processor and a memory. A computer program is stored in the memory and can be executed by the processor to implement a non-singular sliding mode control method for a quadrotor UAV according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, Computer-readable instructions are stored on the computer-readable storage medium. When the computer-readable instructions are executed by the processor of the device where the computer-readable storage medium is located, a non-singular sliding mode control method for a quadrotor UAV according to any one of claims 1-5 is implemented.

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