Non-singular sliding mode control method, device, equipment and medium for quadrotor drone

Abstract

The present invention provides a non-singular sliding mode control method, device, equipment, and medium for a quadcopter drone, relating to the technical field of drone flight control. The present invention establishes a quadcopter body coordinate system and an inertial coordinate system, and establishes a quadcopter attitude model based on the laws of rigid body motion, taking into account air resistance and external unknown disturbances. A predefined time disturbance observer is constructed by introducing auxiliary equations, and external disturbances are rapidly estimated by adjusting the predefined time in combination with the Lyapunov function. A non-singular predefined time sliding mode controller is then designed. The quadcopter is controlled to perform attitude tracking using the non-singular predefined time sliding mode controller, and the attitude tracking error of the quadcopter is controlled to converge within a predefined time by adjusting the predefined time parameters. The present invention is capable of rapidly estimating external disturbances within a preset time and flexibly controlling the convergence rate of the quadcopter drone.

Description

Technical Field

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

[0002] Quadrotors (UAVs) have been widely used in both military and civilian applications due to their excellent stability, ease of operation, small size, and light weight. However, as a typical underactuated, strongly coupled system, quadrotors are highly sensitive to external environmental factors, particularly to unknown disturbances during flight, which increases their control difficulty. To address these challenges, researchers have proposed various control methods, such as adaptive control, neural network control, and observer-based interference rejection control. While these methods have improved the system's interference rejection capabilities to a certain extent, they still have limitations. For example, adaptive control and neural network control require complex parameter adjustment procedures, while traditional finite-time or fixed-time disturbance observers can achieve rapid convergence of the disturbance estimation error, their convergence time is often limited by the system's initial state and cannot be flexibly adjusted. Furthermore, sliding mode control, a commonly used nonlinear control method, while highly robust, is prone to singularity problems in practical applications, affecting system stability and control accuracy.

[0003] In the prior art, the design of disturbance observers and controllers for quadrotor drones primarily focuses on the study of finite-time and fixed-time control algorithms. For example, existing literature has proposed a number of finite-time disturbance observers and fixed-time disturbance observers to estimate the state and external disturbances of a quadrotor drone, thereby improving the system's anti-interference capability. However, these methods can generally only ensure that the disturbance estimation error converges within a finite or fixed time, and the convergence time is closely related to the initial state, making it difficult to meet application scenarios with strict convergence time requirements. Furthermore, there is limited research on the combination of existing predefined-time control algorithms and observers, making it difficult to achieve rapid and accurate disturbance estimation and efficient control of attitude tracking errors in practical applications.

[0004] In view of this, this application is hereby filed. Summary of the Invention

[0005] The present invention aims to provide a non-singular sliding mode control method, device, equipment and medium for a quadrotor drone, so as to solve the technical problem that the existing quadrotor drone attitude control method is difficult to achieve rapid convergence and high-precision attitude tracking in the presence of external unknown disturbances and model uncertainties.

[0006] In order to solve the above technical problems, the present invention is implemented through the following technical solutions:

[0007] A non-singular sliding mode control method for a quadrotor unmanned aerial vehicle, comprising:

[0008] S1, establish the quadrotor drone body coordinate system and inertial coordinate system, and assume that the quadrotor drone body structure is a rigid body with strict symmetry, uniform mass distribution, center of mass and geometric center of gravity coinciding, and its mass and moment of inertia do not change with time;

[0009] S2, based on the rigid body motion law, taking into account the air resistance and external unknown disturbances, establishes the attitude model of the quadrotor drone, and uses the component torque of the quadrotor drone as the control input;

[0010] S3, introduces auxiliary equations to construct a predefined time disturbance observer, and combines Lyapunov function to quickly estimate external disturbances by adjusting the predefined time;

[0011] S4, designing a non-singular predefined-time sliding mode controller based on the posture model and the predefined-time disturbance observer;

[0012] S5, controlling the quadrotor drone to perform attitude tracking according to the non-singular predefined time sliding mode controller, and controlling the attitude tracking error of the quadrotor drone to converge within a predefined time by adjusting the predefined time parameters.

[0013] Preferably, the quad-rotor drone adopts an X-shaped layout, and the posture model of the quad-rotor drone is established as follows:

[0014] Define the body coordinate system b as ; The inertial coordinate system e is ;

[0015] According to the law of rigid body motion, the torque balance equation of the quadrotor UAV attitude is established, and the expression is:

[0016] ;

[0017] in, is the moment of inertia of the quadrotor; is the angular momentum, , 、 、 For four-rotor drones 、 、 Angular velocity of three-axis rotation; for The first derivative of ; T is the transpose sign;

[0018] is the resultant torque acting on the quadrotor, and its three-axis components in the body coordinate system are expressed as:

[0019] ;

[0020] in, 、 、 Respectively around 、 、 The component moments of the three-axis quadrotor; 、 、 Respectively around 、 、 Moment of inertia of the three axes; 、 、 They are 、 、 The first derivative of ;

[0021] Assuming that the quadrotor of the drone is symmetrical, The moment of inertia of the asymmetric part is 0, that is ;

[0022] Assuming that the attitude of the quadrotor drone changes slightly during flight, the relationship between angular velocity and angle is expressed as:

[0023] ;

[0024] in, is the roll angle, is the pitch angle, is the yaw angle; 、 、 are the corresponding first-order derivatives respectively;

[0025] Four-rotor drone 、 、 The component torques on the three axes are used as control inputs, respectively, and are expressed as:

[0026] ;

[0027] Considering the air resistance and external unknown disturbances that the propellers experience during quadrotor flight, the attitude model of the quadrotor drone is expressed as follows:

[0028] ;

[0029] ;

[0030] ;

[0031] in, is the inertia constant of the propeller; 、 、 For quadcopter drones 、 、 Component moments on the three axes; 、 、 are the second-order derivatives of the roll angle, pitch angle, and yaw angle respectively; 、 、 They are respectively the air resistance coefficient and the air resistance Expressed as:

[0032] ;

[0033] 、 、 They are three different external unknown disturbances.

[0034] Preferably, the auxiliary equation is used to estimate the disturbance vector, and its expression is:

[0035] ;

[0036] in, is the second-order derivative of the auxiliary equation state vector Z, 、 、 are the second-order derivatives of the auxiliary equation state quantities of the quadrotor UAV in the body coordinate system; is a positive constant vector in the body coordinate system; , is the moment of inertia The reciprocal of , is the control input vector in the body coordinate system; is the coupling term of the attitude model and the air resistance, expressed as:

[0037] ;

[0038] 、 、 Respectively Corresponding to the body coordinate system 、 、 The value of the axis;

[0039] , is the attitude state of the quadrotor drone Error vector with the auxiliary equation state quantity Z; , is the second-order derivative of the state vector of the quadrotor drone; Respectively Corresponding to the body coordinate system 、 、 The values ​​of the three axes; They represent the coordinates of the quadrotor drone in the body coordinate system. 、 、 Components of the second-order derivatives of the state quantities of the three axes;

[0040] Then, the predefined time disturbance observer is constructed according to the auxiliary equation, and its expression is:

[0041] ;

[0042] ;

[0043] in, is the estimated value of the disturbance vector; is the error state quantity, is the error vector The estimated value of for The second derivative of

[0044] is the error state quantity The first derivative of ; is the normal value control parameter of the disturbance observer, ; is a symbolic function; For predefined time;

[0045] , represents the disturbance error.

[0046] Preferably, the external disturbance is estimated quickly by adjusting the predefined time in combination with the Lyapunov function, specifically:

[0047] Combined with Lyapunov function to deal with disturbance error Taking the time derivative, we can get the disturbance error Can be used at predefined time Inner convergence, the expression is:

[0048] ;

[0049] ;

[0050] in, is the Lyapunov function, a scalar function used to analyze the stability of nonlinear systems; when When, then, class function Expressed as:

[0051] ;

[0052] Scalar functions ; is the parameter variable of the scalar function; ,when hour, ; Normal value parameters for class functions;

[0053] when When , we get the following formula:

[0054] ;

[0055] ;

[0056] express right The derivative of

[0057] Get the estimated error of the perturbation vector , and satisfy the following formula:

[0058] ;

[0059] in, 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 of the quadrotor UAV in the body coordinate system; for The second derivative of is the error state quantity; is the normal value in the body coordinate system; ; is the state quantity of the auxiliary equation in the body coordinate system;

[0060] Thus, when the disturbance error Meet the predefined time At convergence, the estimation error of the perturbation estimation vector is It also meets the convergence within the predefined time, that is, by adjusting the predefined time It can quickly estimate the disturbance of quadrotor drones.

[0061] Preferably, the non-singular predefined time sliding mode controller realizes parameter adjustment of the convergence time of the quadrotor drone in the sliding phase through a non-singular predefined time sliding mode surface;

[0062] The expression of the non-singular predefined time sliding mode surface is:

[0063] ;

[0064] in, is the sliding surface, ; is the posture tracking error, ; is the attitude state 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 drone’s 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 choose ;

[0065] Predefine time control parameters for non-singularity; is the predefined time of the sliding surface; is a sign function; and ;

[0066] Under the action of the non-singular predefined time sliding surface, the attitude tracking error exist Converges within time;

[0067] 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, a non-singular predefined time sliding mode controller is obtained, and its expression is:

[0068] ;

[0069] ;

[0070] in, The component torque of the quadrotor drone in the body coordinate system, i.e., the control input; The coupling term of the attitude model and the value of air resistance in the body coordinate system, ; , Predefine time control parameters for non-singularity; is the estimated value of the disturbance vector; The preset time for the approach phase; represents the Lyapunov function choice ;

[0071] Under the action of non-singular predefined time sliding mode controller, the system state changes in predefined time Converges to the sliding surface and within a predefined time Within, the attitude angle of the quadrotor can track the expected value.

[0072] The present invention also provides a non-singular sliding mode control device for a quadrotor drone, comprising:

[0073] The coordinate system establishment unit is used to establish the coordinate system and inertial coordinate system of the quadrotor drone body, and assumes that the quadrotor drone body structure is a rigid body with strict symmetry, uniform mass distribution, coincidence of center of mass and geometric center of gravity, and its mass and moment of inertia do not change with time;

[0074] The attitude model building unit is used to build the attitude model of the quadrotor drone according to the rigid body motion law, taking into account the air resistance and external unknown disturbances, and uses the component torque of the quadrotor drone as the control input;

[0075] The disturbance observer establishment unit is used to introduce auxiliary equations to construct a predefined time disturbance observer, and combine the Lyapunov function to quickly estimate external disturbances by adjusting the predefined time;

[0076] a sliding mode controller establishing unit, configured to design a non-singular predefined time sliding mode controller based on the posture model and the predefined time disturbance observer;

[0077] The attitude tracking control unit is used to control the quadrotor drone to perform attitude tracking according to the non-singular predefined time sliding mode controller, and control the attitude tracking error of the quadrotor drone to converge within a predefined time by adjusting the predefined time parameters.

[0078] The present invention also provides a non-singular sliding mode control device for a quadrotor drone, comprising a processor and a memory, wherein 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 a quadrotor drone as described above.

[0079] 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, the non-singular sliding mode control method of a quadrotor drone as described above is implemented.

[0080] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0081] This paper designs a novel predefined-time disturbance observer that can quickly estimate external disturbances within a preset time. It also flexibly controls the convergence rate of the quadrotor by adjusting the predefined time parameters, effectively reducing the impact of disturbances on the quadrotor's attitude tracking. Furthermore, 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, further improving the system's control performance. Specifically, the following are the key steps:

[0082] First, the present invention can achieve flexible adjustment of disturbance estimation and attitude tracking convergence rate by adjusting predefined time parameters, thereby meeting the needs of different application scenarios.

[0083] Second, the present invention avoids the singularity problem that may occur in traditional sliding mode control by designing the sliding surface, thereby improving the control accuracy.

[0084] Third, the present invention significantly improves the robustness of the system through the joint design of the disturbance observer and the controller, making it more adaptable to external unknown disturbances and initial state changes.

[0085] Therefore, the present invention not only solves the problem of unadjustable convergence time of disturbance estimation and attitude tracking control in the prior art, but also overcomes the singularity defect in traditional sliding mode control, providing an innovative solution for high-precision attitude control of quadrotor drones. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0087] Figure 1 A schematic diagram of a non-singular sliding mode control method for a quadrotor drone provided in Example 1.

[0088] Figure 2 Schematic diagram of the quadrotor drone provided in Example 1 in the inertial coordinate system and the body coordinate system.

[0089] Figures 3(a), 3(b), and 3(c) are comparison diagrams of the tracking curves of the attitude angles (roll angle, pitch angle, and yaw angle) of the method of the present invention (NPTSM) provided in Example 1, 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.

[0090] Figures 4(a), 4(b), and 4(c) are comparison diagrams of the tracking error curves of the attitude angles (roll angle, pitch angle, and yaw angle) of the method of the present invention (NPTSM) provided in Example 1, 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.

[0091] Figures 5(a), 5(b), and 5(c) are comparison diagrams of the output curves of the method of the present invention (NPTSM) provided in Example 1, the existing predefined time sliding mode control method (PTSM), the existing fixed time sliding mode control method (FTSM), and the controller (u1\u2\u3) of the desired trajectory under the condition of changing the initial state.

[0092] Figure 6 This is a schematic diagram of a non-singular sliding mode control device for a quadrotor drone provided in Example 2.

[0093] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. DETAILED DESCRIPTION

[0094] In order to make the purpose, 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 drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention for which protection is sought, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0095] Example 1

[0096] Embodiment 1 of the present invention provides a non-singular sliding mode control method for a quadrotor drone, which can be implemented by a non-singular sliding mode control device of the quadrotor drone (hereinafter referred to as the control device), and in particular, executed by one or more processors in the control device.

[0097] In this embodiment, the control device may be an electronic device equipped with a processor, which carries a computer program of the non-singular sliding mode control method of the quadrotor drone and can be executed, such as a computer, a smart phone, a smart tablet, a workstation, etc., which is not limited here.

[0098] like Figure 1 As shown, a non-singular sliding mode control method for a quadrotor drone includes steps S1 to S5.

[0099] S1, establish the quadrotor drone body coordinate system and inertial coordinate system, and assume that the quadrotor drone body structure is a rigid body with strict symmetry, uniform mass distribution, coincidence of center of mass and geometric center of gravity, and its mass and moment of inertia do not change with time.

[0100] like Figure 2 The schematic diagram of the quadrotor drone in the inertial coordinate system and the body coordinate system shown in the figure shows that the quadrotor drone of this embodiment adopts an "X"-shaped layout, and the propellers f1 and f3 of the quadrotor drone rotate clockwise, and the propellers f2 and f4 rotate counterclockwise.

[0101] In order to accurately describe the structure and motion principle of the UAV, the body coordinate system b is defined as , the inertial reference system e is .

[0102] In order to better analyze, the following assumptions are made before modeling the quadrotor drone:

[0103] Assumption 1: The quadrotor drone body structure is a rigid body with strict symmetry, uniform mass distribution, and the center of mass coincident with the geometric center of gravity.

[0104] Assumption 2: The mass and moment of inertia of the quadrotor drone do not change with time.

[0105] S2, according to the law of rigid body motion, taking into account the air resistance and external unknown disturbances, establish the attitude model of the quadrotor drone, and use the component torque of the quadrotor drone as the control input.

[0106] According to the law of rigid body motion, the torque balance equation of the quadrotor UAV attitude is established, and the expression is:

[0107] , formula (1)

[0108] in, is the moment of inertia of the quadrotor; is the angular momentum, , 、 、 For four-rotor drones 、 、 Angular velocity of three-axis rotation; for The first derivative of ; T is the transpose sign;

[0109] is the resultant torque acting on the quadrotor, and its three-axis components in the body coordinate system are expressed as:

[0110] , formula (2)

[0111] in, 、 、 Respectively around 、 、 The component moments of the three-axis quadrotor; 、 、 Respectively around 、 、 Moment of inertia of the three axes; 、 、 They are 、 、 The first derivative of ;

[0112] Assuming that the quadrotor of the drone is symmetrical, The moment of inertia of the asymmetric part is 0, that is ;

[0113] Assuming that the attitude of the quadrotor drone changes slightly during flight, the relationship between angular velocity and angle is expressed as:

[0114] ;

[0115] in, is the roll angle (Roll), is the pitch angle (Pitch), is the yaw angle (Yaw); 、 、 are the corresponding first-order derivatives respectively;

[0116] Four-rotor drone 、 、 The component torques on the three axes are used as control inputs, respectively, and are expressed as:

[0117] , formula (3)

[0118] Considering the air resistance and external unknown disturbances that the propellers experience during quadrotor flight, the attitude model of the quadrotor drone is expressed as follows:

[0119] , formula (4)

[0120] in, is the inertia constant of the propeller; 、 、 For quadcopter drones 、 、 Component moments on the three axes; 、 、 are the second-order derivatives of the roll angle, pitch angle, and yaw angle respectively; 、 、 They are respectively the air resistance coefficient and the air resistance Expressed as:

[0121] ;

[0122] 、 、 They are three different external unknown disturbances.

[0123] S3, an auxiliary equation is introduced to construct a predefined time disturbance observer, and the Lyapunov function is combined to quickly estimate the external disturbance by adjusting the predefined time.

[0124] In this embodiment, the control objective of the present invention is to accurately estimate external disturbances and achieve attitude tracking control of a quadrotor drone within a predefined time. External disturbances are quickly and accurately estimated and compensated for in the control law. Therefore, the present invention designs a disturbance observer and controller based on the theory of predefined time stability. The following basic knowledge is required in designing the disturbance observer and controller:

[0125] Function definition: scalar continuous function ,if is strictly monotonically increasing, and ;when hour, ,but belong The function is expressed as , is the parameter variable of the scalar function. The following examples illustrate several function.

[0126] , formula (5)

[0127] , formula (6)

[0128] , formula (7)

[0129] set up is a differentiable function, and there exists is a continuous positive definite, radially unbounded function. If for any , so that the function The time derivative of satisfies the following formula:

[0130] , formula (8)

[0131] in, is the control parameter, , ,and It is a nonlinear system The state quantity, origin is the only equilibrium point of the system, then The nonlinear system corresponding to the function The trajectory can achieve predefined time stability, and the upper bound of the convergence time is , the proof is as follows:

[0132] According to the above formula (8), we can get:

[0133] , formula (9)

[0134] From formula (9), we can see that Decreases over time, eventually , integrating both sides of the formula over time yields:

[0135] , formula (10)

[0136] In formula (10), for The initial value of The definition of the class function shows , and the control parameters The range of , so it can be rewritten as:

[0137] ;

[0138] Therefore, The time to converge to zero is less than ,Depend on From the definition of the class function, we can see that when When it converges to zero, ,at this time It can be seen that is a continuous positive definite, radially unbounded function, when When , then the system state quantity Ability to Internal stability.

[0139] In order to facilitate the design of subsequent observers and controllers, the quadrotor UAV attitude model is simplified as follows:

[0140] , formula (11)

[0141] Where, is the second-order derivative of the state vector of the quadrotor drone; They represent the coordinates of the quadrotor drone in the body coordinate system. 、 、 Components of the second derivatives of the state vector of the three axes;

[0142] , is the moment of inertia The reciprocal of is the disturbance vector; , is the control input vector in the body coordinate system;

[0143] is the coupling term of the attitude model and the air resistance, expressed as:

[0144] ;

[0145] 、 、 Respectively Corresponding to the body coordinate system 、 、 The value of the axis.

[0146] In this embodiment, an auxiliary equation is introduced to estimate the disturbance vector, and its expression is:

[0147] , formula (12)

[0148] in, is the second-order derivative of the auxiliary equation state vector Z, 、 、 are the second-order derivatives of the auxiliary equation state quantities of the quadrotor UAV in the body coordinate system; is a positive constant vector in the body coordinate system; , is the attitude state of the quadrotor drone Error vector with the auxiliary equation state quantity Z; Respectively Corresponding to the body coordinate system 、 、 The values ​​of the three axes.

[0149] Then, the predefined time disturbance observer is constructed according to the auxiliary equation, and its expression is:

[0150] , formula (13)

[0151] , formula (14)

[0152] in, is the estimated value of the disturbance vector; is the error state quantity, is the error vector The estimated value of for The second derivative of

[0153] is the error state quantity The first derivative of ; is the normal value control parameter of the disturbance observer, ; is a symbolic function; is the predefined time of the disturbance observer;

[0154] , represents the disturbance error.

[0155] According to the expression of the predefined time disturbance observer, it is proved that the disturbance error It can converge within a predefined time. Subtract the value from both sides of equation (14) The following formula can be obtained:

[0156] , formula (15)

[0157] For analysis The convergence of Lyapunov function is combined with the Lyapunov function to prove that the error of the disturbance observer can converge within a predefined time. The choices are as follows:

[0158] , formula (16)

[0159] Taking the time derivative of the Lyapunov function, we get:

[0160] , formula (17)

[0161] according to Class function definition, when When, and The class function selection is:

[0162] ;

[0163] in, For the normal value parameter of the class function, when When, you know , then the time derivative formula of the Lyapunov function can be rewritten as:

[0164] , formula (18)

[0165] From the above formula (18), we can see that the error At a predefined time Internal convergence.

[0166] Through equations (12), (13), and (14), we can obtain the estimated error of the disturbance vector: , and satisfy the following formula:

[0167] , formula (19)

[0168] in, 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 of the quadrotor UAV in the body coordinate system; for The second derivative of is the error state quantity; is the normal value in the body coordinate system; ; is the state quantity of the auxiliary equation in the body coordinate system; for The second derivative of .

[0169] According to the above, when the disturbance error Meet the predefined time At convergence, the estimation error of the perturbation estimation vector is It also meets the convergence within the predefined time, that is, by adjusting the predefined time It can quickly estimate the disturbance of quadrotor drones.

[0170] S4. Design a non-singular predefined-time sliding mode controller based on the posture model and the predefined-time disturbance observer.

[0171] In this embodiment, in order to avoid the singularity problem in the traditional predefined time sliding mode control, a non-singular predefined time sliding mode controller is designed. The non-singular predefined time sliding mode controller realizes the convergence time of parameter adjustment of the quadrotor drone in the sliding phase through the non-singular predefined time sliding mode surface;

[0172] The expression of the non-singular predefined time sliding mode surface is:

[0173] , formula (20)

[0174] in, is the sliding surface, ; is the posture tracking error, ; is the attitude state 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 drone’s 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 choose ;

[0175] Predefine time control parameters for non-singularity; is the predefined time of the sliding surface; is a symbolic function; .

[0176] The sliding surface is designed by adjusting the parameters The constraints of the controller are avoided, which avoids the occurrence of singular phenomena and improves the performance of the subsequent controller design.

[0177] Under the action of the non-singular predefined time sliding surface, the attitude tracking error exist Converges within time.

[0178] when When , the sliding surface formula (20) can be evolved into:

[0179] , formula (21)

[0180] Depend on The operational relationship can be obtained as follows:

[0181] , formula (22)

[0182] Further, by The operational relationship can be obtained as follows:

[0183] , formula (23)

[0184] When choosing is the Lyapunov function, and its time derivative is expressed as:

[0185] ;

[0186] when The class function is selected as When, you know ,but:

[0187] , formula (24)

[0188] Therefore, according to the formula, the design of the sliding surface makes the convergence time of the sliding stage meet the preset time parameter Inside.

[0189] Then, based on 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, a non-singular predefined time sliding mode controller (i.e., control law) is designed, which is expressed as:

[0190] , formula (25)

[0191] , formula (26)

[0192] in, The component torque of the quadrotor drone in the body coordinate system, i.e., the control input; The coupling term of the attitude model and the value of air resistance in the body coordinate system, ; , Predefine time control parameters for non-singularity; is the estimated value of the disturbance vector; The preset time for the approach phase; represents the Lyapunov function choice ;

[0193] Under the action of non-singular predefined time sliding mode controller, the system state changes in predefined time Converges to the sliding surface and within a predefined time Within, the attitude angle of the quadrotor can track the expected value.

[0194] When the parameter When, avoid middle The negative exponential term appears, which enables the designed controller to avoid singularity problems during attitude control.

[0195] At the same time, under the action of non-singular predefined time sliding mode controller, the system state can be Reaching the sliding surface .

[0196] By taking the time derivative of the sliding surface formula (20), we can obtain:

[0197] , formula (27)

[0198] Combined with the non-singular predefined time sliding mode controller formula (25), we can get:

[0199] , formula (28)

[0200] When choosing is the Lyapunov function, and taking its time derivative, we can get:

[0201] , formula (29)

[0202] The time is known from the observer hour, ,according to The formula shows , the above formula is scaled as follows:

[0203] , formula (30)

[0204] when The class function is selected as When, you know Then formula (30) can be rewritten as:

[0205] , formula (31)

[0206] Therefore, under the control law, the system state is in the predefined time Converges to the sliding surface and within a predefined time The inner quadrotor attitude angle can track the expected value.

[0207] S5, controlling the quadrotor drone to perform attitude tracking according to the non-singular predefined time sliding mode controller, and controlling the attitude tracking error of the quadrotor drone to converge within a predefined time by adjusting the predefined time parameters.

[0208] During attitude tracking, the attitude angle of the quadrotor UAV is made to track the desired trajectory, and then the attitude angle tracking trajectory curve and the attitude angle tracking error curve are analyzed. By adjusting the predefined time parameters, the attitude tracking error is controlled to converge within the predefined time to meet the different mission requirements of the UAV.

[0209] In another preferred embodiment, in order to verify the effectiveness of the control method proposed in this article, the control method of the present invention is simulated using the matlab / simulink simulation platform. In the simulation experiment, the control system parameters of the quadcopter drone are set as follows:

[0210] 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 non-singular predefined time sliding mode controller are set to The external disturbance amount of the quadrotor UAV is set as , the attitude angle tracking trajectory target is set to .

[0211] In order to verify the tracking performance of the controller and observer designed by the present invention, the tracking performance of the control system under different control schemes is discussed under the condition of changing the initial state. In the simulation experiment, the control algorithm of the present invention (NPTSM) is compared with the predefined time sliding mode control method (PTSM) 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 , wherein the preset time parameters of the NPTSM of the present invention and the prior art PTSM are both set to ( is the predefined time for convergence to the sliding surface, is the predefined time for convergence to the desired value), the simulation results are represented by Figure 3(a), Figure 3(b), Figure 3(c), Figure 4(a), Figure 4(b), Figure 4(c), Figure 5(a), Figure 5(b), and Figure 5(c). In the simulation result figures, PT is used to represent the preset convergence time of the observer or controller of the present invention, and Desired trajectory is the desired trajectory.

[0212] In this embodiment, the Predefined Time Sliding Mode Control (PTSM) method is an advanced sliding mode control variant designed to address the singularity issues inherent in traditional sliding mode control and achieve control system convergence within a predetermined timeframe. By introducing a specific time function to adjust the system's dynamic behavior, it achieves more flexible and smoother control performance while maintaining robustness. For example, in spacecraft attitude tracking control, PTSM can predefine the completion time for attitude adjustments based on mission requirements.

[0213] Fixed-time sliding mode control (FTSM): This method ensures system convergence within a finite time. However, the upper bound of this convergence time is independent of the system's initial state and depends solely on the control parameters. This property allows FTSM to guarantee convergence even when the initial state cannot be accurately determined, but the specific convergence time cannot be directly preset. This method is suitable for scenarios where the initial state is unknown or difficult to measure accurately. For example, in trajectory tracking for omnidirectional mobile robots, it can achieve fast fixed-time convergence, improving trajectory tracking accuracy and system robustness.

[0214] 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, and yaw angle) of the quadrotor under different control schemes and the attitude angle tracking error curves. Figures 3(a) and 4(a) are roll angles, Figures 3(b) and 4(b) are pitch angles, and Figures 3(c) and 4(c) are yaw angles. 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 converge within 0.5s. The results prove that:

[0215] Even with changes to the system's initial state, the convergence time of the proposed algorithm remains within the preset timeframe. Furthermore, Figures 3(a), 3(b), 3(c), 4(a), 4(b), and 4(c) show that the convergence time of the quadrotor attitude angle is approximately 0.6 seconds under the PTSM algorithm, while the convergence time is as long as 2.5 seconds under the FTSM algorithm. Simulation results demonstrate that the proposed control algorithm converges faster than the PTSM and FTSM algorithms, demonstrating its superiority. Figures 5(a), 5(b), and 5(c) show that the control outputs of the PTSM and FTSM algorithms exhibit prolonged chattering.

[0216] In summary, the simulation experimental results show that the predefined time disturbance observer and the non-singular predefined time sliding mode controller designed in the present invention can both complete the tracking of the expected value within the preset time. By adjusting the preset time parameters of this control scheme, the convergence rate of the quadrotor UAV can be improved.

[0217] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0218] The present invention combines Lyapunov stability theory, and the designed controller and observer 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 kept within the predetermined upper limit, which proves the insensitivity of the system of the present invention to the change of the initial state and avoids the problem of the convergence time depending on the initial state in traditional sliding mode control. The observer is combined with the Lyapunov function through auxiliary equations to accurately estimate external disturbances within a predefined time and improve control robustness. The designed sliding surface controller eliminates control singularities and avoids the singularity problem caused by negative exponential terms in traditional sliding mode control. Compared with the existing traditional fixed-time control method, the method of the present invention has advantages in convergence rate.

[0219] Example 2

[0220] like Figure 6 As shown, the second embodiment of the present invention further provides a non-singular sliding mode control device for a quadrotor drone, comprising:

[0221] The coordinate system establishment unit is used to establish the coordinate system and inertial coordinate system of the quadrotor drone body, and assumes that the quadrotor drone body structure is a rigid body with strict symmetry, uniform mass distribution, coincidence of center of mass and geometric center of gravity, and its mass and moment of inertia do not change with time;

[0222] The attitude model building unit is used to build the attitude model of the quadrotor drone according to the rigid body motion law, taking into account the air resistance and external unknown disturbances, and uses the component torque of the quadrotor drone as the control input;

[0223] The disturbance observer establishment unit is used to introduce auxiliary equations to construct a predefined time disturbance observer, and combine the Lyapunov function to quickly estimate external disturbances by adjusting the predefined time;

[0224] a sliding mode controller establishing unit, configured to design a non-singular predefined time sliding mode controller based on the posture model and the predefined time disturbance observer;

[0225] The attitude tracking control unit is used to control the quadrotor drone to perform attitude tracking according to the non-singular predefined time sliding mode controller, and control the attitude tracking error of the quadrotor drone to converge within a predefined time by adjusting the predefined time parameters.

[0226] Example 3

[0227] The third embodiment of the present invention also provides a non-singular sliding mode control device for a quadrotor drone, 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 of the quadrotor drone as described above.

[0228] Example 4

[0229] The fourth embodiment of the present invention also provides a computer-readable storage medium, which stores computer-readable instructions. When the computer-readable instructions are executed by the processor of the device where the computer-readable storage medium is located, the non-singular sliding mode control method of the quadrotor drone as described above is implemented.

[0230] In the several embodiments provided in 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 the devices, methods, and computer program products according to multiple embodiments of the present invention. In this regard, each box in the flowchart or block diagram can represent a module, program segment, or part of a code, which contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the boxes can also occur in an order different from that marked in the drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, as well as the combination of boxes in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified functions or actions, or can be implemented using a combination of dedicated hardware and computer instructions.

[0231] In addition, the functional modules in the various embodiments of the present invention may be integrated together to form an independent part, or each module may exist independently, or two or more modules may be integrated to form an independent part.

[0232] If the functions are implemented in the form of software modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, electronic device, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned storage media include various media that can store program code, such as USB flash drives, mobile hard drives, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical disks. It should be noted that, in this document, the terms "comprise," "include," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or device that includes a series of elements includes not only those elements but also other elements not explicitly listed, or also includes elements inherent to such process, method, article, or device. Without further constraints, an element defined by the phrase "comprises a..." does not preclude the existence of additional identical elements in the process, method, article or apparatus that includes the element.

[0233] 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", "an", "the" and "the" used in the embodiments of the present invention and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise.

[0234] It should be understood that the term "and / or" as used herein is merely a description of the relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the associated objects are in an "or" relationship.

[0235] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0236] The "first" and "second" mentioned in the embodiments are merely used to distinguish similar objects and do not represent a specific ordering of the objects. It is understood that the specific order or precedence of "first" and "second" can be interchanged where appropriate. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate, so that the embodiments described herein can be implemented in an order other than that illustrated or described herein.

[0237] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A non-singular sliding mode control method for a quadrotor drone, characterized in that: include: Establish the quadrotor drone body coordinate system and inertial coordinate system, and assume that the quadrotor drone body structure is a rigid body with strict symmetry, uniform mass distribution, coincidence of center of mass and geometric center of gravity, and its mass and moment of inertia do not change with time; According to the law of rigid body motion, taking into account air resistance and external unknown disturbances, the attitude model of the quadrotor drone is established, and the component torque of the quadrotor drone is used as the control input; Auxiliary equations are introduced to construct a predefined time disturbance observer, and the Lyapunov function is combined to quickly estimate external disturbances by adjusting the predefined time. Designing a non-singular predefined-time sliding mode controller based on the posture model and the predefined-time disturbance observer; Controlling the quadrotor drone to perform attitude tracking according to the non-singular predefined time sliding mode controller, and controlling the attitude tracking error of the quadrotor drone to converge within a predefined time by adjusting the predefined time parameter; The auxiliary equation is used to estimate the disturbance vector, and its expression is: ； in, is the second-order derivative of the auxiliary equation state vector Z, 、 、 are the second-order derivatives of the auxiliary equation state quantities of the quadrotor UAV in the body coordinate system; is a positive constant vector in the body coordinate system; , is the moment of inertia of the quadrotor The reciprocal of , is the control input vector in the body coordinate system; is the coupling term of the attitude model and the air resistance, expressed as: ； in, 、 、 Respectively Corresponding to the body coordinate system 、 、 The value of the axis; is the roll angle, is the pitch angle, is the yaw angle; 、 、 are the corresponding first-order derivatives respectively; is the inertia constant of the propeller; 、 、 Four rotors 、 、 Moment of inertia of the three axes; 、 、 are the air resistance coefficient; , is the attitude state of the quadrotor drone Error vector with the auxiliary equation state quantity Z; , is the second-order derivative of the state vector of the quadrotor drone; Respectively Corresponding to the body coordinate system 、 、 The values ​​of the three axes; They represent the coordinates of the quadrotor drone in the body coordinate system. 、 、 Components of the second-order derivatives of the state quantities of the three axes; 、 、 are the second-order derivatives of the roll angle, pitch angle, and yaw angle respectively; Then, the predefined time disturbance observer is constructed according to the auxiliary equation, and its expression is: ； ； in, is the estimated value of the disturbance vector; is the error state quantity, is the error vector The estimated value of for The second derivative of is the normal value in the body coordinate system; is the error state quantity The first derivative of ; is the normal value control parameter of the disturbance observer, ; is a symbolic function; is the predefined time of the disturbance observer; , represents the disturbance error.

2. The non-singular sliding mode control method for a quadrotor drone according to claim 1 is characterized in that The four-rotor UAV adopts an X-shaped layout, and the posture model of the four-rotor UAV is established as follows: Define the body coordinate system b as ; The inertial coordinate system e is ; According to the law of rigid body motion, the torque balance equation of the quadrotor UAV attitude is established, and the expression is: ； in, is the moment of inertia of the quadrotor; is the angular momentum, , 、 、 For four-rotor drones 、 、 Angular velocity of three-axis rotation; for The first derivative of ; T is the transpose sign; is the resultant torque acting on the quadrotor, and its three-axis components in the body coordinate system are expressed as: ； in, 、 、 Respectively around 、 、 The component moments of the three-axis quadrotor; 、 、 Respectively around 、 、 Moment of inertia of the three axes; 、 、 They are 、 、 The first derivative of ; Assuming that the quadrotor of the drone is symmetrical, The moment of inertia of the asymmetric part is 0, that is ; Assuming that the attitude of the quadrotor drone changes slightly during flight, the relationship between angular velocity and angle is expressed as: ； in, is the roll angle, is the pitch angle, is the yaw angle; 、 、 are the corresponding first-order derivatives respectively; Four-rotor drone 、 、 The component torques on the three axes are used as control inputs, respectively, and are expressed as: ； Considering the air resistance and external unknown disturbances that the propellers experience during quadrotor flight, the attitude model of the quadrotor drone is expressed as follows: ； ； ； in, is the inertia constant of the propeller; 、 、 For quadcopter drones 、 、 Component moments on the three axes; 、 、 are the second-order derivatives of the roll angle, pitch angle, and yaw angle respectively; 、 、 They are respectively the air resistance coefficient and the air resistance Expressed as: ； 、 、 They are three different external unknown disturbances.

3. The non-singular sliding mode control method for a quadrotor drone according to claim 2, characterized in that ,Combined with the Lyapunov function, the external disturbance is quickly estimated by adjusting the predefined time, specifically: Combined with Lyapunov function to deal with disturbance error Taking the time derivative, we can get the disturbance error Can be used at predefined time Inner convergence, the expression is: ； ； in, is the Lyapunov function, a scalar function used to analyze the stability of nonlinear systems; when When, then, class function Expressed as: ； Scalar functions ; is the parameter variable of the scalar function; ,when hour, ; Normal value parameters for class functions; when When , we get the following formula: ； ； express right The derivative of Get the estimated error of the perturbation vector , and satisfy the following formula: ； in, 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 of the quadrotor UAV in the body coordinate system; for The second derivative of is the error state quantity; is the normal value in the body coordinate system; ; is the state quantity of the auxiliary equation in the body coordinate system; Thus, when the disturbance error Meet the predefined time At convergence, the estimation error of the perturbation estimation vector is It also meets the convergence within the predefined time, that is, by adjusting the predefined time It can quickly estimate the disturbance of quadrotor drones.

4. The non-singular sliding mode control method for a quadrotor drone according to claim 3 is characterized in that ,The non-singular predefined time sliding mode controller realizes parameter adjustment of the ,convergence time of the quadrotor UAV in the sliding phase through ,the non-singular predefined time sliding mode surface; The expression of the non-singular predefined time sliding mode surface is: ； in, is the sliding surface, ; is the posture tracking error, ; is the attitude state 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 drone’s 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 choose ; Predefine time control parameters for non-singularity; is the predefined time of the sliding surface; is a sign function; and ; Under the action of the non-singular predefined time sliding surface, the attitude tracking error exist Converges within time; 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, a non-singular predefined time sliding mode controller is obtained, and its expression is: ； ； in, The component torque of the quadrotor drone in the body coordinate system, i.e., the control input; The coupling term of the attitude model and the value of air resistance in the body coordinate system, ; , Predefine time control parameters for non-singularity; is the estimated value of the disturbance vector; The preset time for the approach phase; represents the Lyapunov function choice ; Under the action of non-singular predefined time sliding mode controller, the system state changes in predefined time Converges to the sliding surface and within a predefined time Within, the attitude angle of the quadrotor can track the expected value.

5. A non-singular sliding mode control device for a quadrotor drone, used to implement the non-singular sliding mode control method for a quadrotor drone according to any one of claims 1 to 4, characterized in that: include: The coordinate system establishment unit is used to establish the coordinate system and inertial coordinate system of the quadrotor drone body, and assumes that the quadrotor drone body structure is a rigid body with strict symmetry, uniform mass distribution, coincidence of center of mass and geometric center of gravity, and its mass and moment of inertia do not change with time; The attitude model building unit is used to build the attitude model of the quadrotor drone according to the rigid body motion law, taking into account the air resistance and external unknown disturbances, and uses the component torque of the quadrotor drone as the control input; The disturbance observer establishment unit is used to introduce auxiliary equations to construct a predefined time disturbance observer, and combine the Lyapunov function to quickly estimate external disturbances by adjusting the predefined time; a sliding mode controller establishing unit, configured to design a non-singular predefined time sliding mode controller based on the posture model and the predefined time disturbance observer; The attitude tracking control unit is used to control the quadrotor drone to perform attitude tracking according to the non-singular predefined time sliding mode controller, and control the attitude tracking error of the quadrotor drone to converge within a predefined time by adjusting the predefined time parameters.

6. A non-singular sliding mode control device for a quadrotor drone, characterized in that: The invention comprises a processor and a memory, wherein a computer program is stored in the memory, and the computer program can be executed by the processor to implement a non-singular sliding mode control method for a quadrotor drone as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-readable instructions, and 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 drone as described in any one of claims 1 to 4 is implemented.

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