Four-rotor unmanned aerial vehicle adaptive fault-tolerant control method based on event triggering

Abstract

The invention discloses a quad-rotor unmanned aerial vehicle adaptive fault-tolerant control method based on event triggering. For actuator multiplicative / additive faults caused by motor efficiency degradation, centroid offset and the like, an attitude-position unified dynamical model is established under external disturbance, and a position-attitude double-ring structure is adopted: a position ring generates an expected attitude and total thrust by using a radial basis function neural network (RBF) backstepping adaptive control; the attitude ring compensates a composite fault based on RBF backstepping adaptive control, introduces an event trigger mechanism, updates control input only when an error exceeds a threshold value, and maintains the control input at a zero order at other moments. A Lyapunov method proves that a closed-loop system realizes consistent final bounded stability in the presence of a composite fault and external disturbance, and a trigger interval right lower bound is given to avoid a Zeno phenomenon. According to the method, the trajectory tracking precision can be improved and the calculation and communication overhead can be reduced under the fault working condition without adding hardware, and a powerful reference is provided for specific implementation of engineering practice.

Description

An event-triggered adaptive fault-tolerant control method for quadrotor UAVs Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle error control, and specifically to an event-triggered adaptive fault-tolerant control method for a quadcopter unmanned aerial vehicle. Background Technology

[0002] Rotary-wing unmanned aerial vehicles (UAVs) are widely used in inspection, surveying, logistics, and public safety due to their simple structure, high maneuverability, and low takeoff and landing requirements. Traditional quadrotor control methods often employ a position-attitude dual-loop structure, using linear PID controllers or LQR controllers based on precise models for trajectory tracking. However, in real-world engineering environments, quadrotors are susceptible to various problems, such as multiplicative actuator failures caused by motor efficiency degradation and propeller damage; additive actuator failures caused by structural deformation, load changes, and center of mass shift; and external disturbances like wind and airflow disturbances further increasing model uncertainty. Under the combined effect of these faults and disturbances, conventional control methods are prone to performance degradation and even instability. Traditional fault-tolerant control methods typically require fault diagnosis modules or redundant sensors and actuators, resulting in high hardware costs and complex implementation. Furthermore, most existing fault-tolerant control laws update control inputs and adaptive parameters in real-time over continuous time, placing a heavy burden on computation and communication, which is detrimental to engineering applications on resource-constrained embedded platforms. Therefore, there is an urgent need for an adaptive fault-tolerant control method for quadrotor UAVs that can compensate for multiplicative / additive actuator faults and external disturbances, and reduce the control update frequency, without increasing hardware redundancy. Summary of the Invention

[0003] Purpose of the Invention: To address the problems mentioned in the background art, this invention discloses an event-triggered adaptive fault-tolerant control method for quadrotor unmanned aerial vehicles (UAVs). Considering multiplicative faults, additive faults, and external disturbances, the method achieves online compensation for unknown nonlinearities and faults through a position-attitude dual-loop structure and radial basis function (RBF) neural network backstepping adaptive control. Furthermore, an event-triggered mechanism is introduced into the attitude loop, updating the control input only when the error exceeds a set threshold, thereby improving trajectory tracking accuracy under fault conditions while reducing computational and communication overhead.

[0004] Technical solution:

[0005] This invention discloses an event-triggered adaptive fault-tolerant control method for a quadcopter unmanned aerial vehicle (UAV), the method comprising the following steps:

[0006] S1: Establish a six-DOF attitude-position dynamics model for a quadrotor UAV and a thrust and torque distribution motor speed model;

[0007] S2: Establish a unified fault model that includes multiplicative faults and additive faults;

[0008] S3: Construct a position-attitude cascade system based on the unified fault model, and divide the system into a position subsystem and an attitude subsystem;

[0009] S4: Select the current position vector and the desired position vector of the position subsystem to establish a position error system. The position subsystem introduces an RBF neural network and combines the backstepping method to design an adaptive fault-tolerant control law for the position loop to obtain virtual control quantities. Solve the virtual control quantities as the total thrust command and the desired pitch and roll angles, which serve as the reference inputs of the attitude subsystem.

[0010] S5: Based on the attitude subsystem, establish an equivalent system of angle error and fault, introduce RBF neural network, combine backstepping method to design attitude adaptive fault-tolerant control law, generate attitude control torque command, and obtain the speed command of each motor according to the total thrust command and the attitude control torque command.

[0011] S5.1: The attitude loop of the attitude adaptive fault-tolerant control law introduces an event triggering mechanism.

[0012] Furthermore, the six-DOF attitude-position dynamics model of the quadcopter UAV described in S1 is constructed as follows:

[0013]

[0014]

[0015]

[0016] in, The attitude angle of the quadcopter drone. Indicates the physical location of the quadcopter drone in space. These represent the lift, mass, and gravitational acceleration of the quadcopter, respectively. It is the moment of inertia of a quadcopter drone about its three axes. It is the angular velocity about the three axes. It is the torque about three axes;

[0017] The thrust and torque distribution motor speed model is constructed as follows:

[0018]

[0019] In the formula, It refers to the rotational speed of the four motors on a quadcopter drone. , These are the propeller thrust coefficient and torque coefficient, respectively. It is the distance from the center of the machine body to any motor.

[0020] Furthermore, the failure model for a quadcopter drone is as follows:

[0021]

[0022] In the formula, This is the actual output torque vector. The desired torque control vector is given by the attitude controller. For a multiplicative fault matrix, For additive fault vectors, for The identity matrix; the thrust control and attitude torque control variables are combined to form a unified fault model that includes multiplicative and additive faults, as follows:

[0023]

[0024] In the formula, the position vector velocity vector Attitude angle vector angular velocity vector Moment of inertia , , Total thrust control quantity.

[0025] Furthermore, the dynamic equations of the position subsystem and attitude subsystem described in S3 are as follows:

[0026] The dynamic equations of the position subsystem are as follows:

[0027]

[0028] In the formula, the position vector velocity vector , Total thrust control, the forces acting on the position subsystem are gravity and along the fuselage. The total thrust of the shaft determines the attitude angle. By rotation matrix Affects the direction of thrust;

[0029] The dynamic equations of the attitude subsystem are as follows:

[0030]

[0031] In the formula, the angular velocity vector Moment of inertia , This is the actual output torque vector. For external disturbances, the position subsystem generates total thrust based on the desired trajectory. The attitude subsystem tracks the desired attitude angle. And output attitude torque The two together constitute a position-attitude cascade system.

[0032] Furthermore, the construction of the position error system and the introduction of the RBF neural network in S4 specifically includes:

[0033] Select position subsystem state position ,speed The effects of actuator failure and external disturbances on the position loop are uniformly incorporated into the unknown nonlinear term. ;

[0034] Define the position tracking error and design the virtual control law Introducing the desired position vector Position error Construct Lyapunov functions ,right Differentiate, combine Design virtual control law ,make Contains , making China regarding The term is negative, thus obtaining the virtual control law. Stable position error;

[0035] Introducing speed error Obtain the error dynamics and define the velocity error. ,Will Substitution Get speed error dynamics Also obtain This will be used for the next step of the Lyapunov design.

[0036] Constructing Lyapunov functions ,exist Based on this, by introducing velocity error and RBF weights, we obtain:

[0037]

[0038] In the formula, The error matrix for weight estimation in the RBF neural network. It is a symmetric positive definite adaptive gain matrix;

[0039] Using RBF neural networks to approximate unknown nonlinear terms in the dynamics of position system errors With the derivative of the virtual control law Treat them all as unknown functions, that is... And using RBF neural networks to Perform online approximation. In the formula, .

[0040] Furthermore, the steps for designing the position loop adaptive fault-tolerant control law using the backstepping method described in S4 are as follows:

[0041] Design robust terms and virtual control quantities Robust term design for z2 The upper bound, used to offset approximation errors and external disturbances, is used to design the position controller output based on this:

[0042]

[0043] right Taking the derivative, we get:

[0044]

[0045] from Cross-start design weight adaptive law and add The correction term yields:

[0046]

[0047] Using the Cauchy-Schwarz inequality, inequality properties, and the upper bound of the RBF approximation error, we can finally obtain...

[0048] .

[0049] Furthermore, the construction of the angle error and fault equivalent system described in S5, and the introduction of the RBF neural network, specifically includes:

[0050] Based on the dynamic equations of the attitude subsystem Select attitude angle vector angular velocity vector To represent the system state, multiplicative faults of actuators, additive faults, and external disturbances are incorporated into the unknown nonlinear terms of the attitude subsystem and written in standard nonlinear form.

[0051] The desired attitude angle obtained from the solution For reference, the attitude angle error is defined. Construct the Lyapunov function for attitude angle error. Design virtual control laws ,

[0052] Based on the virtual control law, angular velocity error is introduced, and the angular velocity error is defined as follows: Differentiating and substituting into the dynamic equations of the attitude subsystem, we get:

[0053]

[0054] Separate the terms that are linearly related to the control input from the unknown nonlinear terms, and identify the multiplicative faults in the actuator. Additive faults External disturbances and derivatives of virtual control laws are all considered as unknown nonlinear functions in the same region. It can be written as:

[0055]

[0056] In the formula, It consists of attitude angle, angular velocity, and attitude control torque. Final simplification. for: ;

[0057] Constructing Lyapunov functions Introducing RBF weights, we get:

[0058]

[0059] In the formula, The error matrix for weight estimation in the RBF neural network. It is a symmetric positive definite adaptive gain matrix;

[0060] Using RBF neural networks to approximate unknown nonlinear terms and address multiplicative faults in actuators Additive faults External disturbances and derivatives of virtual control laws are all considered as unknown nonlinear functions in the same region. And using RBF neural networks to Perform online approximation:

[0061] ;

[0062] In the formula, It consists of attitude angle, angular velocity, and attitude control torque.

[0063] Furthermore, the steps for designing the attitude adaptive fault-tolerant control law using the backstepping method described in S5 are as follows:

[0064] Design robustness terms and attitude control torque ,right Design robust terms The control law is selected as follows:

[0065]

[0066] In the formula, Symmetric positive definite gain matrix, Robust compensation term, used to offset RBF approximation error and upper bound of faults and disturbances;

[0067] right Taking the derivative, we get:

[0068]

[0069] from Cross-start design weight adaptive law and add The correction term yields:

[0070]

[0071] Using the Cauchy-Schwarz inequality, inequality properties, and the upper bound of the RBF approximation error, we can finally obtain:

[0072] .

[0073] Furthermore, the specific steps in S5.1 include:

[0074] Design an event-triggered attitude control law, assuming the trigger sequence of the attitude loop is as follows: The event-triggered attitude control law is designed as follows:

[0075]

[0076] With the introduction of the event-triggered mechanism, control input is updated only at the trigger moment, and within adjacent trigger intervals... The value remains unchanged from the previous trigger moment. ;

[0077] Define attitude measurement error as Define the angular velocity measurement error Combine these two errors to construct a trigger error vector:

[0078]

[0079] Select state-related trigger rules: In the formula, design parameters When the above inequality is true for the first time, an event is determined to be triggered, and this moment is recorded as the next trigger moment. And update the attitude control torque in real time. and neural network weight estimation Simultaneous error Reset to zero, the trigger time sequence satisfies the following design:

[0080]

[0081] The adaptive law is updated in continuous-time form, that is: In the formula, It is a symmetric positive definite adaptive gain matrix, at the trigger time. Place Participate in calculating new control laws Between two consecutive triggers, It evolves continuously according to the differential equation, while the control torque remains constant. .

[0082] Beneficial effects:

[0083] 1. This invention incorporates actuator multiplicative faults, additive faults, and external disturbances into a unified dynamic framework, and performs control law design and compensation under the same model. It eliminates the need for additional fault diagnosis modules or redundant sensors and actuators for fault-tolerant control, thereby reducing the configuration threshold of this invention while enhancing the versatility and adaptability of the method.

[0084] 2. This invention introduces RBF neural networks and backstepping methods to design position loop adaptive fault-tolerant control rates and attitude adaptive fault-tolerant control rates, and performs online approximation and compensation for model uncertainties, unknown nonlinearities and equivalent fault / disturbance terms, thereby further improving trajectory / attitude tracking accuracy and enhancing fault tolerance robustness.

[0085] 3. This invention introduces an event-triggered update strategy into the attitude loop. During non-triggered periods, the control input is maintained by zero-order hold, reducing the number of control updates and lowering computational and communication overhead. At the same time, a positive lower bound is given for the trigger interval to avoid the Zeno phenomenon and further ensure engineering feasibility. To address the problem that the lack of control updates during the zero-order hold period may cause a decrease in compensation capability, the adaptive parameters are updated according to a continuous-time adaptive law, so that the approximation compensation capability continues to evolve, achieving a balance between "reducing update frequency" and "maintaining compensation effect". Attached Figure Description

[0086] Figure 1 is a block diagram of the overall operational structure of the method of the present invention;

[0087] Figure 2 is a schematic diagram of the quadcopter configuration and coordinate system of the present invention;

[0088] Figure 3 is a three-dimensional trajectory tracking simulation diagram of an embodiment of the present invention;

[0089] Figure 4 is a simulation diagram of three-axis position tracking according to an embodiment of the present invention;

[0090] Figure 5 is a simulation diagram of three-axis attitude angle tracking according to an embodiment of the present invention;

[0091] Figure 6 is a graph showing the event triggering time interval in an embodiment of the present invention. Detailed Implementation

[0092] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0093] As shown in Figure 1, this invention discloses an adaptive fault-tolerant control method for a quadrotor unmanned aerial vehicle based on event triggering. The method steps are as follows:

[0094] Step 1: Establish the six-DOF attitude-position dynamics model and the thrust and torque distribution motor speed model for the quadcopter UAV as follows:

[0095]

[0096]

[0097]

[0098] in, The attitude angle of the quadcopter drone. Indicates the physical location of the quadcopter drone in space. These represent the lift, mass, and gravitational acceleration of the quadcopter, respectively. It is the moment of inertia of a quadcopter drone about its three axes. It is the angular velocity about the three axes. It is the torque about three axes.

[0099] The relationship between the thrust and torque distribution motor speed in the “X” configuration is as follows:

[0100]

[0101] In the formula, It refers to the rotational speed of the four motors on a quadcopter drone. , These are the propeller thrust coefficient and torque coefficient, respectively. It is the distance from the center of the machine body to any motor.

[0102] Figure 2 shows the 'X' configuration of the quadcopter UAV and its body coordinate system, including the origin of the body coordinate system. Body coordinate axis The spatial arrangement of the four motors and the thrust they generate With rotation direction and angular velocity , in G represents the distance from the center of the machine body to the motor, and G is the direction of gravity.

[0103] Step 2: The fault model for the quadcopter drone is as follows:

[0104]

[0105] In the formula, This is the actual output torque vector. The desired torque control vector is given by the attitude controller. For a multiplicative fault matrix, For additive fault vectors, for Identity matrix. Based on the dynamic model described in step 1, the thrust control quantity and attitude torque control quantity are combined into a unified input vector and integrated with the fault model of the quadcopter UAV. Step 2 describes the following unified dynamic model:

[0106]

[0107] The nonlinear term F(X) and the control matrix G(X) are defined as follows:

[0108]

[0109] In the formula, the position vector velocity vector Attitude angle vector angular velocity vector Moment of inertia , , Total thrust control quantity.

[0110] The relationship between the Euler angle derivative and the body angular velocity is as follows:

[0111]

[0112] In the formula,

[0113]

[0114] Euler angles The rotation matrix from the body coordinate system to the ground coordinate system is defined as follows:

[0115]

[0116] Step 3: Divide the system into a position subsystem and an attitude subsystem, forming a position-attitude cascade system. The dynamic equations of the position subsystem are written as:

[0117]

[0118] In the formula, the position vector velocity vector , Total thrust control, the forces acting on the position subsystem are gravity and along the fuselage. The total thrust of the shaft determines the attitude angle. By rotation matrix It affects the direction of thrust.

[0119] The dynamic equations of the attitude subsystem are written as follows:

[0120]

[0121] In the formula, the angular velocity vector Moment of inertia , This is the actual output torque vector. This is due to external disturbances. The position subsystem generates total thrust based on the desired trajectory. The attitude subsystem tracks the desired attitude angle. And output attitude torque The two together constitute a position-attitude cascade system.

[0122] Step 4: For the position subsystem obtained in Step 3, select the current position vector and the desired position vector to establish a position error system; introduce a radial basis function neural network to approximate the unknown nonlinear terms in the position subsystem online, and design an adaptive fault-tolerant control law for the position loop using the backstepping method to obtain virtual control quantities. Solve the virtual control quantities into total thrust and desired pitch and roll angles, which are used as reference inputs for the attitude subsystem.

[0123] (1) Select the position subsystem state position ,speed :

[0124]

[0125] The effects of actuator failure and external disturbances on the position loop are uniformly incorporated into the unknown nonlinear term. , written as:

[0126]

[0127] In the formula, g(x) is the control gain, here , This is the virtual control quantity output by the position loop.

[0128] (2) Define the position tracking error and design the virtual control law. First, we introduce the desired position vector. Position error Construct Lyapunov functions ,right Differentiate, combine Design virtual control law ,make Contains , making China regarding The term is negative, thus obtaining the virtual control law. This stabilizes the position error.

[0129] (3) Introducing speed error To obtain the error dynamics, the velocity error is first defined. ,Will Substitution Get speed error dynamics Also obtain This will be used for the next step of the Lyapunov design.

[0130] (4) Constructing Lyapunov functions ,exist Based on this, by introducing velocity error and RBF weights, we obtain:

[0131]

[0132] In the formula, The error matrix for weight estimation in the RBF neural network. It is a symmetric positive definite adaptive gain matrix.

[0133] (5) Use RBF neural network to approximate the unknown nonlinear term, and reduce the unknown nonlinear term in the dynamic error of the position system. With the derivative of the virtual control law Treat them all as unknown functions, that is... And using RBF neural networks to Perform online approximation. In the formula, .

[0134] (6) Design robust terms and control laws virtual control quantity , This represents the virtual control quantity output by the position loop controller. As the control output of the position loop, it is used in subsequent calculations to obtain the total thrust and desired attitude angle (pitch / roll). The "control law" refers to the control algorithm / expression used to calculate this virtual control quantity u1; that is, the control quantity u1 is obtained through the control law. These two are not different control quantities, but rather two ways of expressing the same variable u1: the "output quantity" and the "control law that produces this output." First, robustness term design is performed on z2. The upper bound, used to offset approximation errors and external disturbances, is used to design the position controller output based on this:

[0135]

[0136] (7) Taking the derivative, we get:

[0137]

[0138] from Cross-start design weight adaptive law and add The correction term yields:

[0139]

[0140] (8) Using the Cauchy-Schwarz inequality, inequality properties, and the upper limit of the RBF approximation error, we can finally obtain

[0141]

[0142] By Lyapunov theory and the comparison principle, it can be proved that... The uniformity is eventually bounded, and the systematic error will converge to a point centered at the origin with a radius of... Within the specified region, it is demonstrated that the designed adaptive control law based on the RBF neural network can maintain system stability even with model uncertainties and external disturbances, and the error can be limited to an adjustable range. Due to the gain matrix... It is a symmetric positive definite matrix, and has positive constants. and constants Therefore, for the convenience of subsequent explanations, it will be... Designed for

[0143] (9) Assume that the attitude angle required to satisfy the control law is The position controller outputs a virtual control quantity. It needs to be converted into body attitude angle commands. (pitch angle) and (Roll angle). The following variation is derived from the position subsystem in step 1:

[0144]

[0145] The rotation matrix from the body coordinate system to the ground coordinate system described in step 2 is expressed as follows:

[0146]

[0147] Extracting the x and y components, we get:

[0148]

[0149] Here, virtual control variables are defined. , We can obtain:

[0150]

[0151] Rearranging the above equation into matrix form:

[0152]

[0153] Solving for the roll and pitch angles, we get:

[0154]

[0155]

[0156] Therefore, the total thrust can be obtained:

[0157]

[0158] In the formula, The second derivative of the desired height trajectory with respect to time, i.e., the desired... Axial acceleration.

[0159] Step 5: Using the attitude subsystem obtained in Step 3 and the desired attitude angle calculated in Step 4 as references, construct attitude angle error and angular velocity error. Equip actuator multiplicative faults, additive faults, and external disturbances as unknown nonlinear terms. Introduce an RBF neural network to approximate the unknown nonlinear terms online. Combine this with a backstepping method to design an attitude adaptive fault-tolerant control law and generate attitude control torque commands. Based on the total thrust command obtained in Step 4 and the attitude control torque commands, calculate the speed commands of each motor through a predetermined thrust and torque distribution relationship. The steps are as follows:

[0160] (1) Based on the dynamic equations of the attitude subsystem obtained in step 3 Select attitude angle vector angular velocity vector To represent the system state, the multiplicative faults of the actuators, additive faults, and external disturbances are uniformly incorporated into the unknown nonlinear terms of the attitude subsystem and written in standard nonlinear form, in preparation for subsequent adaptive control design.

[0161] (2) The desired attitude angle obtained from step 4 For reference, the attitude angle error is defined. Construct the Lyapunov function for attitude angle error. Design virtual control laws This is used to provide the desired angular velocity signal, so that the attitude angle error tends to converge under ideal conditions.

[0162] (3) Based on the virtual control law, angular velocity error is introduced, and the angular velocity error is defined as follows: Differentiating and substituting into the dynamic equations of the attitude subsystem, we get:

[0163]

[0164] Separate the terms that are linearly related to the control input from the unknown nonlinear terms, and identify the multiplicative faults in the actuator. Additive faults External disturbances and derivatives of virtual control laws are all considered as unknown nonlinear functions in the same region. It can be written as:

[0165]

[0166] In the formula, It consists of attitude angle, angular velocity, and attitude control torque. Final simplification. for: This will be used for the next step of the Lyapunov design.

[0167] (4) Constructing Lyapunov functions Introducing RBF weights, we get:

[0168]

[0169] In the formula, The error matrix for weight estimation in the RBF neural network. It is a symmetric positive definite adaptive gain matrix.

[0170] (5) Approximate the unknown nonlinear term with an RBF neural network to resolve the multiplicative fault of the actuator. Additive faults External disturbances and derivatives of virtual control laws are all considered as unknown nonlinear functions in the same region. And using RBF neural networks to To perform an online approximation,

[0171] .

[0172] In the formula, It consists of attitude angle, angular velocity, and attitude control torque.

[0173] (6) Design robust terms and attitude control torque First of all Design robust terms The control law is selected as follows:

[0174]

[0175] In the formula, Symmetric positive definite gain matrix, The robust compensation term is used to offset the upper bound of RBF approximation error and faults / disturbances.

[0176] (7) Taking the derivative, we get:

[0177]

[0178] from Cross-start design weight adaptive law and add The correction term yields:

[0179]

[0180] (8) Using the Cauchy-Schwarz inequality, inequality properties, and the upper limit of the RBF approximation error, we can finally obtain

[0181]

[0182] By Lyapunov theory and the comparison principle, it can be proved that... The uniformity is eventually bounded, and the systematic error will converge to a point centered at the origin with a radius of... Within a given region, the adaptive fault-tolerant stability of the attitude subsystem under multiplicative faults, additive faults, and external disturbances is demonstrated, and the error can be limited to an adjustable range. Due to the gain matrix... It is a symmetric positive definite matrix, and has positive constants. and constants Therefore, for the convenience of subsequent explanations, it will be... Designed for

[0183] (9) The total thrust obtained in step 4 The attitude control torque obtained in step 5 Combined into control vector Based on the thrust and torque distribution relationship given in step 1,

[0184]

[0185] In the formula, It refers to the rotational speed of the four motors on a quadcopter drone. , These are the propeller thrust coefficient and torque coefficient, respectively. This is the distance from the center of the machine body to any motor. Solving for this gives the square of the angular velocity of each motor. Then, the square root of each component is taken and saturation processing is performed in conjunction with the physical constraints of the motor to obtain the final speed command for the four motors. This enables the distribution of total thrust and attitude torque to motor speed.

[0186] Based on the attitude adaptive fault-tolerant controller established in step 5, an event triggering mechanism is introduced into the attitude loop to construct event triggering conditions. When the triggering conditions are met, the attitude control torque and neural network weight estimation are updated. The control input is maintained between adjacent triggering times, and the adaptive parameters are continuously updated according to a predetermined adaptive law. Stability analysis of the position-attitude cascade system is performed based on the unified Lyapunov function, proving that under the presence of actuator multiplicative faults, additive faults, and external disturbances, the closed-loop system error is consistent and eventually bounded and stable. Step 6 includes the following sub-steps:

[0187] (1) Based on the attitude control law obtained in step 5, design an event-triggered attitude control law. First, assume that the triggering time sequence of the attitude loop is as follows: The event-triggered attitude control law is designed as follows:

[0188]

[0189] With the introduction of the event-triggered mechanism, control input is updated only at the trigger moment, and within adjacent trigger intervals... The value remains unchanged from the previous trigger moment. Therefore, we can conclude that:

[0190]

[0191] (2) Since the attitude control law uses a "hold value" at the triggering moment, it is necessary to define the measurement error and the triggering error. This invention defines the attitude measurement error as follows: Define the angular velocity measurement error Then, these two errors are combined to construct a trigger error vector:

[0192]

[0193] (3) In order to reduce the number of triggers while ensuring control performance, the present invention selects the following state-related triggering rules: In the formula, design parameters When the above inequality is true for the first time, an event is determined to be triggered, and this moment is recorded as the next trigger moment. And update the attitude control torque in real time. and neural network weight estimation Simultaneous error Reset to zero. The trigger time sequence satisfies the following design:

[0194]

[0195] (4) Considering the need for continuous estimation of neural network weights, the adaptive law is still updated in continuous time form, that is: In the formula, It is a symmetric positive definite adaptive gain matrix. The difference between this and attitude control law design is as follows: at the trigger time... Place Participate in calculating new control laws Between two consecutive triggers, It evolves continuously according to the differential equation, while the control torque remains constant. .

[0196] (5) Lyapunov functions for position and orientation obtained in steps 4 and 5 and The unified Lyapunov function for designing position-attitude cascade systems is:

[0197]

[0198] Under the event-triggered control law, Differentiation can be decomposed into ,

[0199] In the formula, These correspond to the Lyapunov derivatives of position and attitude under a continuous control law, respectively. The influence of the control law on the Lyapunov derivative is introduced by the event triggering. Furthermore, because... , Therefore:

[0200]

[0201] This term can be estimated using the Lipschit property of the attitude control law, assuming the existence of a constant. , making Thus Designed for In the formula This is a constant introduced in the analysis to estimate the upper bound of the event-triggered hold error term, and is not used as an adjustment parameter of the control law.

[0202] (6) Based on the event triggering conditions designed in sub-step 3 of step 6. and the design of sub-step 5 We can obtain:

[0203]

[0204] In sub-step 5, the derivative of the unified Lyapunov function for the position-attitude cascade system satisfies

[0205]

[0206] In the formula, For the reason The constant obtained by combination. According to the comparison principle, under the presence of multiplicative faults, additive faults, and external disturbances in the actuator, the error state of the system will eventually become bounded and stable.

[0207] (7) First, from the adaptive fault-tolerant control law in steps 4 and 5 and the attitude loop event-triggered control law, it can be seen that within the closed-loop bounded region, the attitude angle and angular velocity and their derivatives are bounded. Further, from... As can be seen from the definition, there exists a constant. This makes it possible for all ,have The error is reset to zero at the instant of each trigger. Then in any trigger interval Inside And because the triggering condition requires that, The moment is first satisfied

[0208] Therefore there is This gives us the lower bound of the trigger interval. It can be concluded that the triggering interval of the event has a strict positive lower bound. This means that the number of triggers is limited within any finite time interval, thus effectively avoiding the Zeno phenomenon.

[0209] To reduce the number of triggers while ensuring control performance, this invention selects the following state-related triggering rules: , .

[0210] The simulation results of the control system are as follows:

[0211] Figure 3 shows the three-dimensional trajectory tracking results under the method of this invention. It can be seen that the actual flight trajectory basically coincides with the desired spiral trajectory. Figure 4 shows the three-axis position tracking curve, with the position error remaining within a small range. Figure 5 shows the tracking of roll angle, pitch angle, and yaw angle. The attitude can quickly converge to the desired value even with actuator failure and disturbances. Figure 6 shows the interval between event triggering moments. It can be seen that after the system enters steady state, the control update interval is significantly larger than the integral step size, indicating that this invention can reduce the control update frequency while ensuring control performance, thereby reducing the computational and communication burden. In summary, the method of this invention can still maintain good position and attitude tracking performance and has a low control update frequency even with combined actuator failures and external disturbances. Compared with traditional periodic adaptive control methods, it has better fault tolerance and engineering practical value.

[0212] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent transformations or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. An event-triggered adaptive fault-tolerant control method for a quadrotor unmanned aerial vehicle, characterized in that, The method includes the following steps: S1: Establish a six-degree-of-freedom attitude-position dynamics model and a thrust and torque distribution motor speed model for a quadcopter UAV; S2: Establish a unified fault model that includes multiplicative and additive faults; S3: Construct a position-attitude cascade system based on the unified fault model, and divide the system into a position subsystem and an attitude subsystem. S4: Select the current position vector and the desired position vector of the position subsystem to establish a position error system. The position subsystem introduces an RBF neural network and designs an adaptive fault-tolerant control law for the position loop using the backstepping method to obtain virtual control quantities. Solve the virtual control quantities as the total thrust command and the desired pitch angle and roll angle, which serve as the reference inputs for the attitude subsystem. S5: Based on the attitude subsystem, establish an equivalent system for angular error and fault. Introduce an RBF neural network and design an adaptive fault-tolerant control law for the attitude using the backstepping method to generate attitude control torque commands. Calculate the speed commands of each motor based on the total thrust command and the attitude control torque commands. S5.1: The attitude loop of the adaptive fault-tolerant control law for the attitude introduces an event triggering mechanism.

2. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 1, characterized in that, The six-DOF attitude-position dynamics model of the quadcopter UAV described in S1 is constructed as follows: ； ； ;in, The attitude angle of the quadcopter drone. Indicates the physical location of the quadcopter drone in space. These represent the lift, mass, and gravitational acceleration of the quadcopter, respectively. It is the moment of inertia of a quadcopter drone about its three axes. It is the angular velocity about the three axes. It is the torque around the three axes; the thrust and torque distribution motor speed model is constructed as follows: In the formula, It refers to the rotational speed of the four motors on a quadcopter drone. , These are the propeller thrust coefficient and torque coefficient, respectively. It is the distance from the center of the machine body to any motor.

3. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 1, characterized in that, The failure model for a quadcopter drone is as follows: In the formula, This is the actual output torque vector. The desired torque control vector is given by the attitude controller. For a multiplicative fault matrix, For additive fault vectors, for The identity matrix; the thrust control and attitude torque control variables are combined to form a unified fault model that includes multiplicative and additive faults, as follows: In the formula, the position vector velocity vector Attitude angle vector angular velocity vector Moment of inertia ， ， Total thrust control quantity.

4. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 3, characterized in that, The dynamic equations of the position subsystem and attitude subsystem described in S3 are as follows: Dynamic equation of the position subsystem: In the formula, the position vector velocity vector ， Total thrust control, the forces acting on the position subsystem are gravity and along the fuselage. The total thrust of the shaft determines the attitude angle. By rotation matrix Influences the thrust direction; the dynamic equations of the attitude subsystem: In the formula, the angular velocity vector Moment of inertia ， This is the actual output torque vector. For external disturbances, the position subsystem generates total thrust based on the desired trajectory. The attitude subsystem tracks the desired attitude angle. And output attitude torque The two together constitute a position-attitude cascade system.

5. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 4, characterized in that, S4 The construction of the position error system and its introduction into the RBF neural network specifically includes: selecting the position subsystem state position. ,speed The effects of actuator failure and external disturbances on the position loop are uniformly incorporated into the unknown nonlinear term. Define the position tracking error and design the virtual control law. Introducing the desired position vector Position error Construct Lyapunov functions ,right Differentiate, combine Design virtual control law ,make Contains , making China regarding The term is negative, thus obtaining the virtual control law. Stabilizing position error; introducing velocity error Obtain the error dynamics and define the velocity error. ,Will Substitution Get speed error dynamics Also obtain This is used for the next step of Lyapunov design; constructing Lyapunov functions. ,exist Based on this, by introducing velocity error and RBF weights, we obtain: In the formula, The error matrix for weight estimation in the RBF neural network. The gain matrix is ​​a symmetric positive definite adaptive gain matrix; the unknown nonlinear term is approximated using an RBF neural network, thus reducing the unknown nonlinear term in the dynamic error of the position system. With the derivative of the virtual control law Treat them all as unknown functions, that is... And using RBF neural networks to Perform online approximation. In the formula, 。 6. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 5, characterized in that, The steps for designing the position loop adaptive fault-tolerant control law using the backstepping method described in S4 are as follows: Design the robust term and the virtual control quantity. Robust term design for z2 The upper bound, used to offset approximation errors and external disturbances, is used to design the position controller output based on this: ； right Taking the derivative, we get: ;from Cross-start design weight adaptive law and add The correction term yields: ； Using the Cauchy-Schwarz inequality, inequality properties, and the upper bound of the RBF approximation error, we can finally obtain... 。 7. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 6, characterized in that, S5 describes the construction of the angular error and fault equivalent system and the introduction of an RBF neural network, specifically including: based on the attitude subsystem dynamic equations... Select attitude angle vector angular velocity vector For the system state, multiplicative faults of actuators, additive faults, and external disturbances are uniformly incorporated into the unknown nonlinear terms of the attitude subsystem and written in standard nonlinear form to obtain the desired attitude angle. For reference, the attitude angle error is defined. Construct the Lyapunov function for attitude angle error. Design virtual control laws Based on the virtual control law, angular velocity error is introduced, and the angular velocity error is defined as follows: Differentiating and substituting into the dynamic equations of the attitude subsystem, we get: Separate the terms that are linearly related to the control input from the unknown nonlinear terms, and identify multiplicative faults in the actuator. Additive faults External disturbances and derivatives of virtual control laws are all considered as unknown nonlinear functions in the same region. It can be written as: In the formula, It consists of attitude angle, angular velocity, and attitude control torque. Final simplification. for: Construct Lyapunov functions Introducing RBF weights, we get: In the formula, The error matrix for weight estimation in the RBF neural network. The gain matrix is ​​a symmetric positive definite adaptive gain matrix; an RBF neural network is used to approximate the unknown nonlinear term, and the multiplicative fault of the actuator is addressed. Additive faults External disturbances and derivatives of virtual control laws are all considered as unknown nonlinear functions in the same region. And using RBF neural networks to Perform online approximation: In the formula, It consists of attitude angle, angular velocity, and attitude control torque.

8. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 7, characterized in that, The steps for designing the attitude adaptive fault-tolerant control law using the backstepping method described in S5 are as follows: Design the robust term and attitude control torque. ,right Design robust items The control law is selected as follows: In the formula, Symmetric positive definite gain matrix, Robust compensation term, used to offset RBF approximation error and upper bound of faults and disturbances; right Taking the derivative, we get: ;from Cross-start design weight adaptive law and add The correction term yields: Using the Cauchy-Schwarz inequality, inequality properties, and the upper bound of the RBF approximation error, we can finally obtain: 。 9. The event-triggered adaptive fault-tolerant control method for quadrotor UAVs according to claim 8, characterized in that, The specific steps in S5.1 include: designing an event-triggered attitude control law, assuming the triggering sequence of the attitude loop is as follows. The event-triggered attitude control law is designed as follows: With the introduction of the event-triggered mechanism, control input is updated only at the trigger moment, and within adjacent trigger intervals... The value remains unchanged from the previous trigger time. The attitude measurement error is defined as... Define the angular velocity measurement error Combine these two errors to construct a trigger error vector: Select state-related triggering rules: In the formula, design parameters When the above inequality is true for the first time, an event is determined to be triggered, and this moment is recorded as the next trigger moment. And update the attitude control torque in real time. and neural network weight estimation Simultaneous error Reset to zero, the trigger time sequence satisfies the following design: The adaptive law is updated in continuous-time form, that is: In the formula, It is a symmetric positive definite adaptive gain matrix, at the trigger time. Place Participate in calculating new control laws Between two consecutive triggers, It evolves continuously according to the differential equation, while the control torque remains constant. 。

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