Fault-tolerant control algorithm for multi-rotor aerial rescue unmanned aerial vehicle

Abstract

The application discloses a fault-tolerant control algorithm for a multi-rotor aerial rescue unmanned aerial vehicle, and aims at solving the problem that the multi-rotor aerial rescue unmanned aerial vehicle cannot continue to complete a rescue task due to actuator failure when performing rescue. The method firstly establishes a basic mathematical model of the multi-rotor aerial rescue unmanned aerial vehicle without failure. Then, the influence of actuator failure on the basic mathematical model is considered, and a mathematical model of the multi-rotor aerial rescue unmanned aerial vehicle with actuator failure is established. An actuator failure observer is designed to observe actuator failure information, and the obtained failure information is transmitted to a position subsystem controller and an attitude subsystem controller. Finally, a control law of the multi-rotor aerial rescue unmanned aerial vehicle is designed. The application can be used for fault-tolerant control of the multi-rotor aerial rescue unmanned aerial vehicle with actuator failure.

Description

Technical Field

[0001] This invention addresses the issue of actuator failures that can occur when multi-rotor aerial rescue drones perform aerial rescue missions. It proposes an actuator failure-tolerant control algorithm, which belongs to the field of fault-tolerant control. Background Technology

[0002] When multi-rotor aerial rescue drones perform aerial rescue missions in scenarios such as fires, mountainous areas, oceans, and earthquake ruins, actuator malfunctions can occur, causing the drone to malfunction. Therefore, designing actuator fault-tolerant control algorithms for multi-rotor aerial rescue drones is crucial. Summary of the Invention

[0003] This invention addresses the issue of actuator failure in multi-rotor aerial rescue drones during rescue missions. The aim is to observe fault information through an observer and transmit the fault information to a fractional-order sliding mode controller to reconstruct the control law, ensuring that the drone can perform roll, pitch, and yaw movements while maintaining sufficient lift.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: First, a mathematical model of actuator failure in a multi-rotor aerial rescue UAV is established. Then, an actuator failure observer is built to obtain the UAV's failure information. Finally, controllers are designed for the UAV's position and attitude subsystems respectively, and the control is reconstructed using the failure information obtained from the observer.

[0005] The control method includes the following steps: Step 1: Establish a mathematical model for actuator failure in a multi-rotor aerial rescue drone, which includes the following steps; Step 1.1: Establish a mathematical model for actuator-less failure of a multi-rotor aerial rescue drone: Where x, y, and z are the position coordinates of the centroid of the multi-rotor aerial rescue drone; θ, γ, and ψ are the Euler angles of the multi-rotor aerial rescue drone; u1, u2, u3, and u4 are the control inputs for the altitude, roll, pitch, and yaw channels of the multi-rotor aerial rescue drone, respectively; m is the mass of the multi-rotor aerial rescue drone; I xx I yy I zz Let x, y, and z be the moments of inertia of the multi-rotor aerial rescue drone in the x, y, and z axes, respectively; g be the gravitational acceleration of the multi-rotor aerial rescue drone; Step 1.2: Establish a mathematical model of actuator failure for the multi-rotor aerial rescue drone. Mathematical equations after introducing fault terms Where, d x d y d z d θ d γ d ψ External interference with multi-rotor aerial rescue drones; i (i = 1, 2, 3) are the control inputs for the multi-rotor aerial rescue drone under fault-free conditions; u x u y u z u θ u γ u ψ This is an actuator fault item. Let u f =[u x u y u z u θ u γ u ψ ] T And there is u i and u f The expression: Further rewriting equation (2) yields: Among them, o i The fault impact factor, fault impact factor o i The condition is satisfied that 0 ≤ o1(t) ≤ 1. When o1(t) = 0, all actuators experience multiplicative faults. When o1(t) = 1, all actuators operate normally, and the fault impact factors o2, o3, and o4 ≥ 1. Impact factor o i The specific expression is as follows: Step 2, establish an actuator fault observer: Combining the fault models (5) and (6) of multi-rotor aerial rescue UAVs, Equation (7) is designed as an actuator fault observer. in, The observed value is the disturbance caused by the actuator fault, and this value satisfies... The actuator fault observer observation error is defined as follows: Theorem 2.1: If there exists a symmetric matrix P = P T >0, Q>0, L∈R 12×12 ,constant If γ > 0, then G can be derived from equation (9) to form equation (10). G = (PB) T C -1 (10) To address multiplicative actuator faults, a fault estimation algorithm for multirotor aerial rescue UAVs is designed as follows: Where α1 is the adaptive adjustment parameter. When the observer's state error... There is an error in the estimation of actuator failure factors. To avoid unstable observer behavior when the error approaches zero, an external perturbation with a smooth sign function is designed to be adaptively applied as follows: Where α3 is a positive number; the value of Δ is 0.001; Choose the Lyapunov function: Differentiating the Lyapunov function in the above equation, we get: Define H1 = P T e x , From Lemma 2.1 and Assumption 2.2, we can obtain: Let Θ = (A - LC) T P+P(A-LC), Equation (14) can be further simplified to obtain: Let α3 = η in equation (16), then we have: By mathematically deriving the second term on the right side of equation (16), we can obtain: According to hypothesis 2.1, there exist positive constants. satisfy Furthermore, based on equations (17) and (18), we have the following expression: Based on the Lyapunov stability criterion, an observer designed for actuator failure can ensure the residual e. x It is bounded and convergent; Step 3: Design control laws for the position subsystem of the multi-rotor aerial rescue UAV: Dynamic model of the position subsystem when the actuator fails: in, This is the control input for the altitude channel of the UAV system in case of actuator failure. Define the virtual control input for the position subsystem of the multi-rotor aerial rescue UAV: Combining equations (20) and (21), we can obtain: In the formula: P = [xyz] T The matrix represents the position coordinates of a multi-rotor aerial rescue drone. d p =[d x d y d z ] T G = [0 0 g] T Define the position tracking error of a multi-rotor aerial rescue drone: e p =PP d (twenty three) In the formula: P d =[x d y d z d ] T Desired location coordinates for a multi-rotor aerial rescue drone Choose the following fractional integral sliding surface: In the formula: s1=[s x s y s z ] T -1 < r1 < 0; c1, β p h p positive number Differentiating equation (24) above, we have: make Then we have: The fractional-order sliding mode reaching law differs significantly from the traditional sliding mode reaching law in both theory and application. This method is defined using a fractional-order calculus equation. By adjusting the coefficients k2 and the fractional order r1, the velocity at which the system reaches the sliding surface can be precisely controlled. The fractional-order sliding mode reaching law chosen for this purpose is: In the formula: k2>0. Combining equations (26) and (27), we can obtain: Define separately and For the total mass m and external disturbance d of the multi-rotor aerial rescue drone system p The estimated value. To make the multi-rotor aerial rescue UAV with actuator failure robust to mass changes and external disturbances, an adaptive control strategy is combined with a fault-tolerant controller. Therefore, the position control input in the event of actuator failure... for: Substituting equations (28) and (29) into equation (25) yields: For the quality of disturbances and changes caused by the external environment of the UAV, the adaptive law is designed as follows: In the formula: γ1 and γ2 are positive constants; Combining equations (28) and (29), we can obtain: Because there is Therefore, the following result can be derived: To address disturbances and changes in mass caused by the external environment, the deviations of disturbance and mass are defined: In the formula: Because changes in external environmental disturbances and the overall mass of the drone change slowly, therefore... To demonstrate the stability of the position-tolerant controller for the designed multi-rotor aerial rescue UAV, the Lyapunov function is designed as follows: Differentiating the Lyapunov function (35) above and substituting equation (30) into the derivative of the Lyapunov function, we have: Substituting the adaptive law (31) into the above equation (36), we have: Since -1 < r1 < 0, we have so Therefore, the controlled system (20) under study reaches a steady state within a specified finite time range and maintains that state; And because Equation (33) can be rewritten as: It can be derived from equations (5) and (21) that: Furthermore, the control law for position-tolerant control can be derived: At the same time, due to γ d θ d Since the variation is small, the arctangent function can be used to obtain γ. d θ d The value of can be obtained. The target control signal for the actuator fault attitude subsystem can then be obtained: Step 4: Design control laws for the attitude subsystem of the multi-rotor aerial rescue UAV: A matrix-form attitude subsystem model for actuator failure: Define the attitude tracking error of a multi-rotor aerial rescue drone: e χ =χ-χ d (44) Design the following sliding surface: In the formula: s2=[s θ s γ s ψ ] T -1 < r2 < 0; c2, β χ h χ Non-zero positive numbers Differentiating equation (45) above, we have: Choose the following fractional sliding mode reaching law: In the formula: k4 > 0. Substituting equation (43) into equation (46) gives: To address the disturbances d caused by external environmental influences to the attitude subsystem χ Design an adaptive law for attitude perturbation: In the formula: γ3 is a positive number. Combining equations (47) and (49), the attitude controller input for a fault in the attitude subsystem of a multi-rotor aerial rescue UAV can be obtained as: Based on the designed fault observer, the estimation of the actuator fault impact factor is as follows: and The following result can be derived: Combining equations (39) and (51), the specific inputs to the attitude controller can be obtained as follows: The external disturbance estimation error of the attitude subsystem is defined as: To prove the stability of the attitude fault-tolerant controller for a multi-rotor aerial rescue UAV, a Lyapunov function is designed: Differentiating the Lyapunov function (56) above and substituting equation (48) into the derivative of the Lyapunov function, we have: Substituting the adaptive law (49) into the above equation (57), we have: And because when -1 < r2 < 0, we have Then we have: Therefore, the attitude subsystem (43) of the multi-rotor air rescue UAV studied reaches a steady state within a specified finite time range and maintains that state.

[0006] The present invention has the following advantages: (1) This invention converts actuator failure into its impact on four control channels, and obtains a mathematical model of the UAV after actuator failure; (2) The present invention estimates the actuator fault information through an observer and transmits the estimation result to the controller to realize the reconfiguration of the controller; (3) The controller adopts a fractional sliding mode control algorithm with strong robustness, which enables the UAV to perform tasks more stably. Attached Figure Description

[0007] Figure 1 This is a fault-tolerant control block diagram; Figures 2-5 A graph showing the impact factors of actuator failure; Figure 6 This is a 3D curve tracking diagram of the drone; Figures 7-9 The graph shows the x, y, and z position tracking curves of the UAV. Figures 10-12 The Euler angle tracking curve for the UAV; Figure 13 This is a plot of the drone's position error curve. Figure 14 This is a graph showing the attitude error of the UAV. Detailed Implementation

[0008] The control method of the present invention will be further explained and described with reference to the accompanying drawings.

[0009] The fault-tolerant control algorithm for multi-rotor aerial rescue UAVs provided in this application includes the following process: (a) Establishing a mathematical model for actuator failure in a multi-rotor aerial rescue drone, specifically including the following steps. Where x, y, and z are the position coordinates of the centroid of the multi-rotor aerial rescue drone; θ, γ, and ψ are the Euler angles of the multi-rotor aerial rescue drone; u1, u2, u3, and u4 are the control inputs for the altitude, roll, pitch, and yaw channels of the multi-rotor aerial rescue drone, respectively; m is the mass of the multi-rotor aerial rescue drone; I xx I yy I zz , , and , respectively, represent the moments of inertia of the multi-rotor aerial rescue drone in the x, y, and z axes; g is the gravitational acceleration of the multi-rotor aerial rescue drone; and the mathematical equations after introducing fault terms. Where, d x d y d z d θ d γ d ψ External interference with multi-rotor aerial rescue drones; i (i = 1, 2, 3) are the control inputs for the multi-rotor aerial rescue drone under fault-free conditions; u x u y u z u θ u γ u ψ This is an actuator fault item. Let u f =[ux u y u z u θ u γ u ψ ] T And there is u i and u f The expression: Further rewriting equation (2) yields: Among them, o i The fault impact factor, fault impact factor o i The condition is satisfied that 0 ≤ o1(t) ≤ 1. When o1(t) = 0, all actuators experience multiplicative faults. When o1(t) = 1, all actuators operate normally, and the fault impact factors o2, o3, and o4 ≥ 1. Impact factor o i The specific expression is as follows: (b) Establish an actuator fault observer: Combining the fault models (5) and (6) of multi-rotor aerial rescue UAVs, Equation (7) is designed as an actuator fault observer: in, The observed value is the disturbance caused by the actuator fault, and this value satisfies... The actuator fault observer observation error is defined as follows: Theorem 2.1: If there exists a symmetric matrix P = P T >0, Q>0, L∈R 12×12 ,constant If γ > 0, then G can be derived from equation (9) to form equation (10). G = (PB) T C -1 (10) To address multiplicative actuator faults, a fault estimation algorithm for multirotor aerial rescue UAVs is designed as follows: Where α1 is the adaptive adjustment parameter. When the observer's state error... There is an error in the estimation of actuator failure factors. To avoid unstable observer behavior when the error approaches zero, an external perturbation with a smooth sign function is designed to be adaptively applied as follows: Where α3 is a positive number; the value of Δ is 0.001. Choose the Lyapunov function: Differentiating the Lyapunov function in the above equation, we get: Define H1 = P T e x , From Lemma 2.1 and Assumption 2.2, we can obtain: Let Θ = (A - LC) T P+P(A-LC), Equation (14) can be further simplified to obtain: Let α3 = η in equation (16), then we have: By mathematically deriving the second term on the right side of equation (16), we can obtain: According to hypothesis 2.1, there exist positive constants. satisfy Furthermore, based on equations (17) and (18), we have the following expression: Based on the Lyapunov stability criterion, an observer designed for actuator failure can ensure the residual e. x It is bounded and convergent. (c) Design of control laws for the position subsystem of multi-rotor aerial rescue UAVs: Dynamic model of the position subsystem when the actuator fails: in, This is the control input for the altitude channel of the UAV system in case of actuator failure. Define the virtual control input for the position subsystem of the multi-rotor aerial rescue UAV: Combining equations (20) and (21), we can obtain: In the formula: P = [xyz]T The matrix represents the position coordinates of a multi-rotor aerial rescue drone. d p =[d x d y d z ] T G = [00g] T Define the position tracking error of a multi-rotor aerial rescue drone: e p =PP d (twenty three) In the formula: P d =[x d y d z d ] T Desired location coordinates for a multi-rotor aerial rescue drone Choose the following fractional integral sliding surface: In the formula: s1=[s x s y s z ] T -1 < r1 < 0; c1, β p h p positive number Differentiating equation (24) above, we have: make Then we have: The fractional-order sliding mode reaching law differs significantly from the traditional sliding mode reaching law in both theory and application. This method is defined using a fractional-order calculus equation. By adjusting the coefficients k2 and the fractional order r1, the velocity at which the system reaches the sliding surface can be precisely controlled. The fractional-order sliding mode reaching law chosen for this purpose is: In the formula: k2>0. Combining equations (26) and (27), we can obtain: Define separately and For the total mass m and external disturbance d of the multi-rotor aerial rescue drone system p The estimated value. To make the multi-rotor aerial rescue UAV with actuator failure robust to mass changes and external disturbances, an adaptive control strategy is combined with a fault-tolerant controller. Therefore, the position control input in the event of actuator failure... for: Substituting equations (28) and (29) into equation (25) yields: For the quality of disturbances and changes caused by the external environment of the UAV, the adaptive law is designed as follows: In the formula: γ1 and γ2 are positive constants. Combining equations (28) and (29), we can obtain: Because there is Therefore, the following result can be derived: To address disturbances and changes in mass caused by the external environment, the deviations of disturbance and mass are defined: In the formula: Because changes in external environmental disturbances and the overall mass of the drone change slowly, therefore... To demonstrate the stability of the position-tolerant controller for the designed multi-rotor aerial rescue UAV, the Lyapunov function is designed as follows: Differentiating the Lyapunov function (35) above and substituting equation (30) into the derivative of the Lyapunov function, we have: Substituting the adaptive law (31) into the above equation (36), we have: Since -1 < r1 < 0, we have so Therefore, the controlled system (20) under study reaches a steady state within a specified finite time range and maintains that state; And because Equation (33) can be rewritten as: It can be derived from equations (5) and (21) that: Furthermore, the control law for position-tolerant control can be derived: At the same time, due to γ d θd Since the variation is small, the arctangent function can be used to obtain γ. d θ d The value of can be obtained. The target control signal for the actuator fault attitude subsystem can then be obtained: (d) Design of control laws for the attitude subsystem of multi-rotor aerial rescue UAVs: A matrix-form attitude subsystem model for actuator failure: Define the attitude tracking error of a multi-rotor aerial rescue drone: e χ =χ-χ d (44) Design the following sliding surface: In the formula: s2=[s θ s γ s ψ ] T -1 < r2 < 0; c2, β χ h χ It is a non-zero positive number; Differentiating equation (45) above, we have: Choose the following fractional sliding mode reaching law: In the formula: k4 > 0. Substituting equation (43) into equation (46) gives: To address the disturbances d caused by external environmental influences to the attitude subsystem χ Design an adaptive law for attitude perturbation: In the formula: γ3 is a positive number. Combining equations (47) and (49), the attitude controller input for a fault in the attitude subsystem of a multi-rotor aerial rescue UAV can be obtained as: Based on the designed fault observer, the estimation of the actuator fault impact factor is as follows: and The following result can be derived: Combining equations (39) and (51), the specific inputs to the attitude controller can be obtained as follows: The external disturbance estimation error of the attitude subsystem is defined as: To prove the stability of the attitude fault-tolerant controller for a multi-rotor aerial rescue UAV, a Lyapunov function is designed: Differentiating the Lyapunov function (56) above and substituting equation (48) into the derivative of the Lyapunov function, we have: Substituting the adaptive law (49) into the above equation (57), we have: And because when -1 < r2 < 0, we have Then we have: Therefore, the attitude subsystem (43) of the multi-rotor air rescue UAV studied reaches a steady state within a specified finite time range and maintains that state.

[0010] To verify the effectiveness of this invention, the following experiments and analyses were conducted: To verify the performance of the designed fault-tolerant control, the simulation time was set to 30 seconds, and a spiral ascent trajectory was designed with the following expected values:

[0011] The initial positions of the multi-rotor aerial rescue drone are x0 = 0, y0 = 0, z0 = 0, and the initial attitude angles are θ0 = γ0 = ψ0 = 0.

[0012] The fault-tolerant control parameters of the position subsystem of the multi-rotor aerial rescue UAV are set as c1 = 0.9, r1 = 0.9, β p =0.9, h p =10, k2=4, γ1=80, γ2=1.2, d p =0.2sin(t).

[0013] The fault-tolerant control parameters of the position and attitude subsystem of the multi-rotor aerial rescue UAV are set as c2 = 1.5, r2 = 0.9, β χ =1.5, h χ =10, k4=2, γ3=80, d χ =0.2sin(t).

[0014] The observer parameters are set to η = 2.2, α1 = 3.2, and P = 15.07 × I. 12×12 , γ = 3.8.

[0015] To simulate actuator failures caused by propellers, motors, and other equipment during a multi-rotor aerial rescue drone's operation, the simulation was performed as follows: At 5 seconds, the drone's No. 1 motor experienced a 30% multiplicative loss, while the other motors operated normally. At 10 seconds, the drone's No. 9 motor experienced a 30% multiplicative loss, at which point both the upper and lower coaxial motors failed simultaneously, while the other motors continued to operate normally. The simulation results are shown in the curves below. Figures 2-14 As shown; Figures 2-5 This demonstrates how a designed observer can estimate actuator malfunctions when a multi-rotor aerial rescue drone is spiraling upwards. Figure 6 The three-dimensional motion trajectory of a multi-rotor aerial rescue drone during its spiral ascent is shown. Figures 7-9 This demonstrates the tracking capabilities of the position subsystem of a multi-rotor aerial rescue drone during its spiral ascent motion. Figures 10-12 The tracking of the attitude subsystem of a multi-rotor aerial rescue drone during spiral ascent was demonstrated. Figures 13-14 The study further demonstrates the position and attitude errors of a multi-rotor aerial rescue drone within a 0-30s timeframe. It can be observed that when an actuator malfunctions in the multi-rotor aerial rescue drone system, the observer accurately estimates the fault value, and the drone's position and attitude accurately track the expected value. Only when an actuator malfunction occurs is there an error within 0.01, and tracking is restored within 1.5s. This is because the observer transmits the estimated fault impact factor to the fractional-order sliding mode fault-tolerant controller, reconstructing the control laws of the four channels. Furthermore, the fractional-order sliding mode control algorithm itself is robust enough to handle small faults, ensuring system convergence. In addition, the fractional-order calculus factor introduced by the fractional-order sliding mode control algorithm further enhances the robustness of the entire system and improves its fault-tolerance performance. In summary, the observer designed for multi-rotor aerial rescue drones experiencing actuator malfunctions during aerial rescue operations can quickly and accurately estimate actuator faults, and the designed controller ensures that the multi-rotor aerial rescue drone can still operate normally after an actuator malfunction.

Claims

1. A fault-tolerant control method for multi-rotor aerial rescue drones, the method comprising the following steps: Step 1: Establish a fault model for the actuators of the multi-rotor aerial rescue drone; Step 2: Design a fault observer for the actuators of a multi-rotor aerial rescue UAV; Step 3: Design the fault-tolerant control law for the position subsystem of the multi-rotor aerial rescue UAV; Step four: Design the fault-tolerant control law for the attitude subsystem of the multi-rotor aerial rescue UAV; Step 5: Use MATLAB / Simulink to simulate and verify the algorithm; Step one specifically includes the following process: The actuator failure model for the multi-rotor aerial rescue UAV is established as follows: （1） in, x , y , z These are the coordinates of the center of mass of the multi-rotor aerial rescue drone; , , Euler angles for multi-rotor aerial rescue drones; , , , These are the control inputs for the altitude, roll, pitch, and yaw channels of the multi-rotor aerial rescue drone; m For the quality of multi-rotor aerial rescue drones; , , These are multi-rotor aerial rescue drones. x , y , z Moment of inertia in the axial direction; g For the gravitational acceleration of multi-rotor aerial rescue drones; , , , , , External interference with multi-rotor aerial rescue drones; , , , , , For actuator fault items; step two specifically includes the following processes: Define the actuator fault observer model: （2） in, The inputs to the control system include the state variables of the position subsystem and the attitude subsystem; The output of the control system; The impact of external disturbances on drones; For the nonlinear part of the system, the matrix , , , , , , , , , , , , , , , , .

2. The control method according to claim 1, characterized in that, Step three specifically includes the following process: Dynamic model of the position subsystem when the actuator fails: （3） in, This is the control input for the altitude channel of the UAV system in case of actuator failure. Define the virtual control input for the position subsystem of the multi-rotor aerial rescue UAV: （4） Combining equations (3) and (4), we can obtain: （5） In the formula: The matrix represents the position coordinates of a multi-rotor aerial rescue drone. , , , Define the position tracking error of a multi-rotor aerial rescue drone: （6） In the formula: The coordinates are the desired location coordinates for the multi-rotor aerial rescue drone. Choose the following fractional integral sliding surface: （7） In the formula: ; ; , , It is a positive number. Differentiating equation (7) above, we have: （8） make , Then we have: （9） The fractional-order sliding mode reaching law differs significantly from the traditional sliding mode reaching law in both theory and application. This method is defined by a fractional-order calculus equation and adjusts the coefficients... and fractional order r 1. The speed at which the system reaches the sliding surface can be precisely adjusted. Therefore, a fractional-order sliding mode reaching law is selected: （10） In the formula: Combining equations (9) and (10), we can obtain: （11） Define separately and The total mass of the multi-rotor aerial rescue drone system m and external disturbances To ensure the robustness of multi-rotor aerial rescue drones experiencing actuator failures to mass variations and external disturbances, an adaptive control strategy is combined with a fault-tolerant controller. Therefore, the position control input during actuator failure... for: （12） Substituting equations (11) and (12) into equation (8) yields: （13） For the quality of disturbances and changes caused by the external environment of the UAV, the adaptive law is designed as follows: （14） In the formula: , For positive integers, Combining equations (11) and (12), we can obtain: （15） Because there is Therefore, the following result can be derived: （16） To address disturbances and changes in mass caused by the external environment, the deviations of disturbance and mass are defined: （17） In the formula: ; Because changes in external environmental disturbances and the overall mass of the drone are slow, therefore... , To demonstrate the stability of the position fault-tolerant controller for the designed multi-rotor aerial rescue UAV, the Lyapunov function is designed as follows: （18） Differentiating the Lyapunov function (18) above and substituting equation (13) into the derivative of the Lyapunov function, we have: （19） Substituting the adaptive law (14) into the above equation (19), we have: （20） And because Sometimes, ,so （21） Therefore, the controlled system (3) under study reaches a steady state within a specified finite time range and maintains this state, and because Equation (16) can be rewritten as: （22） It can be derived from equations (1) and (4) that: （23） Furthermore, the control law for position-tolerant control can be derived: （24） At the same time, due to , Since the variation is small, the arctangent function can be used to obtain the result. , The value of can be used to obtain the target control signal of the actuator fault attitude subsystem: （25）。 3. The control method according to claim 2, characterized in that, Step four specifically includes the following process: A matrix-form attitude subsystem model for actuator failure: （26） ， ， Define the attitude tracking error of a multi-rotor aerial rescue drone: （27） Design the following sliding surface: （28） In the formula: ; ; , , It is a non-zero positive number. Differentiating the above equation, we have: （29） Choose the following fractional sliding mode reaching law: （30） In the formula: Substituting equation (26) into equation (29), we get: （31） To address the disturbances to the attitude subsystem caused by external environmental influences Design an adaptive law for attitude perturbation: （32） In the formula: Since the input is positive, combining equations (30) and (32), the attitude controller input for a fault in the attitude subsystem of a multi-rotor aerial rescue UAV can be obtained as follows: （33） The estimated actuator failure impact factor is based on the designed fault observer. , j = 2, 3, 4, and The following result can be derived: （34） Based on the above formula, the specific input to the attitude controller can be obtained as follows: （35） （36） （37） The external disturbance estimation error of the attitude subsystem is defined as: （38） To prove the stability of the attitude fault-tolerant controller for a multi-rotor aerial rescue UAV, a Lyapunov function is designed: （39） Differentiating the Lyapunov function (39) above and substituting equation (31) into the derivative of the Lyapunov function, we have: （40） Substituting the adaptive law (32) into the above equation (40), we have: （41） And because when Sometimes, Then we have: （42） Therefore, the attitude subsystem (26) of the multi-rotor air rescue UAV studied reaches a steady state within a specified finite time range and maintains that state.

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