A fractional-order recursive sliding mode trajectory tracking control method for quadrotor UAV

Abstract

The present invention discloses a fractional-order recursive sliding mode trajectory tracking control method for a quadrotor unmanned aerial vehicle (UAV). The method employs an adaptive fractional-order robust control method and utilizes an adaptive gain adjustment method to estimate the unknown upper bounds of model uncertainty and external disturbances. This method offsets the lumped disturbance in the UAV model, improves the trajectory tracking performance of the UAV, and enables stable and rapid trajectory tracking of the UAV. The present invention provides a fractional-order recursive sliding mode trajectory tracking control method for a quadrotor unmanned aerial vehicle (UAV). This method improves the stability and robustness of the entire system, meets the precision requirements of the control input for trajectory tracking of the UAV, and significantly improves the trajectory tracking accuracy of the UAV.

Description

Technical Field

[0001] The present invention relates to a fractional-order recursive sliding mode trajectory tracking control method for a quad-rotor unmanned aerial vehicle (UAV), belonging to the technical field of UAV motion control. Background Art

[0002] Quadrotors (UAVs) are widely used in both civilian and military applications due to their vertical takeoff, simple structure, and strong terrain adaptability. However, they are also underactuated, strongly coupled, and highly nonlinear. During mission execution, they are susceptible to internal disturbances such as model uncertainty and aerodynamic parameter uncertainty, as well as external environmental disturbances such as gusts. These multiple sources of interference severely impact trajectory tracking accuracy, making the design of flight control systems challenging. To address the trajectory tracking problem for quadrotors, researchers at home and abroad have developed numerous effective control methods, including PID control, adaptive control, robust control, sliding mode control, and neural network control. Sliding mode control is the most widely used in quadrotor control system design due to its fast response, strong robustness, and ease of implementation. However, the discontinuous switching characteristics of traditional sliding mode control can cause system chattering. To address this drawback, commonly used methods include the boundary layer method, reaching law method, or methods combined with neural networks. However, the boundary layer method can lead to steady-state errors; the reaching law method can overestimate if parameters are improperly adjusted; and the design of the neural network method is overly complex, making it an unsuitable sliding mode controller. Therefore, it is necessary to propose a trajectory tracking control method that can suppress chattering while having strong anti-interference ability and fast convergence performance. Summary of the Invention

[0003] Objective: To overcome the shortcomings of the prior art, the present invention provides a fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV. An adaptive fractional-order robust control method is adopted, and an adaptive gain adjustment method is used to estimate the unknown upper bounds of model uncertainty and external disturbances, thereby offsetting the lumped interference in the UAV model, improving the trajectory tracking performance of the quadrotor UAV, and achieving stable and fast quadrotor UAV trajectory tracking.

[0004] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is:

[0005] A fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV comprises the following steps:

[0006] Step 1: Construct a quadrotor UAV dynamic model for a quadrotor UAV with uncertain model and unknown disturbance.

[0007] Step 2: Set the quadrotor UAV trajectory tracking flight position target and attitude angle target. The flight position target is used to make the UAV position error converge to 0 and remain stable; the attitude angle target is used to make the UAV roll angle, pitch angle and yaw angle errors converge to 0 and remain stable.

[0008] Step 3: Based on the flight position target, a fractional-order recursive sliding surface of the position subsystem in the quadrotor UAV dynamics model is designed. The fractional-order recursive sliding surface of the position subsystem is processed using the sliding mode variable structure control method, and the unknown upper bounds of the uncertainty and disturbance in the position subsystem are estimated using the adaptive gain adjustment method. The estimated value of the unknown upper bound replaces the actual value, and finally the control input of the position subsystem is obtained.

[0009] Step 4: Inversely solve the desired pitch and roll angles of the quadrotor based on the desired yaw angle and the control input of the position subsystem.

[0010] Step 5: Use the inversely solved pitch angle and roll angle as the reference input of the attitude subsystem in the quadrotor UAV dynamic model, and design the fractional-order recursive sliding surface of the attitude subsystem based on the attitude angle target. Process the fractional-order recursive sliding surface of the attitude subsystem through the sliding mode variable structure control method, and use the adaptive gain adjustment method to estimate the unknown upper bounds of uncertainty and disturbance in the attitude subsystem. Replace the actual value with the estimated value of the unknown upper bound to finally obtain the control input of the attitude subsystem.

[0011] Step 6: Use the obtained control input of the position subsystem and the control input of the attitude subsystem as the input of the quadrotor UAV dynamics model to achieve the quadrotor UAV trajectory tracking flight position target and attitude angle target.

[0012] As a preferred solution, the calculation formula of the quadrotor drone dynamics model is as follows:

[0013]

[0014] Among them, x, y, z represent the values ​​on the x, y, and z axes respectively, φ represents the roll angle, θ represents the pitch angle, ψ represents the yaw angle, g represents the acceleration of gravity, l represents the distance from the center of the propeller to the center of gravity, m represents the mass of the aircraft, and I x , I y , I zRespectively represent the moment of inertia of the aircraft around the x, y, and z axes, K1, K2, and K3 represent the air resistance coefficients in the three coordinate directions, and K4, K5, and K6 represent the air resistance coefficients in the three rotation directions. u1 represents the control input of the position subsystem, u2, u3, and u4 represent the control input of the attitude subsystem, u1 controls the vertical take-off and landing of the drone, u2 controls the roll channel of the drone, u3 controls the pitch channel of the drone, and u4 controls the yaw channel of the drone. τ i , i=1,2,3 represents the uncertain part of the model on the position channel, τ i , i=4,5,6 represents the uncertain part of the model on the attitude channel; d i , i=1,2,3 represents the external disturbance on the moving position, d i , i=4,5,6 represents the external disturbance on the rotation angle.

[0015] As a preferred option, For the location subsystem.

[0016] For the attitude subsystem.

[0017] As a preferred solution, according to the position control target, the actual position coordinates of the quadcopter are (x, y, z), and the expected position coordinates are (x d ,y d ,z d ), obtain the position tracking error e x =xx d ,e y =yy d ,e z =zz d Converges to 0 and remains stable.

[0018] According to the attitude control target, the attitude control target is obtained. The actual attitude angle of the quadrotor drone is (φ,θ,ψ), and the expected attitude angle is (φ d ,θ d ,ψ d ), obtain the posture tracking error e φ =φ-φ d ,e θ =θ-θ d ,e ψ =ψ-ψ d Converges to 0 and remains stable.

[0019] As a preferred solution, the step 3 comprises the following steps:

[0020] Based on the quadrotor drone position subsystem, the control input u of the quadrotor drone in the X, Y and Z directions is designed.x 、u y 、u z , the calculation formula is as follows:

[0021]

[0022] Design the fractional-order non-singular terminal sliding surface of the position subsystem, and the calculation formula is as follows:

[0023]

[0024] The fractional-order recursive sliding surface is designed from the fractional-order non-singular terminal sliding surface. The calculation formula is as follows:

[0025]

[0026] Among them, σ Ix ,σ Iy ,σ Iz is the intermediate variable of the design, c1, c2, λ are positive constant gains, α1, α2 are fractional orders, b1, b2, β are constant orders. D(*) represents the fractional order function, σ x , σ y , σ z represent the fractional-order non-singular terminal sliding surface in the X, Y, and Z directions, respectively, s x 、s y 、s z Represent the fractional-order recursive sliding surface in the X, Y, and Z directions respectively.

[0027] Without considering the disturbance, the equivalent control law can be obtained by setting the fractional-order recursive sliding surface equal to 0. The calculation formula is as follows:

[0028]

[0029] Among them, u xeq 、u yeq 、u zeq Represent the equivalent control laws in the X direction, Y direction and Z direction respectively.

[0030] The switching control law is designed according to the adaptive control method. The calculation formula is as follows:

[0031]

[0032] Among them, u xsw 、u ysw 、u zsw Represent the switching control laws in the X, Y and Z directions respectively, k1, k2 are positive constant gains, ν is the exponent of the reaching law, η1, η2, η3 are the adaptive law gains, and ε is the boundary of the designed sliding surface, which is a very small positive number.

[0033] in, is the estimated value of the unknown upper bound of each channel uncertainty and disturbance, and its derivative is:

[0034]

[0035] The control input u1 of the final position subsystem is calculated as follows:

[0036]

[0037] As a preferred solution, according to the desired yaw angle ψ d and control input u x ,u y ,u z , the desired roll angle φ can be inversely solved d and pitch angle θ d , the calculation formula is as follows:

[0038]

[0039] As a preferred solution, the specific steps of step 5 are as follows:

[0040] The desired roll angle φ obtained by reverse solution d and pitch angle θ d As the reference input of the attitude subsystem,

[0041] Design the fractional-order non-singular terminal sliding mode surface of the attitude subsystem. The calculation formula is as follows:

[0042]

[0043] The fractional-order recursive sliding surface is designed from the fractional-order non-singular terminal sliding surface. The calculation formula is as follows:

[0044]

[0045] Among them, σ Iφ ,σ Iθ ,σ Iψ is the intermediate variable of the design, c1, c2, λ are positive constant gains, α1, α2 are fractional orders, b1, b2, β are constant orders. D(*) represents the fractional order function, σ φ , σ θ , σ ψ represent the fractional-order non-singular terminal sliding mode surfaces in the φ, θ, and ψ directions, respectively, and s φ 、s θ 、s ψRepresent the fractional-order recursive sliding surface in the φ, θ, and ψ directions respectively. Without considering the disturbance, let the fractional-order recursive sliding surface equal to 0 to obtain the equivalent control law. The calculation formula is as follows:

[0046]

[0047] Among them, u φeq 、u θeq 、u ψeq Represent the equivalent control laws in the φ direction, θ direction and ψ direction respectively.

[0048] The switching control law is designed according to the adaptive control method. The calculation formula is as follows:

[0049]

[0050] Among them, k1, k2 are positive constant gains, ν is the exponent of the reaching law, η1, η2, η3 are the adaptive law gains, and ε is the boundary of the designed sliding surface, which is a very small positive number. φsw 、u θsw 、u ψsw Represent the switching control laws in the φ direction, θ direction and ψ direction respectively.

[0051] in, is the estimated value of the unknown upper bound of each channel uncertainty and disturbance, and its derivative is:

[0052]

[0053] The control input of the final attitude subsystem is calculated as follows:

[0054]

[0055] Beneficial effects: The present invention provides a quadrotor UAV fractional-order recursive sliding mode trajectory tracking control method. First, a quadrotor UAV dynamics model including model uncertainty and external interference is established, and it is decoupled into an attitude subsystem and a position subsystem. Secondly, based on the fractional-order control theory, fractional-order recursive sliding mode surfaces are designed for the position subsystem and the attitude subsystem respectively. Finally, an adaptive gain adjustment method is used to estimate the unknown upper bounds of model uncertainty and external disturbances, and an adaptive fractional-order recursive sliding mode controller is designed to ensure that the system state can reach the designed sliding mode surface. The present invention can be applied to quadrotor UAV trajectory tracking control, and has excellent anti-interference performance and tracking accuracy. Its advantages are as follows:

[0056] 1. The present invention discloses a fractional-order recursive sliding mode trajectory tracking control method for a quadrotor unmanned aerial vehicle (UAV). The designed adaptive fractional-order recursive sliding mode controller has two layers of sliding surfaces. The first layer is a fractional-order non-singular terminal sliding mode surface, which can achieve finite-time convergence of the system state. The introduction of fractional-order calculus operators effectively improves the overall control quality. The second layer is an integral sliding mode surface. Since it contains integral elements, it reduces system chattering and improves the stability and robustness of the entire system.

[0057] 2. The present invention discloses a fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV. An adaptive gain adjustment method is used to estimate the unknown upper bounds of model uncertainty and disturbances. The estimated value is updated in real time according to the motion state of the UAV, meeting the accuracy requirements of the control input for the trajectory tracking of the quadrotor UAV.

[0058] 3. The present invention discloses a fractional-order recursive sliding mode trajectory tracking control method for a quad-rotor UAV, which enables the UAV position and attitude to have faster convergence speed and excellent tracking stability, and significantly improves the trajectory tracking accuracy of the quad-rotor UAV. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a control flow chart of the quadrotor drone of the present invention.

[0060] Figure 2 The three-dimensional flight trajectory of the quadrotor UAV under adaptive sliding mode control (ASMC), Super-Twisting sliding mode control (STA) and adaptive fractional-order recursive sliding mode control (AFRSMC) of this method.

[0061] Figure 3 The x-channel response curves of the quadrotor drones of ASMC, STA, and AFRSMC are shown.

[0062] Figure 4 Response curves of the y-channel of the quadrotor UAV of ASMC, STA and AFRSMC.

[0063] Figure 5 The z-channel response curves of the quadrotor drones of ASMC, STA, and AFRSMC are shown.

[0064] Figure 6 ψ channel response curves of the quadrotor drones of ASMC, STA, and AFRSMC.

[0065] Figure 7 Response curves of the θ and φ channels of the quadrotor drone based on this method.

[0066] Figure 8 This is the control input response curve of the quadrotor UAV based on this method. DETAILED DESCRIPTION

[0067] The present invention will be further described below with reference to specific embodiments.

[0068] A fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV comprises the following steps:

[0069] Step 1: Construct a quadrotor UAV dynamic model for a quadrotor UAV with uncertain model and unknown disturbance.

[0070] Step 2: Set the quadrotor UAV trajectory tracking flight position target and attitude angle target. The flight position target is used to make the UAV position error converge to 0 and remain stable; the attitude angle target is used to make the UAV roll angle, pitch angle and yaw angle errors converge to 0 and remain stable.

[0071] Step 3: Based on the flight position target set in step 2, the fractional-order recursive sliding surface of the position subsystem in the quadrotor UAV dynamics model is designed. The fractional-order recursive sliding surface of the position subsystem is processed using the sliding mode variable structure control method, and the unknown upper bounds of the uncertainty and disturbance in the position subsystem are estimated using the adaptive gain adjustment method. The estimated value of the unknown upper bound replaces the actual value, and finally the control input of the position subsystem is obtained.

[0072] Step 4: Inversely solve the desired pitch and roll angles of the quadrotor based on the desired yaw angle and the control input of the position subsystem.

[0073] Step 5: Use the inversely solved pitch angle and roll angle as the reference input of the attitude subsystem in the quadrotor UAV dynamic model, and design the fractional-order recursive sliding surface of the attitude subsystem according to the attitude angle target set in step 2. Process the fractional-order recursive sliding surface of the attitude subsystem through the sliding mode variable structure control method, and use the adaptive gain adjustment method to estimate the unknown upper bounds of uncertainty and disturbance in the attitude subsystem. Replace the actual value with the estimated value of the unknown upper bound to finally obtain the control input of the attitude subsystem.

[0074] Step 6: Use the obtained control input of the position subsystem and the control input of the attitude subsystem as the input of the quadrotor UAV dynamics model to achieve the quadrotor UAV trajectory tracking flight position target and attitude angle target.

[0075] like Figure 1 As shown, further, step 1 includes the following steps:

[0076] In the process of constructing the mathematical model of the quadrotor UAV with model uncertainty and external disturbance, two independent sets of spatial coordinate systems are used, namely the body coordinate system ( b ,X b ,Y b ,Zb ) and the inertial coordinate system (O e ,X e ,Y e ,Z e ). The position in the inertial coordinate system is [x,y,z] T , the roll angle is φ, the pitch angle is θ, and the yaw angle is ψ. The dynamic model of the quadrotor drone can be obtained, and the calculation formula is as follows:

[0077]

[0078] Among them, g represents the acceleration of gravity, l represents the distance from the center of the propeller to the center of gravity, m represents the mass of the aircraft, and I x , I y , I z Respectively represent the moment of inertia of the aircraft around the x, y, and z axes, K1, K2, and K3 represent the air resistance coefficients in the three coordinate directions, and K4, K5, and K6 represent the air resistance coefficients in the three rotation directions. u1 represents the control input of the position subsystem, u2, u3, and u4 represent the control input of the attitude subsystem, u1 controls the vertical take-off and landing of the drone, u2 controls the roll channel of the drone, u3 controls the pitch channel of the drone, and u4 controls the yaw channel of the drone. τ i , i=1,2,3 represents the uncertain part of the model on the position channel, τ i , i=4,5,6 represents the uncertain part of the model on the attitude channel; d i , i=1,2,3 represents the external disturbance on the moving position, d i , i=4,5,6 represents the external disturbance on the rotation angle.

[0079] in, For the location subsystem.

[0080] For the attitude subsystem.

[0081] Furthermore, the implementation process of step 2 is as follows:

[0082] During flight, drones must complete two control tasks: position control and attitude control. Position control ensures that the tangential, normal, and vertical errors converge to zero and remain stable, resulting in precise tracking. Attitude control ensures that the roll, pitch, and yaw errors converge to zero, ensuring stable flight.

[0083] Position control target: The actual position coordinates of the quadcopter are (x, y, z), and the expected position coordinates are (x d ,y d,z d ); The position control goal requires that the actual position coordinates of the UAV can quickly converge to the desired position coordinates and maintain stable tracking, and finally achieve the position tracking error e x =xx d ,e y =yy d ,e z =zz d Converges to 0 and remains stable.

[0084] Attitude control target: The actual attitude angle of the quadcopter is (φ,θ,ψ), and the expected attitude angle is (φ d ,θ d ,ψ d ); The attitude control goal requires that the actual attitude angle of the UAV can quickly converge to the expected value and maintain stable tracking, and finally achieve the attitude tracking error e φ =φ-φ d ,e θ =θ-θ d ,e ψ =ψ-ψ d Converges to 0 and remains stable.

[0085] Furthermore, the implementation process of step 3 is as follows:

[0086] According to the position control target set in step 2, design the quadrotor drone position controller to realize the position control of the quadrotor drone.

[0087] Based on the quadrotor drone position subsystem, the control input u of the quadrotor drone in the X, Y and Z directions is designed. x 、u y 、u z for:

[0088]

[0089] The fractional-order non-singular terminal sliding mode surface of the designed position subsystem is:

[0090]

[0091] The fractional-order recursive sliding surface designed from the fractional-order non-singular terminal sliding surface is:

[0092]

[0093] Among them, σ Ix ,σ Iy ,σ Iz is the intermediate variable of the design, c1, c2, λ are positive constant gains, α1, α2 are fractional orders, b1, b2, β are constant orders. D(*) represents the fractional order function, σx , σ y , σ z represent the fractional-order non-singular terminal sliding surface in the X, Y, and Z directions, respectively, s x 、s y 、s z Represent the fractional-order recursive sliding surface in the X, Y, and Z directions respectively.

[0094] Without considering the disturbance, let the fractional-order recursive sliding surface equal to 0 and the equivalent control law can be obtained as follows:

[0095]

[0096] Among them, u xeq 、u yeq 、u zeq Represent the equivalent control laws in the X direction, Y direction and Z direction respectively.

[0097] Due to the presence of interference, the state of the position subsystem will leave the sliding surface. In order to improve the anti-interference ability and suppress chattering, the switching control law is designed according to the adaptive control method as follows:

[0098]

[0099] Among them, u xsw 、u ysw 、u zsw Represent the switching control laws in the X, Y and Z directions respectively, k1, k2 are positive constant gains, ν is the exponent of the reaching law, η1, η2, η3 are the adaptive law gains, and ε is the boundary of the designed sliding surface, which is a very small positive number.

[0100] in, is the estimated value of the unknown upper bound of each channel uncertainty and disturbance, and its derivative is:

[0101]

[0102] The control input u1 of the position subsystem of the final position subsystem is:

[0103]

[0104] Furthermore, the implementation process of step 4 is as follows:

[0105] According to the desired yaw angle ψ d and the control input u obtained in step 3 x ,u y ,u z , the desired roll angle φ can be inversely solved d and pitch angle θ d .

[0106]

[0107] Furthermore, the implementation process of step 5 is as follows:

[0108] The desired roll angle φ obtained in step 4 d and pitch angle θ d As the reference input of the attitude subsystem, the attitude controller of the quadrotor UAV is designed.

[0109] The designed fractional-order non-singular terminal sliding mode surface of the attitude subsystem is:

[0110]

[0111] The fractional-order recursive sliding surface designed from the fractional-order non-singular terminal sliding surface is:

[0112]

[0113] Among them, σ Iφ ,σ Iθ ,σ Iψ is the intermediate variable of the design, c1, c2, λ are positive constant gains, α1, α2 are fractional orders, b1, b2, β are constant orders. D(*) represents the fractional order function, σ φ , σ θ , σ ψ represent the fractional-order non-singular terminal sliding mode surfaces in the φ, θ, and ψ directions, respectively, and s φ 、s θ 、s ψ Represent the fractional-order recursive sliding surface in the φ, θ, and ψ directions respectively. Without considering the disturbance, let the fractional-order recursive sliding surface equal to 0 and the equivalent control law can be obtained as:

[0114]

[0115] Among them, u φeq 、u θeq 、u ψeq Represent the equivalent control laws in the φ direction, θ direction and ψ direction respectively.

[0116] Due to the presence of interference, the system state will leave the sliding surface. In order to improve the anti-interference ability and suppress chattering, the switching control law is designed according to the adaptive control method as follows:

[0117]

[0118] Among them, k1, k2 are positive constant gains, ν is the exponent of the reaching law, η1, η2, η3 are the adaptive law gains, and ε is the boundary of the designed sliding surface, which is a very small positive number. φsw 、u θsw 、u ψsw Represent the switching control laws in the φ direction, θ direction and ψ direction respectively.

[0119] in is the estimated value of the unknown upper bound of each channel uncertainty and disturbance, and its derivative is:

[0120]

[0121] The control input of the final attitude subsystem is:

[0122]

[0123] In order to verify the tracking accuracy and anti-disturbance performance of the present invention, the algorithm of the present invention is compared with adaptive sliding mode control (ASMC) and Super-Twisting sliding mode control (STA) based on the MATLAB / SIMLINK environment, taking into full consideration the model uncertainty and the existence of external disturbances. The initial conditions of the system are set as: [x, y, z] T =[2,1,0] T ,[φ,θ,ψ] T =[0,0,0] T .

[0124] The expected trajectory is set to: x d =0.5cos(0.5t),y d =0.5sin(0.5t), z d =0.1t+2,ψ d =π / 3,θ d , Obtained by solving the virtual control law.

[0125] The external disturbance and model uncertainty are set as: d i =0.1sin(t)+0.5,τ i =-0.1(-t+1)e -t+1 , where i = 1, 2, 3, 4, 5, 6.

[0126] The dynamic parameters of the quadrotor drone of the present invention are shown in Table 1, and the controller parameters are shown in Table 2.

[0127] Table 1 Quadrotor UAV parameters

[0128]

[0129]

[0130] Table 2 Controller parameters

[0131]

[0132] The present invention provides a fractional-order recursive sliding mode trajectory tracking control method for a quadrotor unmanned aerial vehicle (UAV). The algorithm of the present invention is compared with adaptive sliding mode control (ASMC) and Super-Twisting sliding mode control (STA). Figures 2 to 5 They are the three-dimensional cylindrical trajectory effect diagram and the response curve of the three-channel position. It can be seen that the control method proposed in the present invention can track the desired trajectory within 1s, has a faster convergence speed, higher tracking accuracy, and no overshoot phenomenon. Figure 6 is the ψ channel response curve. It can be seen that the control method proposed in the present invention has better steady-state effect, better accuracy, smoother curve, and no overshoot phenomenon. Figure 7 The approach From the θ response curve, it can be seen that the control method proposed in the present invention can converge asymptotically to 0 within 1s, achieving rapid and stable posture and achieving the purpose of stably tracking the desired trajectory. Figure 8 This is the input response curve of this method. It can be seen that the control input jitter is small and within the specific limit range.

[0133] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV, characterized by: The following steps are involved: Step 1: Construct a quadrotor UAV dynamics model for a quadrotor UAV with uncertain model and unknown disturbances; Step 2: Set the quadrotor UAV trajectory tracking flight position target and attitude angle target. The flight position target is used to make the UAV position error converge to 0 and remain stable; the attitude angle target is used to make the UAV roll angle, pitch angle and yaw angle errors converge to 0 and remain stable. Step 3: Based on the flight position target, a fractional-order recursive sliding surface is designed for the position subsystem in the quadrotor UAV dynamics model. This surface is processed using the sliding mode variable structure control method. The unknown upper bounds of the uncertainty and disturbance in the position subsystem are estimated using the adaptive gain adjustment method. The estimated values ​​of the unknown upper bounds are used instead of the actual values ​​to ultimately obtain the control input for the position subsystem. Step 4: Inversely solve the desired pitch and roll angles of the quadrotor based on the desired yaw angle and the control input of the position subsystem; Step 5: Use the inversely solved pitch and roll angles as reference inputs for the attitude subsystem in the quadrotor UAV dynamics model. Design a fractional-order recursive sliding surface for the attitude subsystem based on the attitude angle target. Process the fractional-order recursive sliding surface using the sliding mode variable structure control method. Use the adaptive gain adjustment method to estimate the unknown upper bounds of uncertainty and disturbances in the attitude subsystem. Replace the actual values ​​with the estimated unknown upper bounds to ultimately obtain the control input for the attitude subsystem. Step 6: Use the obtained control input of the position subsystem and the control input of the attitude subsystem as the input of the quadrotor UAV dynamics model to achieve the quadrotor UAV trajectory tracking flight position target and attitude angle target.

2. The fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV according to claim 1, characterized in that: The calculation formula of the quadrotor UAV dynamics model is as follows: Among them, x, y, z represent the values ​​on the x, y, and z axes respectively, φ represents the roll angle, θ represents the pitch angle, ψ represents the yaw angle, g represents the acceleration of gravity, l represents the distance from the center of the propeller to the center of gravity, m represents the mass of the aircraft, and I x , I y , I z Respectively represent the moment of inertia of the body around the x, y, and z axes, K1, K2, and K3 represent the air resistance coefficients in the three coordinate directions, and K4, K5, and K6 represent the air resistance coefficients in the three rotation directions; u1 represents the control input of the position subsystem, u2, u3, and u4 represent the control input of the attitude subsystem, u1 controls the vertical take-off and landing of the drone, u2 controls the roll channel of the drone, u3 controls the pitch channel of the drone, and u4 controls the yaw channel of the drone; τ i , i=1,2,3 represents the uncertain part of the model on the position channel, τ i , i=4,5,6 represents the uncertain part of the model on the attitude channel; d i , i=1,2,3 represents the external disturbance on the moving position, d i , i=4,5,6 represents the external disturbance on the rotation angle.

3. The fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV according to claim 2, characterized in that: is the position subsystem; For the attitude subsystem.

4. The fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV according to claim 3, characterized in that: According to the position control target, the actual position coordinates of the quadcopter are (x, y, z), and the expected position coordinates are (x d ,y d ,z d ), obtain the position tracking error e x =xx d ,e y =yy d ,e z =zz d Converges to 0 and remains stable; According to the attitude control target, the attitude control target is obtained. The actual attitude angle of the quadrotor drone is (φ,θ,ψ), and the expected attitude angle is (φ d ,θ d ,ψ d ), obtain the posture tracking error e φ =φ-φ d ,e θ =θ-θ d ,e ψ =ψ-ψ d Converges to 0 and remains stable.

5. The fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV according to claim 4, characterized in that: The step 3 comprises the following steps: Based on the quadrotor drone position subsystem, the control input u of the quadrotor drone in the X, Y and Z directions is designed. x 、u y 、u z , the calculation formula is as follows: Design the fractional-order non-singular terminal sliding surface of the position subsystem, and the calculation formula is as follows: The fractional-order recursive sliding surface is designed from the fractional-order non-singular terminal sliding surface. The calculation formula is as follows: Among them, σ Ix ,σ Iy ,σ Iz is the intermediate variable of the design, c1, c2, λ are positive constant gains, α1, α2 are fractional orders, b1, b2, β are constant orders; D(*) represents the fractional order function, σ x , σ y , σ z represent the fractional-order non-singular terminal sliding surface in the X, Y, and Z directions, respectively, s x 、s y 、s z Represent the fractional-order recursive sliding surface in the X, Y, and Z directions respectively; Without considering the disturbance, the equivalent control law can be obtained by setting the fractional-order recursive sliding surface equal to 0. The calculation formula is as follows: Among them, u xeq 、u yeq 、u zeq Represent the equivalent control laws in the X direction, Y direction and Z direction respectively; The switching control law is designed according to the adaptive control method. The calculation formula is as follows: Among them, u xsw 、u ysw 、u zsw Represent the switching control laws in the X, Y, and Z directions respectively, k1, k2 are positive constant gains, ν is the exponent of the reaching law, η1, η2, η3 are the adaptive law gains, and ε is the boundary of the designed sliding surface, which is a very small positive number; in, is the estimated value of the unknown upper bound of each channel uncertainty and disturbance, and its derivative is: The control input u1 of the final position subsystem is calculated as follows:

6. The fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV according to claim 5, characterized in that: According to the desired yaw angle ψ d and control input u x ,u y ,u z , the desired roll angle φ can be inversely solved d and pitch angle θ d , the calculation formula is as follows:

7. The fractional-order recursive sliding mode trajectory tracking control method for a quadrotor UAV according to claim 6, characterized in that: The specific steps of step 5 are as follows: The desired roll angle φ obtained by reverse solution d and pitch angle θ d As the reference input of the attitude subsystem, the fractional-order non-singular terminal sliding mode surface of the attitude subsystem is designed. The calculation formula is as follows: The fractional-order recursive sliding surface is designed from the fractional-order non-singular terminal sliding surface. The calculation formula is as follows: Among them, σ Iφ ,σ Iθ ,σ Iψ is the intermediate variable of the design, c1, c2, λ are positive constant gains, α1, α2 are fractional orders, b1, b2, β are constant orders; D(*) represents the fractional order function, σ φ , σ θ , σ ψ represent the fractional-order non-singular terminal sliding mode surfaces in the φ, θ, and ψ directions, respectively, and s φ 、s θ 、s ψ Represent the fractional-order recursive sliding mode surfaces in the φ, θ, and ψ directions respectively; Without considering the disturbance, the equivalent control law can be obtained by setting the fractional-order recursive sliding surface equal to 0. The calculation formula is as follows: Among them, u φeq 、u θeq 、u ψeq Represent the equivalent control laws in the φ direction, θ direction and ψ direction respectively; The switching control law is designed according to the adaptive control method. The calculation formula is as follows: Among them, k1, k2 are positive constant gains, ν is the exponent of the reaching law, η1, η2, η3 are the adaptive law gains, ε is the boundary of the designed sliding surface, which is a very small positive number; u φsw 、u θsw 、u ψsw Represent the switching control laws in the φ direction, θ direction and ψ direction respectively; in, is the estimated value of the unknown upper bound of each channel uncertainty and disturbance, and its derivative is: The control input of the final attitude subsystem is calculated as follows:

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