Unmanned aerial vehicle preset sliding mode wind disturbance resistance control method based on MRPs

Abstract

The invention discloses an unmanned aerial vehicle preset sliding mode wind disturbance resistance control method based on MRPs. The method comprises the following steps: establishing an unmanned aerial vehicle position dynamic model based on MRPs; calculating a position tracking error according to the position dynamics model, and determining a position tracking error limit meeting a preset performance function by using the preset performance function; performing inverse function operation on the position tracking error, and converting the position tracking error into a conversion error without constraint conditions; calculating an improved over-torsion sliding mode surface by using the conversion error; and calculating a preset sliding mode control input quantity of the unmanned aerial vehicle according to the overtwist sliding mode surface. The method has the advantages that the complex wind disturbance is considered, the MRP-based unmanned aerial vehicle position dynamic model is established, the preset performance control is introduced to effectively limit the position offset of the unmanned aerial vehicle, and the improved over-torque sliding mode control method is combined, so that the robustness and tracking precision of unmanned aerial vehicle trajectory tracking control under the complex wind disturbance condition can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle control, and in particular relates to a preset sliding mode anti-wind disturbance control method for unmanned aerial vehicle based on MRPs (Modified Rodriguez Parameters). Background Art

[0002] With the rapid development of unmanned aerial vehicle technology, drones have become an indispensable tool widely used in various fields. Using drones to detect damage to aircraft skin can significantly improve the detection efficiency. However, when using drones to detect damage to aircraft skin, in complex external environments such as wind disturbances, the flight position offset of the drone is large, which may cause a collision with the aircraft, causing safety problems and property losses. Therefore, while improving the robustness of the controller, it is particularly important to constrain the position offset of the drone through control methods to ensure flight safety.

[0003] Aiming at the position tracking control problem of UAV under wind disturbance, the H∞ and backstepping sliding mode control methods can handle the modeling uncertainty and upper bound of wind disturbance, and the designed position control method has certain robustness. However, in actual situations, complex wind disturbances pose challenges to the position offset limit of the three-axis direction of the UAV. The existing control methods are difficult to effectively solve this problem. The safety of the UAV cannot be effectively guaranteed during flight operations such as inspection tasks. Summary of the invention

[0004] In order to solve the above problems, the object of the present invention is to provide a UAV preset sliding mode anti-wind disturbance control method based on MRPs.

[0005] In order to achieve the above object, the MRPs-based UAV preset sliding mode anti-wind disturbance control method provided by the present invention comprises the following steps performed in sequence:

[0006] 1) Based on the MRPs attitude representation method, the position dynamics model of the UAV under complex wind disturbance is established;

[0007] 2) Calculating the position tracking error of the UAV according to the above position dynamics model, and using a preset performance function to determine the position tracking error limit that satisfies the preset performance function, thereby limiting the position tracking error of the UAV;

[0008] 3) Perform an inverse function calculation on the above position tracking error to obtain the unconstrained conversion error;

[0009] 4) The above conversion error is differentiated with respect to time, and the power reaching law is introduced to calculate the improved super-torsion sliding mode surface, so as to ensure the stability of the UAV under complex wind disturbances;

[0010] 5) According to the above-mentioned hypertorsion sliding surface, the constant velocity reaching law and the exponential reaching law are introduced to calculate the output of the preset sliding mode control of the UAV, thereby completing the design of the preset sliding mode anti-wind disturbance controller of the UAV.

[0011] In step 1), the method for establishing the position dynamics model of the UAV based on the MRPs attitude representation method is:

[0012] First, the position dynamics model of the UAV under complex wind disturbance is established based on MRPs:

[0013]

[0014] Among them, x represents the position coordinate of the center of mass of the drone in the x-axis direction in the global coordinate system O-xyz, represents the acceleration in the x-axis direction; y represents the position coordinate of the center of mass of the drone in the y-axis direction in the global coordinate system O-xyz. represents the acceleration in the y-axis direction; z represents the position coordinate of the center of mass of the drone in the z-axis direction in the global coordinate system O-xyz. represents the acceleration in the z-axis direction, σ1, σ2, σ3 represent the transformation angles of the x-axis, y-axis, and z-axis in the body coordinate system O-x'y'z' and the global coordinate system O-xyz, σ=[σ1 σ2 σ3] T is the vector representation of the MRP parameters, U1 represents the total thrust in the z' direction in the body coordinate system, and the vector F T =[F Tx F Ty F Tz ] T It represents wind force in N, m represents the mass of the drone in Kg, and g represents the acceleration due to gravity.

[0015] In step 2), the position tracking error of the UAV is calculated according to the above position dynamics model, and a position tracking error limit satisfying the preset performance function is determined by using a preset performance function, thereby limiting the position tracking error of the UAV:

[0016] First, the position tracking error of the UAV is expressed as:

[0017] e x =xx d (2)

[0018] Among them, x represents the position coordinate of the center of mass of the drone in the x-axis direction in the global coordinate system O-xyz, and x d represents the desired target position of the UAV;

[0019] Then, a preset performance function ρ that limits the position tracking error is constructed, and the formula is:

[0020]

[0021] Among them, k j Represents the convergence speed parameter of the position transient response, ρ0,ρ ∞ represent the initial value and steady-state value of the preset performance function respectively;

[0022] Then, using the preset performance function ρ, the limit of the position tracking error is expressed as:

[0023]

[0024] in, and δ represent preset performance control parameters.

[0025] In step 3), the method of performing an inverse function calculation on the position tracking error to obtain the unconstrained conversion error is:

[0026] For the above tracking error e x Perform an inverse function calculation to obtain the conversion error without constraints, the formula is:

[0027]

[0028] Wherein, Λ represents the position tracking error that meets the preset performance control parameters.

[0029] In step 4), the method of differentiating the above conversion error with respect to time, introducing the power reaching law, and calculating the improved super-torsion sliding mode surface to ensure the stability of the UAV under complex wind disturbance conditions is:

[0030] First, calculate the conversion error ε x The derivative with respect to time is given by:

[0031]

[0032] Then, the power reaching law is introduced to calculate the improved super-torsion sliding surface, and the formula is:

[0033]

[0034] Among them, μ,c and The constant that represents the conversion error that meets the design requirements of improved supertorsional sliding surface accuracy and stability, sgn(ε x )|ε x | 1-μ It represents the power reaching law that makes the sliding surface satisfy the rapid stability condition.

[0035] In step 5), the method of introducing the constant velocity reaching law and the exponential reaching law according to the above-mentioned super-torsion sliding mode surface, calculating the preset sliding mode control output of the UAV, and thus completing the design of the preset sliding mode anti-wind disturbance controller of the UAV is:

[0036] First, the constant speed reaching law and exponential reaching law are introduced to calculate the output of the preset sliding mode control of the UAV. The formula is:

[0037]

[0038] in, and denote the control gain, represents the constant velocity reaching law that ensures the stability of the sliding mode control system, represents the exponential reaching law that ensures the stability of the sliding mode control system.

[0039] The MRPs-based UAV preset sliding mode anti-wind disturbance control method provided by the present invention has the following advantages:

[0040] Considering that complex wind disturbances in the actual environment will exert forces on each axis of the drone, a mathematical model is established based on the modified Rodriguez parameters, and an improved hypertorsion sliding mode controller is designed, so that the drone can strictly limit the position deviation within the preset range under complex wind disturbances. It can keep the drone with a small position deviation and fast response capability during flight to ensure flight stability. It can consider the complex wind disturbances in the actual environment, artificially pre-set the system performance control conditions, and realize the robustness of the drone's flight process under wind disturbances in real application scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A flow chart of the MRPs-based UAV preset sliding mode anti-wind disturbance control method provided by the present invention;

[0042] Figure 2 A structural diagram of a preset sliding mode anti-wind disturbance controller for a UAV provided in an embodiment of the present invention;

[0043] Figure 3 A three-dimensional position tracking diagram in combination with preset performance control parameters under complex wind disturbances provided by an embodiment of the present invention;

[0044] Figure 4 A three-dimensional position tracking error diagram combined with preset performance control parameters under complex wind disturbances provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The MRP-based UAV preset sliding mode anti-wind disturbance control method provided by the embodiment of the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] like Figure 1As shown, the MRPs-based UAV preset sliding mode anti-wind disturbance control method provided by the present invention includes the following steps performed in sequence:

[0047] 1) Based on the MRPs attitude representation method, the position dynamics model of the UAV under complex wind disturbance is established;

[0048] First, the position dynamics model of the UAV under complex wind disturbance is established based on MRPs:

[0049]

[0050] Among them, x represents the position coordinate of the center of mass of the drone in the x-axis direction in the global coordinate system O-xyz, represents the acceleration in the x-axis direction; y represents the position coordinate of the center of mass of the drone in the y-axis direction in the global coordinate system O-xyz. represents the acceleration in the y-axis direction; z represents the position coordinate of the center of mass of the drone in the z-axis direction in the global coordinate system O-xyz. represents the acceleration in the z-axis direction, σ1, σ2, σ3 represent the transformation angles of the x-axis, y-axis, and z-axis in the body coordinate system O-x'y'z' and the global coordinate system O-xyz, σ=[σ1 σ2 σ3] T is the vector representation of the MRP parameters, U1 represents the total thrust in the z' direction in the body coordinate system, and the vector F T =[F Tx F Ty F Tz ] T It represents wind force in N, m represents the mass of the drone in Kg, and g represents the acceleration due to gravity.

[0051] 2) Calculating the position tracking error of the UAV according to the above position dynamics model, and using a preset performance function to determine the position tracking error limit that satisfies the preset performance function, thereby limiting the position tracking error of the UAV;

[0052] First, the position tracking error of the UAV is expressed as:

[0053] e x =xx d (2)

[0054] Among them, x represents the position coordinate of the center of mass of the drone in the x-axis direction in the global coordinate system O-xyz, and x d represents the desired target position of the UAV;

[0055] Then, a preset performance function ρ that limits the position tracking error is constructed, and the formula is:

[0056]

[0057] Among them, k j Represents the convergence speed parameter of the position transient response, ρ0,ρ ∞ represent the initial value and steady-state value of the preset performance function respectively;

[0058] Then, using the preset performance function ρ, the limit of the position tracking error is expressed as:

[0059]

[0060] in, and δ represent preset performance control parameters.

[0061] 3) Perform an inverse function calculation on the above position tracking error to obtain the unconstrained conversion error;

[0062] For the above tracking error e x Perform an inverse function calculation to obtain the conversion error without constraints, the formula is:

[0063]

[0064] Wherein, Λ represents the position tracking error that meets the preset performance control parameters.

[0065] 4) The above conversion error is differentiated with respect to time, and the power reaching law is introduced to calculate the improved super-torsion sliding mode surface, so as to ensure the stability of the UAV under complex wind disturbances;

[0066] First, calculate the conversion error ε x The derivative with respect to time is given by:

[0067]

[0068] Then, the power reaching law is introduced to calculate the improved super-torsion sliding surface, and the formula is:

[0069]

[0070] Among them, μ,c and The constant that represents the conversion error that meets the design requirements of improved supertorsional sliding surface accuracy and stability, sgn(ε x )|ε x | 1-μ It represents the power reaching law that makes the sliding surface satisfy the rapid stability condition.

[0071] 5) According to the above-mentioned hypertorsion sliding surface, the constant velocity reaching law and the exponential reaching law are introduced to calculate the output of the preset sliding mode control of the UAV, thereby completing the design of the preset sliding mode anti-wind disturbance controller of the UAV.

[0072] First, the constant speed reaching law and exponential reaching law are introduced to calculate the output of the preset sliding mode control of the UAV. The formula is:

[0073]

[0074] in, and l represent the control gain, represents the constant velocity reaching law that ensures the stability of the sliding mode control system, represents the exponential reaching law that ensures the stability of the sliding mode control system.

[0075] The effect of the present invention can be further illustrated by the following simulation results.

[0076] Experimental setup: First, based on the UAV’s moment of inertia and mass parameters, the wind disturbance velocity range is set to [-10, 10] m / s, the preset maximum error boundary is ±0.5 m, and the preset performance control parameters are set to δ=1 and the steady-state value of the preset performance function ρ ∞ = 0.5. In Matlab, we design Figure 2 The preset sliding mode anti-wind disturbance controller of the UAV shown in the figure simulates the limited position offset control performance of the UAV when all axes are subject to complex wind disturbances. The UAV parameter settings of this experiment are shown in Table 1:

[0077] Table 1. UAV model parameters

[0078]

[0079] Figure 3 A three-dimensional position tracking diagram combined with preset performance control under wind disturbance provided by an embodiment of the present invention, Figure 4 A three-dimensional position tracking error diagram combined with preset performance control under wind disturbance provided by an embodiment of the present invention.

[0080] from Figure 3 It can be seen that within the 40-second simulation time, the position of the UAV in the x-axis, y-axis, and z-axis directions can reach the expected position within 2 seconds, and under the condition of continuous complex wind disturbances, the actual position of the UAV is controlled to be consistent with the expected position, achieving effective position tracking.

[0081] from Figure 4 It can be seen that within the 40-second simulation time, the position error of the UAV in the x-axis, y-axis, and z-axis directions can reach 0 within 2 seconds, and in the case of continuous complex wind disturbances, the position error has almost no fluctuation, and the position error will not exceed the performance envelope.

[0082] This position constraint ensures the safety of the inspected aircraft and the UAV during the aircraft skin inspection process. It can be seen that the method of the present invention can limit the position deviation of the UAV under external complex wind disturbance conditions and has strong robustness.

[0083] The method of the present invention is verified by building a simulation model. The simulation results show that the method of the present invention can quickly and stably track the input signal under complex wind disturbance conditions and has good anti-interference ability.

Claims

1. A preset sliding mode anti-wind disturbance control method for an unmanned aerial vehicle based on MRPs, characterized in that: The method comprises the following steps performed in sequence: 1) Based on the MRPs attitude representation method, the position dynamics model of the UAV under complex wind disturbance is established; 2) Calculating the position tracking error of the UAV according to the above position dynamics model, and using a preset performance function to determine the position tracking error limit that satisfies the preset performance function, thereby limiting the position tracking error of the UAV; 3) Perform an inverse function calculation on the above position tracking error to obtain the unconstrained conversion error; 4) The above conversion error is differentiated with respect to time, and the power reaching law is introduced to calculate the improved super-torsion sliding mode surface, so as to ensure the stability of the UAV under complex wind disturbances; 5) According to the above-mentioned hypertorsion sliding surface, the constant velocity reaching law and the exponential reaching law are introduced to calculate the output of the preset sliding mode control of the UAV, thereby completing the design of the preset sliding mode anti-wind disturbance controller of the UAV.

2. The MRPs-based UAV preset sliding mode anti-wind disturbance control method according to claim 1 is characterized by: In step 1), the method for establishing the position dynamics model of the UAV based on the MRPs attitude representation method is: First, the position dynamics model of the UAV under complex wind disturbance is established based on MRPs: Among them, x represents the position coordinate of the center of mass of the drone in the x-axis direction in the global coordinate system O-xyz, represents the acceleration in the x-axis direction; y represents the position coordinate of the center of mass of the drone in the y-axis direction in the global coordinate system O-xyz. represents the acceleration in the y-axis direction; z represents the position coordinate of the center of mass of the drone in the z-axis direction in the global coordinate system O-xyz. represents the acceleration in the z-axis direction, σ1, σ2, σ3 represent the transformation angles of the x-axis, y-axis, and z-axis in the body coordinate system O-x'y'z' and the global coordinate system O-xyz, σ=[σ1σ2 σ3] T is the vector representation of the MRP parameters, U1 represents the total thrust in the z' direction in the body coordinate system, and the vector F T =[F Tx F Ty F Tz ] T It represents wind force in N, m represents the mass of the drone in Kg, and g represents the acceleration due to gravity.

3. The MRPs-based UAV preset sliding mode anti-wind disturbance control method according to claim 1, characterized in that: In step 2), the position tracking error of the UAV is calculated according to the above position dynamics model, and a position tracking error limit satisfying the preset performance function is determined by using a preset performance function, thereby limiting the position tracking error of the UAV: First, the position tracking error of the UAV is expressed as: e x =x-x d (2) Among them, x represents the position coordinate of the center of mass of the drone in the x-axis direction in the global coordinate system O-xyz, and x d represents the desired target position of the UAV; Then, a preset performance function ρ that limits the position tracking error is constructed, and the formula is: Among them, k j Represents the convergence speed parameter of the position transient response, ρ0,ρ ∞ represent the initial value and steady-state value of the preset performance function respectively; Then, using the preset performance function ρ, the limit of the position tracking error is expressed as: in, and δ Indicates preset performance control parameters.

4. The MRPs-based UAV preset sliding mode anti-wind disturbance control method according to claim 1, characterized in that: In step 3), the method of performing an inverse function calculation on the position tracking error to obtain the unconstrained conversion error is: For the above tracking error e x Perform an inverse function calculation to obtain the conversion error without constraints, the formula is: Wherein, Λ represents the position tracking error that meets the preset performance control parameters.

5. The MRPs-based UAV preset sliding mode anti-wind disturbance control method according to claim 1, characterized in that: In step 4), the method of differentiating the above conversion error with respect to time, introducing the power reaching law, and calculating the improved super-torsion sliding mode surface to ensure the stability of the UAV under complex wind disturbance conditions is: First, calculate the conversion error ε x The derivative with respect to time is given by: Then, the power reaching law is introduced to calculate the improved super-torsion sliding surface, and the formula is: Among them, μ,c and The constant that represents the conversion error that meets the design requirements of improved supertorsional sliding surface accuracy and stability, sgn(ε x )|ε x | 1-μ It represents the power reaching law that makes the sliding surface satisfy the rapid stability condition.

6. The MRPs-based preset sliding mode anti-wind disturbance control for unmanned aerial vehicles according to claim 1, characterized in that: In step 5), the method of introducing the constant velocity reaching law and the exponential reaching law according to the above-mentioned super-torsion sliding mode surface, calculating the preset sliding mode control output of the UAV, and thus completing the design of the preset sliding mode anti-wind disturbance controller of the UAV is: First, the constant speed reaching law and exponential reaching law are introduced to calculate the output of the preset sliding mode control of the UAV. The formula is: in, and denote the control gain, represents the constant velocity reaching law that ensures the stability of the sliding mode control system, represents the exponential reaching law that ensures the stability of the sliding mode control system.

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