A robust-infinity-based double cascade MPC attitude control method for quadrotor unmanned aerial vehicles

Abstract

The application relates to a robust infinite-based double cascade MPC four-rotor unmanned aerial vehicle attitude control method, and a kind of robust infinite control and double cascade model predictive control (MPC) combination technology is designed.The method improves the attitude control precision and stability of unmanned aerial vehicle under random air flow disturbance by designing robust infinite controller, angle ring MPC controller and angular velocity ring MPC controller.Robust infinite controller ensures the initial stability of the system under disturbance condition, angle ring MPC optimizes attitude angle, and angular velocity ring MPC accurately controls angular velocity.Compared with traditional PID and ADRC controller, the method has significant advantages in disturbance response speed, stability and tracking accuracy.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) control technology, and specifically relates to an attitude control method for a quadrotor UAV based on robust infinity dual-cascade MPC. Background Technology

[0002] With the rapid development of drone technology, quadcopter drones have been widely used in military, agriculture, logistics and other fields. However, in actual flight, quadcopter drones often encounter various uncertain environmental factors, among which random airflow interference is a particularly common and challenging problem. Random airflow can affect the flight stability and control accuracy of drones.

[0003] To study the impact of wind disturbances on UAV control, current UAV control methods mainly include PID, sliding mode, and backstepping control. Some researchers have also proposed using neural networks to compensate for the uncertainties caused by disturbances. Although researchers have made continuous technological innovations in UAV control algorithms, when the random airflow is too large or too complex, UAV tracking always suffers from inaccurate tracking and poor attitude control stability. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings and deficiencies of the prior art and to propose a robust infinite dual-cascade MPC attitude control method for quadrotor UAVs, which solves the problems of low tracking accuracy and stable attitude control when UAVs encounter random airflow interference.

[0005] To achieve the above objectives, the technical solution provided by this invention is as follows:

[0006] A dual-cascade MPC control method based on robust infinite control includes the following steps:

[0007] Step 1: Determine the state-space equations for the continuous attitude angle channels of the quadcopter UAV as follows:

[0008]

[0009] in, Let ${... This represents the pitch, roll, and yaw angles of a quadcopter UAV. Matrix A c B c C c These represent the parameters of the system's state-space equations. This is the control input for the attitude angle of the quadcopter drone.

[0010] Step 2: Design a robust infinite controller to perform preliminary control of the UAV's attitude angles, and use the control results as input to the MPC controller;

[0011] Step 3: Discretize the state-space equations of the quadrotor UAV attitude angle channels to obtain the discretized state-space model of the quadrotor UAV attitude angles:

[0012]

[0013] in, These represent the state variables, control input variables, and control output variables of the attitude angle nominal system, respectively.

[0014] Step 4: For the control input variables of the continuous-time state model and the discrete-time state model in Step 1 The conversion relationship between the two is shown below:

[0015]

[0016] Among them, T s and The sampling time and control input matrix represent the attitude angles;

[0017] Step 5: Use the matrix K of the robust infinite controller as the initial control law to ensure that the initial state of the system is stable within a certain range;

[0018] Step 6: Design the angle loop MPC controller, optimize the objective function and calculate the optimal control input by discretizing the attitude angle dynamics model;

[0019] Step 7: Determine the kinematic equations for the attitude angular velocity of the UAV:

[0020]

[0021] Where θ, φ and These represent the pitch angle, roll angle, and yaw angle of the drone during its movement. and These represent the pitch angle angular rate, roll angle angular rate, and yaw angle angular rate, respectively. Approximate to p, Approximate to q Approximate to r;

[0022] Step 8: Design an angular velocity loop MPC controller to achieve precise control of the attitude angle by combining the velocity changes of the attitude angle.

[0023] Furthermore, the robust infinite controller in step 2 has the following workflow:

[0024] Step 2.1: Solve the generalized algebraic Riccati equation to obtain the gain matrix of the robust infinite controller. The Riccati equation has the following form:

[0025]

[0026] Where: x k This is a solution to the Riccati equation. R and Q are weight matrices. and These represent the parameters of the system state equations;

[0027] Step 2.2: via u k =-Kx k To implement the constraints, where x k This is a solution to the Riccati equation.

[0028] Furthermore, in step 6, the angle loop MPC controller's workflow includes the following steps:

[0029] Step 6.1: Take the difference between the state variables at two adjacent moments to obtain the difference equations for the attitude angles of the quadcopter UAV at two adjacent moments:

[0030]

[0031] Step 6.2: Determine the incremental model of the discrete state-space equations as follows:

[0032]

[0033] Step 6.3: Derive the control increment form of the attitude angle state increment through the difference equation of two adjacent moments of the UAV attitude angle:

[0034]

[0035] Step 6.4: Determine the incremental form of the difference equations for the quadcopter UAV:

[0036]

[0037] Step 6.5: For the nominal model of attitude angles, select the objective optimization function:

[0038]

[0039] Step 6.6: Obtain the optimal control input sequence for the attitude angle at time k:

[0040]

[0041] Step 6.7: Determine the system input Δu at time k. ζ The value of (k) is used to select the optimal input sequence ΔU. ζ * The first element of (k) yields the system input expression as follows:

[0042]

[0043] Step 6.8: Finally, obtain the actual control input expression for the attitude angle at time k:

[0044] Δu ζ (k)=K ζmpc E ζ (k+1|k)=Δu f (k)+Δu s (k).

[0045] Furthermore, in step 8, the angular velocity loop MPC controller's workflow includes the following steps:

[0046] Step 8.1: Establish the state-space equations for the attitude angle control system with disturbances as follows:

[0047]

[0048] y = Cx + Du

[0049] in:

[0050]

[0051] Where x = [p, q, r, φ, θ, ψ] T u = [τ φ ,τ θ ,τ ψ ] T , σ i (i = u, v, w) represents the turbulence intensity in the x, y, and z directions, and L i (i = u, v, w) represents the turbulence scale in the x, y, and z directions, and V represents the flight speed of the UAV.

[0052] Step 8.2: The design of the subsequent MPC angular velocity loop controller is the same as the angle loop setting.

[0053] The dual-cascade MPC control method based on robust infinite control proposed in this invention has the following advantages compared with the prior art:

[0054] 1. Improve system stability: By setting the MPC angle loop as the main controller and the angular velocity loop as the auxiliary controller, the oscillations caused by real-time attitude adjustment are reduced, enabling the UAV to recover balance more quickly after encountering disturbances, thereby enhancing the robustness and stability of the system.

[0055] 2. Reduced computational complexity: Robust infinite control introduces angle loop preprocessing data, which reduces the MPC controller's need to process real-time data, lowers computational complexity, and improves the efficiency of the control system;

[0056] 3. Optimized control accuracy: By using the MPC optimization algorithm, the deviation between the prediction error and the control target is minimized, ensuring high accuracy of UAV attitude control, especially when dealing with complex environments or disturbances, it shows better control performance. Attached Figure Description

[0057] Figure 1 The flowchart is a method for attitude control of a quadrotor UAV based on robust infinity dual-cascade MPC proposed in this invention.

[0058] Figure 2 This is a schematic diagram of the attitude control structure for a quadrotor UAV based on robust infinity dual-cascade MPC proposed in this invention.

[0059] Figure 3 The random airflow disturbance curve in Experiment Example 1;

[0060] Figure 4 The trajectory tracking curve in the X-axis direction in Experiment Example 1;

[0061] Figure 5 The Y-axis trajectory tracking curve in Experiment Example 1;

[0062] Figure 6 The trajectory tracking curve in the Z-axis direction in Experiment Example 1;

[0063] Figure 7 The pitch angle trajectory tracking curve in Experiment Example 1;

[0064] Figure 8 The roll angle trajectory tracking curve in Experiment Example 1;

[0065] Figure 9 The yaw angle trajectory tracking curve in Experiment Example 1;

[0066] Figure 10 The root mean square error curve of yaw angle in Experiment Example 1;

[0067] Figure 11 The root mean square error curve of pitch angle in Experiment Example 1;

[0068] Figure 12 The root mean square error curve of the roll angle in Experiment Example 1;

[0069] Figure 13 The yaw angle and angular velocity curves from Experiment Example 1;

[0070] Figure 14 The roll angle angular velocity curve in Experiment Example 1;

[0071] Figure 15 The pitch angle and angular velocity curves are from Experiment Example 1. Detailed Implementation

[0072] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application. These fall within the protection scope of the present application.

[0073] Example 1

[0074] This application discloses a dual-cascade MPC control method based on robust infinite control, comprising the following steps:

[0075] Step 1: Determine the state-space equations for the continuous attitude angle channels of the quadcopter UAV as follows:

[0076]

[0077] in, Let ${... This represents the pitch, roll, and yaw angles of a quadcopter UAV. Matrix A c B c C c These represent the parameters of the system's state-space equations. This is the control input for the attitude angle of the quadcopter drone;

[0078] Step 2: Design a robust infinite controller to perform preliminary control of the UAV's attitude angles, and use the control results as input to the MPC controller;

[0079] Step 3: Discretize the state-space equations of the quadrotor UAV attitude angle channels to obtain the discretized state-space model of the quadrotor UAV attitude angles:

[0080]

[0081] in, These represent the state variables, control input variables, and control output variables of the attitude angle nominal system, respectively.

[0082] Step 4: For the control input variables of the continuous-time state model and the discrete-time state model in Step 1 The conversion relationship between the two is shown below:

[0083]

[0084] Among them, T s and The sampling time and control input matrix represent the attitude angles;

[0085] Step 5: Use the matrix K of the robust infinite controller as the initial control law to ensure that the initial state of the system is stable within a certain range;

[0086] Step 6: Design the angle loop MPC controller, optimize the objective function and calculate the optimal control input by discretizing the attitude angle dynamics model;

[0087] Step 7: Determine the kinematic equations for the attitude angular velocity of the UAV:

[0088]

[0089] Where θ, φ and These represent the pitch angle, roll angle, and yaw angle of the drone during its movement. and These represent the pitch angle angular rate, roll angle angular rate, and yaw angle angular rate, respectively. Approximate to p, Approximate to q Approximate to r;

[0090] Step 8: Design an angular velocity loop MPC controller to achieve precise control of the attitude angle by combining the velocity changes of the attitude angle.

[0091] Furthermore, the robust infinite controller in step 2 has the following workflow:

[0092] Step 2.1: Solve the generalized algebraic Riccati equation to obtain the gain matrix of the robust infinite controller. The Riccati equation has the following form:

[0093]

[0094] Where: x k This is a solution to the Riccati equation. R and Q are weight matrices. and These represent the parameters of the system state equations;

[0095] Step 2.2: via u k =-Kx k To implement the constraints, where x k This is a solution to the Riccati equation.

[0096] Furthermore, in step 6, the angle loop MPC controller's workflow includes the following steps:

[0097] Step 6.1: Take the difference between the state variables at two adjacent moments to obtain the difference equations for the attitude angles of the quadcopter UAV at two adjacent moments:

[0098]

[0099] Step 6.2: Determine the incremental model of the discrete state-space equations as follows:

[0100]

[0101] Step 6.3: Derive the control increment form of the attitude angle state increment through the difference equation of two adjacent moments of the UAV attitude angle:

[0102]

[0103] Step 6.4: Determine the incremental form of the difference equations for the quadcopter UAV:

[0104]

[0105] Step 6.5: For the nominal model of attitude angles, select the objective optimization function:

[0106]

[0107] Step 6.6: Obtain the optimal control input sequence for the attitude angle at time k:

[0108]

[0109] Step 6.7: Determine the system input Δu at time k. ζ The value of (k) is used to select the optimal input sequence ΔU. ζ * The first element of (k) yields the system input expression as follows:

[0110]

[0111] Step 6.8: Finally, obtain the actual control input expression for the attitude angle at time k:

[0112] Δu ζ (k)=K ζmpc E ζ (k+1|k)=Δu f (k)+Δu s (k).

[0113] Furthermore, in step 8, the angular velocity loop MPC controller's workflow includes the following steps:

[0114] Step 8.1: Establish the state-space equations for the attitude angle control system with disturbances as follows:

[0115]

[0116] in:

[0117]

[0118] Where x = [p, q, r, φ, θ, ψ] T u = [τ φ ,τ θ ,τ ψ ] T , σ i (i = u, v, w) represents the turbulence intensity in the x, y, and z directions, and L i (i = u, v, w) represents the turbulence scale in the x, y, and z directions, and V represents the flight speed of the UAV.

[0119] Step 8.2: The design of the subsequent MPC angular velocity loop controller is the same as the angle loop setting.

[0120] The following simulation demonstrates the effectiveness and feasibility of the dual-cascade MPC control method based on robust infinite control disclosed in this application, as shown in the following details:

[0121] The parameters of the UAV in the simulation experiment are listed below: mass of the quadcopter UAV m = 0.698 kg, distance from the rotor center to the center of mass d = 0.171 m, and gravitational acceleration g = 9.8 m / s². -2 Lift coefficient C T =7.6184×10 (-8) ×(60 / (2×pi)) 2 N·s -2 X / Y moment of inertia J xx / J yy =0.0034 kg·m 2 Anti-torque coefficient C m =2.6839×10 (-9) ×(60 / (2×pi)) 2 N·m·s -2 Rotor moment of inertia J m =1.302×10 (-6) Kg·m 2 and Z-axis rotational inertia J zz =0.0060 kg·m 2 .

[0122] The simulation results are as follows:

[0123] In the figure, target is the target tracking curve, proportional-integral-derivative (PID) controller and active disturbance rejection controller (ADRC) are control experimental curves, and cascade MPC control based on robust infinite control (H-MMPC) is the attitude control algorithm designed in this invention. Figures 3-9It can be concluded that after the disturbance occurs, the UAV experiences a small disturbance around 2.9s, 31.7s, and 71.7s. However, by comparison, the amplitude and duration of the H-MMPC disturbance are smaller than those of the ADRC and PID controllers, respectively, but the overall difference is not significant. This is because the position loop uses traditional MPC, ADRC, and PID controllers.

[0124] The design using the H-MMPC controller in the attitude loop is significantly superior to ADRC and PID, exhibiting better robustness. This is evident in the pitch-time curves, where the H-MMPC controller shows fewer amplitude fluctuations and jitters, smaller jitter amplitudes, and shorter convergence times. This phenomenon is even more pronounced in the roll-time curve, where amplitude fluctuations remain essentially within a maximum of 0.005, negligible for a UAV. However, in the yaw-time curve, traditional ADRC and PID curves initially exhibit a small jitter, while the H-MMPC controller stably follows the target curve with excellent tracking performance. Overall, different control methods show varying response speeds when adjusting the target angle. It can be observed that the H-MMPC controller consistently responds fastest when disturbances occur. Furthermore, in terms of stability, H-MMPC and ADRC consistently approach the target curve most of the time, demonstrating better stability. PID, on the other hand, exhibits larger fluctuations during disturbances and shows relatively poor stability.

[0125] Figure 10 , 11 Figures 1 and 12 show the root mean square error curves for pitch, roll, and yaw angles. As can be seen in the figures, error fluctuations occur around 11, 30, 51, and 91 seconds. This is due to the addition of a disturbance to the UAV around these time points, simulating random airflow disturbances. However, the UAV's attitude quickly stabilizes after the controller adjusts. After each peak in the error value, the error rapidly decreases and approaches zero, indicating that the proposed control algorithm has strong recovery capability. Except for fluctuations after the applied disturbance, the overall error level remains low, further demonstrating the good stability of this control algorithm.

[0126] Figure 13 , 14 Figure 15 shows the angular velocity curves for pitch, roll, and yaw angles. The attitude angles of a quadcopter UAV serve as an auxiliary loop in attitude control, and their overall velocity change trend always changes with disturbances. When random airflow disturbances increase, the angular velocity of the attitude angles will also change, but its trend differs from that of the attitude angles. Once the UAV control is stable, the angular velocity of the attitude angles will always be at zero and will not fluctuate.

[0127] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions that are any combination of the above technical features. It should be noted that for those skilled in the art, various improvements and modifications can be made without departing from the principle of this invention, and these modifications are also considered within the scope of protection of this invention.

Claims

1. A robust infinite-cascade dual-cascade MPC attitude control method for a quadrotor UAV, used for flight attitude control of the UAV. The core design of this method is to set the model predictive control (MPC) angle loop as the main controller, responsible for the main adjustment of the UAV attitude, while the MPC angular velocity loop serves as an auxiliary controller. The MPC angle loop has a long control cycle and prioritizes attitude adjustment, while the MPC angular velocity loop is used to quickly respond to angular velocity changes with a short control cycle. The attitude controller is based on model predictive control and minimizes the deviation between the prediction error and the control target through optimization algorithms. In order to reduce the computational complexity of the MPC controller and enhance the robustness of the system, robust infinite control is introduced into the MPC angle loop. This robust infinite control first preprocesses the data to reduce the sensitivity of the system to external disturbances, and then transmits the processed data to the MPC angle loop controller, thereby improving the stability and accuracy of attitude control. The method includes the following steps: Step 1: Determine the state-space equations for the continuous attitude angle channels of the quadcopter UAV as follows: in, Let ${... Matrix A represents the pitch, roll, and yaw angles of a quadcopter drone. c B c C c These represent the parameters of the system's state-space equations. This is the control input for the attitude angle of the quadcopter drone; Step 2: Design a robust infinite controller to perform preliminary control of the UAV's attitude angles, and use the control results as input to the MPC controller; Step 3: Discretize the state-space equations of the quadrotor UAV attitude angle channels to obtain the discretized state-space model of the quadrotor UAV attitude angles: in, These represent the state variables, control input variables, and control output variables of the attitude angle nominal system, respectively. Step 4: For the control input variables of the continuous-time state model and the discrete-time state model in Step 1 The conversion relationship between the two is shown below: Among them, T s and The sampling time and control input matrix represent the attitude angles; Step 5: Use the matrix K of the robust infinite controller as the initial control law to ensure that the initial state of the system is stable within a certain range; Step 6: Design the angle loop MPC controller, optimize the objective function and calculate the optimal control input by discretizing the attitude angle dynamics model; Step 7: Determine the kinematic equations for the attitude angular velocity of the UAV: Where θ, φ and These represent the pitch angle, roll angle, and yaw angle of the drone during its movement. and These represent the pitch angle angular rate, roll angle angular rate, and yaw angle angular rate, respectively. Approximate to p, Approximate to q Approximate to r; Step 8: Design an angular velocity loop MPC controller to achieve precise control of the attitude angle by combining the velocity changes of the attitude angle.

2. The attitude control method for a quadrotor UAV based on robust infinity dual-cascade MPC according to claim 1, characterized in that, The robust infinite controller described in step 2 has the following workflow: Step 2.1: Solve the generalized algebraic Riccati equation to obtain the gain matrix of the robust infinite controller; the Riccati equation has the following form: Where: x k These are solutions to the Riccati equation, where R and Q are weight matrices. and These represent the parameters of the system state equations; Step 2.2: via u k =-Kx k To implement the constraints, where x k This is a solution to the Riccati equation.

3. The attitude control method for a quadrotor UAV based on robust infinity dual-cascade MPC according to claim 1, characterized in that, The angle loop MPC controller described in step 6 has the following workflow: Step 6.1: Take the difference between the state variables at two adjacent moments to obtain the difference equations for the attitude angles of the quadcopter UAV at two adjacent moments: Step 6.2: Determine the incremental model of the discrete state-space equations as follows: Step 6.3: Derive the control increment form of the attitude angle state increment through the difference equation of two adjacent moments of the UAV attitude angle: Step 6.4: Determine the incremental form of the difference equations for the quadcopter UAV: Step 6.5: For the nominal model of attitude angles, select the objective optimization function: Step 6.6: Obtain the optimal control input sequence for the attitude angle at time k: Step 6.7: Determine the system input Δu at time k. ζ The value of (k) is used to select the optimal input sequence. The first element yields the system input expression as follows: Step 6.8: Finally, obtain the actual control input expression for the attitude angle at time k: Δu ζ (k)=K ζmpc E ζ (k+1|k)=Δu f (k)+Δu s (k)。 4. The attitude control method for a quadrotor UAV based on robust infinity dual-cascade MPC according to claim 1, characterized in that, The angular velocity loop MPC controller described in step 8 has the following working steps: Step 8.1: Establish the state-space equations for the attitude angle control system with disturbances as follows: y = Cx + Du in: Where x = [p, q, r, φ, θ, ψ] T u = [τ φ ,τ θ ,τ ψ ] T , σ i (i = u, v, w) represents the turbulence intensity in the x, y, and z directions, and L i (i = u, v, w) represents the turbulence scale in the x, y, and z directions, and V represents the flight speed of the UAV. Step 8.2: The design of the subsequent MPC angular velocity loop controller is the same as the angle loop setting.

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