Four-rotor unmanned aerial vehicle differential flatness control method based on optimized LQR

Abstract

The invention discloses a quadrotor unmanned aerial vehicle differential flatness control method based on an optimized LQR, and the method comprises the steps: a system receives the control reference quantity of an unmanned aerial vehicle from a planning end, and obtains the physical constraint information of the unmanned aerial vehicle from an actual environment; constructing a constraint function based on an LQR algorithm, and limiting the maximum value of the acceleration of the control instruction; adding constraint conditions, and determining a feasible solution range of the optimization problem; according to an unmanned aerial vehicle thrust margin limit acceleration instruction calculated in real time, optimal acceleration output is solved under constraint conditions, and the control target of the unmanned aerial vehicle in a complex environment is achieved under the condition that physical constraint information of the unmanned aerial vehicle is met. According to the method, the reference target and the physical constraint are combined, and on the basis of the advantages of excellent differential flatness control performance and relatively low calculation power overhead, an NMPC optimization algorithm is introduced into acceleration vector calculation of the differential flatness controller, so that efficient and safe movement of the unmanned aerial vehicle in a complex environment is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of quad-rotor unmanned aerial vehicle motion control, and in particular to a quad-rotor unmanned aerial vehicle differential flatness control method based on optimized LQR. Background Art

[0002] In the control of quadrotor drones, linearizing the quadrotor model and then performing proportional-integral-derivative (PID) or linear quadratic regulation (LQR) control is a common and mature control method. Linearizing complex nonlinear dynamic models into simple linear models can significantly reduce the difficulty of controller design. However, these two control methods also have many limitations. First, the effectiveness of the linearized model is highly dependent on the approximate assumptions near the working point, that is, the yaw angle, pitch angle, and roll angle of the drone need to be kept within a small range. When the drone performs large-angle flight operations, such as rapid rolls or violent maneuvers, this linearization assumption often fails, resulting in a large deviation between the model and the actual system dynamics. In addition, linear controllers are inherently difficult to cope with complex aerodynamic disturbances and significant nonlinear dynamic characteristics in high-speed flight, such as the coupling effect between rotors and the nonlinear change of air resistance. These factors will reduce the robustness of the controller, thereby affecting the stability and response performance of the system.

[0003] In the prior art, differential flat controllers (DFBCs) have shown significant improvements in trajectory tracking performance during high-speed flight. The differential flatness characteristic is a dynamic system property that allows the system to calculate the control input directly from the desired trajectory without solving complex dynamic equations. In quadrotor drone control, the differential flat control method directly calculates the attitude, angular velocity, and acceleration from the given trajectory to achieve high-precision tracking of the predetermined trajectory. However, since this method does not inherently rely on optimization solutions, it cannot guarantee the optimality of the control input or the satisfaction of the constraints. Therefore, additional optimization strategies may be required to ensure the optimality of the control input when facing operational constraints.

[0004] Another control algorithm is model predictive control (NMPC), which is able to predict future states for multiple time steps and calculate the corresponding control inputs. Thanks to the progress of hardware and nonlinear optimization solvers in recent years, nonlinear model predictive control based on full-state dynamics can meet real-time requirements. NMPC can fully utilize the performance of the UAV and take into account actuator saturation constraints. However, running NMPC on hardware with limited computing power is still very challenging. In addition, NMPC may face numerical convergence problems when the system delay is large or the model error is significant, which manifests as a high instability or crash rate. It can be seen that NMPC is more suitable for highly dynamic mission scenarios that require full exploitation of platform performance and handling dynamically infeasible trajectories.

[0005] Therefore, how to introduce the NMPC optimization algorithm into the acceleration vector calculation of the differential flat controller of the quadrotor UAV, while reducing the computing power overhead and allowing the quadrotor UAV to adapt to obtain the optimal control effect in different complex environments, needs further research. Summary of the invention

[0006] The problem to be solved by the present invention is: to provide a differential flat control method for a quadrotor unmanned aerial vehicle based on optimized LQR, introduce the NMPC optimization algorithm into the acceleration vector calculation of the differential flat controller, while reducing the computing power overhead, allowing the quadrotor unmanned aerial vehicle to adapt to obtain the optimal control effect in different complex environments.

[0007] The present invention adopts the following technical solution: a differential flat control method for a quadrotor drone based on optimized LQR, comprising the following steps: Step 1: Data collection: The control system receives the control reference of the UAV from the planning end and obtains the physical constraint information of the UAV from the actual environment; constructs the body coordinate system and rotation matrix of the quadcopter UAV, and calculates the expected acceleration of the UAV through the control reference; Step 2: Construct constraint function: The control system generates the control command of the UAV by combining the control reference and the physical constraint, and calculates the control command acceleration; constructs the constraint function based on the LQR algorithm to limit the maximum value of the control command acceleration; Step 3, adding constraints: adding physical constraints of the drone to determine the range of feasible solutions to the optimization problem; the constraints are real-time linear constraints, including obstacle avoidance constraints in path planning and constraints of the dynamics model; Step 4. Solve for the optimal acceleration: Based on the real-time calculated UAV thrust margin limit acceleration instruction, the control system uses the interior point algorithm to solve the real-time optimal acceleration that meets the physical constraints of the UAV, and pass the optimal acceleration to the differential flat controller for control. The output of the desired attitude is passed to the flight control software for tracking, thereby achieving the control target of the UAV in a complex environment.

[0008] Preferably, in step 1, the control reference quantity provides an expected flight trajectory for the UAV, which is obtained from the planning end through trajectory planning calculation, including a reference speed and a reference acceleration of the UAV.

[0009] The reference coordinate system is defined in world coordinates and is expressed as ; Define the drone's body coordinate system, expressed as The body coordinate system is fixed to the quadrotor drone, and the origin and the center of mass of the drone are coincide; The quadcopter drone is subject to The gravitational acceleration g in the direction of the body coordinate system is rotated relative to the world coordinate system by the rotation matrix express, , Represents the rotation matrix from the body coordinate system to the world coordinate system; The desired acceleration vector of the quadrotor drone is calculated by controlling the reference quantity.

[0010] Preferably, in step 1, the physical constraint information is obtained from the actual environment, which is the state variable of the drone in the current environment, including: maximum speed, maximum acceleration, and motion capacity limit. The specific method is as follows: Step 1.1, obtain the maximum lift generated by the quadcopter rotor, subtract gravity, and obtain the current thrust margin that can provide the drone with agile flight; Step 1.2: By obtaining the current state of the UAV, the thrust margin is mapped to the UAV body coordinate system to obtain the dynamic constraint of the thrust. When solving the objective function, dynamic boundary conditions are added so that the target value does not exceed the maximum physical limit.

[0011] Preferably, in step 2, the acceleration of the drone control command is calculated by considering the influence of gravity acceleration and air resistance. ; Use zxy sequence to describe the rotation of the quadrotor and define intermediate variables and , by the acceleration and the reference yaw angle , the calculated aircraft attitude The corresponding three-axis orthogonal unit vectors .

[0012] Preferably, in step 2, select the three-axis position and speed As state variable, choose acceleration As input variables, a constraint function is constructed based on the LQR algorithm, and the LQR optimization is described as: ; Among them, the objective function For minimizing state cost and input energy, represents the prediction time domain, Indicates The state variables at time, Indicates The optimization variable at time, Represents the state variable at the terminal moment; subscripts Q and R represent matrices and ,matrix and It is a diagonal matrix. The diagonal elements represent the weights assigned to the state variables or inputs. The weight values ​​indicate the convergence speed of the corresponding state or input. Subscript Represents the terminal status, matrix is the diagonal matrix associated with the terminal states.

[0013] Preferably, in step 3, the physical constraint condition of the drone is added, and the expression is: ; ; ; ; Among them, formula (11b) and (11c) are the initial state constraint and dynamic constraint respectively. Indicates the initial value of the state at the start of the optimizer iteration. Indicates The optimization variable value at time is the system matrix and is the input matrix; Formulas (11d) and (11e) represent the state and input limits, respectively. , Respectively represent the upper and lower bounds of the state variable, Respectively represent the upper and lower bounds of the optimization variable.

[0014] Preferably, in step 4, the acceleration instruction is limited according to the thrust margin of the drone calculated in real time, and the specific method is as follows:

[0015] Get the lift and maximum lift corresponding to the current throttle of the drone motor. When applying dynamic constraints, convert the drone thrust margin into thrust components in the three-axis direction, recorded as ;

[0016] Convert the thrust margin into acceleration margin and solve for the current UAV acceleration margin , as the optimization variable Physical constraints added to solve the optimization function in formula (11e); the acceleration margin Substitute into formula (11e) and calculate the dynamic boundary conditions of the objective function to obtain the optimized , which is used to ensure that the target value obtained when solving the objective function does not exceed the maximum physical limit.

[0017] Preferably, in step 4, the interior point algorithm is specifically as follows: The state equation and control input of the quadrotor system are modeled by CasADi software, the optimization objective function and constraints are constructed, and the LQR problem is transformed into an optimization problem. The optimization problem is solved using the interior point solver provided by the CasADi software, and the control input is iteratively optimized in each control cycle until convergence to the optimal solution; Update the drone control system status according to the optimal control input to ensure trajectory tracking accuracy and system stability.

[0018] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects: 1. The differential flat control method for a quadrotor UAV based on optimized LQR of the present invention, based on the advantages of excellent differential flat control performance and low computing power overhead, introduces the optimization algorithm based on NMPC into the acceleration vector calculation of the differential flat controller, which makes up for the problem that the traditional DFBC controller cannot obtain the optimal control output in real time according to the environment; since the acceleration vector calculation itself is linear, the optimized LQR problem constructed in this way will not bring about the problem of fast flight linearization failure caused by the linearization of the nonlinear model of the quadrotor UAV faced by the classic LQR problem, and at the same time, the solution of the linear model will not cause the optimization algorithm to cause the problem of excessive computing power overhead of the edge computing unit, which greatly improves the control tracking performance.

[0019] 2. The differential flat control method of the quadrotor UAV based on the optimized LQR introduces the optimization problem into the differential flat control algorithm. By combining the reference target and physical constraints, the quadrotor UAV can adaptively obtain the optimal control effect in different complex environments and achieve efficient and safe movement. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a flow chart of the differential flat control method based on optimizing LQR of the present invention; Figure 2 A physical constraint flow chart for obtaining a quadrotor drone for the present invention; Figure 3 It is a schematic diagram of the coordinate system definition and propeller serial number definition of the present invention; Figure 4 This is a comparison diagram of trajectory tracking effects of an embodiment of the present invention; Figure 5 This is a comparison diagram of the root mean square error of trajectory tracking according to an embodiment of the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the application is further elaborated in detail below in conjunction with the accompanying drawings. The described embodiments are only a part of the embodiments involved in the present invention. All non-innovative embodiments of other researchers in the field on this embodiment belong to the protection scope of the present invention. At the same time, for the step numbering in the embodiment of the present invention, it is only set for the convenience of explanation, and the order between the steps is not limited in any way. The execution order of each step in the embodiment can be adaptively adjusted according to the understanding of those skilled in the art.

[0022] In one embodiment of the present invention, a differential flat control method for a quadrotor drone based on optimized LQR is provided. Figure 1 As shown, the following steps are included: Step 1, data collection: The control system receives the control reference of the UAV from the planning end, including the reference speed or reference acceleration. These references provide the expected flight trajectory for the UAV. At the same time, the control system obtains the physical constraint information of the UAV from the environment. These constraints may include maximum acceleration, maximum speed, and other movement capacity restrictions. This information is used as input to provide a basis for the subsequent construction of constraint functions.

[0023] Step 2: Construct constraint function: This constraint function is the core part of the optimization problem. It combines the control reference and physical constraints to ensure that the generated control instructions can achieve the goal in practical applications and meet the physical limitations of the drone. For example, in high-speed flight missions, the constraint function will limit the maximum value of acceleration to avoid exceeding the hardware capabilities of the drone.

[0024] Step 3: Add constraints: After building the constraint function, the control system further adds constraints that define the range of feasible solutions to the optimization problem. The added constraints are real-time linear restrictions, such as obstacle avoidance constraints in path planning or restrictions in the dynamics model.

[0025] Step 4: Solve for the optimal acceleration: The control system uses the interior point method as the optimization algorithm to solve the optimal acceleration output under constraints. The interior point method is a linear / nonlinear optimization method that can efficiently handle optimization problems with complex constraints. The final generated acceleration output not only satisfies the physical constraints, but also effectively achieves the control objectives of the UAV.

[0026] In this embodiment, the physical constraints of the drone are obtained from the environment, such as Figure 2 As shown, the main steps include: First, obtain the maximum lift that the drone rotor can generate, subtract gravity, and get the current thrust margin that can provide agile flight; Secondly, by obtaining the current UAV state, the thrust margin is mapped to the UAV body coordinate system to obtain the dynamic constraint of the thrust.

[0027] In this embodiment, vectors are represented by bold lowercase letters, and matrices are represented by bold uppercase letters. Unless otherwise specified, other symbols represent scalars.

[0028] Orthogonal basis Define a world coordinate system The reference coordinate system is represented by an orthogonal basis Define a body coordinate system Represents the body coordinate system, both coordinate systems are described in world coordinates.

[0029] The body coordinate system is fixed to the quadrotor drone, and its origin coincides with the center of mass of the drone, such as Figure 3 As shown, the quadcopter is subjected to The effect of gravitational acceleration g in the direction.

[0030] Furthermore, in this embodiment, the symbol represents the position of the center of mass of the drone, and uses its corresponding derivative (speed , acceleration , jerk , jerk ). The rotation of the body coordinate system relative to the world coordinate system is described by the rotation matrix It can also be represented by quaternion In describing the rotation, Represents the rotation matrix from the body coordinate system to the world coordinate system.

[0031] In this embodiment, the subscript Used to indicate the reference value obtained from the reference trajectory. Used to represent the expected value calculated by the outer loop controller. Used to represent control instruction values ​​that are directly passed to the underlying controller for calculation.

[0032] In traditional outer loop control, the desired acceleration vector of the quadrotor drone is Calculated from position error, velocity error and reference trajectory, the expression is as follows: ; in, The acceleration, position and velocity values ​​obtained directly from the reference trajectory are usually calculated by trajectory planning; are the current state variables obtained by the sensor or estimator, A proportionality factor that determines how much the error affects acceleration.

[0033] Furthermore, the expected acceleration The effects of gravity acceleration and air resistance are ignored, so it cannot be used directly for attitude calculation or underlying control execution. It is used to directly calculate the acceleration of attitude or underlying control instructions. , expressed as: ; in, Indicates that the quadcopter is subject to negative The influence of gravitational acceleration g in the direction, Represents the rotation matrix The transpose of Indicates the drag coefficient of the drone during flight.

[0034] This embodiment uses the order of zxy to describe the rotation of the quadrotor, so the intermediate variable is defined and , expressed as: ; in, is the reference yaw angle obtained from the reference trajectory.

[0035] Furthermore, in the body coordinate system, , and They must be orthogonal to each other and must be unit vectors. Under this constraint, the rotation matrix of the drone control command use: ; It is expressed as: ; in, Expressed by acceleration and the reference yaw angle The calculated aircraft attitude The corresponding three-axis orthogonal unit vectors.

[0036] LQR is an optimization control algorithm that aims to minimize a quadratic cost function to achieve a balance between system performance and control energy. This embodiment further calculates the control input by solving a set of linear equations to ensure the stability and optimality of the system response.

[0037] To apply LQR to acceleration control, select the three-axis position and speed As state variable, choose acceleration As input variables, as shown in formulas (9) and (10): ; in, Represents the position variable of the quadrotor's center of mass in the world coordinate system, represents the velocity variable of the quadrotor center of mass in the world coordinate system, Represents the acceleration variable of the quadrotor's center of mass in the world coordinate system; Respectively represent the optimization function state variables and optimization variables.

[0038] Therefore, the LQR optimization is described as: ; Among them, the objective function in formula (11a) is Used to minimize state cost and input energy, predict time domain It will affect the accuracy of the prediction output. Values ​​can provide more accurate predictions, but at the same time increase the computational cost; Indicates The state variables at time, Indicates The optimization variable at time, A state variable representing a terminal moment.

[0039] matrix and It is a diagonal matrix whose diagonal elements represent the weights assigned to the state variables or inputs. A larger weight value indicates that the corresponding state or input can converge faster. is the diagonal matrix associated with the terminal states.

[0040] The initial state constraints and dynamic constraints are expressed in equations (11b) and (11c), respectively, and equations (11d) and (11e) represent the limits of the state and input.

[0041] According to formulas 3 and 4, the system matrix and the input matrix It is expressed as: ; in, Represents the period of the controller, and the missing elements in the matrix are 0.

[0042] Furthermore, in flight missions in highly dynamic or complex environments, excessive acceleration commands often lead to thrust saturation or insufficient power for the drone. The core of this problem is that it is difficult for drones to meet their physical constraints in highly dynamic or complex environments.

[0043] During flight, if the acceleration command is too large, the required thrust may exceed the maximum output capacity of the motor and propeller, resulting in thrust saturation. Thrust saturation will cause the actual output force to be unable to meet the control requirements, causing the aircraft's attitude and trajectory to deviate, and may even cause loss of control.

[0044] Therefore, by applying dynamic constraints, the acceleration command can be limited according to the thrust margin calculated in real time to avoid trajectory deviation caused by thrust saturation.

[0045] The thrust margin is the additional force generated by the rotation of the four rotors of the drone to offset gravity and provide agile flight. It is a scalar, but when applying dynamic constraints, it needs to be converted into thrust components in the three-axis direction, recorded as .

[0046] ; Convert the thrust margin to acceleration margin: ; The calculated The range constraint is added to the constraint equation (11e) of the optimization problem to ensure that the target value solved does not exceed the maximum physical limit, thereby improving the accuracy of trajectory tracking.

[0047] Finally, the optimal acceleration obtained is passed to the differential flat controller for control, and the desired attitude is output and transmitted to the Pixhawk flight control software for tracking to achieve the control target of the UAV in a complex environment.

[0048] Furthermore, the LQR method with added constraints in the present invention is compared with the classical controller in real machine trajectory tracking, as shown in Figure 4 and Figure 5 shown.

[0049] Figure 4 The tracking effect of the "8"-shaped trajectory within the range of 2*2 is shown. It can be seen that the LQR algorithm with added constraints proposed in the present invention has better tracking performance than the traditional DFBC algorithm, and the trajectory curve is more in line with the expected curve.

[0050] Figure 5 The root mean square error (RMSE) of the calculated trajectory tracking is shown. It can be seen that the root mean square error of the LQR method with added constraints proposed in the present invention is lower than the tracking error of the traditional DFBC controller, and the tracking effect is better.

[0051] It can be seen that the differential flat control method for quadrotor UAV based on optimized LQR proposed in the present invention combines reference targets and physical constraints. Based on the advantages of excellent differential flat control performance and low computing power overhead, the optimization algorithm of NMPC is introduced into the acceleration vector calculation of the differential flat controller, which can ensure that the quadrotor UAV can achieve efficient and safe movement in complex environments.

[0052] 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 principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A differential flat control method for a quadrotor drone based on optimized LQR, characterized in that: The steps include: Step 1: Data collection: The control system receives the control reference of the UAV from the planning end and obtains the physical constraint information of the UAV from the actual environment; constructs the body coordinate system and rotation matrix of the quadcopter UAV, and calculates the expected acceleration of the UAV through the control reference; Step 2: Construct constraint function: The control system generates the control command of the UAV by combining the control reference and the physical constraint, and calculates the control command acceleration; constructs the constraint function based on the LQR algorithm to limit the maximum value of the control command acceleration; Step 3, adding constraints: adding physical constraints of the drone to determine the range of feasible solutions to the optimization problem; the constraints are real-time linear constraints, including obstacle avoidance constraints in path planning and constraints of the dynamics model; Step 4. Solve for the optimal acceleration: Based on the real-time calculated UAV thrust margin limit acceleration instruction, the control system uses the interior point algorithm to solve the real-time optimal acceleration that meets the physical constraints of the UAV, and pass the optimal acceleration to the differential flat controller for control. The output of the desired attitude is passed to the flight control software for tracking, thereby achieving the control target of the UAV in a complex environment.

2. The differential flat control method of a quadrotor drone based on optimized LQR according to claim 1, characterized in that: In step 1, the control reference quantity provides the expected flight trajectory for the UAV, which is obtained from the planning end through trajectory planning calculation, including the reference speed and reference acceleration of the UAV; The reference coordinate system is defined in world coordinates and is expressed as ; Define the drone's body coordinate system, expressed as The body coordinate system is fixed to the quadrotor drone, and the origin and the center of mass of the drone are coincide; The quadcopter drone is subject to The gravitational acceleration g in the direction of the body coordinate system is rotated relative to the world coordinate system by the rotation matrix express, .

3. The differential flat control method of a quadrotor drone based on optimized LQR according to claim 2 is characterized in that: In step 1, the physical constraint information of the drone is obtained from the actual environment. The physical constraint information is the state variables of the drone in the current environment, including: maximum speed, maximum acceleration, and motion capacity limit. The specific method is as follows: Step 1.1, obtain the maximum lift generated by the quadcopter rotor, subtract gravity, and obtain the current thrust margin for the drone flight; Step 1.2: By obtaining the current state of the UAV, the thrust margin is mapped to the UAV body coordinate system to obtain the dynamic constraint of the thrust, which is used to add dynamic boundary conditions when solving the objective function so that the target value does not exceed the maximum physical limit.

4. The differential flat control method of a quadrotor drone based on optimized LQR according to claim 2 is characterized in that: In step 1, the desired acceleration vector of the quadrotor drone is calculated by controlling the reference quantity, and the expression is: ； in, is the expected acceleration of the UAV; To control the reference speed in the reference quantity, To control the reference acceleration in the reference quantity, for location; are the current position and speed of the UAV obtained by the sensor or estimator respectively; A proportionality factor that determines how much the error affects acceleration.

5. The differential flat control method for a quadrotor drone based on optimized LQR according to claim 4 is characterized in that: In step 2, the acceleration of the drone control command is calculated by considering the effects of gravity acceleration and air resistance. , the expression is: ； in, Indicates that the quadcopter is subject to negative The influence of gravitational acceleration g in the direction, Represents the rotation matrix The transpose of Indicates the drag coefficient of the drone during flight; Use zxy sequence to describe the rotation of the quadrotor and define intermediate variables and , the expression is: ； in, is the reference yaw angle obtained from the reference trajectory; Rotation matrix in body coordinate system middle, , and They are mutually orthogonal and are all unit vectors, and the expression is: ； Rotation matrix of drone control instructions , the expression is: ； in, Expressed by acceleration and the reference yaw angle The calculated aircraft attitude The corresponding three-axis orthogonal unit vectors.

6. The differential flat control method for a quadrotor drone based on optimized LQR according to claim 5 is characterized in that: In step 2, the constraint function is constructed based on the LQR algorithm as follows: Step 2.1, select the three-axis position and speed As state variable, choose acceleration As input variables, the expression is: ； in, Represents the position variable of the center of mass of the quadrotor drone in the world coordinate system, represents the velocity variable of the center of mass of the quadrotor drone in the world coordinate system, Represents the acceleration variable of the center of mass of the quadrotor drone in the world coordinate system; Represent the constraint functions state variables and optimization variables; Step 2.2: Create a constraint function and describe the LQR optimization as: ； Among them, the objective function For minimizing state cost and input energy, represents the prediction time domain, Indicates The state variables at time, Indicates The optimization variable at time, State variables representing terminal moments; Subscript Q , R Representation Matrix and ,matrix and It is a diagonal matrix. The diagonal elements represent the weights assigned to the state variables or inputs. The weight values ​​indicate the convergence speed of the corresponding state or input. Subscript Represents the terminal status, the matrix is the diagonal matrix associated with the terminal states.

7. The differential flat control method for a quadrotor drone based on optimized LQR according to claim 6 is characterized in that: In step 3, add the physical constraints of the drone, the expression is: ； ； ； ； Among them, formula (11b) and formula (11c) are the initial state constraint and dynamic constraint respectively. Indicates the initial value of the state at the start of the optimizer iteration. Indicates The optimization variable value at time is the system matrix and is the input matrix; Formula (11d) and Formula (11e) represent the state and input limits respectively, , Respectively represent the upper and lower bounds of the state variable, Respectively represent the upper and lower bounds of the optimization variable.

8. The differential flat control method for a quadrotor drone based on optimized LQR according to claim 7, characterized in that: System Matrix and the input matrix , the expression is: ； in, Represents the period of the controller, and the missing elements in the matrix are 0.

9. The differential flat control method for a quadrotor drone based on optimized LQR according to claim 8, characterized in that: In step 4, the acceleration command is limited according to the real-time calculated UAV thrust margin. The specific method is as follows: Get the lift and maximum lift corresponding to the current throttle of the drone motor. When applying dynamic constraints, convert the drone thrust margin into thrust components in the three-axis direction, recorded as : ； in, Indicates the current throttle value of the drone. Indicates the lift size corresponding to the current throttle. It indicates the maximum combined lift provided by the motor manufacturer when the motor runs at the maximum speed. Represents the rotation matrix from the body coordinate system to the world coordinate system; Convert the thrust margin to acceleration margin: ； in, Indicates the current acceleration margin of the drone; represents the mass of the quadrotor; The acceleration margin obtained is , put it into formula (11e), calculate the dynamic boundary conditions of the objective function, and get the optimized , which is used to ensure that the target value obtained when solving the objective function does not exceed the maximum physical limit.

10. The differential flat control method of a quadrotor drone based on optimized LQR according to claim 1, characterized in that: In step 4, the interior point algorithm is as follows: The state equation and control input of the quadrotor system are modeled by CasADi software, the optimization objective function and constraints are constructed, and the LQR problem is transformed into an optimization problem. The optimization problem is solved using the interior point solver provided by the CasADi software, and the control input is iteratively optimized in each control cycle until convergence to the optimal solution; Update the drone control system status according to the optimal control input to ensure trajectory tracking accuracy and system stability.

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