A method for analyzing flight characteristics of a quadcopter

Abstract

This invention provides a method for analyzing the flight characteristics of quadrotor aircraft. This method uses the separated vortex method to obtain unsteady flow field data and employs a discrete blade approach to couple this data to the aerodynamic center of the quadrotor, realistically simulating the unsteady disturbance of vortex ring turbulence on the quadrotor. This invention can quickly and accurately provide the response characteristics and control variable changes of a quadrotor under vortex ring turbulence disturbance, significantly reducing experimental risks and saving human and material resources. It can be used to analyze control margins in the vortex ring state of a quadrotor and to analyze pilot work data.

Description

Technical Field

[0001] This invention belongs to the field of flight dynamics and computational fluid dynamics, and particularly relates to a method for analyzing the flight characteristics of a quadcopter. Background Technology

[0002] Currently, research in the field of vortex-ring states mainly revolves around conventional single-rotor helicopters. This technology first acquires a vortex-ring flow field database through empirical models, experiments, or numerical simulations, and then couples it into a quadcopter flight dynamics model using a data transfer strategy to analyze the flight characteristics of the vortex-ring state. However, this approach suffers from low accuracy.

[0003] In the analysis of flight characteristics of quadrotor aircraft under vortex-ring conditions, one method employs slip mesh technology based on unstructured grids to numerically simulate the aerodynamic characteristics of multirotor aircraft. This method uses CFD calculations to obtain the aerodynamic characteristics and flow field laws of the slip zone in this state, thereby conducting equilibrium characteristic analysis of the quadrotor aircraft. However, this method uses Reynolds-averaged Navier-Stokes equations to solve the flow field in the vortex-ring state, which cannot obtain high-precision unsteady flow field data, resulting in low accuracy in the analysis of unsteady vortex-ring turbulence in quadrotor aircraft. Summary of the Invention

[0004] To address the problem that existing methods for analyzing the flight characteristics of quadrotors under vortex-ring conditions cannot obtain high-precision unsteady flow field data, resulting in low accuracy in analyzing unsteady vortex-ring turbulence in quadrotors, this invention provides a method for analyzing the flight characteristics of quadrotors under unsteady vortex-ring turbulence disturbances. The technical solution is as follows: Firstly, a method for analyzing the flight characteristics of a quadrotor is provided. The method uses the separated vortex method to obtain unsteady flow field data and uses the discrete blade method to couple the unsteady flow field data to the aerodynamic center of the quadrotor, so as to realistically simulate the unsteady disturbance of vortex ring turbulence on the quadrotor.

[0005] The method specifically includes: Step 1: Obtain unsteady flow field data using the separated eddy method; Step 2: Using a discrete blade method, the unsteady flow field data is reconstructed, and a quadrotor flight dynamics model under the influence of vortex ring turbulence is established based on the reconstructed unsteady flow field data. Step 3: Analyze the flight characteristics using the established quadcopter flight dynamics model.

[0006] In step 1, the separated vortex method is used to numerically calculate the vortex ring turbulent flow field: an unstructured grid is generated using grid generation software, and the number of prism layers, grid growth rate, and first layer height in the unstructured grid are set to ensure that the y+ condition of the wall function used in the turbulence model calculation is met; the flow field region is cylindrical in shape, and the bottom of the flow field region is set as the velocity inlet boundary condition, while the top and sidewalls of the flow field region are set as the pressure outlet boundary conditions, and the time step is set to obtain unsteady flow field data.

[0007] In step 2, when recombining the unsteady flow field data, the rotor and fuselage are discretized and regarded as several aerodynamic load calculation points. The unsteady flow field data is recombined in the form of a structured grid, and the recombined unsteady flow field data is imported into each aerodynamic load calculation point to simulate the interference of vortex ring turbulence on the quadcopter.

[0008] Step 2 includes: The first step is to establish a single rotor inflow model and calculate the rotor induced velocity distribution based on the rotor inflow model. The rotor inflow model is as follows:

[0009] in, For the dimensionless induced velocity of the rotor, These are the dimensionless term of the uniform inflow to the rotor, the sine component, and the cosine component, respectively. The blade azimuth angle; The second step is to calculate the aerodynamic loads on each rotor based on the rotor-induced velocity distribution: 21. When performing rotor aerodynamic modeling, the blade is divided into several micro-segments. The recombined unsteady flow field data is imported into the center of each micro-segment. The distribution of micro-segments gradually becomes denser from the blade root to the blade tip, and the area of ​​the annulus formed by the inner and outer boundaries of each micro-segment is the same. The coordinates of the center position of each micro-segment are calculated. 22. Calculate the tangential velocity, spanwise velocity, and normal velocity at the center of each rotor micro-segment based on the position coordinates and flow field data of each micro-segment; 23. Calculate the aerodynamic load of each micro-element by calculating the tangential velocity, spanwise velocity, and normal velocity at the center of the rotor micro-element; 24. Sum the aerodynamic loads of each micro-element segment to obtain the force at the root of a single blade and the flapping torque generated by a single blade relative to the flapping hinge, thus obtaining the aerodynamic loads of each rotor. The third step is to establish the equations of motion for rotor blade flapping. The fourth step is to establish an aerodynamic model of the fuselage; The fifth step is to establish the dynamic equations of the aircraft to obtain the flight dynamics model of the quadcopter.

[0010] The process of establishing the equations for rotor blade flapping motion is as follows: The first-order expression for the flapping motion of a rigid rotor is established as follows:

[0011] In the formula, , , In order, they are the equivalent flapping offset, the blade mass static moment, and the moment of inertia. This refers to the blade flapping stiffness when it is not rotating. The rotor speed, To increase the frequency of the swinging motion, Calculate the torque acting at the swing hinge:

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] In the formula, , , , , , , These represent the centrifugal torque, flapping inertial torque, aerodynamic torque, Coriolis torque caused by the quadrotor fuselage angular velocity, inertial torque caused by the fuselage angular acceleration, torque caused by the fuselage acceleration, blade gravity torque, and torque generated by the torsion spring, respectively, acting at the flapping hinge. Waving the horn for the paddle blades, For the angular acceleration of the swing, , , , Let x be the x and y components of the propeller angular velocity and angular velocity in the rotor shaft system. The linear velocity and angular velocity components along the x and y axes of the fuselage are respectively taken as the mechanical system. It is the acceleration due to gravity. The algebraic sum of all torques at the flapping hinge should be zero, thus yielding the rotor blade flapping motion equations: .

[0020] In establishing the airframe dynamics equations, the resultant forces and moments generated by each rotor, along with the resultant forces and moments generated by the fuselage based on the fuselage aerodynamic model, are summed at the airframe's center of gravity. This yields the resultant forces and moments acting on the four rotors at their center of gravity in the airframe coordinate system. The resultant forces and moments in each direction are expressed as follows:

[0021]

[0022] In the formula, , These are the fuselage pitch angle and roll angle, respectively. The total mass of the quadcopter The components of the forces and torques generated by the fuselage along the x, y, and z axes in the body coordinate system. These represent the components of the aerodynamic forces generated by each rotor along the x, y, and z axes in the body coordinate system. The components of the aerodynamic torque generated by each rotor along the x, y, and z axes in the body coordinate system; Using Newton's second law and the law of angular momentum, the equations of motion for the quadrotor's center of gravity shift and its rotation about the center of gravity can be obtained as follows:

[0023]

[0024] In the formula, The components of velocity and angular velocity along the x, y, and z axes in the fuselage-centric coordinate system are respectively given. , , , , , , , , , Let x, y, and z be the moments of inertia of the aircraft's rotational system around the aircraft. For inertial product, By combining the equations of motion for rotor blade flapping with the equations of motion for the airframe, a quadcopter flight dynamics model can be obtained, which is simplified as follows: .

[0025] The force at the root of a single blade is:

[0026] In the formula, These represent the radial, tangential, and normal aerodynamic forces of the micro-element segment, respectively. The number of infinitesimal segments.

[0027] The flapping torque generated by a single blade relative to the flapping hinge is:

[0028] In the formula, and These represent the number of blade micro-segments and the distance from the center of each blade micro-segment to the flapping hinge, respectively. Where is the blade radius.

[0029] The beneficial effects of this invention are at least as follows: This invention employs the concept of nested meshes to discretize the blade rotational motion into... At each station, by matching the blade motion with the unsteady vortex ring turbulent flow field on the time scale, the unsteady disturbance calculation of the quadrotor under the vortex ring turbulent flow field was realized.

[0030] This invention enables the rapid and accurate determination of the response characteristics and control parameters of a quadrotor under vortex ring turbulent flow field interference. The simulation cycle for a single calculation process is only about 10 days. Compared with test flights, this invention can significantly reduce test risks and save on human and material resources. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the computational domain grid. Figure 2 This is a schematic diagram of the aerodynamic load calculation points for a quadcopter. Figure 3 This is a schematic diagram of the vortex ring turbulence data output area; Figure 4 A schematic diagram showing the segmentation of the blade micro-element; Figure 5 This is a flowchart of the method of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] The features and illustrative embodiments of various aspects of the present invention will now be described in detail. Numerous specific details are set forth in the following detailed description to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without requiring some of these specific details. The following description of embodiments is merely intended to provide a better understanding of the invention by illustrating examples of the invention. The invention is by no means limited to any specific setups and methods set forth below, but covers any improvements, substitutions, and modifications to structures, methods, and devices without departing from the spirit of the invention. Well-known structures and techniques are not shown in the drawings and the following description to avoid unnecessarily obscuring the invention.

[0034] It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other, and the various embodiments can be referenced and cited from each other.

[0035] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0036] To overcome the shortcomings of existing technologies, this invention establishes a method for analyzing the flight characteristics of quadrotors under unsteady vortex-ring turbulence. A high-precision vortex separation method is employed to obtain high-precision unsteady flow field data. Furthermore, a discrete blade approach is used to couple the flow field data to the aerodynamic center of the quadrotor, thereby more realistically simulating the unsteady disturbances of vortex-ring turbulence on the quadrotor.

[0037] The core content of this invention mainly comprises three parts: high-precision acquisition of unsteady vortex ring turbulent flow field data, flight dynamics modeling of a quadrotor aircraft coupled with an unsteady vortex ring state flow field, and data transfer strategy from unsteady vortex ring turbulent flow field data to the flight dynamics model. See also... Figure 5 The method of the present invention specifically includes: (1) High-precision numerical simulation of vortex ring turbulent flow field based on the separated vortex method This invention employs a high-precision vortex separation method to numerically calculate the turbulent flow field of vortex rings. An unstructured mesh is generated using mesh generation software: 10 prism layers, a mesh growth rate of 1.1, and a first layer height of 8.5 × 10⁻⁶. -5 m ensures that the y+ condition of the wall function used in the turbulence model calculation is satisfied. The nested mesh element count for a single blade is approximately 500,000, while the background mesh element count is approximately 7 million. See also Figure 1 The flow field region is cylindrical in shape, with the bottom set as the velocity inlet boundary condition and the top and sidewalls set as the pressure outlet boundary conditions. The time step is set to approximately 0.00024 s, which is the time required for the rotor to rotate 1°.

[0038] This step allows you to obtain high-precision unsteady flow field data.

[0039] (2) Data transmission strategy based on unidirectional coupling This invention establishes a data transfer strategy based on the concept of "one-way coupling," considering only the interference of vortex ring turbulence on the quadrotor. In this method, the rotor and fuselage are discretized and treated as several aerodynamic load calculation points, such as... Figure 2 As shown in the figure. There are 10 aerodynamic load calculation points on each blade and one on the fuselage, for a total of 41 aerodynamic load calculation points. Flow field data is imported into each point to simulate the interference of vortex ring turbulence on the quadrotor.

[0040] Before data transfer, an effective vortex ring turbulence field must be obtained, encompassing all regions traversed by each aerodynamic component of the quadcopter within the vortex ring. Unsteady vortex ring turbulence data obtained through CFD calculations are required. It cannot be directly used in quadrotor flight dynamics models yet; its storage method needs to be reorganized into a structured grid format to facilitate interpolation of the aerodynamic centers of each quadrotor component. See Figure 3 .

[0041] Because the rotor blades not only rotate around the center of rotation but also exhibit periodic flapping, and because the spatial positions of each blade micro-segment change due to variations in the aircraft's attitude, the process of transferring flow field data to the rotor aerodynamic model is quite complex. This will be explained in detail here using the interpolation process of the blade micro-segments.

[0042] The first step, to simulate the periodic motion of the propeller blades, is to divide one revolution of the blades into... Each station. Assuming at time... The instantaneous velocity field of the vortex ring turbulence is The coordinates of the blade segment in the blade coordinate system are: Then its coordinates in the body coordinate system can be expressed as:

[0043] in, This represents the rotor's position in the airframe coordinate system. This is the transformation matrix from the blade system to the engine system.

[0044] Continuing the transformation to an inertial frame of reference:

[0045] This is the transformation matrix from the machine system to the inertial system.

[0046] The second step is to obtain the position coordinates of the blade micro-segment in the inertial frame. Then, the distance derivative weighted method is used to interpolate the vortex ring turbulent flow field data, as shown in the following equation:

[0047]

[0048] In the formula, This represents the velocity component to be interpolated at the center of the blade micro-segment. For the velocity components of data points adjacent to the center of the micro-segment, Here are the position coordinates of the adjacent point. This represents the distance from the adjacent point to the center of the micro-segment. To adjust the exponent of the reciprocal of the distance weight, This represents the number of adjacent data points. The vortex ring turbulent flow field data is stored in the form of a structured grid; the center of each blade micro-segment will eventually fall within a rectangular cell of the data domain. . This ensures high interpolation accuracy.

[0049] The third step is to use the above interpolation method to obtain the perturbation velocity components of the vortex ring turbulent flow field at the center of the micro-segment in the inertial frame. Then, the velocity component is transformed into the blade coordinate system, thus completing one interpolation process. After transformation, the velocity components of the turbulent flow field in the vortex ring at the center of the micro-segment are:

[0050] The fourth step involves performing steps one through three on the other micro-segments of the blade.

[0051] Fifth step, upon reaching step (4), one can obtain The aerodynamic force and torque of the blade at time t. Repeat steps (1) to (4) for the other blades and sum them to obtain the results. The aerodynamic forces and torques of the entire rotor at any given moment.

[0052] In the sixth step, the propeller moves forward one station. On the one hand, the spatial position of the propeller micro-segment is updated, and on the other hand, time advances forward simultaneously. At this time, the micro-segment of the propeller blade is Interpolate the turbulent flow field data of the vortex ring at time t, and repeat steps (1) to (4) and (6) to simulate the unsteady interference between the rotor blade and the turbulent vortex structure during the periodic motion.

[0053] The interpolation process for the aerodynamic centers of other components of the quadrotor is similar to that of the rotor, but these aerodynamic centers are all located on the fuselage. It only involves coordinate transformations between the body coordinate system, the inertial coordinate system, and the inertial frame. The data transfer process is relatively simple and will not be elaborated upon here. This section allows the high-precision vortex ring turbulent flow field obtained in the first part to be imported into the quadrotor flight dynamics model established in the second part.

[0054] (3) Flight dynamics model of quadrotor considering the influence of vortex ring turbulence The first step is to determine the inflow model for a single rotor. This invention uses a first-harmonic form of the Pitt-Prters static non-uniform inflow model to calculate the rotor-induced velocity distribution, thereby ensuring sufficient accuracy.

[0055]

[0056] The second step is to calculate the aerodynamic loads on each rotor segment. Considering the influence of vortex ring turbulence, this section divides the blade into several micro-segments when modeling the rotor aerodynamics, and imports turbulent flow field data at the center of each micro-segment. Furthermore, considering that the outer edge of the blade is farther from the center of rotation and is the main area generating aerodynamic loads, the distribution of micro-segments gradually increases in density from the blade root to the blade tip, ensuring that the area of ​​the annulus formed by the inner and outer boundaries of each micro-segment is the same. A schematic diagram of the blade micro-segment distribution is shown below. Figure 4 As shown. Figure 4 In the context of dimensionless waving hinge bias , This represents the dimensionless distance from the blade root tangent to the flapping hinge. and Let be the chord lengths at the blade tip and root, respectively. Then, the distance from the center of the first blade segment starting from the root to the flapping hinge is:

[0057] The distance from the center of the other blade micro-element segment to the flapping hinge is:

[0058] Taking the left front rotor as an example, the tangential velocity at the center of the rotor micro-element segment Spread speed and normal velocity The following are represented as follows:

[0059]

[0060]

[0061] Let be the flow velocity.

[0062] The force at the root of a single blade is obtained by summing the aerodynamic forces of each micro-element segment as follows:

[0063] The swinging torque generated relative to the swinging hinge is:

[0064] In the formula, and These represent the number of blade micro-segments and the distance from the center of the blade micro-segment to the flapping hinge, respectively.

[0065] The third step is to determine the flapping motion model for each rotor. The first-order expression for the flapping motion of the rigid rotor is as follows:

[0066] In the formula, , , In order, they are the equivalent flapping offset, the blade mass static moment, and the moment of inertia. It is the blade flapping stiffness when it is not rotating.

[0067] The flapping motion equations of the rotor can be established using the above method. During the blade motion, the torques acting at the flapping hinge mainly include: centrifugal torque. , swinging inertial torque Aerodynamic torque Coriolis torque caused by the angular velocity of the quadrotor fuselage Inertial torque caused by fuselage angular acceleration Caused by fuselage acceleration Blade gravity torque and the torque generated by the torsion spring Their expressions are as follows:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] The algebraic sum of the above torques at the flapping hinge should be zero. Based on this, the equation of motion for the rotor blade flapping can be obtained:

[0076] The fourth step is to determine the fuselage aerodynamic model. The fuselage model is modeled using the same method as traditional helicopter fuselage models, so it will not be described in detail here.

[0077] The fifth step is to determine the dynamic equations of the airframe. Summing the resultant forces and moments generated by each rotor and fuselage at the airframe's center of gravity yields the resultant forces and moments acting on the center of gravity of the four rotors in the airframe coordinate system. The resultant forces and moments in each direction are expressed as follows:

[0078]

[0079] In the formula, the subscript Represents the fuselage, , These are the fuselage pitch angle and roll angle, respectively. This is the total mass of the quadcopter.

[0080] Using Newton's second law and the theorem of angular momentum, the dynamic equations for the movement of the quadrotor's center of gravity and its rotation about the center of gravity can be obtained as follows:

[0081]

[0082] Combining the blade flapping motion equations with the quadrotor rigid body dynamics equations yields the quadrotor flight dynamics equations, which are simplified as follows:

[0083] This invention employs the concept of "nested meshes" to discretize the blade rotational motion into... At each station, by matching the blade motion with the unsteady vortex ring turbulent flow field on the time scale, the unsteady disturbance calculation of the quadrotor under the vortex ring turbulent flow field was realized.

[0084] This invention enables the rapid and accurate determination of the response characteristics and control parameters of a quadrotor under vortex ring turbulent flow field interference. The simulation cycle for a single calculation process is only about 10 days. Compared with test flights, this invention can significantly reduce test risks and save on human and material resources.

[0085] The above description merely illustrates embodiments of the present invention and is quite specific and detailed; however, it should not be construed as limiting the scope of the patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention. Furthermore, any parts of the present invention not described in detail are conventional techniques.

Claims

1. A method for analyzing the flight characteristics of a quadcopter, characterized in that, Unsteady flow field data were obtained using the separated vortex method, and the unsteady flow field data were coupled to the aerodynamic center of the quadrotor using the discrete blade method to realistically simulate the unsteady disturbance of vortex ring turbulence on the quadrotor.

2. The method according to claim 1, characterized in that, The method specifically includes: Step 1: Obtain unsteady flow field data using the separated eddy method; Step 2: Using a discrete blade method, the unsteady flow field data is reconstructed, and a quadrotor flight dynamics model under the influence of vortex ring turbulence is established based on the reconstructed unsteady flow field data. Step 3: Analyze the flight characteristics using the established quadcopter flight dynamics model.

3. The method according to claim 2, characterized in that, In step 1, the separated vortex method is used to numerically calculate the vortex ring turbulent flow field: an unstructured mesh is generated using mesh generation software, and the number of prism layers, mesh growth rate, and first layer height in the unstructured mesh are set to ensure that the wall function used in the turbulence model calculation is satisfied. condition; The flow field region is cylindrical in shape. The bottom of the flow field region is set as the velocity inlet boundary condition, and the top and sidewalls of the flow field region are set as the pressure outlet boundary conditions. A time step is set to obtain unsteady flow field data.

4. The method according to claim 2, characterized in that, In step 2, when recombining the unsteady flow field data, the rotor and fuselage are discretized and regarded as several aerodynamic load calculation points. The unsteady flow field data is recombined in the form of a structured grid, and the recombined unsteady flow field data is imported into each aerodynamic load calculation point to simulate the interference of vortex ring turbulence on the quadcopter.

5. The method according to claim 2, characterized in that, Step 2 includes: The first step is to establish a single rotor inflow model and calculate the rotor induced velocity distribution based on the rotor inflow model. The rotor inflow model is as follows: , in, For the dimensionless induced velocity of the rotor, These are the dimensionless term of the uniform inflow to the rotor, the sine component, and the cosine component, respectively. The blade azimuth angle; The second step is to calculate the aerodynamic loads on each rotor based on the rotor-induced velocity distribution: (21) When performing rotor aerodynamic modeling, the blade is divided into several micro-segments. The recombined unsteady flow field data is imported into the center of each micro-segment. The distribution of micro-segments gradually becomes denser from the blade root to the blade tip. The inner and outer boundaries of each micro-segment are ensured to have the same area. The coordinates of the center position of each micro-segment are calculated. (22) Calculate the tangential velocity, spanwise velocity and normal velocity of the rotor micro-segment center based on the position coordinates and flow field data of each micro-segment; (23) Calculate the aerodynamic load of each micro-element by calculating the tangential velocity, spanwise velocity and normal velocity at the center of the rotor micro-element; (24) The aerodynamic loads of each micro-element segment are summed to obtain the force at the root of a single blade and the flapping torque generated by a single blade relative to the flapping hinge, thus obtaining the aerodynamic loads of each rotor. The third step is to establish the equations of motion for rotor blade flapping. The fourth step is to establish an aerodynamic model of the fuselage; The fifth step is to establish the dynamic equations of the aircraft to obtain the flight dynamics model of the quadcopter.

6. The method according to claim 5, characterized in that, The process of establishing the equations of motion for rotor blade flapping is as follows: The first-order expression for the flapping motion of a rigid rotor is established as follows: ， In the formula, In order, they are the equivalent flapping offset, the blade mass static moment, and the moment of inertia. This refers to the blade flapping stiffness when it is not rotating. The rotor speed, To increase the frequency of the swinging motion, Calculate the torque acting at the swing hinge: ， ， ， ， ， ， ， ， In the formula, These represent the centrifugal torque, flapping inertial torque, aerodynamic torque, Coriolis torque caused by the quadrotor fuselage angular velocity, inertial torque caused by the fuselage angular acceleration, torque caused by the fuselage acceleration, blade gravity torque, and torque generated by the torsion spring, respectively, acting at the flapping hinge. Waving the horn for the paddle blades, For the angular acceleration of the swing, Let x be the x and y components of the propeller angular velocity and angular velocity in the rotor shaft system. The linear velocity and angular velocity components along the x and y axes of the fuselage are respectively taken as the mechanical system. It is the acceleration due to gravity; The algebraic sum of all torques at the flapping hinge should be zero, thus yielding the rotor blade flapping motion equations: .

7. The method according to claim 5, characterized in that, When establishing the dynamic equations of the aircraft, the resultant forces and moments generated by each rotor, as well as the resultant forces and moments generated by the fuselage based on the fuselage aerodynamic model, are summed at the center of gravity of the aircraft. This yields the resultant forces and moments acting on the center of gravity of the four rotors in the aircraft coordinate system. The resultant forces and moments in each direction are expressed as follows: ， ， In the formula, These are the fuselage pitch angle and roll angle, respectively, and m is the total mass of the quadcopter. The components of the forces and torques generated by the fuselage along the x, y, and z axes in the body coordinate system. These represent the components of the aerodynamic forces generated by each rotor along the x, y, and z axes in the body coordinate system. The components of the aerodynamic torque generated by each rotor along the x, y, and z axes in the body coordinate system; Using Newton's second law and the law of angular momentum, the equations of motion for the quadrotor's center of gravity shift and its rotation about the center of gravity can be obtained as follows: ， ， In the formula, The components of velocity and angular velocity along the x, y, and z axes in the fuselage-centric coordinate system are respectively given. , , , , , , , , , Let x, y, and z be the moments of inertia of the aircraft's rotational system around the aircraft. For inertial product, By combining the equations of motion for rotor blade flapping with the equations of motion for the airframe, a quadcopter flight dynamics model can be obtained, which is simplified as follows: .

8. The method according to claim 5, characterized in that, The force at the root of a single blade is: ， In the formula, These represent the radial, tangential, and normal aerodynamic forces of the micro-element segment, respectively. The number of infinitesimal segments.

9. The method according to claim 5, characterized in that, The flapping torque generated by a single blade relative to the flapping hinge is: ， In the formula, and These represent the number of blade segments and the distance from the center of each blade segment to the flapping hinge, respectively, with R being the blade radius.

Images