A Dynamic Modeling Method for a Variable Center of Mass Unmanned Aerial Vehicle

Abstract

This invention discloses a dynamic modeling method for a variable center of mass unmanned aerial vehicle (UAV), belonging to the field of UAV dynamic modeling. The method includes: establishing a ground coordinate system and a body coordinate system; defining a system configuration including the body, a pitch channel moving battery, and a roll channel moving battery; calculating the system's center of mass position; establishing a system translational dynamic model; establishing a system rotational dynamic model considering additional inertial torque, additional Coriolis torque, and additional gyroscopic torque; establishing a moving battery dynamic model; and forming a complete eight-degree-of-freedom nonlinear dynamic model. This invention uses the UAV's own battery as a moving mass block, accurately describing the complex dynamic phenomena and strong coupling relationships generated during battery movement. Compared with existing technologies, it significantly reduces system complexity and cost, providing a reliable theoretical basis for the design of variable center-of-mass UAV control systems.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of unmanned aerial vehicle dynamics modeling, and particularly relates to a dynamics modeling method of a variable center of mass unmanned aerial vehicle. BACKGROUND

[0002] As a new emerging attitude control method, the variable center of mass control technology changes the system center of mass position by moving the mass block inside the body, thereby generating a control torque to realize attitude control. Compared with the traditional differential control method of propeller, the variable center of mass control has the advantages of low power consumption and long range. At present, the research on the variable center of mass unmanned aerial vehicle mainly focuses on the field of fixed-wing unmanned aerial vehicle, and the research on the variable center of mass control technology of rotary-wing unmanned aerial vehicle is relatively less. In the existing research on the variable center of mass rotary-wing unmanned aerial vehicle, a special slider is mostly used as a moving mass block, which increases the complexity and cost of the system.

[0003] The prior art has the following problems: firstly, the existing modeling method of the variable center of mass quad-rotor unmanned aerial vehicle usually does not consider the dynamic characteristics of the moving mass block, only regards it as a change of static mass distribution, ignores the additional disturbance torque generated in the moving process, and the modeling accuracy is insufficient. Secondly, the existing modeling method mostly adopts linearization processing, which cannot accurately describe the strong nonlinearity and strong coupling characteristics of the variable center of mass system, and affects the design accuracy of the control system. Finally, in the existing research, the moving mass block mostly uses a special slider, which increases the complexity of the system, and the modeling method using the battery of the unmanned aerial vehicle as the moving mass block has not been reported. Therefore, there is an urgent need for a variable center of mass quad-rotor unmanned aerial vehicle dynamics modeling method which can accurately consider the dynamic characteristics of the moving battery. SUMMARY

[0004] To solve the above technical problems, the application provides a dynamics modeling method of a variable center of mass unmanned aerial vehicle, comprising:

[0005] A ground coordinate system and a body coordinate system are established, and all vectors are bidirectionally mapped between the ground coordinate system and the body coordinate system through the conversion matrix of the ground coordinate system and the body coordinate system as an intermediary;

[0006] The system configuration including the body part, the pitch channel moving battery and the roll channel moving battery is defined in the body coordinate system;

[0007] According to the system configuration, the position vector of the system center of mass relative to the body origin is calculated in the body coordinate system;

[0008] The translation dynamics model of the system center of mass is established with the ground coordinate system as the inertial reference frame, and the translation equation is mapped to the body coordinate system through the conversion matrix;

[0009] Using the body coordinate system as a reference system, the absolute angular momentum of the system about the center of mass is calculated based on the position vector of the system's center of mass, and a rotational dynamics model of the system is established.

[0010] A dynamic model of the moving battery is established in the body coordinate system and correlated with the inertial acceleration in the ground coordinate system through the transformation matrix;

[0011] By integrating the translational dynamics model, rotational dynamics model, battery motion dynamics model, and attitude kinematics model after coordinate system transformation, an eight-degree-of-freedom nonlinear dynamics model of the variable center of mass UAV is constructed.

[0012] Optionally, establishing the ground coordinate system and the body coordinate system includes:

[0013] Using the ground coordinate system as the inertial frame, with the origin fixed to the Earth, it is used to describe gravity and inertial acceleration.

[0014] The body coordinate system is used as the body coordinate system, with the origin located at the body's center of mass, to describe the body's attitude and the relative displacement of the battery;

[0015] The inertial quantities in the ground coordinate system are transformed to the body coordinate system using the direction cosine matrix, and the control quantities in the body coordinate system are transformed to the ground coordinate system.

[0016] Optionally, the centroid location of the computing system includes:

[0017] Obtain the original position vectors of the body parts, pitch channel battery, and roll channel battery in the body coordinate system;

[0018] The original position vector is superimposed with the displacement to obtain the real-time position vector of each component in the body coordinate system;

[0019] Based on the formula for the center of mass of a system of particles, the real-time position vector of the system's center of mass relative to the origin of the body is obtained by solving in the body coordinate system.

[0020] Optionally, establishing the system translational dynamics model includes:

[0021] In the ground coordinate system, force analysis is performed on the body, pitch channel battery and roll channel battery respectively, and the equations of Newton's second law for each component are listed.

[0022] The acceleration vector in the ground coordinate system is transformed to the body coordinate system using the direction cosine matrix;

[0023] By integrating the equations of Newton's second law for each component in the body coordinate system, a translational dynamic model of the system's center of mass is obtained.

[0024] Optionally, establishing the system rotational dynamics model includes:

[0025] In the body coordinate system, the position vector of each component relative to the system's center of mass is calculated based on the system's center of mass position vector;

[0026] In the body coordinate system, calculate the absolute angular momentum of the system about the system's center of mass;

[0027] By applying the angular momentum theorem and expressing it in the body coordinate system, the rotational dynamics model of the system is obtained.

[0028] Optionally, the calculation of absolute angular momentum includes:

[0029] In the body coordinate system, calculate the angular momentum of the computer body and each battery about the system's center of mass, respectively;

[0030] The angular velocity vector in the ground coordinate system is transformed to the body coordinate system using the direction cosine matrix;

[0031] By accumulating the angular momentum in the body coordinate system, the total absolute angular momentum of the system about the center of mass is obtained.

[0032] Optionally, establishing the system rotational dynamics model further includes:

[0033] In the body coordinate system, the additional moment of inertia matrix is ​​calculated in real time based on the battery displacement.

[0034] In the body coordinate system, the additional Coriolis torque is calculated based on the battery velocity and the body angular velocity;

[0035] In the body coordinate system, the additional inertial torque is calculated based on the battery acceleration;

[0036] The additional moment of inertia matrix, the additional Coriolis torque, and the additional inertial torque are integrated with the rotor lift torque and anti-torsional torque to form a complete rotational dynamics equation.

[0037] Optionally, establishing the mobile battery dynamics model includes:

[0038] Define the displacement constraints of the pitch and roll channel cells in the body coordinate system;

[0039] The inertial acceleration in the ground coordinate system is mapped to the constraint direction in the body coordinate system through the projection operator;

[0040] By eliminating the constraint forces in the body coordinate system, the dynamic equations of battery motion containing the driving force are obtained.

[0041] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0042] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0043] Compared with the prior art, the present invention has the following advantages and technical effects:

[0044] This invention addresses the shortcomings of existing technologies that treat the moving mass as a static mass distribution change and neglect additional disturbance torques generated during movement, leading to insufficient modeling accuracy. It establishes a complete eight-degree-of-freedom nonlinear dynamic model considering the dynamic characteristics of the moving battery. Compared to existing modeling methods that often employ linearization and fail to accurately describe the strong nonlinearity and coupling characteristics of variable center-of-mass systems, the model established in this invention accurately describes complex dynamic phenomena such as additional inertial torques, Coriolis torques, and gyroscopic torques generated during battery movement, as well as the strong coupling relationship between battery movement and the aircraft's attitude motion. Furthermore, this invention innovatively uses the UAV's own battery as the moving mass, significantly reducing system complexity and cost compared to existing methods that use dedicated sliders. The established precise dynamic model provides a reliable theoretical foundation for the design of variable center-of-mass UAV control systems, supporting precise control under conditions of large-scale battery movement and large-angle maneuvers. It overcomes the limitation of linearized models, which are only applicable to small disturbances, thus fully leveraging the advantages of low power consumption and long range of variable center-of-mass control technology. Attached Figure Description

[0045] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0046] Figure 1 This is a schematic diagram of the planar structure of the UAV according to an embodiment of the present invention.

[0047] Figure 2 For different initial position configurations described in the embodiments of the present invention, I xx Comparison of process curves.

[0048] Figure 3 For different initial position configurations described in the embodiments of the present invention, I yy Comparison of process curves.

[0049] Figure 4 For different initial position configurations described in the embodiments of the present invention, I zz Comparison of process curves.

[0050] Figure 5 M under different initial position configurations as described in the embodiments of the present invention y Comparison of process curves.

[0051] Figure 6 M under different initial position configurations as described in the embodiments of the present invention x Comparison of process curves.

[0052] Figure 7 M under different initial position configurations as described in the embodiments of the present invention z Comparison of process curves.

[0053] Figure 8 For different working conditions described in the embodiments of the present invention, I xx Comparison of process curves.

[0054] Figure 9 For different working conditions described in the embodiments of the present invention, I yy Comparison of process curves.

[0055] Figure 10 For different working conditions described in the embodiments of the present invention, I zz Comparison of process curves.

[0056] Figure 11 M under different working conditions as described in the embodiments of the present invention y Comparison of process curves.

[0057] Figure 12 M under different working conditions as described in the embodiments of the present invention x Comparison of process curves.

[0058] Figure 13 M under different working conditions as described in the embodiments of the present invention z Comparison of process curves. Detailed Implementation

[0059] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0060] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0061] Example 1

[0062] This embodiment provides a dynamic modeling method for a variable center of mass unmanned aerial vehicle (UAV), including:

[0063] Step 1: Coordinate System Establishment and System Configuration Definition. Establish the ground coordinate system OG and the body coordinate system OA; define the variable center of mass UAV system as including the body, the pitch channel moving battery, and the roll channel moving battery, wherein the pitch channel moving battery moves along the XA axis, and the amount of motion is ε. x The rotating channel moves the battery along the YA axis, with a motion amount of ε. y ;

[0064] Step 2: Calculate the system's center of mass. Define the position vectors of the body parts, the pitch channel moving battery, and the roll channel moving battery in the body coordinate system. Determine the position vector of the system's center of mass in the body coordinate system using the center of mass calculation formula.

[0065] Step 3: System translational dynamics modeling. Perform force analysis on the body, pitch channel battery, and roll channel battery in the ground coordinate system, and establish the force equations for each part; calculate the acceleration of the battery; and establish the translational equation of the center of mass in the body coordinate system.

[0066] Step 4: Model the rotational dynamics of the system and calculate the absolute angular momentum of the system about the center of mass; establish the rotational dynamics equations based on the angular momentum theorem; calculate the additional moment of inertia matrix, additional inertial torque, additional Coriolis torque, and additional gyroscopic torque; calculate the rotor lift torque and propeller anti-torque torque.

[0067] Step 5: Model the dynamics of the moving battery and establish the constraints of the battery in the pitch and roll channels; eliminate the constraint forces through the projection operator and constraint conditions, and establish the dynamic equations of battery motion;

[0068] Step Six: Integrate the system's translational dynamics model, attitude rotational dynamics model, battery motion dynamics model, and attitude kinematics model to form a complete eight-degree-of-freedom nonlinear dynamics model.

[0069] The ground coordinate system O G The origin O is fixed to the Earth, X G The axis points due north on the local horizontal plane, Y G The axis is perpendicular to X in the local horizontal plane. G The axis points due east, Z G The axis is perpendicular to X. G -Y G The plane forms a right-handed rectangular coordinate system; the body coordinate system O A The origin O is at the body's center of mass, X A The direction of the axis pointing towards the machine head is positive, Y A The axis is perpendicular to the longitudinal plane and points to the right side of the body, which is positive. A Axis perpendicular to X A -Y AThe plane forms a right-handed rectangular coordinate system.

[0070] The system's center of mass calculation adopts the principle of mass system center of mass calculation, comprehensively considering the mass distribution of the body, the pitch channel moving battery, and the roll channel moving battery:

[0071] The translational dynamics modeling of the system is based on Newton's second law. Force analysis is performed on the airframe, pitch channel battery, and roll channel battery in the ground coordinate system, establishing a set of force equations. Coordinate transformation and vector differentiation are then used to calculate the translational dynamics equations of the variable center of mass UAV.

[0072] The rotational dynamics modeling of the system is based on the angular momentum theorem, establishing a complete rotational dynamics equation that includes additional inertial torque, additional Coriolis torque, and additional gyroscopic torque:

[0073] The total moment of inertia matrix I total Including the moment of inertia of the machine body I a The sum of the additional moment of inertia ΔI and the additional moment of inertia caused by the change in the position of the moving battery, with each element changing in real time with the battery position, allows this additional moment of inertia matrix to accurately reflect the real-time impact of battery movement on the system's rotational characteristics. Each element represents the amount of battery movement ε. x ε y Functions:

[0074] The additional inertial torque M oi Primarily generated by the acceleration of the battery; the additional Coriolis torque M co The additional gyroscopic torque M is generated by the coupling of the battery's moving speed and the body's angular velocity. gy Generated by the change in angular momentum of the battery relative to the body, these three types of additional torques are precisely separated through mathematical derivation by combining like terms, accurately describing the dynamic influence of the moving battery on the rotational dynamics of the system:

[0075] The mobile battery dynamics modeling adopts the constrained multibody system dynamics method, which eliminates constraint forces through projection operators and constraint conditions. This modeling method eliminates the constraint forces of the body on the battery through the projection operator method, and establishes a direct relationship between the battery driving force and the motion state.

[0076] The eight-degree-of-freedom dynamic model forms a complete nonlinear dynamic model by integrating the system translational dynamics model, attitude rotational dynamics model, battery motion dynamics model, and attitude kinematics model. This eight-degree-of-freedom dynamic model includes 3 translational degrees of freedom, 3 rotational degrees of freedom, and 2 battery translational degrees of freedom. It can describe the strong coupling relationship between battery movement and body attitude motion, including the influence of battery position change on the system's center of mass and rotational inertia, the contribution of battery movement speed to the system's Coriolis force and gyroscopic torque, and the feedback effect of body attitude motion on battery dynamics. Compared with existing linearized models or simplified models that ignore battery dynamic characteristics, this model can maintain high modeling accuracy under large-range battery movement and large-angle maneuvering conditions.

[0077] Example 2

[0078] This embodiment provides a dynamic modeling method for a variable center of mass unmanned aerial vehicle (UAV), including:

[0079] First, the necessary mathematical foundation is given: the ground coordinate system O. G To the body coordinate system O A The transformation matrix is:

[0080]

[0081] in:

[0082]

[0083] Expanding yields the complete transformation matrix:

[0084]

[0085] In the formula, φ, θ and ψ are the pitch, roll and yaw angles, respectively.

[0086] The complete angular velocity conversion relationship is as follows:

[0087]

[0088] Under the assumption of a small angle, the above equation simplifies to:

[0089]

[0090] ω X ,ω Y ,ω Z These are the angular velocities for pitch, roll, and yaw, respectively. The first derivative of the pitch angle. The first derivative of the roll angle is given by... The first derivative representing the yaw angle;

[0091] For vector a = [aX ,a Y ,a Z ] T Its cross product matrix is:

[0092]

[0093] Rule 1: The differential of a vector with respect to time, let the vector v be expressed as v in the moving coordinate system B. B In inertial coordinate system I, it is expressed as v I Then we have:

[0094] (dv / dt) I =(dv / dt) B +ω×v B (7)

[0095] Where ω is the angular velocity vector of the moving coordinate system B relative to the inertial coordinate system I.

[0096] Rule 2: The differential rule of the cross product of vectors;

[0097] d(a×b) / dt=da / dt×b+a×db / dt (8)

[0098] Rule 3: The differential rule for the product of scalars and vectors;

[0099] d(k·v) / dt=dk / dt·v+k·dv / dt (9)

[0100] Rule 4: The differential rule of composite vectors. Let r = r0 + ρ, where r0 is the base point position vector and ρ is the relative position vector, then:

[0101] dr / dt=dr0 / dt+dρ / dt+ω×ρ (10)

[0102] d 2 r / dt 2 =d 2 r0 / dt 2 +d 2 ρ / dt 2 +2ω×dρ / dt+dω / dt×ρ+ω×(ω×ρ) (11)

[0103] Rule 5: Differentiation of the coordinate transformation matrix:

[0104]

[0105] Modeling method steps:

[0106] Step 1: Establishing the coordinate system and defining the system configuration;

[0107] Establish two coordinate systems, the first being the ground coordinate system O. G The origin O is fixed to the Earth, X G The axis points due north on the local horizontal plane, Y G The axis is perpendicular to X in the local horizontal plane. G The axis points due east, Z G The axis is perpendicular to X. G -Y G The first plane forms a right-handed rectangular coordinate system; the second is the body coordinate system O. A The origin O is at the body's center of mass, X A The direction of the axis pointing towards the machine head is positive, Y A The axis is perpendicular to the longitudinal plane and points to the right side of the body, which is positive. A Axis perpendicular to X A -Y A The plane forms a right-handed rectangular coordinate system.

[0108] The variable center of mass quadrotor unmanned aerial vehicle system is defined as including the airframe, a pitch channel moving battery, and a roll channel moving battery, wherein: the pitch channel moving battery moves along the X... A Motion along the axial direction, with a motion quantity of ε x ; The rolling channel moves the battery along the Y A Motion along the axial direction, with a motion quantity of ε y .

[0109] Step 2: Calculate the system centroid;

[0110] Define the position vector of the body part in the body coordinate system as:

[0111]

[0112] in, is the position vector of the body part in the body coordinate system, and T is the transpose symbol.

[0113] Define the position vector of the pitch channel moving battery in the body coordinate system as:

[0114]

[0115] in, h represents the position vector of the moving battery in the body coordinate system for the pitch channel. y1 ,h z1 This represents the projection of the battery's initial installation position onto the Y and Z axes. ε x This represents the displacement of the battery in the pitch channel.

[0116] Define the position vector of the rotating channel moving battery in the body coordinate system as:

[0117]

[0118] h x2 ,h z2 This represents the projection of the battery's initial installation position onto the X and Z axes. ε y This represents the displacement of the battery in the rolling channel.

[0119] According to the formula for calculating the center of mass, the position vector of the system's center of mass in the body coordinate system is... for:

[0120]

[0121] m a m is the mass of the machine body, m1 and m2 are the mass of the battery, m c This refers to the total mass of the system.

[0122] Expanding, we get:

[0123]

[0124] Where λ1=m1 / m c λ2=m2 / m c This represents the mass ratio of the battery to the system.

[0125] Step 3: Model the translational dynamics of the system;

[0126] In the ground coordinate system, force analysis is performed on the fuselage, pitch channel battery, and roll channel battery respectively:

[0127] Force equations for the body:

[0128]

[0129] Force equation for the battery in the pitch channel:

[0130]

[0131] Force equation for a rolling channel battery:

[0132]

[0133] Wherein: F ai F represents the constraint force exerted by the machine on the i-th battery. ci F is the driving force of the i-th battery; p For propeller thrust, F d For aerodynamic forces (assumed to be zero during modeling); Let g be the gravity of each part in the ground coordinate system. This represents the position vector of each part in the ground coordinate system.

[0134] The positional relationship of each part in the ground coordinate system:

[0135]

[0136] Calculate battery acceleration using the vector differential rule:

[0137]

[0138] in:

[0139]

[0140] ω a Let be the angular velocity vector of the aircraft relative to the ground coordinate system. Let the first derivative of the position vector of the moving battery in the body coordinate system be the pitch channel. The second derivative of the position vector of the moving battery in the body coordinate system for the pitch channel.

[0141] Simplified version:

[0142]

[0143] Therefore, the acceleration of the pitch channel battery is:

[0144]

[0145] Similarly, the acceleration of the rolling channel battery is:

[0146]

[0147] Substituting equation 24 into equation 18, equation 25 into equation 19, and then into equation 17, we get:

[0148]

[0149] The above equation can be converted into the equation of the translation of the center of mass in the body coordinate system as follows:

[0150]

[0151] Where N = [0, 0, 1] T f is the unit vector along the Z-axis of the body coordinate system. j Let be the lift magnitude of the j-th propeller.

[0152] Step 4: Model the rotational dynamics of the system;

[0153] The absolute angular momentum of the system about its center of mass c is:

[0154]

[0155] Among them: I a It is the moment of inertia of the organism about its own center of mass, rc-a It is the position vector of the body's center of mass a relative to the system's center of mass c, r c-i v is the position vector of the i-th battery relative to the system's centroid c. a and v i Let a be the mass center a of the machine body and the velocity vector of the i-th battery, respectively.

[0156] Position vector from the system's center of mass to the body's center of mass:

[0157] r c-a =-[λ1·ε x +λ2·h x2 ,λ1·h y1 +λ2·ε x ,λ1·h z1 +λ2·h z2 ] T (29)

[0158] Position vectors from the system's center of mass to the centers of mass of each battery:

[0159]

[0160] The velocity of the body's center of mass in the body coordinate system:

[0161]

[0162] This is the transformation matrix from the body coordinate system to the ground coordinate system.

[0163] The battery's velocity in the machine's coordinate system:

[0164]

[0165] According to the theorem of angular momentum:

[0166]

[0167] For term I:

[0168]

[0169] For item II:

[0170]

[0171] Substituting equations 35 and 34 into equation 33 and combining like terms, we get:

[0172]

[0173] Where ΔI is the additional moment of inertia caused by the battery's position change, and its expression is:

[0174]

[0175] The specific elements are as follows:

[0176]

[0177]

[0178] Additional inertial torque M oi for:

[0179]

[0180] Additional Coriolis torque M co for:

[0181]

[0182] Additional gyro torque M gy for:

[0183]

[0184] in:

[0185]

[0186] To calculate the rotor's lift moment, the rotor's coordinates in the body coordinate system are defined as follows:

[0187]

[0188] The lift moment M of the rotor fl for:

[0189]

[0190]

[0191] The propeller's counter-torque M ff for:

[0192]

[0193] Ω j Let d be the rotational speed of the j-th rotor, and d be the anti-torque coefficient.

[0194] Step 5: Dynamic modeling of the mobile battery;

[0195] The constraints for the pitch and roll channel batteries are as follows:

[0196]

[0197] The expressions for constraint force and driving force are:

[0198]

[0199] The projection operator expression is:

[0200] K x =[1,0,0] T K y =[0,1,0] T (54)

[0201] Substituting Equation 24 into Equation 18 and Equation 25 into Equation 19, and transforming to the body coordinate system, and projecting onto the pitch or roll axis, we obtain:

[0202]

[0203] Combining Equation 55 with Equation 27 can eliminate the acceleration term of the body, and the final result is:

[0204]

[0205] in:

[0206]

[0207] Step Six: Complete Eight-DOF Dynamic Model

[0208] System translational dynamics model:

[0209]

[0210] Attitude rotation dynamics model:

[0211]

[0212] Battery dynamics model:

[0213]

[0214] Posture kinematic model:

[0215]

[0216] Example 3

[0217] This embodiment provides a dynamic modeling method for a variable center of mass unmanned aerial vehicle (UAV), including:

[0218] Step 1: Coordinate System Establishment and System Configuration Definition. Establish the ground coordinate system OG and the body coordinate system OA; define the variable center of mass UAV system as including the body, the pitch channel moving battery, and the roll channel moving battery, wherein the pitch channel moving battery moves along the XA axis, and the amount of motion is ε. xThe rotating channel moves the battery along the YA axis, with a motion amount of ε. y ;

[0219] Step 2: Calculate the system's center of mass. Define the position vectors of the body parts, the pitch channel moving battery, and the roll channel moving battery in the body coordinate system. Determine the position vector of the system's center of mass in the body coordinate system using the center of mass calculation formula.

[0220] Step 3: System translational dynamics modeling. Perform force analysis on the body, pitch channel battery, and roll channel battery in the ground coordinate system, and establish the force equations for each part; calculate the acceleration of the battery; and establish the translational equation of the center of mass in the body coordinate system.

[0221] Step 4: Model the rotational dynamics of the system and calculate the absolute angular momentum of the system about the center of mass; establish the rotational dynamics equations based on the angular momentum theorem; calculate the additional moment of inertia matrix, additional inertial torque, additional Coriolis torque, and additional gyroscopic torque; calculate the rotor lift torque and propeller anti-torque torque.

[0222] Step 5: Model the dynamics of the moving battery and establish the constraints of the battery in the pitch and roll channels; eliminate the constraint forces through the projection operator and constraint conditions, and establish the dynamic equations of battery motion;

[0223] Step Six: Integrate the system's translational dynamics model, attitude rotational dynamics model, battery motion dynamics model, and attitude kinematics model to form a complete eight-degree-of-freedom nonlinear dynamics model.

[0224] Based on the system configuration definition in Step 1, the basic parameters are set as follows: fuselage mass mb = 10 kg, pitch channel moving battery mass mp1 = 5 kg, roll channel moving battery mass mp2 = 5 kg. The fuselage characteristic dimensions are 0.8 m × 0.8 m, and the fuselage moment of inertia parameter is set to Ixx = 1.5 kg·m. 2 Iyy = 1.6 kg·m 2 Izz = 2.3 kg·m 2 Its system configuration diagram is as follows: Figure 1 .

[0225] Analysis of additional moment of inertia and additional torque under different initial positions and strokes;

[0226] Based on the system centroid calculation method in step two, three different initial battery installation position configurations are set:

[0227] Position configuration 1: The initial battery positions in the pitch channel are hy1 = 0.1m and hz1 = 0.05m; the initial battery positions in the roll channel are hx2 = 0.1m and hz2 = 0.05m. In this configuration, the battery is close to the body's center of gravity, and according to the center of gravity calculation formula (15), the system's center of gravity offset is small.

[0228] Position Configuration 2: Initial battery positions in the pitch channel: hy1 = 0.2m, hz1 = 0.1m; initial battery positions in the roll channel: hx2 = 0.2m, hz2 = 0.1m. In this configuration, the batteries are far from the body's center of gravity, resulting in a significant shift in the system's center of gravity.

[0229] Position Configuration 3: Pitch channel battery initial positions hy1 = 0.15m, hz1 = 0.15m; Roll channel battery initial positions hx2 = 0.15m, hz2 = 0.15m. This configuration is an intermediate state between the first two.

[0230] Based on the dynamic modeling of the moving battery in step five, the battery motion is set as sinusoidal periodic motion to simulate the actual control process:

[0231] Pitch channel battery motion: ε x (t) = Ap1·sin(2πft), where f = 0.5Hz;

[0232] Rolling channel battery movement: ε y (t)=Ap2·sin(2πft+π / 2).

[0233] Three different strokes were set to verify the adaptability of the model to different motion amplitudes: short stroke Ap1=Ap2=0.05m, medium stroke Ap1=Ap2=0.1m, and long stroke Ap1=Ap2=0.15m.

[0234] Based on the system rotational dynamics model established in step four, calculate the elements of the additional moment of inertia matrix according to formulas (39-44). When the battery moves, the additional moment of inertia changes:

[0235] Calculate the components of the additional torque using formulas (45-47). Additional inertial torque M oi Primarily generated by the acceleration of the battery; additional Coriolis torque M co Generated by the coupling of the battery's moving speed and the body's angular velocity; additional gyroscopic torque M gy It is generated by the change in angular momentum of the battery relative to the body.

[0236] Figure 2 , Figure 3 and Figure 4 The following displays I under different initial position configurations. xx I yy I zzComparison of the timeline curves. Figure 5 , Figure 6 and Figure 7 M were displayed respectively y M x M z Table 1 presents a comparative analysis of the process curves for different initial position configuration parameters.

[0237] Table 1

[0238]

[0239] Analysis of Additional Moment of Inertia and Additional Torque under Different Working Conditions

[0240] This embodiment is based on the complete eight-degree-of-freedom dynamic model in step six, and focuses on verifying the ability of the model of the present invention to accurately describe the strong coupling relationship between battery movement and body posture motion.

[0241] Working condition 1: Center of gravity adjustment in hovering state;

[0242] The control objective is to achieve precise control of the system's center of gravity through fine-tuning of the battery position. According to the system translational dynamics model in step three, in the hovering state, the propeller thrust is mainly used to balance gravity, while battery movement primarily affects the center of gravity position. The system dynamics are relatively simple under this condition, but it lays the foundation for other complex operating conditions.

[0243] Working condition 2: Attitude auxiliary control during pitch maneuvers;

[0244] The pitch maneuver trajectory is set as θ(t) = 15°·sin(0.3πt). This condition verifies the accuracy of the attitude rotation dynamics model in step four of this invention. During the pitch maneuver, according to the attitude kinematics model, the change in body attitude and the battery motion form a strong coupling relationship.

[0245] Operating Condition 3: Attitude compensation control during roll maneuver;

[0246] The roll angle maneuver trajectory is set as φ(t) = 20°·sin(0.25πt). This is the most complex case, which fully demonstrates the accurate description capability of the model of this invention for large-angle maneuvers and strong coupling characteristics.

[0247] Based on the rotational dynamics modeling method in step four, the changes in the additional moment of inertia matrix under each working condition are calculated. Under the hovering condition, the additional moment of inertia is mainly determined by the battery position; under the maneuvering condition, in addition to the influence of the battery position, the coupling effect of the body angular velocity on the additional torque must also be considered.

[0248] The additional torque components under different operating conditions were calculated using formulas (45-47). In the hovering state, the additional Coriolis torque and additional gyroscopic torque are relatively small; in the maneuvering state, these coupled torque terms increase significantly, having a significant impact on the system's dynamic characteristics.

[0249] Figure 8 , Figure 9 and Figure 10 The additional moment of inertia I under different operating conditions is described. xx I yy I zz Comparison of the timeline curves. Figure 11 Figure 12 and Figure 13 The additional torque M is shown under different working conditions. y M x M z Table 2 shows a comparative analysis of the dynamic characteristics under different flight conditions.

[0250] Table 2

[0251]

[0252] The calculations and analyses of the two embodiments above verify that the dynamic modeling method provided by the present invention can accurately describe the influence of the dynamic characteristics of the mobile battery on the system dynamics. The established complete eight-degree-of-freedom nonlinear dynamic model provides a reliable theoretical basis for the control system design of a variable center-of-mass UAV.

[0253] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0254] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0255] The above are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A dynamic modeling method for a variable center of mass unmanned aerial vehicle, characterized in that, The application relates to a method for establishing a nonlinear dynamic model of a variable center of mass unmanned aerial vehicle. The method comprises the following steps: establishing a ground coordinate system and a body coordinate system, and mapping all vectors between the ground coordinate system and the body coordinate system through a conversion matrix of the ground coordinate system and the body coordinate system; defining a system configuration comprising a body part, a pitch channel mobile battery and a roll channel mobile battery in the body coordinate system; calculating a position vector of a system center of mass relative to a body origin in the body coordinate system according to the system configuration; establishing a translation dynamics model of the system center of mass in the ground coordinate system as an inertial reference system, and mapping the translation equation to the body coordinate system through the conversion matrix; calculating absolute momentum moment of the system center of mass according to the position vector of the system center of mass in the body coordinate system, and establishing a rotation dynamics model of the system; establishing a mobile battery dynamics model in the body coordinate system, and correlating the mobile battery dynamics model with inertial acceleration in the ground coordinate system through the conversion matrix; comprehensively establishing an eight-degree-of-freedom nonlinear dynamics model of the variable center of mass unmanned aerial vehicle by comprehensively integrating the translation dynamics model, the rotation dynamics model, the mobile battery dynamics model and an attitude kinematics model after the coordinate system conversion; the translation dynamics model of the system comprises the following steps: analyzing forces of the body, the pitch channel battery and the roll channel battery in the ground coordinate system respectively, and listing Newton's second law equations of the components; converting acceleration vectors in the ground coordinate system to the body coordinate system through a direction cosine matrix; integrating the Newton's second law equations of the components in the body coordinate system, and obtaining the translation dynamics model of the system center of mass; the rotation dynamics model of the system comprises the following steps: calculating position vectors of the components relative to the system center of mass in the body coordinate system according to the position vector of the system center of mass; calculating absolute momentum moment of the system center of mass in the body coordinate system; applying the momentum moment theorem and expressing the momentum moment theorem in the body coordinate system, and obtaining the rotation dynamics model of the system; the mobile battery dynamics model comprises the following steps: defining displacement constraints of the pitch channel battery and the roll channel battery in the body coordinate system; mapping inertial acceleration in the ground coordinate system to the constraint direction of the body coordinate system through a projection operator; 2. The method of claim 1, wherein, eliminating constraint forces in the body coordinate system, and obtaining mobile battery dynamics equations containing driving forces. the ground coordinate system and the body coordinate system comprise the following steps: taking the ground coordinate system as an inertial system, and fixing the origin to the earth, so as to describe gravity and inertial acceleration; taking the body coordinate system as a body coordinate system, and locating the origin at the center of mass of the body, so as to describe the attitude of the body and the relative displacement of the battery; 3. The method of claim 1, wherein, converting inertial quantities in the ground coordinate system to the body coordinate system through a direction cosine matrix, and converting control quantities in the body coordinate system to the ground coordinate system. the position of the system center of mass comprises the following steps: obtaining original position vectors of the body part, the pitch channel battery and the roll channel battery in the body coordinate system; superimposing the original position vectors and displacement quantities, so as to obtain real-time position vectors of the components in the body coordinate system; 4. The method of claim 1, wherein, solving the real-time position vector of the system center of mass relative to the body origin in the body coordinate system according to a mass center formula of a particle system, and obtaining the position of the system center of mass. the absolute momentum moment comprises the following steps: In the body coordinate system, the momentum moments of the body and each battery to the system center of mass are calculated respectively; The angular velocity vector in the ground coordinate system is converted to the body coordinate system through a direction cosine matrix; In the body coordinate system, the total absolute momentum moment of the system to the center of mass is obtained by accumulating each momentum moment.

5. The method of claim 1, wherein, The system rotation dynamics model further comprises: In the body coordinate system, an additional moment of inertia matrix is calculated in real time according to the battery displacement; In the body coordinate system, an additional Coriolis force moment is calculated according to the battery velocity and the body angular velocity; In the body coordinate system, an additional inertial force moment is calculated according to the battery acceleration; The additional moment of inertia matrix, the additional Coriolis force moment and the additional inertial force moment are integrated with the rotor lift moment and the counter-torque moment to form a complete rotation dynamics equation.

6. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, The processor executes the computing program to realize the method in any one of claims 1-5.

7. A computer-readable storage medium storing a computer program, wherein the computer program comprises the following steps of: receiving a request for a resource from a client; determining whether the client is authorized to access the resource; and if the client is authorized to access the resource, providing the resource to the client. The computer program is executed by the processor to realize the method in any one of claims 1-5.

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