Dynamic modeling method for variable-centroid unmanned aerial vehicle

Abstract

The invention discloses a dynamic modeling method for a variable-centroid unmanned aerial vehicle, and belongs to the field of unmanned aerial vehicle dynamic modeling. The method comprises the steps that a ground coordinate system and a vehicle body coordinate system are established; defining a system configuration comprising a machine body part, a pitching channel mobile battery and a rolling channel mobile battery; calculating a system centroid position; establishing a system translation dynamic model; establishing a system rotation dynamical model considering an additional inertia moment, an additional Coriolis moment and an additional gyroscopic moment; establishing a dynamic model of the mobile battery; and a complete eight-degree-of-freedom nonlinear dynamic model is formed. According to the method, the battery of the unmanned aerial vehicle serves as a moving mass block, the complex dynamic phenomenon and the strong coupling relation generated in the battery moving process are accurately described, compared with the prior art, the system complexity and cost are remarkably reduced, and a reliable theoretical basis is provided for design of a variable-centroid unmanned aerial vehicle control system.

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] An absolute momentum moment of the system on the mass center is calculated according to a system mass center position vector with the body coordinate system as a reference system, and a system rotation dynamics model is established;

[0010] A mobile battery dynamics model is established in the body coordinate system, and the inertia acceleration in the ground coordinate system is associated through the conversion matrix;

[0011] The translation dynamics model, the rotation dynamics model, the battery movement dynamics model and the attitude kinematics model after the coordinate system conversion are integrated to form an eight-degree-of-freedom nonlinear dynamics model of the variable mass center unmanned aerial vehicle.

[0012] Optionally, the establishment of the ground coordinate system and the body coordinate system comprises:

[0013] The ground coordinate system is taken as an inertial system, and the origin is fixed to the earth, for describing the gravity and the inertia acceleration;

[0014] The body coordinate system is taken as a body coordinate system, and the origin is located at the mass center of the body, for describing the body attitude and the relative displacement of the battery;

[0015] The inertia quantity in the ground coordinate system is converted to the body coordinate system through a direction cosine matrix, and the control quantity in the body coordinate system is converted to the ground coordinate system.

[0016] Optionally, the calculation of the system mass center position comprises:

[0017] Original position vectors of the body part, the pitch channel battery and the roll channel battery in the body coordinate system are obtained;

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

[0019] According to a mass center formula of a particle system, a real-time position vector of the system mass center relative to the body origin is solved in the body coordinate system, and the system mass center position is obtained.

[0020] Optionally, the establishment of the system translation dynamics model comprises:

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

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

[0023] In the body coordinate system, the Newton's second law equations of each component are integrated to obtain the translation dynamics model of the system mass center.

[0024] Optionally, the establishment of the system rotation dynamics model comprises:

[0025] In the body coordinate system, a position vector of each component relative to the system centroid is calculated according to a system centroid position vector;

[0026] In the body coordinate system, an absolute momentum moment of the system on the system centroid is calculated;

[0027] The momentum moment theorem is applied and expressed in the body coordinate system to obtain a system rotational dynamics model.

[0028] Optionally, the calculation of the absolute momentum moment comprises:

[0029] In the body coordinate system, a momentum moment of the body and each battery on the system centroid is calculated respectively;

[0030] An angular velocity vector in the ground coordinate system is converted to the body coordinate system through a direction cosine matrix;

[0031] In the body coordinate system, each momentum moment is accumulated to obtain a total absolute momentum moment of the system on the centroid.

[0032] Optionally, the establishment of the system rotational dynamics model further comprises:

[0033] In the body coordinate system, an additional rotational inertia matrix is calculated in real time according to a battery displacement amount;

[0034] In the body coordinate system, an additional Coriolis moment is calculated according to a battery velocity and a body angular velocity;

[0035] In the body coordinate system, an additional inertia moment is calculated according to a battery acceleration;

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

[0037] Optionally, the establishment of the mobile battery dynamics model comprises:

[0038] In the body coordinate system, a displacement constraint of a pitch and roll channel battery is defined;

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

[0040] In the body coordinate system, a constraint force is eliminated to obtain a battery motion dynamics equation containing a driving force.

[0041] In another aspect, the application further provides an electronic device comprising 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] In another aspect, the present application also provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the method.

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

[0044] The present application solves the problem of insufficient modeling accuracy in the prior art caused by regarding the moving mass block as a static mass distribution change and ignoring the additional disturbance torque generated during the movement process by establishing a complete eight-degree-of-freedom nonlinear dynamic model considering the dynamic characteristics of the moving battery. Compared with the linearization processing method commonly used in the prior art, which cannot accurately describe the strong nonlinearity and strong coupling characteristics of the variable center-of-mass system, the model established by the present application can accurately describe the complex dynamic phenomena such as additional inertia torque, Coriolis torque and gyroscopic torque generated during the movement of the battery, as well as the strong coupling relationship between the movement of the battery and the attitude motion of the body. At the same time, the present application innovatively uses the battery of the unmanned aerial vehicle itself as the moving mass block, which significantly reduces the system complexity and cost compared with the prior art scheme of using a dedicated slider. The established accurate dynamic model provides a reliable theoretical basis for the design of the variable center-of-mass unmanned aerial vehicle control system, can support accurate control under the conditions of large-scale battery movement and large-angle maneuver, and overcomes the limitation of the linearization model which is only applicable to small perturbation conditions, thereby fully exploiting the advantages of variable center-of-mass control technology in terms of low power consumption and long range. BRIEF DESCRIPTION OF DRAWINGS

[0045] The accompanying drawings, which form a part of the present application, are used to provide a further understanding of the present application, and the illustrative embodiments thereof, and are not intended to limit the present application. In the drawings:

[0046] Figure 1 The unmanned aerial vehicle planar structure diagram described in the embodiment of the present application.

[0047] Figure 2 The I xx History curve comparison.

[0048] Figure 3 The I yy History curve comparison.

[0049] Figure 4 The I zz History curve comparison.

[0050] Figure 5 The M y History curve comparison.

[0051] Figure 6 Mach number under different initial position configurations of the embodiments of the present application x History curve comparison.

[0052] Figure 7 Mach number under different initial position configurations of the embodiments of the present application z History curve comparison.

[0053] Figure 8 Mach number under different working conditions of the embodiments of the present application xx History curve comparison.

[0054] Figure 9 Mach number under different working conditions of the embodiments of the present application yy History curve comparison.

[0055] Figure 10 Mach number under different working conditions of the embodiments of the present application zz History curve comparison.

[0056] Figure 11 Mach number under different working conditions of the embodiments of the present application y History curve comparison.

[0057] Figure 12 Mach number under different working conditions of the embodiments of the present application x History curve comparison.

[0058] Figure 13 Mach number under different working conditions of the embodiments of the present application z History curve comparison. DETAILED DESCRIPTION

[0059] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

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

[0061] Embodiment one

[0062] In this embodiment, a dynamic modeling method of a variable centroid unmanned aerial vehicle is provided, comprising:

[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 constitutes a right-handed rectangular coordinate system.

[0070] The system centroid calculation adopts the principle of mass point system centroid calculation, and comprehensively considers the mass distribution of the body part, the pitch channel mobile battery and the roll channel mobile battery:

[0071] The system translation dynamics modeling is based on Newton's second law, and the force analysis of the body, the pitch channel battery and the roll channel battery is carried out in the ground coordinate system, the force equation set is established, and the variable centroid UAV centroid translation dynamics equation is calculated by using coordinate transformation and vector differential method:

[0072] The system rotation dynamics modeling is based on the theorem of moment of momentum, and the complete rotation dynamics equation including additional inertia moment, additional Coriolis moment and additional gyroscopic moment is established:

[0073] The total rotational inertia matrix I total includes the superposition of the body rotational inertia I a and the additional rotational inertia ΔI, the additional rotational inertia ΔI is caused by the change of the mobile battery position, and each element is real-time with the battery position, the additional rotational inertia matrix can accurately reflect the real-time influence of the battery movement on the system rotation characteristics, each element is a function of the battery movement amount ε x , ε y :

[0074] The additional inertia moment M oi is mainly generated by the acceleration motion of the battery; the additional Coriolis moment M co is generated by the coupling of the battery moving speed and the body angular velocity; the additional gyroscopic moment M gy is generated by the change of the angular momentum of the battery relative to the body, the three types of additional moments are accurately separated by the mathematical derivation method of combining similar terms, which accurately describes the dynamic influence of the mobile battery on the system rotation dynamics:

[0075] The mobile battery dynamics modeling adopts the method of constrained multibody system dynamics, and the constraint force is eliminated by the projection operator and the constraint condition, the direct relationship between the battery driving force and the motion state is established by the projection operator method.

[0076] The eight-degree-of-freedom dynamic model is formed by integrating a system translation dynamic model, an attitude rotation dynamic model, a battery motion dynamic model and an attitude kinematics model, the eight-degree-of-freedom dynamic model including 3 translation degrees of freedom, 3 rotation degrees of freedom and 2 battery movement degrees of freedom, and being capable of describing a strong coupling relationship between battery movement and body attitude movement, including the influence of battery position change on the system center of mass and the moment of inertia, the contribution of battery movement velocity to the system Coriolis force and gyroscopic moment, and the feedback effect of body attitude movement on battery dynamics, compared with existing linearized models or simplified models ignoring battery dynamic characteristics, the model can maintain high modeling accuracy under large range battery movement and large angle maneuvering.

[0077] Embodiment two

[0078] The embodiment provides a dynamic modeling method of a variable center of mass unmanned aerial vehicle, including:

[0079] Firstly, the required mathematical basis is given, the conversion matrix from the ground coordinate system O G to the body coordinate system O A is as follows:

[0080]

[0081] Wherein:

[0082]

[0083] The complete conversion matrix is obtained by expansion:

[0084]

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

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

[0087]

[0088] Under the small angle assumption, the above formula is simplified as:

[0089]

[0090] ω X ,ω Y ,ω Z are respectively the angular velocities of the pitch, the roll and the yaw, denotes the first order differential of the pitch angle, denotes the first order differential of the roll angle, denotes the first order differential of the yaw angle.

[0091] For a 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 in the moving coordinate system B as v B and in the inertial coordinate system I as v I Then:

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

[0095] where ω is the angular velocity vector of the moving coordinate system B with respect to the inertial coordinate system I.

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

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

[0098] Rule 3: The differential rule for the product of a scalar and a vector;

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

[0100] Rule 4: The differential rule for a composite vector, let r = r0 + ρ, where r0 is the position vector of the origin and ρ is the position vector relative to the origin, then:

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

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

[0103] Rule 5: The differential of the coordinate transformation matrix:

[0104]

[0105] Modeling method steps:

[0106] Step 1: Coordinate system establishment and system configuration definition;

[0107] Two coordinate systems are established, the first coordinate system is ground coordinate system O G : the origin O is fixed to the earth, the X G -axis points to the north direction in the local horizontal plane, the Y G -axis is perpendicular to the X G -axis in the local horizontal plane and points to the east direction, and the Z G -axis is perpendicular to the X G -Y G -plane forms a right-handed orthogonal coordinate system; the second coordinate system is body coordinate system O A : the origin O is at the body mass center, the X A -axis points to the nose direction and is positive, the Y A -axis is perpendicular to the longitudinal plane and points to the right side of the body and is positive, and the Z A -axis is perpendicular to the X A -Y A -plane forms a right-handed orthogonal coordinate system.

[0108] The variable mass center quadrotor unmanned aerial vehicle system comprises a body part, a pitch channel mobile battery and a roll channel mobile battery, wherein: the pitch channel mobile battery moves along the X A -axis direction, and the movement amount is ε x ; the roll channel mobile battery moves along the Y A -axis direction, and the movement amount is ε y .

[0109] Step two: system mass center calculation;

[0110] The position vector of the body part in the body coordinate system is defined as:

[0111]

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

[0113] The position vector of the pitch channel mobile battery in the body coordinate system is defined as:

[0114]

[0115] wherein, is the position vector of the pitch channel mobile battery in the body coordinate system, h y1 ,h z1 are the projections of the initial installation position of the battery on the Y-axis and the Z-axis. ε x is the displacement of the battery in the pitch channel.

[0116] The position vector of the roll channel mobile battery in the body coordinate system is defined as:

[0117]

[0118] h x2 ,h z2 is the projection of the initial installation position of the battery on the X-axis and Z-axis. ε y is the displacement of the battery in the roll channel.

[0119] According to the centroid calculation formula, the position vector of the system centroid in the body coordinate system is :

[0120]

[0121] m a is the mass of the body, m1 and m2 are the masses of the batteries, m c is the total mass of the system.

[0122] Expanding it gives:

[0123]

[0124] where λ1 = m1 / m c , λ2 = m2 / m c is the mass ratio of the battery to the system.

[0125] Step three: translational dynamics modeling of the system;

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

[0127] The body force equation is:

[0128]

[0129] The pitch channel battery force equation is:

[0130]

[0131] The roll channel battery force equation is:

[0132]

[0133] where: F ai is the constraint force of the body on the i-th battery; F ci is the driving force of the i-th battery; F p is the propeller pull force, F d is the aerodynamic force (assumed to be zero in modeling); is the gravity of each part in the ground coordinate system. is the position vector of each part in the ground coordinate system.

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

[0135]

[0136] The battery acceleration is calculated using vector differential rules:

[0137]

[0138] Where:

[0139]

[0140] ω a is the angular velocity vector of the body relative to the ground coordinate system, is the first order differential of the position vector of the battery in the body coordinate system in the pitch channel, is the second order differential of the position vector of the battery in the body coordinate system in the pitch channel.

[0141] After simplification:

[0142]

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

[0144]

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

[0146]

[0147] Substitute equation 24 into equation 18, equation 25 into equation 19, and then into equation 17 to obtain:

[0148]

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

[0150]

[0151] Where N = [0, 0, 1] T is the unit vector of the Z axis of the body coordinate system. f j is the lift of the jth propeller.

[0152] Step four: system rotational dynamics modeling;

[0153] The absolute momentum moment of the system on the center of mass c is:

[0154]

[0155] Where: I a is the rotational inertia of the body about its center of mass, rc-a is the position vector of the body center of mass a relative to the system center of mass c, r c-i is the position vector of the i-th battery relative to the system center of mass c, v a and v i are the velocity vectors of the body center of mass a and the i-th battery, respectively.

[0156] Position vector of the system center of mass to the body 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 vector of the system center of mass to the i-th battery center of mass:

[0159]

[0160] Velocity of the body center of mass in the body coordinate system:

[0161]

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

[0163] Velocity of the i-th battery in the body coordinate system:

[0164]

[0165] According to the theorem of the moment of momentum:

[0166]

[0167] For the I term:

[0168]

[0169] For the II term:

[0170]

[0171] Substitute equation 35 and equation 34 into equation 33 and combine like terms to get:

[0172]

[0173] where ΔI is the additional moment of inertia brought by the movement of the battery position, and the expression is:

[0174]

[0175] The specific elements are:

[0176]

[0177]

[0178] The additional inertia moment M oi is:

[0179]

[0180] The additional Coriolis moment M co is:

[0181]

[0182] The additional gyroscopic moment M gy is:

[0183]

[0184] where:

[0185]

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

[0187]

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

[0189]

[0190]

[0191] The counter-torque moment of the propeller M ff is:

[0192]

[0193] Ω j is the rotation speed of the jthrotor, and d is the counter-torque coefficient.

[0194] Step five: Moving battery dynamics modeling;

[0195] The constraint conditions of the pitch and roll channels of the battery are:

[0196]

[0197] The expressions of the constraint force and the driving force are:

[0198]

[0199] The expression of the projection operator is:

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

[0201] Substitute equation 24 into equation 18, equation 25 into equation 19, and convert to the body coordinate system, and project to the pitch or roll axis to obtain:

[0202]

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

[0204]

[0205] Where:

[0206]

[0207] Step six: complete eight-degree-of-freedom dynamic model

[0208] System translational dynamics model:

[0209]

[0210] Attitude rotational dynamics model:

[0211]

[0212] Battery motion dynamics model:

[0213]

[0214] Attitude kinematics model:

[0215]

[0216] Example three

[0217] A variable center of mass unmanned aerial vehicle dynamics modeling method is provided in this embodiment, comprising:

[0218] Step one: 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 unmanned aerial vehicle system including the body part, the pitch channel moving battery and the roll channel moving battery, wherein the pitch channel moving battery moves along the XA axis direction, and the movement amount is ε x; the roll channel moves the battery along the YA axis direction, and the movement amount is ε y ;

[0219] Step two: the system centroid calculation defines the position vector of the body part in the body coordinate system, the position vector of the pitch channel moving battery in the body coordinate system, and the position vector of the roll channel moving battery in the body coordinate system; the position vector of the system centroid in the body coordinate system is determined according to the centroid calculation formula;

[0220] Step three: the system translation dynamics modeling analyzes the force of the body, the pitch channel battery and the roll channel battery respectively in the ground coordinate system, establishes the force equation of each part, calculates the acceleration of the battery, and establishes the centroid translation equation in the body coordinate system;

[0221] Step four: the system rotation dynamics modeling calculates the absolute momentum moment of the system to the centroid; the rotation dynamics equation is established according to the momentum moment theorem; the additional moment of inertia matrix, the additional inertia force moment, the additional Coriolis force moment and the additional gyroscopic force moment are calculated; the rotor lift moment and the propeller counter-torque moment are calculated;

[0222] Step five: the moving battery dynamics modeling establishes the constraint conditions of the pitch and roll channel batteries; the constraint force is eliminated through the projection operator and the constraint condition, and the battery motion dynamics equation is established;

[0223] Step six: the complete eight-degree-of-freedom dynamics model integrates the system translation dynamics model, the attitude rotation dynamics model, the battery motion dynamics model and the attitude kinematics model to form a complete eight-degree-of-freedom nonlinear dynamics model.

[0224] According to the system configuration defined in step one, the following basic parameters are set: the body mass mb=10 kg, the pitch channel moving battery mass mp1=5 kg, the roll channel moving battery mass mp2=5 kg. The body characteristic size is 0.8 m x 0.8 m, and the body rotation inertia parameters are set as Ixx=1.5 kg·m 2 , Iyy=1.6 kg·m 2 , Izz=2.3 kg·m 2 . The system configuration diagram is Figure 1 .

[0225] Analysis of additional moments of inertia and additional moments of force at different initial positions and strokes;

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

[0227] Position configuration one: the initial position of the battery in the pitch channel hy1 = 0.1 m, hz1 = 0.05 m; the initial position of the battery in the roll channel hx2 = 0.1 m, hz2 = 0.05 m. In this configuration, the battery is closer to the center of mass of the machine, and the system center of mass offset is smaller according to the center of mass calculation formula (15).

[0228] Position configuration two: the initial position of the battery in the pitch channel hy1 = 0.2 m, hz1 = 0.1 m; the initial position of the battery in the roll channel hx2 = 0.2 m, hz2 = 0.1 m. In this configuration, the battery is farther away from the center of mass of the machine, and the system center of mass offset is obvious.

[0229] Position configuration three: the initial position of the battery in the pitch channel hy1 = 0.15 m, hz1 = 0.15 m; the initial position of the battery in the roll channel hx2 = 0.15 m, hz2 = 0.15 m. This configuration is an intermediate state of the previous two.

[0230] According to the moving battery dynamics modeling in step five, set the battery motion as a sinusoidal periodic motion to simulate the actual control process:

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

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

[0233] Set three different stroke verification models to adapt to different motion amplitudes: small stroke Ap1 = Ap2 = 0.05 m, medium stroke Ap1 = Ap2 = 0.1 m, and large stroke Ap1 = Ap2 = 0.15 m.

[0234] According to the system rotation 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] According to formulas (45-47), calculate the components of the additional moment. The additional inertia moment M oi is mainly generated by the acceleration motion of the battery; the additional Coriolis moment M co is generated by the coupling of the battery moving speed and the machine angular velocity; the additional gyroscopic moment M gy is generated by the change of the angular momentum of the battery relative to the machine.

[0236] Figure 2 , Figure 3 and Figure 4 show the I xx , I yy , I zzThe history curve comparison of M y , M x , M z , and Table 1 gives the comparison analysis of different initial position configuration parameters. Figure 5 , Figure 6 and Figure 7 respectively show the history curve comparison of M y , M x , M z , and Table 1 gives the comparison analysis of different initial position configuration parameters.

[0237] Table 1

[0238]

[0239] Additional rotational inertia and additional torque analysis 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 accuracy of the model in describing the strong coupling relationship between the battery movement and the body attitude motion.

[0241] Working condition one: mass center adjustment in hovering state

[0242] The control target is to realize accurate control of the system mass center through battery position fine adjustment. According to the system translation dynamics model in step three, the propeller tension is mainly used to balance the gravity in the hovering state, and the battery movement mainly affects the mass center position. The system dynamics under this working condition is relatively simple, but it lays the foundation for other complex working conditions.

[0243] Working condition two: attitude auxiliary control in pitch maneuvering process

[0244] The pitch angle maneuvering trajectory is set as θ(t) = 15°·sin(0.3πt), and this working condition verifies the accuracy of the attitude rotation dynamics model in step four of the application. In the pitch maneuvering process, according to the attitude kinematics model, the body attitude change and the battery movement form a strong coupling relationship.

[0245] Working condition three: attitude compensation control in roll maneuvering process

[0246] The roll angle maneuvering trajectory is set as φ(t) = 20°·sin(0.25πt), and this working condition is the most complex case, fully embodying the accuracy of the model in describing large-angle maneuvering and strong coupling characteristics.

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

[0248] The additional torque components in different working conditions are calculated according to formulas (45-47). In the hovering state, the additional Coriolis torque and the additional gyroscopic torque are small; in the maneuvering state, these coupling torque terms increase significantly, which has an important influence on the system dynamics.

[0249] Figure 8 、 Figure 9 and Figure 10 The history curves of the additional rotational inertia I xx , I yy , I zz in different working conditions are compared, Figure 11 Figure 12 and Figure 13 The changes of the additional torques M y , M x , M z in different working conditions are shown, and Table 2 gives a comparative analysis of the dynamics in different flight conditions.

[0250] Table 2

[0251]

[0252] Through the calculation and analysis of the above two embodiments, it is verified that the dynamic modeling method provided by the present application can accurately describe the influence of the dynamic characteristics of the moving battery on the system dynamics, and the complete eight-degree-of-freedom nonlinear dynamic model provides a reliable theoretical basis for the control system design of the variable center-of-mass unmanned aerial vehicle.

[0253] In another aspect, the present embodiment also provides an electronic device, which includes a memory, a processor, and a computing program stored in the memory and executable on the processor, and the processor implements the method when executing the computing program.

[0254] In another aspect, the present embodiment also provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the method.

[0255] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical scope disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method of dynamic modeling of a variable center of mass unmanned aerial vehicle, the method comprising: include: Establish a ground coordinate system and a body coordinate system, and use the transformation matrix between the ground coordinate system and the body coordinate system as an intermediary to perform bidirectional mapping of all vectors between the ground coordinate system and the body coordinate system; A system configuration comprising the body section, pitch channel moving battery, and roll channel moving battery is defined in the body coordinate system; Based on the system configuration, calculate the position vector of the system's center of mass relative to the origin of the machine in the body coordinate system; Using the ground coordinate system as the inertial reference system, a translational dynamic model of the system's center of mass is established, and the translational equations are mapped to the body coordinate system through the transformation matrix. 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. 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; 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.

2. The method of claim 1, wherein, The establishment of the ground coordinate system and the body coordinate system includes: 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. 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; 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.

3. The method of claim 1, wherein, The centroid location of the computing system includes: Obtain the original position vectors of the body parts, pitch channel battery, and roll channel battery in the body coordinate system; The original position vector is superimposed with the displacement to obtain the real-time position vector of each component in the body coordinate system; 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.

4. The method of claim 1, wherein, The establishment of the system translational dynamics model includes: 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. The acceleration vector in the ground coordinate system is transformed to the body coordinate system using the direction cosine matrix; 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.

5. The method of claim 1, wherein, The establishment of the system rotational dynamics model includes: 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; In the body coordinate system, calculate the absolute angular momentum of the system about the system's center of mass; By applying the angular momentum theorem and expressing it in the body coordinate system, the rotational dynamics model of the system is obtained.

6. The method of claim 1, wherein, The calculation of absolute angular momentum includes: In the body coordinate system, calculate the angular momentum of the computer body and each battery about the system's center of mass, respectively; The angular velocity vector in the ground coordinate system is transformed to the body coordinate system using the direction cosine matrix; 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.

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

8. The method of claim 1, wherein, The method for establishing the mobile battery dynamics model comprises: In the body coordinate system, the displacement constraint of the battery in the pitch and roll channels is defined; The inertial acceleration in the ground coordinate system is mapped to the constraint direction of the body coordinate system through a projection operator; In the body coordinate system, the constraint force is eliminated to obtain a battery motion dynamics equation containing a driving force.

9. 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 1-8.

10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The computer program is executed by the processor to realize the method in any one of claims 1-8.

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