Control method of non-planar agricultural six-rotor UAV based on high-order all-wheel drive system

Abstract

The present invention relates to the field of drone control, and more particularly to a method for controlling a non-planar agricultural six-rotor drone. The present invention aims to address the problem of low control accuracy of existing methods for all-wheel drive non-planar six-rotor drones. The process is as follows: Step 1: Construct an all-wheel drive non-planar six-rotor drone model; Step 2: Construct a system state variable matrix; Step 3: Design a controller based on the all-wheel drive non-planar six-rotor drone model and the system state variable matrix; The specific process is as follows: Step 3i: Convert the all-wheel drive non-planar six-rotor drone model constructed in Step 1 into a high-order all-wheel drive system model based on the system state variable matrix; Step 3ii: Obtain an error tracking model based on the high-order all-wheel drive system model; Step 3iii: Design a controller based on the error tracking model.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) control, and in particular to a control method for a non-planar agricultural six-rotor UAV. Background Art

[0002] my country's grain production has grown continuously for many years, and agricultural production has entered a new stage of development, generating new demands for farmland production. Improving the quality of agricultural products and strengthening early warning capabilities for agricultural disasters have become urgent needs. At the same time, my country's agricultural planting and management model is continuously shifting from a small-scale peasant economy to a "big agriculture" of agricultural cooperatives. Large-scale production has placed higher demands on agricultural equipment.

[0003] Traditional manual pesticide spraying has numerous drawbacks, such as requiring manual intervention in harsh environments and low spraying efficiency. However, drone-based pesticide spraying systems can deliver comprehensive, precise, and all-around spray coverage to farmland. Furthermore, agricultural drones offer immediate response capabilities. When problems are discovered, drones can promptly reach the affected area to apply fertilizer, disinfest, provide feedback, and predict yields. This has led to a nationwide surge in agricultural mechanization and automation, and the use of drones for pesticide spraying has emerged as a key driver of agricultural production. The use of agricultural drones aligns with the new trends of agricultural modernization, informatization, and precision agriculture.

[0004] Agricultural aircraft have been used for pesticide spraying on most farms in my country. Many farms have introduced low-speed agricultural aircraft and successfully completed pesticide spraying operations on large farms. Agricultural fixed-wing aircraft offer advantages such as large payload capacity, high efficiency, and high speed. However, due to their high speed and altitude, they cannot spray accurately and control the drift of droplets. Agricultural helicopters have the advantages of hovering ability, slow flight speed, and effective airflow disturbance over crops. The airflow generated by their main rotors ensures uniform distribution of pesticides, improving their utilization rate. However, helicopters rely on rotor rotation to increase altitude and adjust direction, resulting in high energy consumption and low efficiency. In addition, high repair and maintenance costs make them relatively expensive spraying equipment in the agricultural aviation sector.

[0005] In recent years, research on multi-rotor aircraft has seen significant progress in civilian, agricultural, and military applications. Multi-rotor drones have a simple structure, with the rotors being their only moving parts. Compared to fixed-wing drones, they offer greater maneuverability and hovering capabilities, are less affected by time, location, or land area, and are relatively affordable. Consequently, multi-rotor aircraft have been widely used in pesticide spraying.

[0006] The design of a non-planar hexacopter drone allows it to compensate for gravity in any posture, enabling static hovering in any position. Pesticide spraying drones must adapt to the complex environments of farmland or orchards (e.g., confined spaces and obstacles). In many cases, drones must fly at a specific angle into fields or orchards to spray pesticides at specific locations on plants. However, the attitude and position control of traditional drones are highly coupled, making static hovering difficult for underactuated drones. Non-planar hexacopter drones expand the application scope of future drone development. While operating, non-planar hexacopter drones can achieve unrestricted omnidirectional motion in six degrees of freedom and robustly track arbitrary trajectories in three-dimensional space. This omnidirectional drone offers a unique advantage over traditional drones, significantly facilitating the use of drones for pesticide spraying. Summary of the Invention

[0007] The purpose of the present invention is to solve the problem of low control accuracy of existing methods for all-wheel drive non-planar six-rotor drones, and to propose a control method for non-planar agricultural six-rotor drones based on a high-order all-wheel drive system.

[0008] The specific process of the control method of the non-planar agricultural six-rotor UAV based on the high-order all-wheel drive system is as follows:

[0009] Step 1: Build a full-drive non-planar six-rotor drone model;

[0010] Step 2: Construct the system state variable matrix;

[0011] Step 3: Design a controller based on the all-wheel drive non-planar six-rotor drone model and the system state variable matrix. The specific process is as follows:

[0012] Step 3.1: Convert the all-wheel drive non-planar six-rotor UAV model constructed in step 1 into a high-order all-wheel drive system model based on the system state variable matrix;

[0013] Step 32: Obtain an error tracking model based on the high-order all-wheel drive system model;

[0014] Step 3. Design a controller based on the error tracking model.

[0015] The beneficial effects of the present invention are:

[0016] The present invention proposes a control method for a non-planar agricultural six-rotor UAV based on a high-order all-wheel drive system. In order to more conveniently and intuitively observe the layout of the UAV rotor, Figure 2 The three views after removing the pesticide sprayer are shown. Figure 2 , f1-f6 represent the directions in which the six rotors provide lift, Figure 2 a is the top view of the drone, f 1XY -f6XY They are the directions of the forces after projecting the lift provided by the six rotors onto the plane where the fuselage and the arms are located; Figure 2 Figure c clearly shows that the lift f2 provided by the rotor is not vertically upward, but has an angle γ with the vertical direction, and decomposes the inclined lift in the horizontal and vertical directions into f 2z and f 2xy This non-planar design with passive tilt rotors overcomes the under-actuated characteristics of common multi-rotor configurations. The full rank of the control allocation matrix indicates that this drone with a non-planar design has six independent control variables, so it does not need to tilt while moving on the horizontal plane. In this case, the equipment for spraying pesticides does not require additional rotation and stabilization devices, which enables it to achieve a certain degree of modularity and simplification. When spraying pesticides, the drone will be subject to complex wind interference and easily lose control, and the response speed of the drone is required to be relatively high. Therefore, the present invention uses a finite-time high-order full-wheel drive system method to design an anti-interference controller to improve the robustness and rapid response of the system. Since the mass of the medicine loaded on the belly of the drone will decrease over time, the present invention takes into account the "variable mass" characteristic of the pesticide spraying drone. When the pesticide spraying stops, the mass of the pesticide can be regarded as part of the mass of the drone. In summary, the present invention improves the control accuracy of the full-wheel drive non-planar six-rotor drone. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Flowchart of the present invention;

[0018] Figure 2 The structure diagram of the six-rotor all-wheel drive drone used in the present invention, a is a top view, b is an oblique view, c is a main view, f is a 1xy is the projection of the lift of the first rotor of the UAV onto the xoy plane of the UAV coordinate system, f 2xy is the projection of the lift of the second rotor of the UAV onto the xoy plane of the UAV coordinate system, f 3xy is the projection of the lift of the third rotor of the UAV onto the xoy plane of the UAV coordinate system, f 4xy is the projection of the lift of the fourth rotor of the UAV onto the xoy plane of the UAV coordinate system, f 5xy is the projection of the lift of the fifth rotor of the UAV onto the xoy plane of the UAV coordinate system, f 6xy is the projection of the lift of the sixth rotor of the drone onto the xoy plane of the drone coordinate system, f1 is the direction of the lift generated by the first rotor of the drone, f2 is the direction of the lift generated by the second rotor of the drone, f3 is the direction of the lift generated by the third rotor of the drone, f4 is the direction of the lift generated by the fourth rotor of the drone, f5 is the direction of the lift generated by the fifth rotor of the drone, and f6 is the direction of the lift generated by the sixth rotor of the drone.B is the x-axis of the drone coordinate system, Y B is the y-axis of the drone coordinate system, Z B is the z-axis of the drone coordinate system, O is the center of the drone, and f 2z is the vector obtained by projecting the lift force generated by the No. 2 rotor of the drone toward the z-axis, and γ is the angle between the rotor of each drone and the xoy plane of the drone coordinate system (taken as 30°);

[0019] Figure 3 The following are the position tracking curves of the UAV: ​​a is the position tracking curve in the x-axis direction, b is the position tracking curve in the y-axis direction, and c is the position tracking curve in the z-axis direction.

[0020] Figure 4 is the attitude angle diagram of the UAV, a is the roll angle tracking curve, b is the yaw angle tracking curve, and c is the pitch angle tracking curve;

[0021] Figure 5 Figure 3 is the UAV position tracking curve after interference is applied, a is the tracking error in the x-axis direction after interference is applied, b is the tracking error in the y-axis direction after interference is applied, and c is the tracking error in the z-axis direction after interference is applied. DETAILED DESCRIPTION

[0022] Specific embodiment 1: The specific process of the control method of the non-planar agricultural six-rotor drone based on the high-order full-drive system in this embodiment is as follows:

[0023] Step 1: Build a full-drive non-planar six-rotor drone model;

[0024] Step 2: Construct the system state variable matrix;

[0025] Step 3: Design a controller based on the all-wheel drive non-planar six-rotor drone model and the system state variable matrix. The specific process is as follows:

[0026] Step 3.1: Based on the system state variable matrix, the all-wheel drive non-planar six-rotor UAV model (Equation 1) constructed in Step 1 is converted into a high-order all-wheel drive system model (Equation 13);

[0027] Step 32: Obtain the error tracking model (14) based on the high-order all-wheel drive system model (Equation 13);

[0028] Step 3. Design a controller based on the error tracking model (14).

[0029] Specific embodiment 2: This embodiment differs from the specific embodiment 1 in that in step 1, a full-drive non-planar six-rotor drone model is constructed; the specific process is as follows:

[0030] After theoretical derivation, the following set of equations can describe this all-wheel drive six-rotor drone;

[0031] Select any rotor in the six-rotor drone as the first rotor, and arrange the rotors in order based on the first rotor as the second rotor, the third rotor, the fourth rotor, the fifth rotor, and the sixth rotor;

[0032] Construct the drone coordinate system: take the center of the six-rotor drone as the origin o, the direction of the third rotor pointing to the fifth rotor as the x-axis, the direction of the second rotor as the y-axis, and the z-axis perpendicular to the x and y planes;

[0033] The model of the all-wheel drive non-planar six-rotor drone is expressed as:

[0034]

[0035] Where, represents the second-order derivative of the drone’s position along the x-axis, represents the second-order derivative of the drone’s position along the y-axis, represents the second-order derivative of the drone's position along the z-axis, represents the second-order derivative of the UAV’s roll angle, Represents the second-order derivative of the pitch angle of the drone, Represents the second-order derivative of the yaw angle of the drone; a, b, α p , α q , α r All represent coefficients, d1, d2, d3, d4, d5, d6 represent the interference to the UAV; u1, u2, u3, u4, u5, u6 represent the control matrix of the UAV, u1, u2, u3, u4, u5, u6 and the speed of the six rotors of the UAV The specific relationship is shown in formula (2); g represents the gravitational acceleration of the earth.

[0036] Other steps and parameters are the same as those in the first embodiment.

[0037] Specific embodiment 3: This embodiment differs from specific embodiment 1 or 2 in that the control matrix of the drone is expressed as:

[0038]

[0039] Where, Indicates the square of the first rotor speed of the drone, Indicates the square of the second rotor speed of the drone, Indicates the square of the rotation speed of the third rotor of the drone, Indicates the square of the fourth rotor speed of the drone, Indicates the square of the fifth rotor speed of the drone, It represents the square of the rotation speed of the sixth rotor of the UAV; the superscript T indicates the transpose.

[0040] Other steps and parameters are the same as those in the first or second embodiment.

[0041] Specific embodiment 4: This embodiment differs from any one of the specific embodiments 1 to 3 in that the coefficient m represents the mass of the drone, δm represents the mass of the drone’s payload, and k f represents the lift coefficient, S γ represents sinγ, where γ represents the angle between the UAV rotor and the xoy plane of the UAV coordinate system;

[0042] coefficient

[0043] coefficient l represents the rotor radius, C γ represents cosγ, k τ Represents the counter torque coefficient, I x represents the moment of inertia of the drone along the x-axis;

[0044] coefficient I y represents the moment of inertia of the drone along the y-axis;

[0045] coefficient I z Represents the UAV's moment of inertia along the z-axis.

[0046] The drone can be controlled by adjusting the rotation speed of the rotor.

[0047] Similarly, if the control matrix required at a certain moment is calculated during the control process, the rotational speed of the four rotors at that moment can also be calculated, thereby achieving control of the drone.

[0048] After calculating the determinant of the coefficient matrix, the value is 2, so it can be seen that The coefficient matrix of is full rank, that is, the UAV can reach any state by adjusting the speed of the six rotors.

[0049] The other steps and parameters are the same as those in the first to third embodiments.

[0050] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the system state variable matrix is ​​constructed in step 2; the specific process is as follows:

[0051] Step 2.1. Define the matrix M i ∈R m×m , constant i=0,1,2,...,n-1, n=2; R represents the set of real numbers; m represents the mass of the drone;

[0052] M0 and M1 represent a real matrix with m rows and m columns respectively;

[0053] Based on the matrix M i Construct matrix M (0～(n-1)) ; The expression is:

[0054] M (0～(n-1)) =[M0 M1 … M n-1 ] (4)

[0055] In the formula, M0 represents a real number matrix with m rows and m columns, M1 represents a real number matrix with m rows and m columns, and M n-1 Represents a real matrix with m rows and m columns;

[0056] Based on the matrix M (0～(n-1)) Construct the matrix Γ(M (0～(n-1)) ); the expression is:

[0057]

[0058] Where I represents the identity matrix;

[0059] Step 2: Define the following function:

[0060] sig σ (ζ)=sign(ζ)|ζ| σ (10)

[0061] Where, sig σ (ζ) represents the σ-order index of sig(ζ), |ζ| represents the absolute value of ζ, |ζ| σ represents the σ-order index of |ζ|; σ represents an arbitrary constant, σ≥0;

[0062] ζ represents the system state variable; the system is a full-drive non-planar six-rotor drone;

[0063] where sign(ζ) is expressed as:

[0064]

[0065] For any constant σ, the system state variable ζ, d|ζ| σ+1 / dζ=(σ+1)sig σ (ζ), d[sig σ+1 (ζ)] / dζ=(σ+1)|ζ| σ ;

[0066] Where |ζ| σ+1 represents the σ+1 order index of |ζ|; sig σ+1(ζ) represents the σ+1 order exponent of sig(ζ);

[0067] Step 2: Construct the system state variable matrix ζ based on the system state variable ζ (0～n) .

[0068] Other steps and parameters are the same as those in the embodiment 1 to 1.

[0069] Specific embodiment 6: The difference between this embodiment and the specific embodiments 1 to 5 is that the system state variable matrix ζ is constructed based on the system state variable ζ in steps 2 and 3. (0～n) ; The expression is:

[0070]

[0071] Where, ζ (0～n) represents the system state variable matrix;

[0072] represents the first-order derivative of ζ, ζ (n) represents the nth-order derivative of ζ, n = 2;

[0073] ζ∈R r , R represents the set of real numbers, R r represents the r-dimensional real number set, r = 1;

[0074] The system is a fully driven non-planar six-rotor drone;

[0075] The ζ (n) Expressed as:

[0076] ζ (n) =f(ζ (0～(n-1)) )+T d +L(ζ (0～(n-1)) )u (6)

[0077] Where, f(ζ (0～(n-1)) ) represents the continuous state function, f(ζ (0～(n-1)) )∈R r ζ (0～(n-1)) represents the system state variable matrix,

[0078] T d represents the external disturbance function of the system, T d ∈R r , the system is a fully driven non-planar six-rotor UAV;

[0079] L(ζ (0～(n-1)) ) represents a continuous matrix function, and detL(ζ (0～(n-1)) )≠0, L(ζ (0～(n-1)) )∈Rr×r , R r×r Represents a real matrix with r rows and r columns;

[0080] u represents the control quantity of the system, u∈R r , the system is a fully driven non-planar six-rotor UAV;

[0081] The control quantity u of the system is written as follows:

[0082] u=u0+u a (7)

[0083] Where u0 represents the nominal part of the controller; u a Represents the auxiliary controller, which enables the system to achieve faster state convergence, improve dynamic performance such as robustness and anti-interference ability;

[0084] Here, we choose finite-time control to improve the controller’s control performance for this hexacopter drone;

[0085] The nominal part u0 of the controller is expressed as follows:

[0086]

[0087] Where u * represents the robust controller, which is used to resist the external interference to the UAV;

[0088] ε represents a positive number, The norm of the disturbance to the system The square of represents the norm of the disturbance to the system, W L (M (0～(n-1)) ) represents the parameter matrix, and the superscript T represents the transpose; ζ *(n) represents the desired system state ζ * The nth derivative of

[0089] The purpose of the most basic part of the controller u0 is to convert the linear term M (0～n-1) ζ (0～n-1) Assigned to the closed-loop systemζ (n) =f(ζ (0～(n-1)) ); ensure that the system state variable ζ converges to the ellipsoid region shown below:

[0090]

[0091] Where, (ζ * ) (0～(n-1)) Represents the desired system state ζ * A matrix represents the ellipsoid region to which the desired system state converges, ζ * represents the desired system state, P(ζ-ζ * ) (0～(n-1)) Represents a matrix, ((ζ-ζ * ) (0～(n-1)) ) T P(ζ-ζ * ) (0～(n-1)) The whole represents the ellipsoid region to which the desired system state converges, and κ are two arbitrarily given positive numbers;

[0092] The auxiliary controller u a It is expressed as follows:

[0093] According to the finite-time sliding mode control theory, when the auxiliary controller u a When designed in the following form, the system state variable ζ can converge to the sliding surface within a finite time, thus achieving finite-time control of the system;

[0094]

[0095] Among them, * represents the desired system state, represents the first derivative of the desired system state;

[0096] σ1, σ2, k p 、k d are all constants and satisfy 0<σ1<1,σ2=2σ1 / (1+σ1), k p >0,k d >0;

[0097] In this way, we can track and control the state system of the UAV in a limited time, that is, make the current state ζ reach the desired state ζ within a limited time. d .

[0098] represents sig(ζ * -ζ) of the σ1 order index, express The σ2-order exponent of .

[0099] The other steps and parameters are the same as those in the first to fifth embodiments.

[0100] Specific embodiment seven: This embodiment differs from any one of specific embodiments one to six in that, in step three, the all-wheel drive non-planar six-rotor drone model (Formula 1) constructed in step one is converted into a high-order all-wheel drive system model (Formula 13); the expression is:

[0101]

[0102] Where ζ represents the system state variable, ζ==[x,y,z,φ,θ,ψ] T , x represents the position coordinate of the drone on the x-axis, y represents the position coordinate of the drone on the y-axis, z represents the position coordinate of the drone on the z-axis, φ represents the roll angle of the drone, θ represents the pitch angle of the drone, ψ represents the yaw angle of the drone, and the superscript T represents the transpose;

[0103] The system is a fully driven non-planar six-rotor drone;

[0104] represents the second-order derivative of the system state variable, represents the second-order derivative of the drone’s position along the x-axis, represents the second-order derivative of the drone’s position along the y-axis, represents the second-order derivative of the drone's position along the z-axis, represents the second-order derivative of the UAV’s roll angle, Represents the second-order derivative of the pitch angle of the drone, Represents the second derivative of the UAV's yaw angle;

[0105] f(ζ (0～1) ) represents the continuous state function, f(ζ (0～1) )=[0,0,-g,0,0,0] T , g represents the earth's gravitational acceleration, ζ (0～1) represents the 0th to 1st order derivative of ζ, ζ (0～1) =[ζ ζ] T , Represents the first-order derivative of the system state variable;

[0106] L(ζ (0～1) ) represents a continuous matrix function, Re represents a diagonal matrix, a, b, α p , α q , α r All represent coefficients;

[0107] T d represents the external disturbance function of the system, T d =[d1,d2,d3,d4,d5,d6] T , T d ∈R r ;

[0108] d1 represents the disturbance of the drone's x-axis position coordinates; d2 represents the disturbance of the drone's y-axis position coordinates; d3 represents the disturbance of the drone's z-axis position coordinates; d4 represents the disturbance of the drone's roll angle; d5 represents the disturbance of the drone's pitch angle; and d6 represents the disturbance of the drone's yaw angle.

[0109] The other steps and parameters are the same as those in the first to sixth embodiments.

[0110] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the error tracking model is obtained based on the high-order all-wheel drive system model (Formula 13) in step three-two; the specific process is:

[0111] Assume that the desired position of the hexacopter is ζ * =(x * ,y * ,z * ,φ * ,θ * ,ψ * ) T ,and and It is continuous and differentiable, let the deviation Δ = ζ-ζ * ;

[0112] Where x * Indicates the desired coordinate of the drone on the x-axis, y * Indicates the desired coordinate of the drone on the y-axis, z * Indicates the desired coordinate of the drone on the z-axis, φ * represents the desired roll angle of the drone, θ * represents the desired pitch angle of the drone, ψ * represents the desired yaw angle of the drone, represents the first-order derivative of the desired UAV state, represents the second-order derivative of the desired drone state;

[0113] The high-order all-wheel drive system model (Equation 13) is converted into an error tracking model; the expression is:

[0114]

[0115] Where, represents the second-order derivative of the deviation Δ;

[0116] Δ (0～1) represents the deviation matrix, represents the first derivative of the deviation Δ;

[0117] f(Δ (0～1)) represents a continuous state function, f(Δ (0～1) )=[0,0,-g,0,0,0] T ;

[0118] L(Δ (0～1) ) represents a continuous matrix function, Re represents a diagonal matrix, a, b, α p , α q , α r Both represent coefficients.

[0119] The other steps and parameters are the same as those in the first to seventh embodiments.

[0120] Specific embodiment nine: This embodiment differs from any one of specific embodiments one to eight in that the controller is designed based on the error tracking model formula (14) in step three; the specific process is as follows:

[0121] The controller is shown below

[0122] u=u0+u a (15)

[0123]

[0124] Among them, β1, β2, k p 、k d are all constants, 0<β1<1, β2=2β1 / (1+β1), k p >0,k d >0;

[0125] M (0～1) Represents the matrix, M (0～1) =[M0 M1] T ;

[0126] u * represents the robust controller, which is used to resist the external interference to the UAV;

[0127] The norm of the disturbance to which the system is subjected The square of The norm of the disturbance to which the system is subjected;

[0128] W L (M 0～1 ) represents the parameter matrix, and the superscript T represents the transpose;

[0129] Represents the desired UAV system state ζ * The second derivative of

[0130] sig β1 (ζ* -ζ) represents the function sig(ζ * -ζ) β1-order index;

[0131] Representation function β2-order index;

[0132] In this way, we can track and control the state system of the UAV in a limited time, that is, make the current state (x, y, z, φ, θ, ψ) T Reach the desired state (x * ,y * ,z * ,φ * ,θ * ,ψ * ) T .

[0133] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0134] Specific embodiment 10: This embodiment differs from any one of specific embodiments 1 to 9 in that the parameter matrix W L (M 0～(n-1) ) is obtained as follows:

[0135] 1) Set matrix P and matrix Q to satisfy detN(Q,P)≠0;

[0136] The matrix P represents a real matrix with nr rows and nr columns, the matrix Q represents a real matrix with r rows and nr columns, and detN(Q,P) represents the rank of the matrix N(Q,P);

[0137] The rank of the matrix N(Q,P) is expressed as:

[0138]

[0139] Where, P n-1 represents the n-1 power of the matrix P;

[0140] 2) Based on the matrix N(Q,P) and the matrix P, construct the matrix Γ(M 0～(n-1) ); the expression is:

[0141] Γ(M 0～(n-1) )=N(Q,P)PN -1 (Q,P) (19)

[0142] 3) Based on matrix N(Q,P), matrix P, and matrix Q, construct matrix M 0～(n-1) ; The expression is:

[0143] M 0～(n-1) =-QPn N -1 (Q,P) (20)

[0144] 4) The matrix Γ(M 0～(n-1) ), matrix M 0～(n-1) Substitute the Riccati equation and solve the matrix W(M 0～(n-1) );

[0145] The Riccati equation is Γ T (M 0～1 )W(M 0～(n-1) )+W(M 0～(n-1) )Γ(M 0～1 )≤-κW(M 0～(n-1) );

[0146] In the formula, κ represents an arbitrarily selected positive number, κ>0;

[0147] 5) Based on the matrix W(M 0～(n-1) ) Construct the matrix W L (M 0～(n-1) ); the expression is:

[0148]

[0149] Where, I r represents an r-row and r-column identity matrix.

[0150] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0151] The following examples are used to verify the beneficial effects of the present invention:

[0152] Example 1:

[0153] In order to verify and demonstrate the effectiveness of the controller designed in this invention for the finite-time tracking control method of a non-planar hexacopter drone based on high-order all-wheel drive system theory, the following numerical simulation experiments were carried out.

[0154] The parameters of the drone are: mass m = 7.5 kg, δm = (3-0.02t·δ(t-1)) kg, where t is the simulation time, δ(t-1) is a step function, gravitational acceleration g = 9.8 N / kg, and lift coefficient k f =1.91×10 -3 , counter-torque coefficient k τ =4.21×10 -5 , rotor radius l = 0.45m, I x =0.363kg·m 2 , I y =0.363kg·m 2 , Iz =0.651kg·m 2 , γ=30°. Other parameters in the controller are: κ=8.

[0155] Select position reference trajectory x * =5sin(0.5πt)m,y * =5cos(0.5πt)m,z * =0.5tm; attitude reference trajectory θ * =0.2cos(0.5πt)rad, The numerical experimental results are as follows Figure 3 、 4 As shown;

[0156] The system can achieve relatively good tracking in 0.5 seconds. The finite-time drone controller designed based on the high-order all-wheel drive system can quickly adjust the drone's position to the desired effect, reflecting the rapid tracking of this controller, and can fly to the designated location to perform tasks very accurately and quickly.

[0157] The UAV is subjected to random wind disturbances with an average speed of 6 m / s along the x-axis and y-axis, and a random wind disturbance with an average speed of 3 m / s along the z-axis. Another set of simulation results and the tracking error after 0.5 seconds are obtained as follows: Figure 5 As shown;

[0158] Depend on Figure 5 It can be seen that even after a certain amount of interference is applied, the drone is still able to track the desired position curve. The interference causes the drone to deviate by an average of approximately 0.08m along the x- and y-axes, with a maximum deviation of approximately 0.12m. The average deviation along the z-axis is approximately 0.02m, with a maximum deviation of approximately 0.04m. This demonstrates that this finite-time all-wheel drive controller is highly robust and can effectively withstand external interference caused by factors such as wind during the pesticide spraying process.

[0159] The present invention may have many other embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art may make various corresponding changes and modifications based on the present invention, but these corresponding changes and modifications should all fall within the scope of protection of the claims attached to the present invention.

Claims

1. A control method for a non-planar agricultural hexacopter drone based on a high-order all-wheel drive system, characterized by: The specific process of the method is: Step 1: Build a full-drive non-planar six-rotor drone model; Step 2: Construct the system state variable matrix; the specific process is: Step 2.

1. Define the matrix M i ∈R m×m , constant i=0,1,2,...,n-1, n=2; R represents the set of real numbers; m represents the mass of the drone; M0 and M1 represent a real matrix with m rows and m columns respectively; Based on the matrix M i Construct matrix M (0～(n-1)) ; The expression is: M (0～(n-1)) =[M0 M1 … M n-1 ] (4) In the formula, M0 represents a real number matrix with m rows and m columns, M1 represents a real number matrix with m rows and m columns, and M n-1 Represents a real matrix with m rows and m columns; Based on the matrix M (0～(n-1)) Construct the matrix Γ(M (0～(n-1)) ); the expression is: Where I represents the identity matrix; Step 2: Define the following function: sig σ (ζ)=sign(ζ)|ζ| σ (10) Where, sig σ (ζ) represents the σ-order index of sig(ζ), |ζ| represents the absolute value of ζ, |ζ| σ represents the σ-order index of |ζ|; σ represents an arbitrary constant, σ≥0; ζ represents the system state variable; the system is a full-drive non-planar six-rotor drone; where sign(ζ) is expressed as: For any constant σ, the system state variable ζ, d|ζ| σ+1 / dζ=(σ+1)sig σ (ζ), d[sig σ+1 (ζ)] / dζ=(σ+1)|ζ| σ ; Where |ζ| σ+1 represents the σ+1 order exponent of |ζ|; sig σ+1 (ζ) represents the σ+1 order exponent of sig(ζ); Step 2: Construct the system state variable matrix ζ based on the system state variable ζ (0～n) ; Step 3: Design a controller based on the all-wheel drive non-planar six-rotor drone model and the system state variable matrix; the specific process is as follows: Step 3.1: Convert the all-wheel drive non-planar six-rotor UAV model constructed in step 1 into a high-order all-wheel drive system model based on the system state variable matrix; Step 32: Obtain an error tracking model based on the high-order all-wheel drive system model; Step 3. Design a controller based on the error tracking model.

2. The control method for a non-planar agricultural six-rotor UAV based on a high-order all-wheel drive system according to claim 1, characterized in that: In step 1, a full-drive non-planar six-rotor drone model is constructed; the specific process is as follows: Select any rotor in the six-rotor drone as the first rotor, and arrange the rotors in order based on the first rotor as the second rotor, the third rotor, the fourth rotor, the fifth rotor, and the sixth rotor; Construct the drone coordinate system: take the center of the six-rotor drone as the origin o, the direction of the third rotor pointing to the fifth rotor as the x-axis, the direction of the second rotor as the y-axis, and the z-axis perpendicular to the x and y planes; The model of the all-wheel drive non-planar six-rotor drone is expressed as: Where, represents the second-order derivative of the drone’s position along the x-axis, represents the second-order derivative of the drone’s position along the y-axis, represents the second-order derivative of the drone's position along the z-axis, Represents the second-order derivative of the UAV's roll angle, Represents the second-order derivative of the pitch angle of the drone, Represents the second-order derivative of the yaw angle of the drone; a, b, α p , α q , α r All represent coefficients, d1, d2, d3, d4, d5, and d6 represent the interference to the UAV; u1, u2, u3, u4, u5, and u6 represent the control matrix of the UAV; and g represents the gravitational acceleration of the earth.

3. The control method for a non-planar agricultural hexacopter drone based on a high-order all-wheel drive system according to claim 2, characterized in that: The control matrix of the UAV is expressed as: Where, Indicates the square of the first rotor speed of the drone, Indicates the square of the second rotor speed of the drone, Indicates the square of the rotation speed of the third rotor of the drone, Indicates the square of the fourth rotor speed of the drone, Indicates the square of the fifth rotor speed of the drone, It represents the square of the rotation speed of the sixth rotor of the UAV; the superscript T indicates the transpose.

4. The control method for a non-planar agricultural hexacopter drone based on a high-order all-wheel drive system according to claim 3, characterized in that: The coefficient m represents the mass of the drone, δm represents the mass of the drone’s payload, and k f represents the lift coefficient, S γ represents sinγ, where γ represents the angle between the UAV rotor and the xoy plane of the UAV coordinate system; coefficient coefficient l represents the rotor radius, C γ represents cosγ, k τ Represents the counter torque coefficient, I x represents the moment of inertia of the drone along the x-axis; coefficient I y represents the moment of inertia of the drone along the y-axis; coefficient I z Represents the UAV's moment of inertia along the z-axis.

5. The control method for a non-planar agricultural six-rotor UAV based on a high-order all-wheel drive system according to claim 4, characterized in that: In the steps 2 and 3, the system state variable matrix ζ is constructed based on the system state variable ζ. (0～n) ; The expression is: Where, ζ (0～n) represents the system state variable matrix; represents the first-order derivative of ζ, ζ (n) represents the nth-order derivative of ζ, n = 2; ζ∈R r , R represents the set of real numbers, R r represents the r-dimensional real number set, r = 1; The system is a fully driven non-planar six-rotor drone; The ζ (n) Expressed as: g (n) =f(ζ (0～(n-1)) )+T d +L(ζ (0～(n-1)) )u (6) Where, f(ζ (0～(n-1)) ) represents the continuous state function, f(ζ (0～(n-1)) )∈R r ζ (0～(n-1)) represents the system state variable matrix, T d represents the external disturbance function of the system, T d ∈R r , the system is a fully driven non-planar six-rotor UAV; L(ζ (0～(n-1)) ) represents a continuous matrix function, and detL(ζ (0～(n-1)) )≠0, L(ζ (0～(n-1)) )∈R r×r , R r×r Represents a real matrix with r rows and r columns; u represents the control quantity of the system, u∈R r , the system is a fully driven non-planar six-rotor UAV; The control quantity u of the system is written as follows: u=u0+u a (7) Where u0 represents the nominal part of the controller; u a represents the auxiliary controller; The nominal part u0 of the controller is expressed as follows: Where u * represents the robust controller; ε represents a positive number, The norm of the disturbance to the system The square of represents the norm of the disturbance to the system, W L (M (0～(n-1)) ) represents the parameter matrix, and the superscript T represents the transpose; ζ *(n) represents the desired system state ζ * The nth derivative of ; The auxiliary controller u a It is expressed as follows: Among them, * represents the desired system state, represents the first derivative of the desired system state; σ1, σ2, k p 、k d are all constants and satisfy 0<σ1<1,σ2=2σ1 / (1+σ1), k p >0,k d >0; represents sig(ζ * -ζ) of the σ1 order index, express The σ2-order exponent of .

6. The control method for a non-planar agricultural hexacopter drone based on a high-order all-wheel drive system according to claim 5, characterized in that: In step 31, the all-wheel drive non-planar six-rotor drone model constructed in step 1 is converted into a high-order all-wheel drive system model; the expression is: Where ζ represents the system state variable, ζ==[x,y,z,φ,θ,ψ] T , x represents the position coordinate of the drone on the x-axis, y represents the position coordinate of the drone on the y-axis, z represents the position coordinate of the drone on the z-axis, φ represents the roll angle of the drone, θ represents the pitch angle of the drone, ψ represents the yaw angle of the drone, and the superscript T represents the transpose; The system is a fully driven non-planar six-rotor drone; represents the second-order derivative of the system state variable, represents the second-order derivative of the drone’s position along the x-axis, represents the second-order derivative of the drone’s position along the y-axis, represents the second-order derivative of the drone's position along the z-axis, Represents the second-order derivative of the UAV's roll angle, Represents the second-order derivative of the pitch angle of the drone, Represents the second derivative of the UAV's yaw angle; f(ζ (0～1) ) represents the continuous state function, f(ζ (0～1) )=[0,0,-g,0,0,0] T , g represents the earth's gravitational acceleration, ζ (0～1) represents the 0th to 1st order derivative of ζ, Represents the first-order derivative of the system state variable; L(ζ (0～1) ) represents a continuous matrix function, Re represents a diagonal matrix, a, b, α p , α q , α r All represent coefficients; T d represents the external disturbance function of the system, T d =[d1,d2,d3,d4,d5,d6] T , T d ∈R r ; d1 represents the disturbance of the drone's x-axis position coordinates; d2 represents the disturbance of the drone's y-axis position coordinates; d3 represents the disturbance of the drone's z-axis position coordinates; d4 represents the disturbance of the drone's roll angle; d5 represents the disturbance of the drone's pitch angle; and d6 represents the disturbance of the drone's yaw angle.

7. The control method for a non-planar agricultural hexacopter drone based on a high-order all-wheel drive system according to claim 6, characterized in that: In step 32, an error tracking model is obtained based on a high-order all-wheel drive system model; the specific process is as follows: Assume that the desired position of the hexacopter is ζ * =(x * ,y * ,z * ,φ * ,θ * ,ψ * ) T ,and and It is continuous and differentiable, let the deviation Δ = ζ-ζ * ; Where x * Indicates the desired coordinate of the drone on the x-axis, y * Indicates the desired coordinate of the drone on the y-axis, z * Indicates the desired coordinate of the drone on the z-axis, φ * represents the desired roll angle of the drone, θ * represents the desired pitch angle of the drone, ψ * represents the desired yaw angle of the drone, represents the first-order derivative of the desired UAV state, represents the second-order derivative of the desired drone state; The high-order all-wheel drive system model is converted into an error tracking model; the expression is: Where, represents the second-order derivative of the deviation Δ; Δ (0～1) represents the deviation matrix, represents the first derivative of the deviation Δ; f(Δ (0～1) ) represents a continuous state function, f(Δ (0～1) )=[0,0,-g,0,0,0] T ; L(Δ (0～1) ) represents a continuous matrix function, Re represents a diagonal matrix, a, b, α p , α q , α r Both represent coefficients.

8. The control method for a non-planar agricultural hexacopter drone based on a high-order all-wheel drive system according to claim 7, characterized in that: In step 33, a controller is designed based on the error tracking model (14); the specific process is: The controller is shown below u=u0+u a (15) Among them, β1, β2, k p 、k d are all constants, 0<β1<1, β2=2β1 / (1+β1), k p >0,k d >0; M (0～1) Represents the matrix, M (0～1) =[M0 M1] T ; u * represents the robust controller; The norm of the disturbance to which the system is subjected The square of The norm of the disturbance to which the system is subjected; W L (M 0～1 ) represents the parameter matrix, and the superscript T represents the transpose; Represents the desired UAV system state ζ * The second derivative of Represents the function sig(ζ * -ζ) β1-order index; Representation function The β2-order exponent of .

9. The control method for a non-planar agricultural hexacopter drone based on a high-order all-wheel drive system according to claim 8, characterized in that: The parameter matrix W L (M 0～(n-1) ) is obtained as follows: 1) Set matrix P and matrix Q to satisfy detN(Q,P)≠0; The matrix P represents a real matrix with nr rows and nr columns, and the matrix Q represents a real matrix with r rows and nr columns. detN(Q,P) represents the rank of the matrix N(Q,P); The rank of the matrix N(Q,P) is expressed as: Where, P n-1 represents the n-1 power of the matrix P; 2) Based on the matrix N(Q,P) and the matrix P, construct the matrix Γ(M 0～(n-1) ); the expression is: Γ(M 0～(n-1) )=N(Q,P)PN -1 (Q,P) (19) 3) Based on matrix N(Q,P), matrix P, and matrix Q, construct matrix M 0～(n-1) ; The expression is: M 0～(n-1) =-QP n N -1 (Q,P) (20) 4) The matrix Γ(M 0～(n-1) ), matrix M 0～(n-1) Substitute the Riccati equation and solve the matrix W(M 0～(n-1) ); Riccati equation forC T (M 0～1 )W(M 0～(n-1) )+W(M 0～(n-1) )C(M 0～1 )≤-κW(M 0～(n-1) ); In the formula, κ represents an arbitrarily selected positive number, κ>0; 5) Based on the matrix W(M 0～(n-1) ) Construct the matrix W L (M 0～(n-1) ); the expression is: Where, I r represents an r-row and r-column identity matrix.

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