New-configuration four-rotor unmanned aerial vehicle control method based on robust control

Abstract

The invention discloses a new-configuration four-rotor unmanned aerial vehicle control method based on robust control, and the method comprises the steps: determining the definition of a coordinate system of a new-configuration four-rotor unmanned aerial vehicle, building a kinetic model of the new-configuration four-rotor unmanned aerial vehicle, and designing an attitude ring sliding mode controller and a position ring sliding mode control method. According to the invention, the novel four-rotor unmanned aerial vehicle can rapidly and accurately track the given expected trajectory and attitude angle.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicles, and particularly relates to a control method for a new configuration quadrotor unmanned aerial vehicle based on robust control. Background Art

[0002] In recent years, with the rapid development of quadrotor unmanned aerial vehicle technology, it has been widely used in the fields of military reconnaissance, logistics transportation, environmental monitoring, and urban planning. However, the extensive application scenarios have imposed higher requirements on quadrotor unmanned aerial vehicles. For example, people desire both the stability of quadrotor unmanned aerial vehicles and the flexibility and speed similar to those of helicopters. Traditional configuration quadrotor unmanned aerial vehicles often fail to meet these requirements.

[0003] To address the above problems, researchers have proposed various new configurations for quadrotor UAVs, including adding servos to tilt the arms (Journal: 2012 IEEE International Conference on Robotics and Automation; Authors: M. Ryll, H. H. Bülthoff and P. R. Giordano; Publication Date: 2012; Article Title: Modeling and control of a quadrotor UAV with tilting propellers; Pages: 4606 - 4613), or changing the motor mounting position to achieve more flexible drive, etc. (Journal: 2013 IEEE / RSJ International Conference on Intelligent Robots and Systems; Authors: S. Driessens and P. E. I. Pounds; Publication Date: 2013; Article Title: Towards a more efficient quadrotor configuration; Pages: 1386 - 1392). Dr. James Paulos from the University of Pennsylvania proposed a swashplate - less hub structure (Journal: 2015 IEEE International Conference on Robotics and Automation; Authors: James Paulos and Mark Yim; Publication Date: 2015; Article Title: Flight Performance of a Swashplateless Micro Air Vehicle; Pages: 5284 - 5289). This structure can obtain three - axis forces and torques by adjusting the motor speed, achieving a function similar to that of a helicopter swashplate with only a single motor. Compared with applying a helicopter swashplate to a quadrotor, this swashplate - less hub is more convenient to replace, has a simple mechanical structure, greatly reduces the extra weight, makes the adjustment of the rotor lift direction and the body direction more flexible, and reduces the mechanical complexity and maintenance cost. However, the swashplate - less hub structure also brings new challenges, including complex non - linear dynamics modeling and attitude - position control under external disturbances and modeling uncertainties.

[0004] To address the above problems, sliding mode robust control technology has gradually become a research hotspot in the field of UAV control due to its significant advantages in dealing with nonlinear systems and anti-interference. Sliding mode control can effectively overcome the influence of system modeling errors and external disturbances by designing a reasonable sliding mode surface and control law, thereby achieving precise attitude control and trajectory tracking of UAVs (Journal: IEEE Transactions on Aerospace and Electronic Systems; Authors: Wang H, Ye X, Tian Y, et al.; Publication Date: 2016; Article Title: Model-free–based terminal SMC of quadrotor attitude and position; Pages: 2519-2528). In recent years, research on robust control has mainly focused on traditional quadrotor UAVs (Journal: ISA transactions; Authors: Zheng E H, Xiong J J, Luo J L; Publication Date: 2014; Article Title: Second order sliding mode control for a quadrotor UAV; Pages: 1350-1356), while research on new configuration quadrotor UAVs is relatively scarce. In particular, how to design efficient and robust attitude loop and position loop control algorithms in combination with their unique swashplate-free hub structure remains a technical problem to be solved urgently. Summary of the Invention

[0005] To overcome the deficiencies of the prior art, the present invention provides a control method for a new configuration quadrotor UAV based on robust control, determines the coordinate system definition of the new configuration quadrotor UAV, establishes the dynamic model of the new configuration quadrotor UAV, and further designs an attitude loop sliding mode controller and a position loop sliding mode control method. The present invention enables the new configuration quadrotor UAV to quickly and accurately track the given desired trajectory and attitude angle.

[0006] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0007] Step 1: Determine the coordinate system definition of the new configuration quadrotor UAV;

[0008] The coordinate system definition of the new configuration quadrotor UAV with four swashplate-free hub structures involves four coordinate systems: inertial coordinate system F i , body coordinate system F B , hub coordinate system F H , and rotor coordinate system F R ; among them, the origin of the body coordinate system is located at the centroid of the UAV, the origin of the hub coordinate system is located at the centroid of the hub, and the origin of the rotor coordinate system is located at the hub; the definitions of each coordinate system follow the right-hand rule;

[0009] Step 2: Establish the dynamic model of the new configuration quadrotor UAV;

[0010] Step 2-1: Consider the new configuration quadrotor UAV as a rigid body, which moves under the action of external forces and external torques; According to Newton-Euler equations, the motion equations of the rigid body in the body coordinate system are given as follows:

[0011]

[0012] where, the mass and inertia of the rigid body, the external forces and external torques acting on it are respectively and V = (u, v, w) and Ω = (p, q, r) are the linear velocity and angular velocity in the body coordinate system respectively; The resultant force F ext includes gravity, lift and air resistance; τ represents the torque acting on the UAV in the body coordinate system; u, v, w respectively represent the linear velocities of the three axes of the UAV in the body coordinate system, and p, q, r respectively represent the angular velocities of the three axes of the UAV in the body coordinate system;

[0013] Step 2-2: Define the rotation sequence of Euler angles as "ZYX", and the rotation matrix R ∈ SO3 from the body coordinate system F B to the inertial coordinate system F i is defined as:

[0014]

[0015] where η = (ψ, θ, φ) are the roll angle, pitch angle and yaw angle; s(·) and c(·) are abbreviations of sin(·) and cos(·);

[0016] Step 2-3: Give the translational dynamic equation of the rigid body in the inertial coordinate system F i through the rotation matrix R:

[0017]

[0018] where, ξ = (x, y, z) and are the position and velocity of the UAV in the inertial system; g is the acceleration due to gravity, F is the resultant force other than gravity acting on the body in the body coordinate system F B ; e 3 is the identity matrix [0, 0, 1] T ;

[0019] Step 2-4: Re-express the attitude dynamics in terms of Euler angles;

[0020] First, The relationship between and Ω is as follows:

[0021]

[0022] The Euler matrix Φ(η) is given by the following formula:

[0023]

[0024] Φ(η) has singularities at θ = ±π / 2, and its inverse matrix Ψ(η) = Φ -1 (η) is:

[0025]

[0026] Step 2-5: Take the time derivative of formula (4), and substitute the obtained by solving the second equation in formula (1), to get:

[0027]

[0028] Define the operation from to as sk; for any vector , sk(x) is a skew-symmetric matrix related to the vector product sk(x)y = x × y;

[0029] Step 2-6: Multiply both sides of formula (7) by Ψ(η) T JΨ(η) to transform the formula into the standard six-degree-of-freedom rigid body kinematic equation:

[0030]

[0031] where M(η) = Ψ(η) T J Ψ (η) is a positive definite inertia matrix;

[0032] According to the matrix derivative rule Substitute into formula (4), the Coriolis force and centrifugal force matrix is in the form as shown in the following formula:

[0033]

[0034] Step 2-7: Considering the symmetry of the quadrotor UAV, the inertia J is approximately J = diag(J 1 , J 2 , J 3 ), J 1 , J 2 , J 3 are the moments of inertia of the UAV; therefore, the matrix M(η) is expressed as:

[0035]

[0036] Combining Equation (3) and Equation (8), the non - linear model of the UAV is derived, d F and D τ is the total amount including modeling uncertainties and external disturbances; it is assumed that there is a supremum sup(D) for this disturbance:

[0037]

[0038] The rotor coordinate system F R is obtained by rotating the azimuth angle β and the tilt angle α in the hub coordinate system, and the rotation matrix is expressed as follows:

[0039]

[0040] where, α i and β i represent the tilt angle and azimuth angle of the i - th rotor, R z (·) represents the rotation matrix along the z - axis, and R y (·) represents the rotation matrix along the y - axis;

[0041] The rotation matrix from the rotor coordinate system to the body coordinate system is:

[0042]

[0043] where, ζ i is the angle of the hub mechanism relative to the centroid;

[0044] The lift force F i and torque τ i generated by each swash - plate - less hub structure are as follows:

[0045]

[0046] where, s i is the position of the hub structure relative to the centroid of the UAV body, σ i is the rotation direction of the rotor, k τ is the fitted proportionality coefficient; T i represents the lift force of the i - th rotor;

[0047] Step 3: Design the attitude - loop sliding - mode controller and the position - loop sliding - mode controller;

[0048] Define the position error as e ξ = ξ - ξ d , and the angle error as Design the sliding surface in the following form:

[0049]

[0050] where γ > 0 is the sliding mode control gain; ξ d represents the position setpoint of the new configuration UAV, and η d represents the angle setpoint, and s ξ represents the sliding mode surface of the position loop robust control algorithm, and s η represents the sliding mode surface of the angle loop;

[0051] Differentiating Equation (15) gives the dynamic sliding mode surface:

[0052]

[0053] Substituting into Equation (11), the control laws for the force and moment are designed as follows:

[0054]

[0055] Since the sign function sgn(s) will cause chattering of the controller, the sign function sgn(.) in Equations (17) and (18) is replaced by a saturation function:

[0056]

[0057] where is the boundary layer thickness.

[0058] A computer program that causes a computer to execute the above control method for a new configuration quadrotor UAV.

[0059] An electronic device, comprising: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory so that the electronic device executes the above control method for a new configuration quadrotor UAV.

[0060] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the above control method for a new configuration quadrotor UAV is implemented.

[0061] A chip, comprising: a processor for calling and running a computer program from a memory, so that a device installed with the chip executes the above control method for a new configuration quadrotor UAV.

[0062] A computer program product, the computer program product includes a computer storage medium, the computer storage medium stores a computer program, the computer program includes instructions that can be executed by at least one processor, and when the instructions are executed by the at least one processor, the above control method for a new configuration quadrotor UAV is implemented.

[0063] The beneficial effects of the present invention are as follows:

[0064] 1. The present invention is based on a new configuration of a quadrotor unmanned aerial vehicle (UAV) with a hubless structure without a swashplate. By defining four mutually convertible coordinate systems and using Newton-Euler equations, a nonlinear dynamic equation is established, laying a foundation for subsequent control design.

[0065] 2. Through the design of a control method based on sliding mode robustness, the present invention compensates for the modeling uncertainty of the new configuration quadrotor and unknown external disturbances, and uses the method based on Lyapunov analysis to prove the global asymptotic convergence characteristics of the error.

[0066] 3. The superiority of the designed robust control method is verified through MATLAB numerical simulation, proving that the control method designed by the present invention can enable the new configuration quadrotor UAV to quickly and accurately track the given desired trajectory and attitude angles. Description of the Drawings

[0067] Figure 1 It is a structural diagram of the new configuration quadrotor of the present invention with a hubless structure without a swashplate;

[0068] Figure 2 It is a mechanical structural diagram of the hubless structure without a swashplate of the present invention;

[0069] Figure 3 It is the given desired body attitude angle value and the actual attitude angle value during the MATLAB simulation experiment;

[0070] Figure 4 It is the given desired position value and the actual position value of the quadrotor UAV during the MATLAB simulation experiment;

[0071] Figure 5 It is the torque control amount when the new configuration quadrotor UAV tracks the given attitude angle;

[0072] Figure 6 It is the force control amount when the new configuration quadrotor UAV tracks the given position target.

[0073] Reference numerals: 1 - UAV main body bearing structure frame; 2 - new configuration UAV arm; 3 - UAV power rotor sub-component; 4 - flapping component in the hubless structure without a swashplate; 5 - flapping-lag coupling component; 6 - rotor component; 7 - hub structure bearing base component; 8 - M3 stud. Detailed Embodiment

[0074] The present invention will be further described below in conjunction with the drawings and embodiments.

[0075] The technical problem to be solved by the present invention is that there is no corresponding non - linear dynamic model for a new configuration quadrotor UAV with a hubless swashplate structure, and unknown external disturbances and modeling uncertainties will greatly affect the control accuracy.

[0076] The present invention proposes an attitude loop and position loop control algorithm for a new configuration quadrotor UAV based on sliding - mode robust control to achieve fast and accurate tracking of the given attitude and trajectory of the quadrotor UAV with a hubless swashplate structure. For this purpose, the technical solution adopted by the present invention is that the attitude loop and position loop control method for a new configuration quadrotor UAV based on sliding - mode robust control includes the following steps: determining the coordinate system definition of the new configuration quadrotor UAV, establishing the dynamic model of the new configuration quadrotor UAV, and then designing an attitude loop sliding - mode controller and a position loop sliding - mode control method. The specific steps are as follows:

[0077] Step 1) Determine the coordinate system definition of the new configuration quadrotor UAV;

[0078] As Figure 1 and Figure 2 shown, the coordinate system definition of the new configuration quadrotor UAV with four hubless swashplate structures mainly involves four coordinate systems, the inertial coordinate system \(F_{I}\), the body coordinate system \(F_{B}\), the hub coordinate system \(F_{H}\), and the rotor coordinate system \(F_{R}\). i , the body coordinate system \(F_{B}\) B , the hub coordinate system \(F_{H}\) H , and the rotor coordinate system \(F_{R}\) R . Among them, the origin of the body coordinate system is located at the center of mass of the UAV, the origin of the hub coordinate system is located at the center of mass of the hub, and the origin of the rotor coordinate system is located at the hub. The definition of each coordinate system follows the right - hand rule;

[0079] Step 2) Establish the dynamic model of the new configuration quadrotor UAV;

[0080] The new configuration quadrotor UAV can be considered as a rigid body that moves under the action of external forces and external torques.

[0081] According to Newton - Euler equations, the motion equations of the rigid body in the \(F_{I}\) B coordinate system are given.

[0082]

[0083] Among them, a rigid body with mass \(m\) and inertia \(J\) is subjected to external forces and external torques of \(F=(F_{x},F_{y},F_{z})\) and \(V=(u,v,w)\) and \(\Omega=(p,q,r)\) are the linear velocity and angular velocity in the body coordinate system respectively. The resultant force \(F\) ext includes gravity, lift, air resistance, etc.

[0084] Define the rotation sequence of Euler angles as "ZYX", starting from the body coordinate system \(F_{B}\)B to the inertial coordinate system F i The rotation matrix R ∈ SO3 is defined as:

[0085]

[0086] where η = (ψ, θ, φ) are the roll angle, pitch angle, and yaw angle. s(·) and c(·) are abbreviations for sin(·) and cos(·). Through the rotation matrix R, the translational dynamics equation of the rigid body in the inertial frame F i can be given as:

[0087]

[0088] where ξ = (x, y, z) and are the position and velocity of the UAV in the inertial frame. g in formula (3) is the acceleration due to gravity, and F is the resultant of all other forces acting on the body except gravity in F B For the convenience of control design, the attitude dynamics in this paper is re-expressed in terms of Euler angles. First, The relationship between

[0089]

[0090] The Euler matrix Φ(η) is given by:

[0091]

[0092] It can be seen that Φ(η) has singularities at θ = ±π / 2, which is an inherent limitation of Euler angles. Its inverse matrix Ψ(η) = Φ -1 (η) is:

[0093]

[0094] Taking the time derivative of formula (4) and substituting the solved from the second equation in formula (1), we get:

[0095]

[0096] Define the operation from to as sk. For any vector sk(x) is a skew-symmetric matrix related to the vector product sk(x)y = x × y.

[0097] Multiplying both sides of formula (7) by Ψ(η) T JΨ(η), the formula can be transformed into the standard six-degree-of-freedom rigid body kinematic equation:

[0098]

[0099] where \(M(\eta)=\Psi(\eta)\) T \(J\Psi(\eta)\) is a positive definite inertia matrix. According to the matrix derivative rule Substituting into formula (4), the Coriolis force and centrifugal force matrix is in the following form:

[0100]

[0101] Considering the symmetry of the quadrotor UAV, the inertia \(J\) can be approximated as \(J = diag(J\) 1 , \(J\) 2 , \(J\) 3 ). Therefore, the matrix \(M(\eta)\) can be expressed as:

[0102]

[0103] Combining formula (3) and formula (8), the nonlinear model of the UAV is derived, \(D\) F and \(D\) τ are the total amounts including modeling uncertainties and external disturbances. Assume that there is a supremum \(\sup(D)\) for this disturbance:

[0104]

[0105] Due to the use of the swashplate - less hub structure, there is an angle between the lift direction and the body z - axis direction. The rotor coordinate system \(F\) R is obtained by rotating the azimuth angle \(\beta\) and tilt angle \(\alpha\) of the hub coordinate system. The rotation matrix is expressed as follows:

[0106]

[0107] The rotation matrix from the rotor coordinate system to the body coordinate system is:

[0108]

[0109] where \(\zeta\) i is the angle of the hub mechanism relative to the centroid (\(\zeta\) 1 = 45°, \(\zeta\) 2 = - 135°, \(\zeta\) 3 = - 45°, \(\zeta\) 4 = 135°).

[0110] The lift and moment generated by each swashplate - less hub structure are as follows:

[0111]

[0112] si is the position of the hub structure relative to the centroid of the UAV body, σ i is the rotation direction of the rotor (σ 1 = 1, σ 2 = 1, σ 3 = -1, σ 4 = -1), k τ is the fitting scale coefficient. e 3 is the identity matrix [0, 0, 1] T .

[0113] Step 3) Design the attitude loop sliding mode controller and the position loop sliding mode controller;

[0114] Define the position error as e ξ = ξ - ξ d , and the angle error is Design the sliding surface in the following form:

[0115]

[0116] where γ > 0 is the sliding mode control gain. Differentiate Equation (15) to obtain the dynamic sliding surface:

[0117]

[0118] Substitute it into Equation (11) and design the control law of force and moment as follows:

[0119]

[0120] Since the sign function sgn(s) will cause chattering of the controller, a saturation function is used instead:

[0121]

[0122] where is the boundary layer thickness.

[0123] Embodiment:

[0124] To evaluate the effectiveness of the sliding mode robust control algorithm designed by the present invention, MATLAB is used for simulation. The given trajectory expectation value is:

[0125]

[0126] where g(s) is a second-order transfer function, This is to smooth the given expectation signal and reduce the influence of excessive error on the control system.

[0127] Similarly, the given angle expectation value is:

[0128]

[0129] In formula (21), l(s) is also a second-order transfer function. The initial angle value and position value are both 0.

[0130] Build a nonlinear model of the new configuration quadrotor UAV in MATLAB SIMULINK. Based on the actual 450-level quadrotor UAV, the simulation parameters are designed as follows:

[0131] J = [1.6, 1.6, 3] T ×10 -3 kg·m 2 , m = 2 kg, g = 9.81 m / s 2 , r h = 0.1 m, l = 0.225 m

[0132] The parameters of the sliding mode robust controller are designed as follows:

[0133] γ ξ = [5.6, 5.1, 3] T , γ η = [3, 3, 2] T , k F = [10, 10, 15] T , k τ = [2.5, 1.3, 1.8] T ,

[0134] The external disturbances acting on the position loop and attitude loop are respectively given by D F = [2, 2, 2] T N and D τ = [0.5, 0.5, 0.5] T N·m.

[0135] Figure 3 are the actual attitude angle value and the desired attitude angle value of the new configuration quadrotor UAV in the MATLAB simulation. Figure 4 are the actual position value and the desired position value of the new configuration quadrotor UAV. It can be seen that the robust control algorithm proposed by the present invention can still quickly and accurately track the given desired angles and positions considering the modeling uncertainty and external disturbances.

[0136] Figure 5 , Figure 6 are the force and moment output by the controller under the condition of tracking the given desired values respectively.

[0137] Based on a new configuration of a quadrotor UAV with a hub without a swashplate, the present invention designs a robust control algorithm to compensate for modeling uncertainties and external disturbances. The MATLAB simulation results prove that, in the presence of disturbances in forces and torques, the control algorithm designed by the present invention can also enable the quadrotor UAV to quickly and accurately track the desired angles and trajectories.

Claims

1. A new configuration quadrotor drone control method based on robust control, characterized in that: The steps include: Step 1: Determine the coordinate system definition of the new quadrotor drone; The coordinate system definition of the new quadrotor drone with four swashplate-free hub structures involves four coordinate systems: inertial coordinate system F i , body coordinate system F B , hub coordinate system F H , rotor coordinate system F R ; Among them, the origin of the body coordinate system is located at the center of mass of the UAV, the origin of the hub coordinate system is located at the center of mass of the hub, and the origin of the rotor coordinate system is located at the hub; the definition of each coordinate system follows the right-hand rule; Step 2: Establish the dynamic model of the new quadrotor drone; Step 2-1: The new quadrotor drone is considered as a rigid body, which moves after being acted upon by external forces and torques. The motion equation of the rigid body in the body coordinate system is given according to the Newton-Euler equation: Among them, quality and inertia The external forces and moments on the rigid body are and V = (u, v, w) and Ω = (p, q, r) are the linear velocity and angular velocity in the body coordinate system respectively; the resultant force F ext Including gravity, lift and air resistance; τ represents the torque of the drone in the body coordinate system; u, v, w represent the linear velocity of the three axes of the drone in the body coordinate system, and p, q, r represent the angular velocity of the three axes of the drone in the body coordinate system; Step 2-2: Define the rotation order of Euler angles as "ZYX", from the body coordinate system F B To the inertial coordinate system F i The rotation matrix R∈SO3 is defined as: Where η=(ψ,θ,φ) is the roll angle, pitch angle and yaw angle; s(·) and c(·) are the abbreviations of sin(·) and cos(·); Step 2-3: Use the rotation matrix R to give the rigid body in the inertial coordinate system F i The translational dynamics equations in : where ξ=(x,y,z) and is the position and velocity of the drone in the inertial system; g is the acceleration of gravity, and F is the body coordinate system F B The other forces acting on the body except gravity; e3 is the unit matrix [0,0,1] T ; Step 2-4: Re-express the attitude dynamics using Euler angles; first, The relationship between and Ω is: The Euler matrix Φ(η) is given by: Φ(η) has a singularity at θ=±π / 2, and its inverse matrix Ψ(η)=Φ -1 (η) is: Step 2-5: Calculate the time derivative of formula (4) and solve the second equation in formula (1) to obtain Substitute it in and we get: definition arrive The operation is sk; for any vector In terms of sk(x), sk(x) is a skew-symmetric matrix associated with the vector product sk(x)y=x×y; Step 2-6: Multiply both sides of formula (7) by ψ(η) T JΨ(η), convert the formula into the standard six-degree-of-freedom rigid body kinematic equation: Where, M(η)=Ψ(η) T JΨ(η) is the positive definite inertia matrix; According to the matrix derivation rule Substituting into formula (4), the Coriolis force and centrifugal force matrix The form is as follows: Step 2-7: Considering the symmetry of the quadrotor drone, the inertia J is approximately J=diag(J1,J2,J3), where J1,J2,J3 are the moments of inertia of the drone; therefore, the matrix M(η) is expressed as: Combining formula (3) and formula (8), the nonlinear model of the UAV is derived, D F and D τ is the total amount including modeling uncertainty and external disturbance; assuming that the disturbance has a supremum sup(D): Rotor coordinate system F R The rotation matrix is ​​obtained by rotating the hub coordinate system by the azimuth angle β and the tilt angle α. It is expressed as follows: Among them, α i and β i represents the tilt angle and azimuth angle of the i-th rotor, R z (·) represents the rotation matrix along the z-axis, R y (·) represents the rotation matrix along the y-axis; Rotation matrix from rotor coordinate system to body coordinate system for: in, ζ i is the angle of the propeller hub mechanism relative to the center of mass; The lift F generated by each hub structure without swashplate i and torque τ i As shown below: Among them, s i is the position of the hub structure relative to the center of mass of the UAV body, σ i is the rotation direction of the rotor, k τ is the proportional coefficient of the fitting; T i represents the lift of the i-th rotor; Step 3: Design the attitude loop sliding mode controller and the position loop sliding mode controller; Define the position error as e ζ =ζ-ζ d , the angle error is The design sliding surface is as follows: Where γ>0 is the sliding mode control gain; ξ d represents the position given value of the new configuration UAV, η d Indicates the given angle value, s ξ represents the sliding surface of the position loop robust control algorithm, s η represents the sliding surface of the angle ring; Differentiate equation (15) and obtain the dynamic sliding surface: Substituting into equation (11), the control rate of design force and moment is as follows: Since the sign function sgn(s) can cause controller chattering, the sign function sgn(.) in equations (17) and (18) is replaced by a saturation function: in, is the boundary layer thickness.

2. A computer program, characterized in that The computer program enables a computer to execute the method as claimed in claim 1.

3. An electronic device, characterized in that: include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device executes the method as claimed in claim 1.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method as claimed in claim 1 is implemented.

5. A chip, characterized in that: include: A processor, used to call and run a computer program from a memory, so that a device equipped with the chip executes the method as claimed in claim 1.

6. A computer program product, characterized in that The computer program product comprises a computer storage medium storing a computer program, wherein the computer program comprises instructions executable by at least one processor, and when the instructions are executed by the at least one processor, the method according to claim 1 is implemented.

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