CN109885074A - A finite time convergence attitude control method for quadrotor UAV - Google Patents

Abstract

The present invention relates to the precise control of the attitude of the quadrotor unmanned aerial vehicle. In order to propose a nonlinear attitude controller for the four-rotor unmanned aerial vehicle, the present invention provides a limited time convergence attitude control method of the four-rotor unmanned aerial vehicle. The steps are as follows: 1) Establish a quadrotor UAV dynamics model, and use the Newton-Euler method to establish a quadrotor UAV dynamics model; 2) Non-linear controller design, including roll angle Nonlinear controller design, pitch angle θ nonlinear controller design, yaw angle ψ nonlinear controller design; finally, finite-time convergence control of UAV attitude error is realized. The invention is mainly applied to the situation of precise attitude control of the quadrotor unmanned aerial vehicle.

Description

A finite time convergence attitude control method for quadrotor UAV

technical field

The invention relates to the precise control of the attitude of a quadrotor unmanned aerial vehicle. Aiming at the characteristics of quadrotor UAV system with high degree of nonlinearity, underactuation, strong coupling and uncertainty of disturbance, a nonlinear attitude controller based on second-order sliding mode control is proposed, which realizes the attitude control of UAV. Error finite time convergence result. Specifically, it relates to a finite-time convergence attitude control method for a quadrotor UAV.

Background technique

Multi-rotor UAVs have played an increasingly important role in scientific research, civil and military applications in recent years because of their simple mechanical structure, vertical take-off and landing, hovering capability, and low requirements for the site. Among the many types of multi-rotor UAVs, quad-rotor UAVs are more commonly used. It changes the attitude of the aircraft by changing the relative rotation speed between the four rotors and the magnitude of the single-axis thrust, thereby changing the running trajectory of the aircraft. Therefore, it is very important to study the attitude control of quadrotor UAV for controlling the quadrotor UAV.

For the attitude control of quadrotor UAV, foreign research was carried out earlier. Among them, the original main goal of Stanford University's quadrotor UAV project was to improve the collaborative working ability of quadrotor UAVs through the rational use of multi-agent technology, and thus completed the modification of two quadrotor UAVs successively. The second of these increases the speed of the processor and the accuracy of the sensor compared to the first, resulting in improved control. The quadrotor drone uses two Microchip PIC18F6520 microcontrollers to coordinate communications, sensing, and control activities on the aircraft (Conference: IEEE RSJ International Conference on Intelligent Robots and Systems; Authors: HoffmannGabriel M, Waslander Steven L, Vitus Michael P, et al; Publication Year: 2009; Article Title: Stanford Testbed of Autonomous Rotorcraft for Multi-Agent Control; Pages: 404-405). At present, the drone has achieved autonomous flight indoors and outdoors. A quadrotor drone at the University of Pennsylvania uses a backstepping-based control algorithm to build a vision-based flight control system. At present, tasks such as ground mobile platform landing, target grabbing, and multi-machine cooperation can be realized (Journal: IEEE Robotics&Automatics Magazine; Authors: Michael N, Mellinger D, Lindsey Q, Kumar V; Publication Date: September 2010; Title of the article : The GRASPMultiple Micro-UAV Test Bed Experimental Evaluation of Multirobot AerialControl Algorithms; pp. 56-65). In terms of using advanced sliding mode control algorithms, the University of Alabama in Huntsville uses traditional sliding mode control and super-twisting (super-twisting) algorithms to control quadrotor UAVs (Journal: Automatica; Author: Shtessel Y, Taleb M, Plestan F; Publication Date: May 2012; Article Title: A novel Adaptive-gain Super-twisting Sliding Mode Controller: Methodology and Application; Pages: 759-769). In addition, some scholars have used advanced sliding mode control for UAV fault-tolerant control (Journal: IEEE Transactions on Control Systems Technology; Authors: RyllMarkus, Buelthoff Heinrich H, Giordano Paolo Robuffo; Publication Year: March 2015 ; Article Title: A Novel Overactuated Quadrotor Unmanned Aerial Vehicle: Modeling, Control, and Experimental Validation; Pages: 540-556). Although the domestic quadrotor UAV research started late, it has also achieved certain results. Among them, Tsinghua University, National University of Defense Technology, Tianjin University, Beijing University of Aeronautics and Astronautics and other scientific research institutions have made great contributions to the research and development of quadrotor UAVs in China. At present, the control methods used at home and abroad mainly include feedback linearization, backstepping method, robust control, sliding mode variable structure control, intelligent PID (proportional, integral, differential) control and so on.

Regarding the research on quadrotor UAV control, researchers have made certain achievements, but there are also some limitations: 1) Some existing control designs have made more assumptions and simplifications for the dynamic model of the UAV, For example, some existing results assume that the UAV is flying at a low speed and does not consider the disturbance. But in fact, the disturbance to the drone cannot be ignored. 2) In some control methods, the model of the controlled object is linearized near the equilibrium point, and the controller is designed on this basis, thereby weakening the control effect of the controlled object near the non-equilibrium point.

SUMMARY OF THE INVENTION

In order to overcome the deficiencies of the prior art, the present invention aims to propose a nonlinear attitude controller for a quadrotor UAV. For this reason, the technical solution adopted in the present invention is a method for controlling the attitude of the quadrotor unmanned aerial vehicle with limited time convergence, and the steps are as follows:

1) Establish a quadrotor UAV dynamics model

The present invention adopts the Newton-Euler method to establish a four-rotor UAV dynamics model, and the expression is as follows:

The variables in formula (1) are defined as follows: for drone quality, is the spatial position vector of the UAV in the inertial coordinate system, And g=9.8m/s ² represents the acceleration of gravity, is the translational damping coefficient matrix, K _x , _Ky , and K _z are constant parameters, which are the air damping coefficients of the UAV along the three axes of the body coordinate system, and ^B u _t represents the propeller generated by the UAV in the body coordinate system the combined force of Represents the torque of the lift generated by the propeller acting on the UAV body in the body coordinate system, is the rotational inertia matrix of the UAV, where J _x , J _y , and J _z are the rotational inertias of the UAV around the three axes of the body coordinate system, respectively, is the rotational angular velocity of the drone, is the rotation damping coefficient matrix, K ₁ , K ₂ , and K ₃ are constant parameters, which respectively represent the air damping coefficients of the UAV around the three axes of the body coordinate system. In addition, in formula (1), the expression of R _t is:

in, θ and ψ represent the roll angle, pitch angle and yaw angle of the UAV, respectively. The direction of the force ^B u _t is always perpendicular to the plane of the UAV fuselage, and its magnitude is the lift force f ₁ , f ₂ generated by the four propellers , f ₃ , the sum of f ₄ , namely:

And ^B τ is the linear combination of the lift generated by the four propellers, expressed in the following form:

in Represents the distance from the propeller axis to the geometric center of the UAV, called "half wheelbase", Representing the lift-torque coefficient of the motor and propeller actuator system of the UAV, the equations (2)-(4) are brought into equation (1) to obtain:

Moreover, according to the rotating subsystem of the UAV kinematics model, we get:

For the attitude stabilization control of the UAV, that is, the roll angle, pitch angle and yaw angle of the UAV are all 0, so θ,ψ is very small, as small as is approximately equal to the identity matrix, so equation (5) can be rewritten as:

2) Nonlinear controller design

For the convenience of design, four virtual control quantities are defined:

Bring equation (8) into equation (5) and equation (1) to get:

where A _z , A _θ and A _ψ respectively represent the external disturbances that the UAV receives in this direction;

roll angle The steps to design a nonlinear controller are as follows:

Roll angle channel error represents the desired roll angle, which leads to the following equation:

Next, define the sliding surface

in, constant parameter

The design steps of the pitch angle θ nonlinear controller are as follows:

Pitch angle channel error e _θ = θ _d - θ, θ _d represents the desired pitch angle, which leads to the following equation:

Next, define the sliding mode surface s _θ :

in, Constant parameter k _θ >0;

The design steps of the yaw angle ψ nonlinear controller are as follows:

The yaw angle channel error e _ψ = ψ _d -ψ, where ψ _d represents the desired yaw angle, from which the following equation is obtained:

Next, define the sliding mode surface s _ψ :

in, Constant parameter k _ψ >0;

Get the following formula:

Thus, three new virtual control quantities are obtained U _θ and U _ψ , now, use the super-twisting algorithm to design the control variables:

where β _i and α _i are gains and constants, and β _i >0, α _i >0, i can take θ or ψ.

The characteristics and beneficial effects of the present invention are:

The present invention establishes a dynamic model with unknown disturbance for the quadrotor UAV, designs a nonlinear attitude controller based on the super-twisting control algorithm, realizes the finite-time convergence control of the attitude error of the UAV, and improves the The robustness of the quad-rotor UAV system enables precise control of the quad-rotor UAV attitude.

Description of drawings:

Fig. 1 is the schematic diagram of the quadrotor unmanned aerial vehicle system adopted in the present invention;

Fig. 2 is the four-rotor unmanned aerial vehicle control flow chart of the present invention;

Fig. 3 is the hardware-in-the-loop simulation platform of the four-rotor unmanned aerial vehicle used in the present invention;

Figure 4 is a graph of three attitude angles during the flight of the quadrotor UAV after the control scheme is adopted;

Figure 5 is a graph of the roll angle during the flight of the quadrotor UAV when the control scheme is adopted when it is subjected to external disturbances.

Detailed ways

In order to overcome the existing deficiencies, the present invention will design a nonlinear attitude controller for the quadrotor UAV. The role of the nonlinear attitude controller in the quadrotor UAV system is shown in Figure 2. The technical scheme adopted in the present invention is a nonlinear attitude control method of a quadrotor unmanned aerial vehicle. Proceed as follows:

1) Establish a quadrotor UAV dynamics model

The present invention adopts the Newton-Euler method to establish a four-rotor UAV dynamics model, and the expression is as follows:

The variables in formula (1) are defined as follows: for drone quality, is the spatial position vector of the UAV in the inertial coordinate system. And g=9.8m/s ² represents the acceleration of gravity. is the translational damping coefficient matrix, K _x , _Ky , and K _z are constant parameters, which are the air damping coefficients of the UAV along the three axes of the body coordinate system. ^B u _t represents the resultant force generated by the propeller of the UAV in the body coordinate system. It represents the torque of the lift generated by the propeller acting on the body of the UAV in the body coordinate system. is the rotational inertia matrix of the UAV, where J _x , J _y , and J _z are the rotational inertias of the UAV around the three axes of the body coordinate system, respectively. is the rotational angular velocity of the drone. is the rotation damping coefficient matrix, K ₁ , K ₂ , and K ₃ are constant parameters, which respectively represent the air damping coefficients of the UAV around the three axes of the body coordinate system. In addition, in formula (1), the expression of R _t is:

The direction of the force ^B u _t is always perpendicular to the plane of the UAV fuselage, and its magnitude is the sum of the lift forces f ₁ , f ₂ , f ₃ , and f ₄ generated by the four propellers, namely:

And ^B τ is the linear combination of the lift generated by the four propellers, which can be expressed as the following form:

in Represents the distance from the propeller axis to the geometric center of the UAV, which can be called "half wheelbase", Represents the lift-torque coefficient of the UAV's actuator (motor and propeller) system. Substituting equations (2)-(4) into equation (1), we can get:

Moreover, according to the rotating subsystem of the UAV kinematics model, it can be known that:

Considering that the control goal of this study is the attitude stabilization control of the UAV, that is, the roll angle, pitch angle and yaw angle of the UAV are all 0, so it is assumed that θ,ψ is very small, as small as is approximately equal to the identity matrix, so equation (5) can be rewritten as:

2) Nonlinear controller design

For the convenience of design, four virtual control quantities are defined:

Substituting Equation (8) into Equation (5) and Equation (1), we can get:

where A _z , A _θ and A _ψ represent the external disturbances that the UAV receives in this direction, respectively.

Next, this specification conducts nonlinear controller design.

The controller design of the roll angle channel is carried out first. The present invention selects closed-loop control, therefore, set the roll angle channel error represents the desired roll angle, which leads to the following equation:

Next, the present invention defines a sliding surface:

in, constant parameter The other two attitude angle channels are also processed according to the above method:

Set the pitch angle channel error e _θ = θ _d -θ, θ _d represents the desired pitch angle, and the following equation is obtained:

Next, define the sliding surface:

in, The constant parameter k _θ >0.

Set the yaw angle channel error e _ψ =ψ _d -ψ, ψ _d represents the desired yaw angle, and the following equation is obtained:

Next, the present invention defines a sliding surface:

in, The constant parameter k _ψ >0.

Through the above processing of the three attitude angle channels, the following formula is obtained:

Thus, the present invention obtains three new virtual control quantities U _θ and U _ψ . Now, use the super-twisting algorithm to design the control quantity:

In the formula, the gains are all constants, and β _i >0, α _i >0.

The technical problem to be solved by the present invention is to realize the precise control of the attitude of the quadrotor UAV under the condition of external interference. To this end, it is necessary to establish a dynamic model of the quadrotor UAV containing external disturbances, and design an attitude controller based on the super-twisting algorithm according to this model, so as to achieve precise control of the UAV attitude.

The technical scheme adopted by the present invention is to establish a four-rotor unmanned aerial vehicle dynamics model containing unknown external disturbances, and design a corresponding nonlinear attitude controller, including the following steps:

First, the dynamics model of the quadrotor UAV needs to be established. Figure 1 is a schematic diagram of the quadrotor UAV system used in this paper. In the present invention, the unmanned aerial vehicle is an X-shaped four-rotor unmanned aerial vehicle, and the Newton-Euler method is used to establish a dynamic model of the four-rotor unmanned aerial vehicle, and the expression is as follows:

The variables in formula (1) are defined as follows: for drone quality, is the spatial position vector of the UAV in the inertial coordinate system. And g=9.8m/s ² represents the acceleration of gravity. is the translational damping coefficient matrix, K _x , _Ky , and K _z are constant parameters, which are the air damping coefficients of the UAV along the three axes of the body coordinate system. ^B u _t represents the resultant force generated by the propeller of the UAV in the body coordinate system. It represents the torque of the lift generated by the propeller acting on the body of the UAV in the body coordinate system. is the rotational inertia matrix of the UAV, where J _x , J _y , and J _z are the rotational inertias of the UAV around the three axes of the body coordinate system, respectively. is the rotational angular velocity of the drone. is the rotation damping coefficient matrix, K ₁ , K ₂ , and K ₃ are constant parameters, which respectively represent the air damping coefficients of the UAV around the three axes of the body coordinate system. In addition, in formula (1), the expression of R _t is:

The direction of the force ^B u _t is always perpendicular to the plane of the UAV fuselage, and its magnitude is the sum of the lift forces f ₁ , f ₂ , f ₃ , and f ₄ generated by the four propellers, namely:

And ^B τ is the linear combination of the lift generated by the four propellers, which can be expressed as the following form:

in Represents the distance from the propeller axis to the geometric center of the UAV, which can be called "half wheelbase", Represents the lift-torque coefficient of the UAV's actuator (motor and propeller) system.

Substituting equations (2)-(4) into equation (1), we can get:

Moreover, according to the rotating subsystem of the UAV kinematics model, it can be known that:

Considering that the control goal of this study is the attitude stabilization control of the UAV, that is, the roll angle, pitch angle and yaw angle of the UAV are all 0, so it is assumed that θ,ψ is very small, as small as is approximately equal to the identity matrix, so equation (5) can be rewritten as:

Then, according to the dynamic model, the design of the nonlinear controller based on the super-twisting control algorithm is carried out.

For the convenience of design, four virtual control quantities are defined:

Substituting Equation (8) into Equation (5) and Equation (1), we can get:

where A _z , A _θ and A _ψ represent the external disturbances that the UAV receives in this direction, respectively.

Next, the nonlinear controller design is carried out.

The present invention selects closed-loop control, so set the roll angle channel error represents the desired roll angle, which leads to the following formula:

Next, the present invention defines a sliding surface:

in, constant parameter The other two attitude angle channels are also processed according to the above method. The detailed process is as follows:

Set the pitch angle channel error e _θ = θ _d -θ, θ _d represents the desired pitch angle, and the following equation is obtained:

Next, the present invention defines a sliding surface:

in, The constant parameter k _θ >0.

Set the yaw angle channel error e _ψ =ψ _d -ψ, ψ _d represents the desired yaw angle, and the following equation is obtained:

Next, the present invention defines a sliding surface:

in, The constant parameter k _ψ >0.

This results in the following formula:

make And suppose |ρ|<δ, δ is constant

Thus, the present invention obtains three new virtual control quantities U _θ and U _ψ .

Now, use the super-twisting algorithm to design the control quantity:

In the formula, the gains are all constants, and β _i >0, α _i >0. It can be proved that when the gains α, β satisfy α>δ, β ² >4α, the control system can converge in a finite time. Among them, the transfer function G(s)=C(sI-A) ^-1 B satisfies and:

Specific implementation examples are given below:

1. Introduction to the experimental platform

The present invention uses the experimental platform shown in FIG. 3 to verify the effect of the designed nonlinear controller. This experimental platform is a hardware-in-the-loop simulation platform for a quadrotor UAV. The platform uses a real quadrotor UAV as the controlled object, and loads a real attitude sensor on the UAV, so that the real and intuitive UAV attitude control effect can be obtained, and the result is closer to the actual flight situation. . At the same time, the platform uses the network to establish the communication between the host computer, the target computer and the monitoring computer, which is convenient for data exchange and control.

2. Results of flight experiments

In order to verify the effectiveness and practicability of the nonlinear attitude controller proposed in the present invention, the attitude stabilization experiment of the quadrotor UAV was carried out on the above-mentioned experimental platform. The control goal is that the three attitude angles of the UAV approach zero in a limited time, namely:

And when subjected to external disturbances, it can still return to a stable state.

The parameters involved in this experimental platform are moment of inertia J=diag[1.34,1.31,2.54] ^T ×10 ^-2 kg·m ² , half wheelbase l=0.225m, lift-torque coefficient c=0.25, mass m =1.5kg.

As can be seen from Figure 4, using the super-twisting attitude controller, the error can be controlled within -1° to 1.5°. It can be seen from Figure 5 that when the external disturbance reaches 40°, it can still return to a stable state. Therefore, the nonlinear attitude controller of the quadrotor UAV designed in the present invention has good robustness and can precisely control the attitude angle.

Claims (1)

1. A finite time convergence attitude control method for a quad-rotor unmanned aerial vehicle is characterized by comprising the following steps:

1) establishing a four-rotor unmanned aerial vehicle dynamics model

A Newton-Euler method is adopted to establish a four-rotor unmanned plane dynamic model, and the expression formula is as follows:

the variables in formula (1) are defined as follows:the mass of the unmanned aerial vehicle is the mass of the unmanned aerial vehicle,is a space position vector of the unmanned aerial vehicle under an inertial coordinate system,and isWhich represents the acceleration of the force of gravity,is a translational damping coefficient matrix, K_x,K_y,K_zAre all constant parameters, are respectively the air damping coefficients of the unmanned aerial vehicle along the three axes of the body coordinate system,^Bu_trepresenting the resultant force generated by the propeller of the unmanned plane in a body coordinate system,representing the torque of the lift force generated by the propeller acting on the unmanned aerial vehicle body under the body coordinate system,is a rotational inertia matrix of the drone, wherein J_x,J_y,J_zRespectively the rotational inertia of the unmanned aerial vehicle around three axes of a coordinate system of the body,is the rotation angular velocity of the unmanned aerial vehicle,as a matrix of rotational damping coefficients, K₁,K₂,K₃For a common parameter, the air damping coefficients of the unmanned aerial vehicle around three axes of the coordinate system of the body are respectively expressed, and in addition, the formula(1) In, R_tThe expression of (a) is:

wherein,theta, psi represents roll angle, pitch angle and yaw angle of the unmanned aerial vehicle, respectively, and force^Bu_tIs always perpendicular to the plane where the unmanned aerial vehicle body is located, and the size of the unmanned aerial vehicle generates lift force f for four propellers₁,f₂,f₃,f₄The sum of (a):

and is^Bτ is a linear combination of the four propellers producing lift, expressed in the form:

whereinThe distance from the axis of the propeller to the geometric center of the unmanned aerial vehicle is shown, and is called as the half wheelbase,expressing the lift-torque coefficient of a motor and propeller actuator system of the unmanned aerial vehicle, and bringing the formulas (2) to (4) into formula (1) to obtain:

moreover, according to the rotation subsystem of the kinematics model of the drone, we obtain:

for attitude stabilization control of the unmanned aerial vehicle, namely, the roll angle, pitch angle and yaw angle of the unmanned aerial vehicle are all 0, so thatTheta, psi are small, as small asApproximately equal to the identity matrix, thus, equation (5) is rewritten as:

2) non-linear controller design

For design convenience, four virtual control quantities are defined:

u₁＝f₁+f₂+f₃+f₄

u₂＝f₁+f₂-f₃-f₄

u₃＝-f₁+f₂+f₃-f₄

u₄＝-f₁+f₂-f₃+f₄(8)

bringing formula (8) into formulae (5) and (1) gives:

wherein A is_z,A_θ,A_ψRespectively representing the external disturbance to which the drone is subjected in that direction;

roll angleThe nonlinear controller is designed by the following steps:

cross roll angle channel error The desired roll angle is expressed, thereby yielding the following equation:

next, defining a slip form surface

Wherein,constant parameter

The pitch angle theta nonlinear controller is designed by the following steps:

pitch angle channel error e_θ＝θ_d-θ，θ_dRepresenting the desired pitch angle, the following equation is derived:

next, a slip form surface s is defined_θ：

Wherein,constant value k_θ＞0；

The design steps of the yaw angle psi nonlinear controller are as follows:

yaw angle channel error e_ψ＝ψ_d-ψ，ψ_dThe desired yaw angle is expressed, thereby yielding the following equation:

next, a slip form surface s is defined_ψ：

Wherein,constant value k_ψ＞0；

The following formula is obtained:

thus, three new virtual control quantities are obtainedU_θAnd U_ψNow, the control quantity is designed by using the super-twisting algorithm:

formula (III) β_iAnd α_iIs a gain and is a constant, and β_i＞0,α_i> 0, i is preferredTheta or psi.