CN109885074A - Quadrotor drone finite time convergence control attitude control method - Google Patents
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Abstract
The present invention relates to the postures of quadrotor drone accurately to control, to propose to be directed to a kind of nonlinear attitude control device of quadrotor drone, the present invention, quadrotor drone finite time convergence control attitude control method, steps are as follows: 1) establishing quadrotor drone kinetic model, establish quadrotor drone kinetic model using Newton―Leibniz formula；2) Design of non-linear controllers, including roll angleDesign of non-linear controllers, pitching angle theta Design of non-linear controllers, yaw angle ψ Design of non-linear controllers；The final finite time convergence control control for realizing UAV Attitude error.Present invention is mainly applied to the postures of quadrotor drone accurately to control occasion.
Description
Technical Field
The invention relates to attitude precision control of a quad-rotor unmanned aerial vehicle. Aiming at the characteristics of high nonlinearity, under-actuation, strong coupling, uncertain disturbance and the like of a quad-rotor unmanned aerial vehicle system, the nonlinear attitude controller based on second-order sliding mode control is provided, and the result of finite time convergence of the attitude control error of the unmanned aerial vehicle is realized. In particular to a finite time convergence attitude control method for a quad-rotor unmanned aerial vehicle.
Background
The multi-rotor unmanned aerial vehicle has the characteristics of simple mechanical structure, capability of vertically taking off and landing, hovering, lower requirement on a field and the like, and occupies more and more important positions in the aspects of scientific research, civil use and military use in recent years. In the numerous many rotor unmanned aerial vehicle types, four rotor unmanned aerial vehicle are comparatively commonly used. The attitude of the airplane is changed by changing the relative rotating speed and the single-shaft thrust between the four rotors, so that the running track of the airplane is changed. Therefore, it is crucial to study attitude control of quad-rotor drones for controlling quad-rotor drones.
Attitude control to four rotor unmanned aerial vehicle, the research of foreign was carried out earlier. The primary main objective of the project of the quad-rotor unmanned aerial vehicle of Stanford university is to improve the cooperative working capacity of the quad-rotor unmanned aerial vehicle by reasonably applying a multi-agent technology, and therefore, the two types of quad-rotor unmanned aerial vehicles are modified successively. The second item improves the speed of the processor and the accuracy of the sensor compared to the first item, thereby resulting in an improved control effect. The quad-rotor unmanned aerial vehicle adopts two single-chip microcomputers with the model number of PIC18F6520 of the micro-core company to coordinate communication, sensing and Control activities on the aircraft (Conference: IEEE RSJIntermental Conference on Intelligent Robots and Systems; authors: Hoffmann Gabriel M, Waslander Steven L, Vitus Michael P, etc.; publication year and month: 2009; article title: Stanford test of Autonomus Rotorcraft for Multi-Agent Control; page number: 404-. This unmanned aerial vehicle has realized indoor and outdoor autonomic flight at present. The quad-rotor unmanned aerial vehicle at pennsylvania university uses a control algorithm based on a backstepping method to construct a flight control system based on vision. The tasks of land mobile platform landing, target grabbing, multi-machine collaboration, etc. can be realized (journal: IEEE Robotics & Automatics Magazine; author: Michael N, Mellinger D, Lindsey Q, Kumar V; published year month: 9 2010; article title: The GRASPMultiple Micro-UAV Test Bed expert Evaluation of Multi robot control Algorithms; page number: 56-65). In terms of applying a high-order Sliding Mode control algorithm, the university of Alabama, Hantzville, university of America, controls a quad-rotor unmanned aerial vehicle by applying a traditional Sliding Mode control and a Super-twilling algorithm (journal: Automatica; author: Shtessel Y, Taleb M, Plesan F; published month: 2012: 5 month; article title: A novel Adaptive-gain Super-twilling Sliding Mode Controller: method and Application; page number: 759-. In addition, there are also students who use high-order sliding mode Control for Unmanned Aerial Vehicle fault-tolerant Control (journal: IEEE Transactions on Control Systems Technology; Renderee: RylMarkus, Buelthoff Heinrich H, Giordino Paolo Robuffo; published month: 2015 3 month; article title: A Novel acted Quadrotor Unmanned Aerial Vehicle: Modeling, Control, and Experimental Validation; page: 540-. Although the research of the domestic four-rotor unmanned aerial vehicle starts late, a certain result is obtained. Wherein scientific research institutes such as Qinghua university, national defense science and technology university, Tianjin university, Beijing aerospace university and the like make great contribution to the research and development of the domestic four-rotor unmanned aerial vehicle. At present, the control methods used at home and abroad mainly include feedback linearization, a backstepping method, robust control, sliding mode variable structure control, intelligent PID (proportion, integral and differential) control and the like.
With regard to the research on quad-rotor drone control, researchers have achieved some success today, but there are also some limitations: 1) some existing control designs make more assumptions and simplifications on the dynamic model of the unmanned aerial vehicle, for example, some existing achievements assume that the flying speed of the unmanned aerial vehicle is low, and do not consider the disturbance. But in practice the disturbances experienced by the drone are not negligible. 2) Some control methods linearize the model of the controlled object near the equilibrium point and design the controller based on the linearized model, thereby weakening the control effect of the controlled object near the non-equilibrium point.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a nonlinear attitude controller for a quad-rotor unmanned aerial vehicle. Therefore, the invention adopts the technical scheme that the finite time convergence attitude control method of the quad-rotor unmanned aerial vehicle comprises the following steps:
1) establishing a four-rotor unmanned aerial vehicle dynamics model
The invention adopts Newton-Euler method to establish a four-rotor unmanned plane dynamics model, and the expression 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 g is 9.8m/s2Which represents the acceleration of the force of gravity,is a translational damping coefficient matrix, Kx,Ky,KzAre all constant parameters, are respectively the air damping coefficients of the unmanned aerial vehicle along the three axes of the body coordinate system,Butrepresenting 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 Jx,Jy,JzRespectively 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 the normal reference, the air damping coefficients of the unmanned aerial vehicle around three axes of the body coordinate system are respectively expressed, and in the formula (1), RtThe expression of (a) is:
wherein,theta, psi represents roll angle, pitch angle and yaw angle of the unmanned aerial vehicle, respectively, and forceButIs 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 isBτ 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:
bringing formula (8) into formulae (5) and (1) gives:
wherein A isz,Aθ,AψRespectively 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 Indicating a desired roll angle, thereby obtainingEquation:
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 eθ＝θd-θ，θdRepresenting the desired pitch angle, the following equation is derived:
next, a slip form surface s is definedθ：
Wherein,constant value kθ>0；
The design steps of the yaw angle psi nonlinear controller are as follows:
yaw angle channel error eψ＝ψd-ψ，ψdThe desired yaw angle is expressed, thereby yielding the following equation:
next, a slip form surface s is definedψ：
Wherein,constant value kψ>0；
The following formula is obtained:
thus, three new virtual control quantities are obtainedUθAnd UψNow, the control quantity is designed by using the super-twisting algorithm:
formula (III) βiAnd αiIs a gain and is a constant, and βi>0,αi>0, i is preferableTheta or psi.
The invention has the characteristics and beneficial effects that:
the invention establishes a dynamics model containing unknown interference for the quad-rotor unmanned aerial vehicle, designs a nonlinear attitude controller based on a super-twisting control algorithm, realizes the finite time convergence control of the attitude error of the unmanned aerial vehicle, improves the robustness of the quad-rotor unmanned aerial vehicle system, and realizes the accurate control of the attitude of the quad-rotor unmanned aerial vehicle.
Description of the drawings:
FIG. 1 is a schematic diagram of a quad-rotor drone system for use with the present invention;
FIG. 2 is a flow chart of the four-rotor drone control of the present invention;
FIG. 3 is a hardware-in-the-loop simulation platform for a quad-rotor drone for use with the present invention;
FIG. 4 is a graph of three attitude angles during flight of a quad-rotor drone using a control scheme;
fig. 5 is a graph of roll angle during quad-rotor drone flight when subject to external disturbances after the control scheme is employed.
Detailed Description
In order to overcome the existing defects, the invention designs a nonlinear attitude controller aiming at a four-rotor unmanned aerial vehicle. The non-linear attitude controller is embodied in figure 2 for use in a quad-rotor drone system. The invention adopts the technical scheme that a nonlinear attitude control method of a quad-rotor unmanned aerial vehicle is adopted. The method comprises the following steps:
1) establishing a four-rotor unmanned aerial vehicle dynamics model
The invention adopts Newton-Euler method to establish a four-rotor unmanned plane dynamics model, and the expression 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,the space position vector of the unmanned aerial vehicle under the inertial coordinate system.And g is 9.8m/s2Representing the gravitational acceleration.Is a translational damping coefficient matrix, Kx,Ky,KzThe air damping coefficients are all constant parameters and are the air damping coefficients of the unmanned aerial vehicle along the three axes of the body coordinate system.ButAnd the resultant force generated by the propeller of the unmanned aerial vehicle under the body coordinate system is represented.And the torque of the lift force generated by the propeller acting on the unmanned aerial vehicle body under the body coordinate system is represented.Is a rotational inertia matrix of the drone, wherein Jx,Jy,JzRespectively is the inertia of the unmanned aerial vehicle around the three axes of the coordinate system of the body.Is the angular velocity of rotation of the drone.As a matrix of rotational damping coefficients, K1,K2,K3And the air damping coefficients of the unmanned aerial vehicle around three axes of the coordinate system of the body are respectively expressed as normal parameters. Further, in the formula (1), RtThe expression of (a) is:
force ofButIs 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 isBτ is a linear combination of the four propellers producing lift and can be expressed in the form:
whereinThe distance from the axis of the propeller to the geometric center of the unmanned aerial vehicle is shown, and can be called as a half-wheelbase,representing the lift-torque coefficient of the actuator (motor and propeller) system of the drone. Bringing formulae (2) to (4) into formula (1) can give:
moreover, according to the rotation subsystem of the kinematics model of the drone, it is possible to know:
considering that the control objective of the present study is attitude stabilization control of the drone, i.e., the roll angle, pitch angle, and yaw angle of the drone are all 0, it is assumed thatTheta, psi are small, as small asApproximately equal to the identity matrix, so equation (5) can be rewritten as:
2) non-linear controller design
For design convenience, four virtual control quantities are defined:
bringing formula (8) into formula (5) and formula (1) can yield:
wherein A isz,Aθ,AψRespectively, representing the external disturbances experienced by the drone in that direction.
In the following, the present specification performs a nonlinear controller design.
Firstly, designing a controller of a roll angle channel. The invention selects closed-loop control, so that the roll angle channel error is set The desired roll angle is expressed, thereby yielding the following equation:
next, the invention defines a slip form face:
wherein,constant parameterAnd processing other two attitude angle channels according to the method:
setting pitch angle channel error eθ＝θd-θ，θdRepresenting the desired pitch angle, the following equation is derived:
next, a slip form surface is defined:
wherein,constant value kθ>0。
Channel error of setting yaw angleeψ＝ψd-ψ，ψdThe desired yaw angle is expressed, thereby yielding the following equation:
next, the invention defines a slip form face:
wherein,constant value kψ>0。
Through the above processing of the three attitude angle channels, the following formula is obtained:
therefore, the invention obtains three new virtual control quantitiesUθAnd Uψ. Now, the control quantity is designed by using a super-twisting algorithm:
wherein the gains are all constant, and βi>0,αi>0。
The invention aims to solve the technical problem of realizing the accurate control of the posture of the quad-rotor unmanned aerial vehicle under the condition of external interference. Therefore, a dynamic model of the quad-rotor unmanned aerial vehicle containing external disturbance needs to be established, and a super-twisting algorithm-based attitude controller is designed according to the model, so that the attitude of the unmanned aerial vehicle can be accurately controlled.
The technical scheme adopted by the invention is as follows: establishing a four-rotor unmanned aerial vehicle dynamic model containing external unknown disturbance and designing a corresponding nonlinear attitude controller, wherein the method comprises the following steps:
first, a quad-rotor drone dynamics model needs to be built. Fig. 1 is a schematic diagram of a quad-rotor drone system as used herein. The unmanned aerial vehicle is an X-shaped quadrotor unmanned aerial vehicle, and a dynamics model of the quadrotor unmanned aerial vehicle is established by adopting a Newton-Euler method, wherein the expression 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,the space position vector of the unmanned aerial vehicle under the inertial coordinate system.And g is 9.8m/s2Representing the gravitational acceleration.Is a translational damping coefficient matrix, Kx,Ky,KzThe air damping coefficients are all constant parameters and are the air damping coefficients of the unmanned aerial vehicle along the three axes of the body coordinate system.ButAnd the resultant force generated by the propeller of the unmanned aerial vehicle under the body coordinate system is represented.And the torque of the lift force generated by the propeller acting on the unmanned aerial vehicle body under the body coordinate system is represented.Is a rotational inertia matrix of the drone, wherein Jx,Jy,JzRespectively is the inertia of the unmanned aerial vehicle around the three axes of the coordinate system of the body.Is the angular velocity of rotation of the drone.As a matrix of rotational damping coefficients, K1,K2,K3And the air damping coefficients of the unmanned aerial vehicle around three axes of the coordinate system of the body are respectively expressed as normal parameters. Further, in the formula (1), RtThe expression of (a) is:
force ofButIs 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 isBτ is a linear combination of the four propellers producing lift and can be expressed in the form:
whereinThe distance from the axis of the propeller to the geometric center of the unmanned aerial vehicle is shown, and can be called as a half-wheelbase,representing the lift-torque coefficient of the actuator (motor and propeller) system of the drone.
Bringing formulae (2) to (4) into formula (1) can give:
moreover, according to the rotation subsystem of the kinematics model of the drone, it is possible to know:
considering that the control objective of the present study is attitude stabilization control of the drone, i.e., the roll angle, pitch angle, and yaw angle of the drone are all 0, it is assumed thatTheta, psi are small, as small asApproximately equal to the identity matrix, so equation (5) can be rewritten as:
then, the design of the nonlinear controller based on the super-twisting control algorithm is carried out according to the dynamic model.
For design convenience, four virtual control quantities are defined:
bringing formula (8) into formula (5) and formula (1) can yield:
wherein A isz,Aθ,AψRespectively, representing the external disturbances experienced by the drone in that direction.
The following is a non-linear controller design.
The invention selects closed-loop control, so the roll angle channel error is set Representing the desired roll angle, the following equation is obtained:
next, the invention defines a slip form face:
wherein,constant parameterAnd processing other two attitude angle channels according to the method, wherein the detailed process is as follows:
setting pitch angle channel error eθ＝θd-θ，θdTo representThe pitch angle is desired, from which the following equation is derived:
next, the invention defines a slip form face:
wherein,constant value kθ>0。
Set yaw angle channel error eψ＝ψd-ψ，ψdThe desired yaw angle is expressed, thereby yielding the following equation:
next, the invention defines a slip form face:
wherein,constant value kψ>0。
To give the following formula:
order toAnd suppose | ρ | |<δ, δ being a constant
Therefore, the invention obtains three new virtual control quantitiesUθAnd Uψ。
Now, the control quantity is designed by using a super-twisting algorithm:
wherein the gains are all constant, and βi>0,αi>0. It can be shown that when the gain α satisfies α>δ,β2>4 α, the control system may converge within a limited time, wherein the transfer function g(s) ═ C (sI-a)-1B satisfiesAnd:
specific examples of implementation are given below:
first, introduction of experiment platform
The invention utilizes the experimental platform shown in fig. 3 to verify the effect of the designed nonlinear controller. This experiment platform is four rotor unmanned aerial vehicle hardware in the ring simulation platform. This platform adopts real four rotor unmanned aerial vehicle as the controlled object to loaded real attitude sensor on unmanned aerial vehicle, can obtain real and audio-visual unmanned aerial vehicle attitude control effect from this, also made the result more press close to the actual flight condition. Meanwhile, the platform establishes communication among the upper computer, the target computer and the monitoring computer by utilizing a network, and is convenient for data interaction and control.
Second, flight experiment results
In order to verify the effectiveness and the feasibility of the nonlinear attitude controller provided by the invention, the four-rotor unmanned aerial vehicle attitude stabilization experiment is carried out on the experimental platform. The control target is that three attitude angles of the unmanned aerial vehicle approach to zero in limited time, namely:
and can still be recovered to a stable state when being interfered by the outside.
The experimental platform relates to the parameter values of inertia moment J ═ diag [1.34,1.31,2.54 ]]T×10-2kg·m2The half-axle distance l is 0.225m, the lift-torque coefficient c is 0.25, and the mass m is 1.5 kg.
As can be seen from FIG. 4, the error can be controlled to be within-1 to 1.5 using the super-twisting attitude controller. It can be seen from fig. 5 that the steady state can still be reached when the external disturbance reaches 40 °. Therefore, the nonlinear attitude controller of the quad-rotor unmanned aerial vehicle has good robustness and can accurately 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, Kx,Ky,KzAre all constant parameters, are respectively the air damping coefficients of the unmanned aerial vehicle along the three axes of the body coordinate system,Butrepresenting 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 Jx,Jy,JzRespectively 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, RtThe expression of (a) is:
wherein,theta, psi represents roll angle, pitch angle and yaw angle of the unmanned aerial vehicle, respectively, and forceButIs 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 isBτ 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 isz,Aθ,AψRespectively 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 eθ＝θd-θ，θdRepresenting the desired pitch angle, the following equation is derived:
next, a slip form surface s is definedθ：
Wherein,constant value kθ＞0；
The design steps of the yaw angle psi nonlinear controller are as follows:
yaw angle channel error eψ＝ψd-ψ，ψdThe desired yaw angle is expressed, thereby yielding the following equation:
next, a slip form surface s is definedψ：
Wherein,constant value kψ＞0；
The following formula is obtained:
thus, three new virtual control quantities are obtainedUθAnd UψNow, the control quantity is designed by using the super-twisting algorithm:
formula (III) βiAnd αiIs a gain and is a constant, and βi＞0,αi> 0, i is preferredTheta or psi.
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| CN113110066A (en) * | 2021-05-13 | 2021-07-13 | 河北科技大学 | Finite-time Super-Twisting sliding mode control method for four-rotor aircraft |
| CN113359824A (en) * | 2021-05-31 | 2021-09-07 | 杭州电子科技大学 | Unmanned aerial vehicle cluster control method based on fuzzy model |
| CN116300668A (en) * | 2023-05-26 | 2023-06-23 | 北京航空航天大学杭州创新研究院 | Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference |
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| CN113359824A (en) * | 2021-05-31 | 2021-09-07 | 杭州电子科技大学 | Unmanned aerial vehicle cluster control method based on fuzzy model |
| CN116300668A (en) * | 2023-05-26 | 2023-06-23 | 北京航空航天大学杭州创新研究院 | Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference |
| CN116300668B (en) * | 2023-05-26 | 2023-08-08 | 北京航空航天大学杭州创新研究院 | Layering anti-interference control method for four-rotor unmanned aerial vehicle aiming at rainfall interference |
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