CN109901606A - A kind of mixing finite time control method for quadrotor Exact trajectory tracking - Google Patents
A kind of mixing finite time control method for quadrotor Exact trajectory tracking Download PDFInfo
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Abstract
The present invention provides a kind of mixing finite time control method for quadrotor Exact trajectory tracking.The method of the present invention includes the following steps: the kinematics model for establishing quadrotor unmanned vehicle and and kinetic model；According to the vertical control law of quadrotor unmanned vehicle height tracing error and the design vertical movement of Adaptive Integral sliding-mode surface；According to quadrotor unmanned vehicle horizontal position tracking error, the horizontal control law based on the movement of Backstepping design level；Finite time disturbance observer is designed according to quadrotor unmanned vehicle attitude angle, designs accurate pose stabilization control rule in conjunction with non-singular terminal sliding formwork control ratio and finite time disturbance observer.Quadrotor is divided into height, horizontal position, posture three subsystems by the present invention, has separately designed three kinds of control strategies, can be with fast and stable track following error using mixing control program.The Exact trajectory tracking of quadrotor can be realized in the case where allowing Unknown Parameters and external interference, manipulate more flexible.
Description
Technical field
The present invention relates to unmanned vehicle field more particularly to a kind of mixing for quadrotor Exact trajectory tracking are limited
Duration control method.
Background technique
Quadrotor unmanned vehicle is a kind of drive lacking, close coupling, multivariable, nonlinear complication system, and by weight
The interference of the external environments such as the influence of the several physicals such as power and gyroscopic effect and air-flow, controller design are cumbersome.
Adaptive approach is merely capable of handling continuous and slow time-varying disturbance.Backstepping poor robustness, by external disturbance
It influences greatly, to be easy to cause system unstable.It is sliding although sliding-mode control can overcome the characteristics of Backstepping poor robustness
There is the phenomenon that input is buffeted in mould control.Existed again using the intelligence learnings such as neural network, fuzzy theory algorithm and is needed largely
The problems such as experimental data, high-performance processor, cost is larger, is not suitable for the system of practical application.
It is difficult to meet its dynamic performance index using traditional control method.In order to keep quadrotor drone effective
Ground avoids the factors such as external environment interference and inherent parameters uncertainty from influencing, it is necessary to which quadrotor can effectively be realized by designing one kind
The method of the accurate tracing control in unmanned vehicle track.
Summary of the invention
According to technical problem set forth above, and provide a kind of mixing finite time for quadrotor Exact trajectory tracking
Control method.The present invention by by the independent control strategy of height, horizontal position, posture three subsystems in quadrotor system,
Enable quadrotor fast and stable, realizes Exact trajectory tracking.The technological means that the present invention uses is as follows:
A kind of mixing finite time control method for quadrotor Exact trajectory tracking, includes the following steps:
S1, the kinematics model for establishing quadrotor unmanned vehicle and and kinetic model；
S2, it is hung down according to what quadrotor unmanned vehicle height tracing error and the design of Adaptive Integral sliding-mode surface moved vertically
Straight control law；
S3, according to quadrotor unmanned vehicle horizontal position tracking error, the level based on the movement of Backstepping design level
Control law；
S4, finite time disturbance observer is designed according to quadrotor unmanned vehicle attitude angle, it is sliding in conjunction with non-singular terminal
Mould control law and finite time disturbance observer design accurate pose stabilization control rule.
Further, in the step S1, the kinematics model and and kinetic model of quadrotor unmanned vehicle are established
Specifically:
Kinematics model indicates are as follows:
Wherein R is position spin matrix, is expressed as
T is posture transfer matrix, is expressed as
Wherein, ξ=[x, y, z]T, indicate the absolute position of four rotors, x, y and z indicate quadrotor under earth axes
The specific location and lifting position of unmanned vehicle,It indicates Eulerian angles, i.e. attitude angle, whereinθ
It is respectively roll angle, pitch angle and yaw angle, V=[u, v, w] with ψTWith Ω=[p, q, r]TIndicate linear velocity and the angle of four rotors
Speed, s and c respectively indicate sin and cos,
Kinetic model indicates are as follows:
It is state vector, wherein M indicates the quality of quadrotor,The linear velocity of x, y, z axis direction is respectively represented,Respectively represent roll, pitching, yaw direction
Angular speed propeller blade angular speed are as follows:
ω=ω1-ω2+ω3-ω4
di, i=1,2,3,4
ai, i=1,2 ..., 5
bi, i=1,2,3,
ω1、2、3、4Respectively represent the angular speed a of four rotors of quadrotori、biIndicate preset parameter, UiFor list-directed defeated
Enter, diIndicate the unknown disturbance comprising systematic uncertainty and other unknown numbers.
Further, the vertical specific design method of control law of the step S2 are as follows:
S21, height subsystem mathematical model is constructed according to kinetic model:
The acceleration of gravity of ge expression quadrotor
Height tracing error is defined as:
ez=z-zd
Z indicates the actual height of quadrotor, zdIndicate the reference altitude of quadrotor,
Adaptive Integral synovial membrane mask body indicates are as follows:
cz> 0
SzIndicate sliding-mode surface, kzFor the adaptation coefficient in sliding-mode surface, t indicates the time that the Adaptive Integral sliding formwork carries out；
S22, consider that tracking error and Adaptive Integral sliding-mode surface, the control law for devising vertical movement are as follows:
Adaptive law is designed as
For constant.
Further, the specific design method of the horizontal control law of step S3 are as follows:
S31, controller of the design based on Backstepping, define horizontal cross shaft tracking error are as follows:
ex=x-xd
S32, selection liapunov function
Virtual controlling rule is designed to
ZxIndicate the difference between virtual controlling input and practical control input,
Select liapunov function
To V2Virtual controlling rule is brought into wherein after derivation, is obtained
By selecting suitable cxAnd kxParameter, to ensure
Further, the horizontal control law of step S3 further include:
S33, horizontal vertical pivot tracking error is defined are as follows:
ey=y-yd
Wherein, y indicates the horizontal longitudinal axis physical location of quadrotor, ydIndicate the horizontal longitudinal axis reference position of quadrotor,
S34, selection liapunov function
After taking differential to it, obtain
Virtual controlling variable αyIt is designed asWherein cy> 0 is a constant, meanwhile, available void
Quasi- control variable αyWithBetween error
Virtual controlling restrains vyIt is designed to:
Selection includes eyAnd zyLiapunov function be
Find out V4About the derivative of time, then by control rate vyIt brings into wherein, obtains
By selecting suitable cxAnd kxParameter, to ensure
Further, the accurate pose stabilization control of the step S4 restrains specific design method are as follows: S41, is built with external do
The posture subsystem disturbed:
Wherein f (Ω)=[a1qr+a2qω,a3pr+a4pω,a5pq]TBe it is nonlinear,
U=[u2,u3,u4]TIt is the input vector of controller,
Matrix g is expressed as
Matrix g is the inertial matrix of quadrotor system, and element therein is all the moment of inertia,
Matrix d (t)=[d2,d3,d4]TIt is external disturbance；
S42, according to quadrotor kinetic model, design finite time disturbance observer:
ζ0=-λ1L1/3sig2/3(z0-Ω)+z1
ζ1=-λ2L1/2sig1/2(z1-ζ0)+z2
Wherein, u is the input vector of system, u=[u2, u3, u4]T z0,z1And z2Ω, d andEstimated value, then
Through too long control, unknown external disturbance d can be accurately identified within the limited time.
Further, after the step S4 further include:
S5, simulating, verifying research is carried out to the quadrotor unmanned vehicle model using mixing control program, with conventional hand
Section compares, and further verifies validity and superiority.
The invention has the following advantages that
Quadrotor system is divided into height, horizontal position, posture three subsystems by the present invention, has separately designed three kinds of controls
Strategy enables quadrotor fast and stable, realizes Exact trajectory tracking.Wherein, for the height subsystem of quadrotor,
A kind of Adaptive Integral sliding formwork control ratio is proposed, so that quadrotor is reached Desired Height and has good robustness, can resist
Influence of the extraneous X factor to system.Horizontal position subsystem is controlled using contragradience technology.In order to accurately inhibit
External interference constructs a kind of non-singular terminal sliding formwork control based on finite time disturbance observer for posture subsystem
Strategy, to realize the stability of finite time.It, can be with fast and stable track following error using mixing control program.This hair
The mixing finite time Trajectory Tracking Control method of bright design can allowing Unknown Parameters and in the case where external interference,
It realizes the Exact trajectory tracking of quadrotor, manipulates more flexible.
The present invention can be widely popularized in unmanned vehicle field based on the above reasons.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to do simply to introduce, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without any creative labor, can be with
It obtains other drawings based on these drawings.
Fig. 1 is quadrotor unmanned vehicle algorithm design flow diagram of the present invention.
Fig. 2 is quadrotor unmanned vehicle geometry kinematic sketch of the present invention.
Fig. 3 is that the present invention is based on the quadrotor Exact trajectory tracking control block diagrams of gust disturbances and systematic uncertainty.
Fig. 4 is the present invention and sliding formwork control and the anti-reality for pushing away control method and desired tracking mode contrast schematic diagram.
Fig. 5 is the present invention and sliding formwork control and the anti-track following error contrast schematic diagram for pushing away control method.
Fig. 6 is that the present invention is compared with the actual path tracking performance in sliding formwork control and the anti-three-dimensional space for pushing away control method
Schematic diagram.
Fig. 7 is to be illustrated in posture subsystem of the present invention using the comparison result of FDO-NTSM scheme and NTSM control method
Figure.
Fig. 8 is the present invention rapid convergent effect diagram under complicated unknown disturbances.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
As shown in Figure 1, present embodiment discloses a kind of mixing finite-time controls for quadrotor Exact trajectory tracking
(HFTC) method includes the following steps:
S1, the kinematics model and and kinetic model for establishing quadrotor unmanned vehicle as shown in Figure 2；
As shown in figure 3, S2, being designed and being hung down according to quadrotor unmanned vehicle height tracing error and Adaptive Integral sliding-mode surface
The vertical control law directly moved；
S3, according to quadrotor unmanned vehicle horizontal position tracking error, the level based on the movement of Backstepping design level
Control law；
S4, finite time disturbance observer is designed according to quadrotor unmanned vehicle attitude angle, it is sliding in conjunction with non-singular terminal
Mould control law and finite time disturbance observer FDO-NTSM design accurate pose stabilization control rule.
In the step S1, establish quadrotor unmanned vehicle kinematics model and and kinetic model specifically:
Kinematics model indicates are as follows:
Wherein R is position spin matrix, is expressed as
T is posture transfer matrix, is expressed as
Wherein, ξ=[x, y, z]T, indicate the absolute position of four rotors, x, y and z indicate quadrotor under earth axes
The specific location and lifting position of unmanned vehicle,It indicates Eulerian angles, i.e. attitude angle, whereinθ
It is respectively roll angle, pitch angle and yaw angle, V=[u, v, w] with ψTWith Ω=[p, q, r]TIndicate linear velocity and the angle of four rotors
Speed, s and c respectively indicate sin and cos,
Kinetic model indicates are as follows:
It is state vector, wherein M indicates the quality of quadrotor,The linear velocity of x, y, z axis direction is respectively represented,Respectively represent roll, pitching, yaw direction
Angular speed propeller blade angular speed are as follows:
ω=ω1-ω2+ω3-ω4
di, i=1,2,3,4
ai, i=1,2 ..., 5
bi, i=1,2,3,
ω1、2、3、4Respectively represent the angular speed of four rotors of quadrotor, ai、biIndicate preset parameter, UiFor list-directed
Input, diIndicate the unknown disturbance comprising systematic uncertainty and other unknown numbers.
In order to decouple the drive lacking characteristic of the height subsystem of quadrotor unmanned vehicle, implement as preferred
Mode, the vertical specific design method of control law of the step S2 are as follows:
S21, height subsystem mathematical model is constructed according to kinetic model:
Wherein, geIndicate the acceleration of gravity of quadrotor,
Height tracing error is defined as:
ez=z-zd
Wherein, z indicates the actual height of quadrotor, zdIndicate the reference altitude of quadrotor,
Adaptive Integral synovial membrane face (AISM) is embodied as:
cz> 0
Wherein, SzIndicate sliding-mode surface, kzFor the adaptation coefficient in sliding-mode surface, t indicates what the Adaptive Integral sliding formwork carried out
Time；
S22, consider that tracking error and Adaptive Integral sliding-mode surface, the control law for designing vertical movement are as follows:
Adaptive law design are as follows:
For constant.
The specific design method of the horizontal control law of step S3 are as follows:
S31, controller of the design based on Backstepping, define horizontal cross shaft tracking error are as follows:
ex=x-xd
Wherein, x indicates the horizontal cross shaft physical location of quadrotor, xdIndicate the horizontal cross shaft reference position of quadrotor,
S32, selection liapunov function
Virtual controlling rule is designed to
zxIndicate the difference between virtual controlling input and practical control input,
Select liapunov function
To V2Virtual controlling rule is brought into wherein after derivation, is obtained
By selecting suitable cxAnd kxParameter, to ensure
The horizontal control law of step S3 further include:
S33, horizontal vertical pivot tracking error is defined are as follows:
ey=y-yd
Wherein, y indicates the horizontal longitudinal axis physical location of quadrotor, ydIndicate the horizontal longitudinal axis reference position of quadrotor,
S34, selection liapunov function
After taking differential to it, obtain
Virtual controlling variable αyIt is designed asWherein cy> 0 is a constant,
Meanwhile available virtual controlling variable αyWithBetween error
Virtual controlling restrains vyIt is designed to:
Selection includes eyAnd zyLiapunov function be
Find out V4About the derivative of time, then by control rate vyIt brings into wherein, obtains
By selecting suitable cxAnd kxParameter, to ensure
In order to realize stability of the quadrotor in finite time, as preferred embodiment, the step S4 is accurate
Pose stabilization control restrains specific design method are as follows:
S41, the posture subsystem for being built with external disturbance:
Wherein f (Ω)=[a1qr+a2qω,a3pr+a4pω,a5pq]TBe it is nonlinear,
U=[u2,u3,u4]TIt is the input vector of controller,
Matrix g is expressed as
Matrix g is the inertial matrix of quadrotor system, and element therein is all the moment of inertia,
Matrix d (t)=[d2,d3,d4]TIt is external disturbance；
S42, according to quadrotor kinetic model, design finite time disturbance observer (FDO):
ζ1=-λ2L1/2sig1/2(z1-ζ0)+z2
Wherein, u is the input vector of system, u=[u2, u3, u4]Tz0,z1And z2Ω, d andEstimated value, then pass through
Too long control can accurately identify unknown external disturbance d within the limited time.
After the step S4 further include:
S5, simulating, verifying research is carried out to the quadrotor unmanned vehicle model using mixing control program, with conventional hand
Section compares, and further verifies validity and superiority.
Specifically, initial position and yaw angle (z are selected0,x0,y0,ψ0) it is (0, -2, -2,0).External disturbance becomes at any time
Change relationship are as follows: di(t)=0.5cos (t), i=1,2,3,4.
The desired trajectory of position and yaw angle is
The parameter selection of AISM control is cz=2, kz=1, hz=10,The parameter of Backstepping Controller is selected
It is selected as cx=kx=cy=ky=10.The parameter of NTSM controller based on FDO: λ1=2.8, λ2=1.1, λ3=1.6, L=30,
β=1, m=5, n=3, k=diag (10,10,10)
For the superiority of prominent proposed HFTC scheme, by itself and traditional sliding formwork control SMC and Reverse Step Control technology
Backstepping is compared.Fig. 4 shows practical and desired tracking mode z, x, y and ψ, therefrom it can be seen that HFTC
Scheme can drive four rotors faster, more accurately to track required track relative to sliding formwork control and the anti-control method that pushes away.This
Outside, ze,xe,yeAnd ψeTrack following error it is as shown in Figure 5.In order to intuitively understand the superiority of HFTC scheme, Fig. 6 is provided
The actual path tracking performance of HFTC in three dimensions.
In the control of posture subsystem, the present embodiment uses the ratio of FDO-NTSM scheme and existing NTSM control method
It is as shown in Figure 7 compared with result.As can be seen that the FDO-NTSM scheme proposed can accurately solve the dry of complicated unknown parameter
It disturbs.Fig. 8 shows the variation for 4 control inputs that actuator provides, wherein the total life u of 4 propellers1Finally in 19.6N
Left and right, equal to the gravity of four rotors.Due to complicated unknown disturbances, control input u2And u3There is slight jitter in 4s or so, and
Fast convergence.Control input u4Also there is buffeting in departure time, but smoothened after reaching desired yaw angle.Therefore it can obtain
Conclusion: the significant validity of the algorithm arrangement proposed and superiority are verified.Using mixing control program, fast and stable four
Rotor track following error.Greatly improve the manoeuvrable and tracking accuracy of quadrotor Trajectory Tracking Control System.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (7)
1. a kind of mixing finite time control method for quadrotor Exact trajectory tracking, which is characterized in that including walking as follows
It is rapid:
S1, the kinematics model for establishing quadrotor unmanned vehicle and and kinetic model；
S2, the vertical control to be moved vertically according to quadrotor unmanned vehicle height tracing error and the design of Adaptive Integral sliding-mode surface
System rule；
S3, according to quadrotor unmanned vehicle horizontal position tracking error, the horizontal control based on the movement of Backstepping design level
Rule；
S4, finite time disturbance observer is designed according to quadrotor unmanned vehicle attitude angle, in conjunction with non-singular terminal sliding formwork control
System rule and finite time disturbance observer design accurate pose stabilization control rule.
2. the mixing finite time control method according to claim 1 for quadrotor Exact trajectory tracking, feature
Be, in the step S1, establish quadrotor unmanned vehicle kinematics model and and kinetic model specifically:
Kinematics model indicates are as follows:
Wherein R is position spin matrix, is expressed as
T is posture transfer matrix, is expressed as
Wherein, ξ=[x, y, z]T, indicate the absolute position of four rotors, x, y and z indicate under earth axes quadrotor nobody fly
The specific location and lifting position of row device,It indicates Eulerian angles, i.e. attitude angle, whereinθ and ψ difference
For roll angle, pitch angle and yaw angle, V=[u, v, w]TWith Ω=[p, q, r]TIndicate the linear velocity and angular speed of four rotors, s
Sin and cos are respectively indicated with c,
Kinetic model indicates are as follows:
It is state vector, wherein M indicates the quality of quadrotor,Point
The linear velocity of x, y, z axis direction is not represented,Respectively represent roll, pitching, yaw direction angular speed propeller
Blade angular speed are as follows:
ω=ω1-ω2+ω3-ω4
di, i=1,2,3,4
ai, i=1,2 ..., 5
bi, i=1,2,3,
ω1、2、3、4Respectively represent the angular speed of four rotors of quadrotor, ai、biIndicate preset parameter, UiFor list-directed input,
diIndicate the unknown disturbance comprising systematic uncertainty and other unknown numbers.
3. the mixing finite time control method according to claim 2 for quadrotor Exact trajectory tracking, feature
It is, the vertical specific design method of control law of the step S2 are as follows:
S21, height subsystem mathematical model is constructed according to kinetic model:
Wherein, geIndicate the acceleration of gravity of quadrotor,
Height tracing error is defined as:
ez=z-zd
Wherein, z indicates the actual height of quadrotor, zdIndicate the reference altitude of quadrotor,
Adaptive Integral synovial membrane mask body indicates are as follows:
cz> 0
Wherein, SzIndicate sliding-mode surface, kzFor the adaptation coefficient in sliding-mode surface, t indicate that the Adaptive Integral sliding formwork carries out when
Between；
S22, consider that tracking error and Adaptive Integral sliding-mode surface, the control law for designing vertical movement are as follows:
Adaptive law design are as follows:
For constant.
4. the mixing finite time control method according to claim 2 for quadrotor Exact trajectory tracking, feature
It is, the specific design method of the horizontal control law of step S3 are as follows:
S31, controller of the design based on Backstepping, define horizontal cross shaft tracking error are as follows:
ex=x-xd
Wherein, x indicates the horizontal cross shaft physical location of quadrotor, xdIndicate the horizontal cross shaft reference position of quadrotor,
S32, selection liapunov function
Virtual controlling rule is designed to
zxIndicate the difference between virtual controlling input and practical control input,
Select liapunov function
To V2Virtual controlling rule is brought into wherein after derivation, is obtained
By selecting suitable cxAnd kxParameter, to ensure
5. the mixing finite time control method according to claim 4 for quadrotor Exact trajectory tracking, feature
It is, the horizontal control law of step S3 further include:
S33, horizontal vertical pivot tracking error is defined are as follows:
ey=y-yd
Wherein, y indicates the horizontal longitudinal axis physical location of quadrotor, ydIndicate the horizontal longitudinal axis reference position of quadrotor,
S34, selection liapunov function
After taking differential to it, obtain
Virtual controlling variable αyIt is designed asWherein cy> 0 is a constant,
Meanwhile available virtual controlling variable αyWithBetween error
Virtual controlling restrains vyIt is designed to:
Selection includes eyAnd zyLiapunov function be
Find out V4About the derivative of time, then by control rate vyIt brings into wherein, obtains
By selecting suitable cxAnd kxParameter, to ensure
6. the mixing finite time control method according to claim 2 for quadrotor Exact trajectory tracking, feature
It is, the accurate pose stabilization control of step S4 restrains specific design method are as follows:
S41, the posture subsystem for being built with external disturbance:
Wherein f (Ω)=[a1qr+a2qω,a3pr+a4pω,a5pq]TBe it is nonlinear,
U=[u2,u3,u4]TIt is the input vector of controller,
Matrix g is expressed as
Matrix g is the inertial matrix of quadrotor system, and element therein is all the moment of inertia,
Matrix d (t)=[d2,d3,d4]TIt is external disturbance；
S42, according to quadrotor kinetic model, design finite time disturbance observer:
ζ0=-λ1L1/3sig2/3(z0-Ω)+z1
ζ1=-λ2L1/2sig1/2(z1-ζ0)+z2
Wherein, u is the input vector of system, u=[u2, u3, u4]Tz0,z1And z2Ω, d andEstimated value, then through too long
Control, can accurately identify unknown external disturbance d within the limited time.
7. described in any item mixing finite time controlling parties for quadrotor Exact trajectory tracking according to claim 1~6
Method, which is characterized in that after the step S4 further include:
S5, to using mixing control program quadrotor unmanned vehicle model carry out simulating, verifying research, with conventional means into
Row comparison, further verifies validity and superiority.
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