CN107247464B - A kind of the state constraint control method and system of quadrotor unmanned vehicle - Google Patents
A kind of the state constraint control method and system of quadrotor unmanned vehicle Download PDFInfo
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Abstract
The invention discloses a kind of state constraint control methods of quadrotor unmanned vehicle, which comprises location information, velocity information, posture information and the angular velocity information of step 1) acquisition t moment aircraft；Step 2) calculates the position tracking error and speed tracing error of t moment according to ideal trajectory, and thus control law F among design t+1 moment position；Step 3) designs the control lift T at t+1 moment according to control rate F among the position at t+1 moment；Control lift T of the step 4) according to the t+1 moment, the ideal pose and ideal angular speed at calculating aircraft t+1 moment；Step 5) calculates attitude error and angular speed error according to ideal pose and desirable angle speed；Step 6) designs control law β among the posture at t+1 moment, and thus designs the control moment Γ at t+1 moment, and aircraft is made to reach ideal pose and ideal angular speed at the t+1 moment.Method of the invention is described attitude of flight vehicle using unit quaternion, improves computational efficiency；And improve control precision.
Description
Technical field
The present invention relates to unmanned vehicle fields, and in particular to a kind of state constraint controlling party of quadrotor unmanned vehicle
Method and system.
Background technique
Quadrotor unmanned vehicle is a kind of small-sized unmanned aircraft by four motor driven rotor flyings, is had motor-driven
Property is strong, compact-sized, can be with VTOL and hovering the advantages that, has obtained widely answering in numerous areas in recent years
With.Simultaneously as drive lacking characteristic possessed by its internal system: there are four control input has and there are six controlled volume tools, making
Obtaining the design analysis to quadrotor unmanned aerial vehicle control system has certain difficulty, therefore in terms of theoretical research, four rotations
The controller design of wing unmanned vehicle and analysis are also a research hotspot.
The model of existing quadrotor unmanned vehicle mostly uses greatly Eulerian angles that posture is described, it may occur that Euler
Unusual appearance makes control law fail；Meanwhile Eulerian angles progress attitude description can introduce trigonometric function operation, so that point of system
It analyses increasingly complex；Secondly, existing control method can only guarantee the constringency performance of error, and to the error change of dynamic process
Situation does not account for, although system is stablized, error may have exceeded permissible range in the process of tracking, cannot
Meet control to require, so that control program fails；In addition, the model of system is simplified in conventional control technology,
Modeling error is not only introduced, but also has merely ensured that the respective stability of position and posture, there is no to position and posture
Between coupling analyzed, the stability of closed-loop system is not proven.
Summary of the invention
It is an object of the invention to overcome drawbacks described above existing for the control method of current quadrotor unmanned vehicle, consider
Has many advantages, such as computational efficiency height to unit quaternion, convenient for the design and analysis of system, method of the invention uses unit four
First several pairs of attitude of flight vehicle are described, and avoid Euler's unusual appearance, and barrier constraint letter is introduced in design control law
Number, so that the error of system is limited in specified range, ensure that the precision of track following.
To achieve the above object, the invention proposes a kind of state constraint control method of quadrotor unmanned vehicle, institutes
The method of stating includes:
Location information, velocity information, posture information and the angular velocity information of step 1) acquisition t moment aircraft；
Step 2) calculates the position tracking error and speed tracing error of t moment according to ideal trajectory, and thus designs t+1
Control law F among moment position；
Step 3) designs the control lift T at t+1 moment according to control rate F among the position at t+1 moment；
Control lift T of the step 4) according to the t+1 moment, the ideal pose and ideal angular speed at calculating aircraft t+1 moment；
Step 5) calculates attitude error and angular speed error according to ideal pose and desirable angle speed；
Step 6) designs control law β among the posture at t+1 moment, and thus designs the control moment Γ at t+1 moment, makes to fly
Row device reaches ideal pose and ideal angular speed at the t+1 moment.
In above-mentioned technical proposal, the step 2) specifically:
If the location information of the aircraft of t moment is p, velocity information v, ideal trajectory information is respectively pdWith vd, definition
Position tracking error isSpeed tracing error is
Then control law F among the moment position t+1 are as follows:
Wherein kb1,kb2> 0, the maximum set value allowed by position tracking error and speed tracing error, kz> 0 is control
Gain processed.
In above-mentioned technical proposal, the step 3) specifically:
F, which is projected in inertial coodinate system, to be indicated are as follows: F=(Fx,Fy,Fz)T, then lift T is controlled are as follows:
Wherein, m is the quality of aircraft.
In above-mentioned technical proposal, the step 4) specifically:
DefinitionUnit quaternionFor the ideal appearance of quadrotor
State, ηdFor QdScalar component, ωdFor the ideal angular speed of aircraft；
Then ηdAre as follows:
Ideal angular speed is ωdAre as follows:
Wherein, I3For the unit diagonal matrix of three ranks, S (qd) it is 3 × 3 skew symmetric matrixes:
In above-mentioned technical proposal, the step 5) specifically:
If the posture information of the aircraft of t moment is unit quaternary number Q=(qT,η)T=(q1,q2,q3,η)T, q=(q1,
q2,q3)TFor the vector section of Q, η is the scalar component of Q；Angular velocity information is ω=(ωx,ωy,ωz)T；
The coordinate system established using the posture Q of aircraft is the body coordinate system of aircraft, with the ideal pose Q of aircraftd
The coordinate system of foundation is the ideal coordinates system of aircraft, then the posture between the body coordinate system of aircraft and ideal coordinates system is missed
DifferenceAnd angular speed errorAre as follows:
Wherein,For the spin matrix of ideal coordinates system to body coordinate system,
In:
R (Q)=(η2-||q||2)I3+2qqT-2ηS(q)
R(Qd)=(ηd 2-||qd||2)I3+2qdqd T-2ηdS(qd)
Q=(qT,η)T=(q1,q2,q3,η)T, q=(q1,q2,q3)T；ω=(ωx,ωy,ωz)T。
In above-mentioned technical proposal, the step 6) specifically:
Define matrixAre as follows:
IfFor inertial matrix,
Control law among the posture of design are as follows:
Wherein, kβ> 0 is control gain,
Column vector
Design control moment Γ are as follows:
Wherein, intermediate variable Ω:kΩ> 0 is control gain,
M1For diagonal matrix:
If when t=0,First three items be respectively as follows:Then kb31、kb32、kb33All for greater than zero
Constant, and meet
A kind of state constraint control system of quadrotor unmanned vehicle, including memory, processor and it is stored in storage
Computer program that is on device and can running on a processor, which is characterized in that the processor is realized when executing described program
The step of above method.
Present invention has an advantage that
1, method of the invention is described attitude of flight vehicle using unit quaternion, improves computational efficiency, avoids
Unusual appearance；
2, basis (such as cavern, the narrow interior space) under certain narrow environments appoints quadrotor drone track following
The required precision of business needs to limit speed and the position of unmanned plane at this time, guarantees the precision of track following, method of the invention
By introducing barrier constraint function, designs controller (being divided into positioner and attitude controller), guarantee location tracking
The required precision of error and Velocity Pursuit error, to avoid the generation of collision indirectly.
Detailed description of the invention
Fig. 1 is quadrotor structure chart；
Fig. 2 a is the x-axis error tracking figure of simulation example；
Fig. 2 b is the y-axis error tracking figure of simulation example；
Fig. 2 c is the z-axis error tracking figure of simulation example；
Fig. 3 a is the x-axis velocity error tracing figure of simulation example；
Fig. 3 b is the y-axis velocity error tracing figure of simulation example；
Fig. 3 c is the z-axis velocity error tracing figure of simulation example；
Fig. 4 is the space three-dimensional track following figure of simulation example；
Fig. 5 a is the quaternary number q of simulation exampled1Tracing figure；
Fig. 5 b is the quaternary number q of simulation exampled2Tracing figure；
Fig. 5 c is the quaternary number q of simulation exampled3Tracing figure；
Fig. 5 d is the quaternary number η of simulation exampledTracing figure.
Specific embodiment
The present invention will be described in detail in the following with reference to the drawings and specific embodiments.
A kind of state constraint control method of quadrotor unmanned vehicle, which comprises
Step 1) establishes the kinetics equation of quadrotor drone aircraft；
As shown in Figure 1, defining the coordinate system E={ e that direction is north, east, ground1,e2,e3It is inertial reference system；Define origin
Before quadrotor geometric center direction is, it is right, under coordinate system B={ b1,b2,b3It is body coordinate system, it is fixed to be all satisfied the right hand
Then.In order to avoid Euler's unusual appearance and operation efficiency is improved, the posture of aircraft is described using unit quaternion.Define unit
Quaternary number isWherein claimFor unit quaternary number vector section, claimFor unit four
Each component of first number scalar component, unit quaternion meets qTq+η2=1.To be sat from inertial coodinate system to ontology
The spin matrix of system is marked, is defined as:
R (Q)=(η2-||q||2)I3+2qqT-2ηS(q) (1)
Wherein I3For the unit diagonal matrix of three ranks, | | | | it is the European norm of vector.S (q) is 3 × 3 skew symmetric matrixes:
The structure of quadrotor is as shown in Figure 1, its kinematics and dynamic differential equation indicate are as follows:
Formula (2) is referred to as location subsystem, and formula (3) is posture subsystem.Wherein, m is vehicle mass, and g is gravity acceleration
Degree,For inertial matrix,For body angular speed.Fly for quadrotor to be designed
Row device inputs lift,For input torque to be designed.
Observation type (2) is it is found that control input is T, and system state variables are p, and the dimension of control amount is less than system mode
The dimension in space, therefore location subsystem is a under-actuated systems.Observation type (3) is it is found that control input is Γ, aircraft appearance
State variable is unit quaternary number Q=(qT,η)T=(q1,q2,q3,η)T, q=(q1,q2,q3)TFor the vector section of Q, η is the mark of Q
Measure part；Angular velocity information is ω=(ωx,ωy,ωz)T；, which drives entirely.In order to enable a system to tracking one
Three-dimensional ideal trajectoryOne reasonable control target is to guarantee position p=(px,py,pz)TAnd some
Tracking of the attitude angle to instruction, remaining two attitude angle are stayed calm or are servo-actuated.
DefinitionFor the ideal pose of quadrotor, ωdFor machine
The ideal angular speed of body.Attitude error between body coordinate system and ideal coordinates systemAnd angular speed errorAre as follows:
Wherein,For the spin matrix of ideal coordinates system to body coordinate system,
Derivative relation meetsWherein:
R (Q)=(η2-||q||2)I3+2qqT-2ηS(q)
R(Qd)=(ηd 2-||qd||2)I3+2qdqd T-2ηdS(qd)
Quaternary number Q=(qT,η)T=(q1,q2,q3,η)T, q=(q1,q2,q3)T；Angular velocity information is ω=(ωx,ωy,
ωz)T。
Step 2) designs intermediate control law；
By the differential equation and Fig. 2 of location subsystem it is found that the direction of T always with the vertical pivot b of body coordinate system3Altogether
Line can not track three-dimensional ideal trajectory only by T simultaneously.Therefore, to have in particular moment quadrotor certain
Specific posture, to utilize ideal pose QdLift T is projected on each axis of inertial coodinate system to generate component.
Lift T is combined into ideal pose Q required for the momentd, can synthesize a three-dimensional control force is
Defining position tracking error isSpeed tracing error isControl law among design position
F is
Wherein kb1,kb2> 0, the maximum set value allowed by location error and velocity error, kz> 0 is control gain.
Using intermediate control law (6), can systematic error finally be met
Wherein,Subscript " j " is vector x, y, the side z under inertial coodinate system
To component.
The solution of step 3) control lift T
Formula (6) illustrates the variation of F actual value, after obtaining location information p and velocity information v, believes with ideal trajectory
Cease pdWith vdAvailable location error is made the difference respectivelyWithThe value of F at various moments to known to.But F is only one
A virtual intermediate control force, is by T and QdIt synthesizes to obtain by the operation relation of formula (5), if therefore wanting the F in formula (6)
Act on system, it is necessary to by the anti-size for solving actual control lift T of formula (5), and be driven by motor and generate lift T reality
Now to the control of system.
In order to solve T, component of the F in each reference axis of inertial coodinate system is used, projecting in inertial coodinate system indicates
Are as follows: F=(Fx,Fy,Fz)T.Formula (5) is expanded into
Control law F among position, which is substituted into formula (2), to be obtained:
Wherein:
Indicate the posture Q and ideal pose Q of current quadrotor dronedTo position
It is influenced caused by system, the error caused by spin matrix is
For known (Fx,Fy,Fz)T, targeted attitude is solved by above formulaAnd actual lift
T, totally five unknown quantitys.Again because of QdMeet the constraint of unit vector, therefore there are four unknown quantitys for the practical tool of above-mentioned equation group, do not have
There is unique solution.One group of solution in order to obtain can fix QdIn some component enable q without loss of generalityd3=0, then:
By the summed square of above formula front two row, can obtain:
It is solved an equation (12) by method of completing the square, an available solution are as follows:
Since the modulus value of unit quaternion is 1, substituting into formula (11) can be obtained:
Formula (13) substitution formula (14) can be obtained:
Therefore, after the design for completing the F as described by formula (6), actual control lift T can be solved are as follows:
Step 4) ideal poseSolution
Formula (16) are substituted into formula (13), solve ηdAre as follows:
The first two equation of convolution (11), can solve:
According to unit quaternion kinematical equation, available ideal angular speed is ωdAre as follows:
The design of step 5) control moment Γ；
Design control moment Γ carrys out tracking step 4 below) obtained ideal pose.
According to the definition of the quaternary number kinematical equation in formula (3) and attitude error in formula (4), the appearance of model can establish
State error system is as follows:
Wherein,MatrixIs defined as:
IfFor inertial matrix；
Control law β among posture is introduced, is enabled
Derivation can obtain
Then
Design control law among posture are as follows:
Wherein, kβ> 0 is control gain, column vector
Final design control moment Γ are as follows:
Wherein, kΩ> 0 is control gain, diagonal matrix
If when t=0,First three items be respectively as follows:Then kb31、kb32、kb33All for greater than zero
Constant, and meet
Stability analysis:
The quadrotor unmanned vehicle model as described in formula (2) and formula (3), control input by formula (6), formula (16) and
Formula (25), (26) are given, work as initial errorAndMeet
It can prove the equal bounded of all signals of closed-loop system,Asymptotic convergence to zero point, and
It proves as follows:
Construct lyapunov function
Formula (30) derivation is obtained
Wherein,kb31, kb32, kb33
For the constant greater than zero.
Control law formula (6), formula (16) and formula (25), (26) are substituted into formula (31), are obtained
Again because of M1Positive definite diagonal matrix, thereforeAgain because of kz、α、kβ、kΩIt is all larger than zero, whenWhen, haveΩ ≡ 0,ThereforeResult is substituted into equation (26) and substitutes into posture sub-system error
Known to equation (22)Result is substituted into known to location subsystem error equation
Therefore, the equalization point of closed-loop system isR (Q)=I3.According to LaSalle invariant set
Principle it is found that as t → ∞,
Lemma 1: it is directed to error dynamics systematic (34):
WhereinThere are continuously differentiable and the function V of positive definite1And V2, kbi> 0, i=1,2.Such as set position
For x1, speed x2, define location error e1=x1-yd, velocity errorMeet ei→-kbiOr ei→kbi
When, there is Vi(zi)→∞.Assuming that | e1(0) | < kbi, takeIf meeting formula (35)
Then | ei(t) | < kbi,
According to lemma 1, formula (29) available proof.
Simulating, verifying:
Taking quality is m=0.5kg；Acceleration of gravity is g=9.8m/s2；Inertial matrix are as follows:
If=diag (0.039,0.039,0.012) kgm2.Control gain are as follows: kz=5, kb1=0.6, kb2=0.3,
kb31=0.6, kb32=0.6, kb33=0.6, kβ=20, kΩ=10.System variable original state are as follows:
P (0)=(0,0,0)TM, v (0)=(0,0,0)TM/s,
Reference locus are as follows: pd=(0.5cos (t), 0.5sin (t), t/10)Tm.The following Fig. 2 a of simulation result, Fig. 2 b, figure
2c, Fig. 3 a, Fig. 3 b, Fig. 3 c, Fig. 4, Fig. 5 a, Fig. 5 b, Fig. 5 c and Fig. 5 d.
Above-described specific embodiment has carried out further the purpose of the present invention, technical scheme and beneficial effects
It is described in detail, it should be understood that being not intended to limit the present invention the foregoing is merely a specific embodiment of the invention
Protection scope, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should all include
Within protection scope of the present invention.
Claims (2)
1. a kind of state constraint control method of quadrotor unmanned vehicle, which comprises
Location information, velocity information, posture information and the angular velocity information of step 1) acquisition t moment aircraft；
Step 2) calculates the position tracking error and speed tracing error of t moment according to ideal trajectory, and thus designs the t+1 moment
Control law F among position；
Step 3) designs the control lift T at t+1 moment according to control rate F among the position at t+1 moment；
Control lift T of the step 4) according to the t+1 moment, the ideal pose and ideal angular speed at calculating aircraft t+1 moment；
Step 5) calculates attitude error and angular speed error according to ideal pose and desirable angle speed；
Step 6) designs control law β among the posture at t+1 moment, and thus designs the control moment Γ at t+1 moment, makes aircraft
Reach ideal pose and ideal angular speed at the t+1 moment；
The step 2) specifically:
If the location information of the aircraft of t moment is p, velocity information v, ideal trajectory information is respectively pdWith vd, define position
Tracking error isSpeed tracing error is
Then control law F among the moment position t+1 are as follows:
Wherein kb1,kb2> 0, the maximum set value allowed by position tracking error and speed tracing error, kz> 0 is that control increases
Benefit；
The step 3) specifically:
F, which is projected in inertial coodinate system, to be indicated are as follows: F=(Fx,Fy,Fz)T, then lift T is controlled are as follows:
Wherein, m is the quality of aircraft；
The step 4) specifically:
DefinitionUnit quaternionFor the ideal pose of quadrotor, ηdFor
QdScalar component, ωdFor the ideal angular speed of aircraft；
Then ηdAre as follows:
According to unit quaternion kinematical equation, ideal angular speed is ωdAre as follows:
Wherein, I3For the unit diagonal matrix of three ranks, S (qd) it is 3 × 3 skew symmetric matrixes:
The step 5) specifically:
If the posture information of the aircraft of t moment is unit quaternary number Q=(qT,η)T=(q1,q2,q3,η)T, q=(q1,q2,q3)T
For the vector section of Q, η is the scalar component of Q；Angular velocity information is ω=(ωx,ωy,ωz)T；
The coordinate system established using the posture Q of aircraft is the body coordinate system of aircraft, with the ideal pose Q of aircraftdIt establishes
Coordinate system is the ideal coordinates system of aircraft, then the attitude error between the body coordinate system of aircraft and ideal coordinates systemWith
And angular speed errorAre as follows:
Wherein,For the spin matrix of ideal coordinates system to body coordinate system, in which:
R (Q)=(η2-||q||2)I3+2qqT-2ηS(q)
R(Qd)=(ηd 2-||qd||2)I3+2qdqd T-2ηdS(qd)
Q=(qT,η)T=(q1,q2,q3,η)T, q=(q1,q2,q3)T, ω=(ωx,ωy,ωz)T；
The step 6) specifically:
Define matrixAre as follows:
IfFor inertial matrix, in the posture of design
Between control law are as follows:
Wherein, kβ> 0 is control gain,
Column vector
Design control moment Γ are as follows:
Wherein, intermediate variable Ω:kΩ> 0 is control gain,
M1For diagonal matrix:
If when t=0,First three items be respectively as follows:Then kb31、kb32、kb33It is all normal greater than zero
Number, and meet
2. a kind of state constraint control system of quadrotor unmanned vehicle, including memory, processor and it is stored in memory
On and the computer program that can run on a processor, which is characterized in that the processor realizes power when executing described program
Benefit requires the step of 1 the method.
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