CN110531777A - Quadrotor attitude control method and system based on Auto Disturbances Rejection Control Technique - Google Patents
Quadrotor attitude control method and system based on Auto Disturbances Rejection Control Technique Download PDFInfo
- Publication number
- CN110531777A CN110531777A CN201910745681.7A CN201910745681A CN110531777A CN 110531777 A CN110531777 A CN 110531777A CN 201910745681 A CN201910745681 A CN 201910745681A CN 110531777 A CN110531777 A CN 110531777A
- Authority
- CN
- China
- Prior art keywords
- control
- angular
- controller
- disturbance rejection
- control amount
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Abstract
The invention discloses a kind of quadrotor attitude control method and system based on Auto Disturbances Rejection Control Technique, can effectively improve the robustness of quadrotor gesture stability.This method realizes the angular speed ring control in gesture stability using Active Disturbance Rejection Control;In automatic disturbance rejection controller, given angular speed and angular acceleration is obtained after carrying out smoothing and noise-reducing process to given angular velocity signal using Nonlinear Tracking Differentiator;Observer uses Second Order Eso, using the feedback angular speed of controlled device and the control amount u (t- τ) of addition motor response delay, each scalariform state of angular velocity Controlling model and the inside and outside portion acted on model disturbance and the summation of system Unmarried pregnancy are observed estimation;It is made the difference using the output quantity and specified rate of observer and preliminary control amount is calculated by nonlinear Control rate, the disturbance estimator obtained using observer is compensated on the basis of the preliminary control amount, obtains final output control amount u (t).
Description
Technical field
The invention belongs to quadrotor control technology fields, are related to a kind of quadrotor based on Auto Disturbances Rejection Control Technique
Spacecraft Attitude Control and system.
Background technique
Quadrotor is the aircraft that one kind is capable of VTOL (vertical take-off and landing, VTOL),
It belongs to non co axial formula disc-shaped flying craft on total arrangement, and compared with conventional rotary aircraft, quadrotor structure is more
Compact, the lift of generation is bigger, and the opposite rotor of two pairs of rotation directions can cancel out each other anti-twisted torque, therefore not need anti-
Torque paddle.Due to quadrotor drone compared to fixed wing aircraft can VTOL, freely hover, with very strong maneuver energy
Power executes task particularly suitable for complex condition.As quadrotor drone in recent years is in the extensive of civilian and military field
Using not only increasing productivity level, while also changing the mode of operation of modern war.
Quadrotor has there are three translational degree of freedom, three rotational freedoms, total six-freedom degree, but only four
A control input.Therefore, quadrotor is a kind of typical under-actuated systems.Meanwhile quadrotor is that have by force
The quiet time-dependent system of the characteristics such as coupling, non-linear, multivariable, and will receive in low-latitude flying the effect of several physical
And wind such as disturbs at the interference of external environments, influences control effect and even results in unstability, it is therefore desirable to design a kind of reliable and stable
Positional control algorithm can guarantee a series of requirements such as stabilization and the precision of control in the case where dynamic situation is thanksed for your hospitality in the external world.
Auto Disturbances Rejection Control Technique be by Chinese Academy of Sciences's mathematics and systematic science research institute system Han Jingqing researcher
And its research group's Founding and development of leader, the idea of classic control had both been inherited and developed to Auto Disturbances Rejection Control Technique, simultaneously
The thought of modern control theory is absorbed again.So-called active disturbance rejection, refers to: Unmarried pregnancy and unknown outer disturb all are attributed to object
Unknown disturbance, estimated with inputoutput data and recompensed, to realize the dynamic feedback linearization of dynamical system, then
Nonlinear Feedback Control rule is constituted using nonlinear configurations to improve the control performance of its closed-loop system.
There is related scholar to be applied to Auto Disturbances Rejection Control Technique in the relevant control of quadrotor at present, still
Its effect need to be further strengthened.
Summary of the invention
In view of this, the defect that the present invention is poor for interference rejection ability in existing quadrotor gesture stability, provides
A kind of quadrotor attitude control method and system based on Auto Disturbances Rejection Control Technique can effectively improve quadrotor and fly
The interference rejection ability and tracking accuracy of row device entirety, so as to effectively improve the robustness of quadrotor gesture stability.
In order to solve the above-mentioned technical problem, the present invention is implemented as follows:
A kind of quadrotor attitude control method based on Auto Disturbances Rejection Control Technique is controlled using active disturbance rejection angular speed
Device realizes the angular speed ring control in gesture stability;In active disturbance rejection angular rate control unit, using Nonlinear Tracking Differentiator to given
Angular velocity signal v carries out smoothing and noise-reducing process, and by input signal itself v after smoothing and noise-reducing process1And its derivative v2As giving
Fixed angular speed and angular acceleration;Observer use Second Order Eso, use the feedback angular speed y of controlled device with
And the control amount u (t- τ) of motor response delay τ is added, it each scalariform state of angular velocity Controlling model and acts on model
The disturbance of inside and outside portion be observed estimation with the summation of system Unmarried pregnancy;The Attitude rate estimator amount z that observer is exported1
With angular speed specified rate v1It makes the difference, by Attitude rate estimator amount z1Differential obtains angular acceleration estimator and angular acceleration specified rate v2
It makes the difference, preliminary control amount u is calculated by nonlinear Control rate in two differences0, the disturbance estimator that is obtained using observer
In the preliminary control amount u0On the basis of compensate, obtain final control amount output u (t).
Preferably, the gesture stability uses double -loop control structure, and inner ring angular speed ring uses the active disturbance rejection angular speed
Controller realizes that outer ring angle ring is realized using PD angle controller.
Preferably, this method further comprises: establishing PID attitude controller;It is risen manually using the control of PID attitude controller
Journey is flown over, after aircraft enters automatic mode and steadily hovering, starts while running PID attitude controller and by active disturbance rejection angle
The active disturbance rejection attitude controller of speed control and PD angle controller composition, but at this time still using the defeated of PID attitude controller
Output is as actual output control amount;And judge the active disturbance rejection attitude controller and the counted control of PID attitude controller meter
Whether amount processed differs in a certain range, if the output quantity of active disturbance rejection attitude controller does not dissipate and the control of two controllers output
Numerical quantity differs within the set range, then is switched to the active disturbance rejection attitude controller control.
Preferably, the Nonlinear Tracking Differentiator is constructed using steepest comprehensive function fhan;In steepest comprehensive function, it is quick because
Sub- r uses 104Magnitude data, filtering factor h1Using 10-2Magnitude data.
The invention also discloses a kind of the quadrotor attitude control system based on Auto Disturbances Rejection Control Technique, the system
Including active disturbance rejection attitude controller, which includes the angle control of the angular rate control unit and outer ring of inner ring
Device;The angular rate control unit is active disturbance rejection angular rate control unit comprising Nonlinear Tracking Differentiator, observer, nonlinear Control rate
Computing module, time delay module and control- action compensation module;
Nonlinear Tracking Differentiator, for carrying out smoothing and noise-reducing process to given angular velocity signal v, after smoothing and noise-reducing process
Input signal v itself1And its derivative v2Subsequent calculating is used for as given angular speed and angular acceleration;
Time delay module is input to observation for that will export formation u (t- τ) after motor response delay τ is added in control amount u (t)
Device;
Observer uses Second Order Eso, using feedback angular speed y and the control that joins delay of controlled device
Amount u (t- τ) processed, each scalariform state of angular velocity Controlling model and the inside and outside portion acted on model disturbance are not built with system
The dynamic summation of mould is observed estimation, obtains Attitude rate estimator amount z1With disturbance estimator, and angular velocity estimator z1It carries out
Differential obtains angular acceleration estimator
Nonlinear Control rate computing module is used for Attitude rate estimator amount z1With angular acceleration estimatorWith carry out autotracking
The specified rate v of differentiator1And v2Correspondence makes the difference, and preliminary control amount u is calculated by nonlinear Control rate in two differences0;
Control- action compensation module, the disturbance estimator for being obtained using observer is in the preliminary control amount u0Basis is enterprising
Row compensation obtains final control amount output u (t).
Preferably, which further comprises PID attitude controller, switching control module and switching switch;
Switching control module, for being switched by control switching, so that PID attitude controller work in manual takeoff phase
Make;After aircraft enters automatic mode and steadily hovering, by control switching switch, so that PID attitude controller and active disturbance rejection appearance
State controller works at the same time, but at this time still using the output quantity of PID attitude controller as actual output control amount;Judgement
Whether PID attitude controller differs in a certain range with the counted control amount of active disturbance rejection attitude controller meter, if active disturbance rejection appearance
The output quantity of state controller does not dissipate and two control amount numerical value differ within the set range, then by control switching switch, switches
For the work of active disturbance rejection attitude controller.
Preferably, the Nonlinear Tracking Differentiator is constructed using steepest comprehensive function fhan;In steepest comprehensive function, it is quick because
Sub- r uses 104Magnitude data, filtering factor h1Using 10-2Magnitude data.
Compared with prior art, advantages of the present invention and good effect:
(1) in practical flight, the posture channel of quadrotor is easy to be influenced and become by various disturbance factors
It obtains unstable.The present invention be added in angular speed control ring the uncertain part of extended state observer real-time estimation position model with
And the summation of inside and outside disturbance, and further by the response time of system in view of making the estimated value obtained in the design of ESO
It is more accurate, finally this part estimated value is compensated on output control amount u, quadrotor appearance can be effectively improved
The robustness of state control.
(2) to Turbo Factor r in automatic disturbance rejection controller and filtering factor h1The restriction of value range is carried out, parameter selection is wanted
Meet delay minimum as far as possible, filtering requirements can be reduced suitably, and limiting in this way is to guarantee that the addition of differentiator will not be led
It causes entire control process excessive lag occur, avoids the oscillation of control system or even unstable.
(3) preferred embodiment of the present invention uses the scheme of active disturbance rejection attitude controller+PID attitude controller, two controllers
It uses stage by stage, takeoff phase uses PID control scheme, solves the problems, such as that takeoff phase observer is not easy to restrain, normal to fly
Row order section uses Active Disturbance Rejection Control scheme, improves the interference rejection ability and tracking accuracy of its flight.By designing reasonable switching
Control strategy guarantees that PID attitude controller is switched to the smooth transition of active disturbance rejection attitude controller handoff procedure.
Detailed description of the invention
Fig. 1 is the compound quadrotor Attitude control model based on active disturbance rejection+PID in the embodiment of the present invention;
Fig. 2 is the schematic diagram of active disturbance rejection attitude controller in Fig. 1;
Fig. 3 is the structural block diagram of active disturbance rejection angular rate control unit in Fig. 2;
Fig. 4 is the quadrotor attitude control system schematic diagram based on active disturbance rejection in the embodiment of the present invention;
Fig. 5 is to increase disturbance angleonly tracking situation (wobble shaft) in practical flight in the case of location fixes;
Fig. 6 is to increase disturbance angleonly tracking situation (pitch axis) in practical flight in the case of location fixes;
Fig. 7 is to increase disturbance control amount in practical flight in the case of location fixes to export situation (wobble shaft);
Fig. 8 is to increase disturbance control amount in practical flight in the case of location fixes to export situation (pitch axis);
Fig. 9 is that gesture stability uses composite controller position tracking circular trace situation (dividing x, y-axis) in practical flight;
Figure 10 is that gesture stability uses composite controller position tracking circular trace situation in practical flight.
Specific embodiment
The preferred embodiment of the present invention provides a kind of quadrotor gesture stability side based on Auto Disturbances Rejection Control Technique
Case, due to quadrotor unmanned vehicle posture kinetic model be a multivariable, close coupling, nonlinear second-order model, therefore
In order to control the convenience with adjustment parameter, dual-loop controller, the i.e. angular speed of the angle controller including outer ring and inner ring are designed
Controller, to control its posture.Through analyzing, the model uncertainty of quadrotor and disturbance are considered as whole
It is applied on inner ring angular speed ring, therefore general PD control device is still taken to outer ring angle ring, and to inner ring angular speed ring design
Active disturbance rejection angular rate control unit.Active disturbance rejection angular rate control unit+PD angle controller constitutes active disturbance rejection attitude controller.
Design for inner ring active disturbance rejection angular rate control unit, it is defeated to outer ring angle controller using Nonlinear Tracking Differentiator first
Control amount out is used as inner ring angular speed given value after carrying out smoothing and noise-reducing process, and derivation obtains inner ring angular acceleration and gives
Value then designs a Second Order Eso, and the present invention is to the control amount u acted on Second Order Eso
(t) it is improved, joined motor response and be delayed to guarantee that each variable for being input to observer matches alignment in time,
And then real-time and accurately the inside and outside portion of each scalariform state of inner ring angular speed Controlling model and effect on the mold can be disturbed
The dynamic summation with system Unmarried pregnancy is observed estimation;Second Order Eso can estimate angular velocity, through micro-
Divide available angular acceleration estimated value;Second Order Eso can also total disturbance quantity suffered by estimating system;Angular speed
Preliminary control amount is calculated by nonlinear Control rate with the error of corresponding estimated value with angular acceleration given value, the preliminary control
After the disturbance estimator that Second Order Eso is estimated is added in amount processed, final control amount output is obtained, to realize
Excellent control to system.
As it can be seen that it is to acting on Second Order Eso that active disturbance rejection angular rate control unit, which designs maximum improvement,
Control amount u (t) improved, joined and represent control amount and generate to the time delay between feedback, so that input
Each variable to observer matches alignment in time, so as to the real-time accurately disturbance of estimating system and gives compensation.
It is easy further, since takeoff phase quadrotor attitudes vibration is larger so that observer diverging causes control to be lost
Surely, therefore the preferred embodiment is normally taken off in takeoff phase using the control of PID attitude controller, is switched again after its posture is steady
For Active Disturbance Rejection Control.Guarantee that PID attitude controller is switched to automatic disturbance rejection controller handoff procedure by design switching control strategy
Smooth transition.
The present invention will now be described in detail with reference to the accompanying drawings and examples.
Fig. 1 is the compound quadrotor gesture stability structure based on active disturbance rejection+PID in the embodiment of the present invention, packet
Active disturbance rejection attitude controller and PID attitude controller are included, the two is switched over using switching switch.
Fig. 2 is the specific schematic diagram of active disturbance rejection attitude controller in Fig. 1.Active disturbance rejection attitude controller is a double -loop control
Device, i.e. outer ring angle controller and inner ring angular rate control unit, to control its posture.Through analyzing, quadrotor nobody fly
The model uncertainty of row device and disturbance are considered as all being applied on inner ring angular speed ring, therefore outer ring angle ring still takes one
As PD angle controller, only to inner ring angular speed ring design active disturbance rejection angular rate control unit.
Fig. 3 is the concrete composition block diagram of active disturbance rejection angular rate control unit in Fig. 2.Compared with existing automatic disturbance rejection controller, increase
Time delay link is added.
It is described below for design and workflow of the invention.
One, quadrotor attitude dynamics model is initially set up, kinetic model is described below:
Wherein, four independent control input quantities, U2For wobble shaft control amount, U3For pitch axis control amount, U4For yaw axis
Control amount, φ, θ, ψ respectively represent the rolling of body posture, pitching, Eulerian angles of the yaw axis under inertial coodinate system, Ixx,Iyy,
IzzRespectively represent the rotary inertia of corresponding channel, JrRotary inertia related with gyroscopic effect is represented, l is represented from each motor
Brachium of the heart to body center.It is non-linear it can be seen that three channels have multivariable, the characteristics of close coupling, therefore generally three
A channel need to separately design corresponding automatic disturbance rejection controller compensate between each channel intercoupling effect and it is suffered
Inside and outside disturbance.
The Controlling model of each axis is described below:
Wherein, x1,x2Respectively represent the state variable of system model, the i.e. value of the angle of corresponding channel and angular speed, f
(x1,x2, w (t), t) represent system model uncertain part and system suffered by inside and outside disturbance summation, bu (t- τ) represent
It exports control amount and considers that executing agency responds the part on time-lag action to system model, wherein τ is the system response delay time,
B is the estimated value of control amount amplification factor in system model.For the control in each channel, the main object of the present invention is exactly to the greatest extent
F (x may quickly and accurately be estimated1,x2, w (t), t) and b, so that finally can be accurate on the basis of PD angle controller
Rapidly the uncertain and disturbance part of model is fallen in compensation.
Two, according to the model of above-mentioned foundation, the Nonlinear Tracking Differentiator in Auto Disturbances Rejection Control Technique gesture stability is designed.
The Nonlinear Tracking Differentiator form is as follows:
Fh=fhan (v1(k)-v(k),v2(k),r,h1)
v1(k+1)=v1(k)+h2v2(k)
v2(k+1)=v2(k)+h2fh
Wherein, input signal v (k) here is to input discrete signal, v1(k) and v2(k) input signal sheet is tracked respectively
Body and its derivative, v1It (k) is the angular velocity information of tracking, v2(k) it is the angular acceleration information of tracking, is v1(k) derivative.
Fhan be steepest comprehensive function, expression formula referring to document 1 (Auto Disturbances Rejection Control Technique, Han Jingqing, " front line science " 20071,
Total 1st phase).r,h1Respectively represent Turbo Factor and filtering factor, h2Represent step factor.Here parameter selection will be as far as possible
It is minimum to meet delay, filtering requirements can be reduced suitably, it is believed that as long as not occurring the king-sized ladder of amplitude or spiking
It can be used, therefore Turbo Factor r of the invention uses 104Magnitude data, filtering factor h1Using 10-2Magnitude data.
Three, it according to quadrotor position control model, designs Second Order Eso (ESO) and considers to be added
System response delay time, the disturbance being applied on inner ring angular speed ring for real-time estimation simultaneously give real-time compensation.
The present invention designs each scalariform state that Second Order Eso is used for observation system, while estimating real system institute
The inside and outside disturbance received, and real-time compensation is given, to enhance the robustness of system.
The Second Order Eso specifically designed is shown below:
E=z1-y
Wherein, y is the value of feedback of real system, i.e., the magnitude of angular velocity that each channel returns.z1Represent this symptom of system
State, i.e., the magnitude of angular velocity in each channel;z2The variable for as characterizing system expansion state, contains the uncertainty of system model
And the summation of suffered inside and outside overall disturbance, the z2Value arrives for compensation after being multiplied with 1/b and exports control amount u (t).Bu generation
Table is applied to the control amount on model, and b is the estimated value of control amount amplification factor in system model, and u is the output of this control program
Control amount, and bu (t- τ) represents the control amount for considering that motor response delay is input to system model, due to the value of feedback y of system
Delay is had contemplated that after system, so that the signals of all input observers is realized synchronization in this way, obtained estimated value is just more
Accurately.Wherein τ represents the action time delay of control amount.
The substantially observer system that is still an error-driven, β01,β02For two observer gains, with system
Sampling step length is related.Theoretically the gain of observer is the bigger the better, and observation speed can be made to accelerate, uncertain to system to realize
Property and the real-time compensation of disturbance, reach an ideal control effect, but due to being passed in practical quadrotor system
Sensor noise is larger, therefore the selection of observer gain cannot be too big, otherwise can amplification system noise, be not easy observer
The case where convergence even dissipates.Ideal effect can be obtained by testing adjusting parameter.
Four, the Attitude rate estimator amount z obtained according to quadrotor Attitude control model obtained above and observer1, with
The angular speed specified rate v that track differentiator obtains1, available error e1And the differential e of error2。
e1=v1-z1
Five, by angular speed and angular acceleration error e1、e2Preliminary control amount u is calculated by nonlinear Control rate0。
For nonlinear Control rate, the present invention uses the form such as following formula:
u0=b1fal(e1,α1,δ1)+b2fal(e2,α2,δ2)
Wherein b1,b2Flow gain is respectively controlled, fal (e, α, δ) is a nonlinear function, the following institute of expression
Show:
Since gamma controller theoretically has " small error, large gain;The characteristic of big error, small gain ", therefore be added
A small amount of non-linear partial can slightly improve the performance of former controller, therefore the value near α, δ selection one reasonable 1 is
It can.
Six, it according to the basic principle of Active Disturbance Rejection Control, obtains the system control rate inside and outside compensating after disturbance and is shown below:
Wherein,It is that total disturbed value that Second Order Eso is estimated compensates the part into control amount.b
It is the estimated value of control amount amplification factor in system model, u is the reality output of this control program.
When in use, for the Controlling model of Fig. 1, reasonable controller switchover policy is designed, may be implemented to fly manually
The smooth transition between active disturbance rejection attitude controller used using PID attitude controller and automatic flight.Its switching control plan
Basic ideas slightly are as follows: after taking off manually using PID attitude controller and enter the basicly stable hovering of automatic mode, start simultaneously
PID attitude controller and active disturbance rejection attitude controller are run, but at this time still using the output quantity of PID attitude controller as practical
Output control amount;Start to judge that the two counts whether counted control amount differs in a certain range at this time, if active disturbance rejection posture
The output quantity of controller does not dissipate and two control amount numerical value differ in a certain range, cuts it may be considered that once carrying out controller
Change theoretically be not in the output of biggish control amount fluctuation, then be switched to the work of active disturbance rejection attitude controller;If active disturbance rejection
Attitude controller diverging or two control amount gaps are larger, then cannot switch, until meeting switching condition.
Based on above method process, the quadrotor appearance based on Auto Disturbances Rejection Control Technique that the present invention also provides a kind of
State control system, as shown in Figure 1, including that active disturbance rejection attitude controller, PID attitude controller, switching control module and switching are opened
It closes.
Switching control module is in manual takeoff phase, by control switching switch, so that PID attitude controller works;Fly
After row device enters automatic mode and steadily hovering, by control switching switch, so that PID attitude controller and active disturbance rejection gesture stability
Device works at the same time, but at this time still using the output quantity of PID attitude controller as actual output control amount;Judge PID posture
Whether controller differs in a certain range with counted two control amount of active disturbance rejection attitude controller meter, if the control based on active disturbance rejection
The output quantity of device processed does not dissipate and two controllers calculate the control amount numerical value difference obtained in a certain range, then is cut by control
Switch is changed, the work of active disturbance rejection attitude controller is switched to.
Active disturbance rejection attitude controller uses double -loop control structure, including inner ring angular speed ring and outer ring angle ring;Inner ring angle
Speed ring realizes that outer ring angle ring is realized using PD angle controller using active disturbance rejection angular rate control unit.On as shown in figure 4,
Stating active disturbance rejection angular rate control unit includes Nonlinear Tracking Differentiator, observer, nonlinear Control rate computing module, time delay module and control
Measure compensating module.
Nonlinear Tracking Differentiator, for carrying out smoothing and noise-reducing process to given angular velocity signal v, after smoothing and noise-reducing process
Input signal v itself1And its derivative v2Subsequent calculating is used for as given angular speed and angular acceleration;
Time delay module is input to observation for that will export formation u (t- τ) after motor response delay τ is added in control amount u (t)
Device;
Observer uses Second Order Eso, using feedback angular speed y and the control that joins delay of controlled device
Amount u (t- τ) processed, each scalariform state of angular velocity Controlling model and the inside and outside portion acted on model disturbance are not built with system
The dynamic summation of mould is observed estimation, obtains Attitude rate estimator amount z1With disturbance estimator, and angular velocity estimator z1It carries out
Differential obtains angular acceleration estimator
Nonlinear Control rate computing module is used for Attitude rate estimator amount z1With angular acceleration estimatorWith carry out autotracking
The specified rate v of differentiator1And v2Correspondence makes the difference, and preliminary control amount u is calculated by nonlinear Control rate in two differences0;
Control- action compensation module, the disturbance estimator for being obtained using observer is in the preliminary control amount u0Basis is enterprising
Row compensation obtains final control amount output u (t).
In order to verify above-mentioned design the Compound Control Technique quadrotor attitude controller based on active disturbance rejection+PID it is effective
Property, the present invention carries out practical flight experiment using the quadrotor based on QAV-250 rack.
Quadrotor is based primarily upon the winged control of ANO-Pioneer open source and is developed in experiment, utilizes the machine of QAV-250
Frame is built.This flies control and is based on STM32F407VG master controller, and highest dominant frequency is used up to 168MHz, inertia measuring module
ICM20602 module, dynamical system use EMAX MT2204KV2300 DC brushless motor, EMAX Sinonk 12A electronics tune
Fast device and 5045 blades.Gross mass is about 650g when body flight, and the load quality for applying disturbance is about 150g.
It is right in location fixes in order to verify the excellent Immunity Performance of inner ring attitude controller in practical flight experiment
Practical quadrotor applies a degree of disturbance, observes posture rolling, the angular response feelings in two channels of pitching respectively
Condition as shown in Figure 5,6, and is analyzed the control amount in corresponding two channels, as shown in Figure 7,8.
In entire flight course, 0s-15s aircraft is in without the floating state that obviously disturbs, and when 15s flies in quadrotor
A load is hung on one horn of row device, and level side not of uniform size is applied to suspension load during 15s-40s
To disturbance, when 40s removes suspension load, is left time aircraft still in floating state.As can be seen that 15s from Fig. 5,6
The angular error of the rolling of aircraft and pitch channel considers the influence base of sensor error when aircraft is in floating state before
Originally be maintained at+- 1deg within, the control precision of the automatic disturbance rejection controller is higher when illustrating in floating state.Apply one when 15s
When the more gentle disturbance of a larger but variation, it can be seen that the angular error in two channels is not applying horizontal direction to load
In the case where the excessive measurement error for changing as violent disturbance and considering sensor, angular error stilled remain in+-
Within 3deg, even if being applied with a more violent disturbance to suspension load level direction in 33s or so, it can be seen that angle
It is still within controllable state, and error is in acceptable range, whole process control delay is lower, illustrates the observer
Performance is more excellent, and the quick and precisely estimation to larger more violent disturbance may be implemented and compensate, reached certain anti-interference
The requirement of ability.
It can be seen that floating state under normal circumstances from Fig. 7,8 simultaneously, the output of two channel controllers is essentially
Zero, 15s suspension load after, observer quickly estimates the disturbance, be embodied in control amount then show as control amount compared with
To reach a stationary value rapidly and smoothly, when 33s applies acutely disturbance, slightly shaken though control amount output has,
Still it restrains quickly, and the output of control amount at this time is close to saturation state, it can be seen that controller still has under limiting condition
There is relatively stable performance, has reached the expected requirement for controlling precision and robustness for it.
In terms of position control, as shown in Figures 9 and 10, using this based on the attitude controller of auto-disturbance rejection technology as bottom control
Device, outer ring use a non-linear placement controller, track a circular trace, it can be seen that it is in x, y two axial controls
Precision controlling is delayed in+- 5cm, and substantially without tracing control, and general effect is good, and precision is comparable to being even more than general PID
Attitude controller, but to be far superior to general PID attitude controller in interference rejection ability.
In conclusion the above is merely preferred embodiments of the present invention, being not intended to limit the scope of the present invention.
All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should be included in of the invention
Within protection scope.
Claims (7)
1. a kind of quadrotor attitude control method based on Auto Disturbances Rejection Control Technique, which is characterized in that use active disturbance rejection
Angular rate control unit realizes the angular speed ring control in gesture stability;In active disturbance rejection angular rate control unit, using tracking differential
Device carries out smoothing and noise-reducing process to given angular velocity signal v, and by input signal itself v after smoothing and noise-reducing process1And its
Derivative v2As given angular speed and angular acceleration;Observer uses Second Order Eso, using controlled device
Feed back angular speed y and be added motor response delay τ control amount u (t- τ), each scalariform state of angular velocity Controlling model and
The summation of the disturbance of inside and outside portion and system Unmarried pregnancy that act on model is observed estimation;The angle that observer is exported
Velocity estimation amount z1With angular speed specified rate v1It makes the difference, by Attitude rate estimator amount z1Differential obtains angular acceleration estimator and adds with angle
Speed preset amount v2It makes the difference, preliminary control amount u is calculated by nonlinear Control rate in two differences0, obtained using observer
Estimator is disturbed in the preliminary control amount u0On the basis of compensate, obtain final control amount output u (t).
2. the method as described in claim 1, which is characterized in that the gesture stability uses double -loop control structure, inner ring angle speed
It spends ring to realize using the active disturbance rejection angular rate control unit, outer ring angle ring is realized using PD angle controller.
3. method according to claim 2, which is characterized in that this method further comprises: establishing PID attitude controller;It adopts
Manual take-off process is controlled with PID attitude controller, after aircraft enters automatic mode and steadily hovering, starts while running
PID attitude controller and the active disturbance rejection attitude controller being made of active disturbance rejection angular rate control unit and PD angle controller, but this
When still use the output quantity of PID attitude controller as actual output control amount;And judge the active disturbance rejection attitude controller
Whether differed in a certain range with the counted control amount of PID attitude controller meter, if the output quantity of active disturbance rejection attitude controller
It does not dissipate and the control amount numerical value of two controllers output differs within the set range, be then switched to the active disturbance rejection attitude controller
Control.
4. the method as described in claim 1, which is characterized in that the Nonlinear Tracking Differentiator uses steepest comprehensive function fhan structure
It builds;In steepest comprehensive function, Turbo Factor r uses 104Magnitude data, filtering factor h1Using 10-2Magnitude data.
5. a kind of quadrotor attitude control system based on Auto Disturbances Rejection Control Technique, which includes active disturbance rejection posture control
Device processed, which is characterized in that the active disturbance rejection attitude controller includes the angular rate control unit of inner ring and the angle controller of outer ring;Institute
Stating angular rate control unit is active disturbance rejection angular rate control unit comprising Nonlinear Tracking Differentiator, observer, nonlinear Control rate calculate mould
Block, time delay module and control- action compensation module;
Nonlinear Tracking Differentiator, for carrying out smoothing and noise-reducing process to given angular velocity signal v, by the input after smoothing and noise-reducing process
Signal v itself1And its derivative v2Subsequent calculating is used for as given angular speed and angular acceleration;
Time delay module is input to observer for that will export formation u (t- τ) after motor response delay τ is added in control amount u (t);
Observer uses Second Order Eso, using the feedback angular speed y and the control amount u that joins delay of controlled device
(t- τ), each scalariform state of angular velocity Controlling model and act on model inside and outside portion disturbance with system Unmarried pregnancy
Summation be observed estimation, obtain Attitude rate estimator amount z1With disturbance estimator, and angular velocity estimator z1Differential is carried out to obtain
Obtain angular acceleration estimator
Nonlinear Control rate computing module is used for Attitude rate estimator amount z1With angular acceleration estimatorWith carry out autotracking differential
The specified rate v of device1And v2Correspondence makes the difference, and preliminary control amount u is calculated by nonlinear Control rate in two differences0;
Control- action compensation module, the disturbance estimator for being obtained using observer is in the preliminary control amount u0On the basis of mended
It repays, obtains final control amount output u (t).
6. system as claimed in claim 5, which is characterized in that the system further comprises PID attitude controller, switching control
Module and switching switch;
Switching control module, for being switched by control switching in manual takeoff phase, so that PID attitude controller works;Fly
After row device enters automatic mode and steadily hovering, by control switching switch, so that PID attitude controller and active disturbance rejection gesture stability
Device works at the same time, but at this time still using the output quantity of PID attitude controller as actual output control amount;Judge PID posture
Whether controller differs in a certain range with the counted control amount of active disturbance rejection attitude controller meter, if active disturbance rejection attitude controller
Output quantity do not dissipate and two control amount numerical value difference within the set range, then by control switching switch, be switched to active disturbance rejection
Attitude controller work.
7. system as claimed in claim 5, which is characterized in that the Nonlinear Tracking Differentiator uses steepest comprehensive function fhan structure
It builds;In steepest comprehensive function, Turbo Factor r uses 104Magnitude data, filtering factor h1Using 10-2Magnitude data.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201910745681.7A CN110531777B (en) | 2019-08-13 | 2019-08-13 | Four-rotor aircraft attitude control method and system based on active disturbance rejection control technology |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN201910745681.7A CN110531777B (en) | 2019-08-13 | 2019-08-13 | Four-rotor aircraft attitude control method and system based on active disturbance rejection control technology |
Publications (2)
Publication Number | Publication Date |
---|---|
CN110531777A true CN110531777A (en) | 2019-12-03 |
CN110531777B CN110531777B (en) | 2020-11-10 |
Family
ID=68663084
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN201910745681.7A Active CN110531777B (en) | 2019-08-13 | 2019-08-13 | Four-rotor aircraft attitude control method and system based on active disturbance rejection control technology |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN110531777B (en) |
Cited By (20)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111103890A (en) * | 2019-12-17 | 2020-05-05 | 西北工业大学 | High-precision strong-robustness approach landing guidance control method |
CN111413865A (en) * | 2020-03-05 | 2020-07-14 | 清华大学 | Disturbance compensation single-loop superheated steam temperature active disturbance rejection control method |
CN111443724A (en) * | 2020-04-20 | 2020-07-24 | 中南大学 | Control method of quad-rotor unmanned aerial vehicle based on active-disturbance-rejection hybrid switching control |
CN111522352A (en) * | 2020-05-09 | 2020-08-11 | 广东工业大学 | Design method of single-parameter active disturbance rejection attitude controller of multi-rotor aircraft |
CN111523076A (en) * | 2020-03-24 | 2020-08-11 | 中国人民解放军军事科学院评估论证研究中心 | Method, device and system for calculating angular acceleration based on Fal function |
CN112034871A (en) * | 2020-08-25 | 2020-12-04 | 南京航空航天大学 | Omnidirectional control method of tiltable multi-rotor aircraft |
CN112666959A (en) * | 2020-11-30 | 2021-04-16 | 航天科工火箭技术有限公司 | Attitude stability control method for carrier rocket in attitude instability state |
CN112947058A (en) * | 2021-03-19 | 2021-06-11 | 中国科学院数学与系统科学研究院 | Active disturbance rejection type PID parameter adjusting method for airplane three-axis angular rate control |
CN112965505A (en) * | 2021-01-29 | 2021-06-15 | 广东汇天航空航天科技有限公司 | Manned aircraft flight attitude control method and system and manned aircraft |
CN113138612A (en) * | 2020-07-28 | 2021-07-20 | 西安天和防务技术股份有限公司 | Active disturbance rejection control method and device for astronomical navigation and electronic equipment |
CN113204193A (en) * | 2021-05-06 | 2021-08-03 | 北京航空航天大学 | Fault-tolerant control method and device for aircraft and electronic equipment |
CN113341943A (en) * | 2020-03-03 | 2021-09-03 | 天津大学 | Repeated operation type unmanned vehicle trajectory tracking control algorithm based on total disturbance instant observation and iterative learning |
CN113419562A (en) * | 2021-07-13 | 2021-09-21 | 天津大学 | Height control method of quad-rotor unmanned aerial vehicle under variable load |
CN113466483A (en) * | 2021-06-17 | 2021-10-01 | 北京控制工程研究所 | On-line intelligent diagnosis method for satellite angular velocity abnormal fault under condition of no gyroscope |
CN113515142A (en) * | 2020-04-10 | 2021-10-19 | 北京三快在线科技有限公司 | Unmanned aerial vehicle trajectory tracking control method and device, unmanned aerial vehicle and storage medium |
CN114153193A (en) * | 2021-11-29 | 2022-03-08 | 北京航天自动控制研究所 | Polarity fault identification method combining extended state observer and BP neural network |
CN115202213A (en) * | 2022-08-02 | 2022-10-18 | 北京理工大学 | Four-rotor aircraft control method based on active disturbance rejection control |
CN115390512A (en) * | 2022-09-08 | 2022-11-25 | 上海交通大学 | Flexible gantry double-drive system and electric-coupling decoupling motion control method thereof |
CN116232282A (en) * | 2023-01-12 | 2023-06-06 | 湖南大学无锡智能控制研究院 | Time-varying time delay estimation method, device and system based on adaptive all-pass filter |
CN116700359A (en) * | 2023-08-08 | 2023-09-05 | 兰笺(苏州)科技有限公司 | Unmanned aerial vehicle disturbance control method and device under load change condition |
Citations (11)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6227482B1 (en) * | 1998-03-27 | 2001-05-08 | Futaba Denshi Kogyo Kabushiki Kaisha | Gyroscope for remote-controlled helicopters |
CN102324746A (en) * | 2011-06-07 | 2012-01-18 | 江苏威凡智能电气科技有限公司 | A kind of high-voltage chain type STATCOM power unit module DC bus-bar voltage control method based on Auto Disturbances Rejection Control Technique |
CN102830622A (en) * | 2012-09-05 | 2012-12-19 | 北京理工大学 | Auto-disturbance-rejection automatic flight control method for four-rotor aircraft |
CN103777641A (en) * | 2014-02-19 | 2014-05-07 | 北京理工大学 | Compound active-disturbances-rejection control method of tracking control over aircraft |
CN104865968A (en) * | 2015-04-22 | 2015-08-26 | 浙江工业大学 | Quad-rotor aircraft hovering control method employing cascade auto disturbances rejection control technology |
CN106444812A (en) * | 2016-10-26 | 2017-02-22 | 华南智能机器人创新研究院 | Attitude control method and system based on quad-rotor unmanned helicopter |
CN106933104A (en) * | 2017-04-21 | 2017-07-07 | 苏州工业职业技术学院 | A kind of quadrotor attitude based on DIC PID and the mixing control method of position |
EP3097013A4 (en) * | 2014-01-21 | 2017-09-27 | Sikorsky Aircraft Corporation | Rotor moment feedback for stability augmentation |
CN107943070A (en) * | 2017-11-01 | 2018-04-20 | 贾杰 | A kind of unmanned helicopter active disturbance rejection flying speed and attitude control method |
CN108958270A (en) * | 2017-05-18 | 2018-12-07 | 成都天府新区光启未来技术研究院 | Aircraft Auto-disturbance-rejection Control and device |
CN109459934A (en) * | 2019-01-15 | 2019-03-12 | 华北电力大学 | A method of depression of order automatic disturbance rejection controller parameter is adjusted based on PID controller |
-
2019
- 2019-08-13 CN CN201910745681.7A patent/CN110531777B/en active Active
Patent Citations (11)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6227482B1 (en) * | 1998-03-27 | 2001-05-08 | Futaba Denshi Kogyo Kabushiki Kaisha | Gyroscope for remote-controlled helicopters |
CN102324746A (en) * | 2011-06-07 | 2012-01-18 | 江苏威凡智能电气科技有限公司 | A kind of high-voltage chain type STATCOM power unit module DC bus-bar voltage control method based on Auto Disturbances Rejection Control Technique |
CN102830622A (en) * | 2012-09-05 | 2012-12-19 | 北京理工大学 | Auto-disturbance-rejection automatic flight control method for four-rotor aircraft |
EP3097013A4 (en) * | 2014-01-21 | 2017-09-27 | Sikorsky Aircraft Corporation | Rotor moment feedback for stability augmentation |
CN103777641A (en) * | 2014-02-19 | 2014-05-07 | 北京理工大学 | Compound active-disturbances-rejection control method of tracking control over aircraft |
CN104865968A (en) * | 2015-04-22 | 2015-08-26 | 浙江工业大学 | Quad-rotor aircraft hovering control method employing cascade auto disturbances rejection control technology |
CN106444812A (en) * | 2016-10-26 | 2017-02-22 | 华南智能机器人创新研究院 | Attitude control method and system based on quad-rotor unmanned helicopter |
CN106933104A (en) * | 2017-04-21 | 2017-07-07 | 苏州工业职业技术学院 | A kind of quadrotor attitude based on DIC PID and the mixing control method of position |
CN108958270A (en) * | 2017-05-18 | 2018-12-07 | 成都天府新区光启未来技术研究院 | Aircraft Auto-disturbance-rejection Control and device |
CN107943070A (en) * | 2017-11-01 | 2018-04-20 | 贾杰 | A kind of unmanned helicopter active disturbance rejection flying speed and attitude control method |
CN109459934A (en) * | 2019-01-15 | 2019-03-12 | 华北电力大学 | A method of depression of order automatic disturbance rejection controller parameter is adjusted based on PID controller |
Non-Patent Citations (5)
Title |
---|
BAOHUA LU等: "State Estimation and Fault Detection for Nonlinear Dynamic Systems", 《PROCEEDINGS OF THE 37TH CHINESE CONTROL CONFERENCE》 * |
LING ZHAO等: "Attitude control for quadrotors subjected to wind disturbances via active disturbance rejection control and integral sliding mode control", 《MECHANICAL SYSTEMS AND SIGNAL PROCESSING》 * |
孔大庆: "基于自抗扰控制技术的四旋翼飞行控制系统研究", 《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》 * |
李杰等: "自抗扰控制: 研究成果总结与展望", 《控制理论与应用》 * |
王彪等: "基于改进自抗扰技术的四旋翼姿态控制", 《系统仿真学报》 * |
Cited By (31)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN111103890A (en) * | 2019-12-17 | 2020-05-05 | 西北工业大学 | High-precision strong-robustness approach landing guidance control method |
CN111103890B (en) * | 2019-12-17 | 2022-11-11 | 西北工业大学 | High-precision strong-robustness approach landing guiding control method |
CN113341943A (en) * | 2020-03-03 | 2021-09-03 | 天津大学 | Repeated operation type unmanned vehicle trajectory tracking control algorithm based on total disturbance instant observation and iterative learning |
CN111413865A (en) * | 2020-03-05 | 2020-07-14 | 清华大学 | Disturbance compensation single-loop superheated steam temperature active disturbance rejection control method |
CN111413865B (en) * | 2020-03-05 | 2021-07-13 | 清华大学 | Disturbance compensation single-loop superheated steam temperature active disturbance rejection control method |
CN111523076A (en) * | 2020-03-24 | 2020-08-11 | 中国人民解放军军事科学院评估论证研究中心 | Method, device and system for calculating angular acceleration based on Fal function |
CN113515142A (en) * | 2020-04-10 | 2021-10-19 | 北京三快在线科技有限公司 | Unmanned aerial vehicle trajectory tracking control method and device, unmanned aerial vehicle and storage medium |
CN111443724B (en) * | 2020-04-20 | 2022-03-11 | 中南大学 | Control method of quad-rotor unmanned aerial vehicle based on active-disturbance-rejection hybrid switching control |
CN111443724A (en) * | 2020-04-20 | 2020-07-24 | 中南大学 | Control method of quad-rotor unmanned aerial vehicle based on active-disturbance-rejection hybrid switching control |
CN111522352A (en) * | 2020-05-09 | 2020-08-11 | 广东工业大学 | Design method of single-parameter active disturbance rejection attitude controller of multi-rotor aircraft |
CN111522352B (en) * | 2020-05-09 | 2022-07-26 | 广东工业大学 | Design method of single-parameter active disturbance rejection attitude controller of multi-rotor aircraft |
CN113138612A (en) * | 2020-07-28 | 2021-07-20 | 西安天和防务技术股份有限公司 | Active disturbance rejection control method and device for astronomical navigation and electronic equipment |
CN112034871A (en) * | 2020-08-25 | 2020-12-04 | 南京航空航天大学 | Omnidirectional control method of tiltable multi-rotor aircraft |
CN112034871B (en) * | 2020-08-25 | 2022-05-24 | 南京航空航天大学 | Omnidirectional control method of tiltable multi-rotor aircraft |
CN112666959A (en) * | 2020-11-30 | 2021-04-16 | 航天科工火箭技术有限公司 | Attitude stability control method for carrier rocket in attitude instability state |
CN112965505A (en) * | 2021-01-29 | 2021-06-15 | 广东汇天航空航天科技有限公司 | Manned aircraft flight attitude control method and system and manned aircraft |
WO2022160618A1 (en) * | 2021-01-29 | 2022-08-04 | 广东汇天航空航天科技有限公司 | Passenger drone flight posture control method and system, and passenger drone |
CN112947058A (en) * | 2021-03-19 | 2021-06-11 | 中国科学院数学与系统科学研究院 | Active disturbance rejection type PID parameter adjusting method for airplane three-axis angular rate control |
CN112947058B (en) * | 2021-03-19 | 2022-07-22 | 中国科学院数学与系统科学研究院 | Active disturbance rejection type PID parameter adjusting method for airplane three-axis angular rate control |
CN113204193A (en) * | 2021-05-06 | 2021-08-03 | 北京航空航天大学 | Fault-tolerant control method and device for aircraft and electronic equipment |
CN113466483A (en) * | 2021-06-17 | 2021-10-01 | 北京控制工程研究所 | On-line intelligent diagnosis method for satellite angular velocity abnormal fault under condition of no gyroscope |
CN113419562B (en) * | 2021-07-13 | 2022-03-29 | 天津大学 | Height control method of quad-rotor unmanned aerial vehicle under variable load |
CN113419562A (en) * | 2021-07-13 | 2021-09-21 | 天津大学 | Height control method of quad-rotor unmanned aerial vehicle under variable load |
CN114153193A (en) * | 2021-11-29 | 2022-03-08 | 北京航天自动控制研究所 | Polarity fault identification method combining extended state observer and BP neural network |
CN115202213A (en) * | 2022-08-02 | 2022-10-18 | 北京理工大学 | Four-rotor aircraft control method based on active disturbance rejection control |
CN115202213B (en) * | 2022-08-02 | 2023-05-12 | 北京理工大学 | Four-rotor aircraft control method based on active disturbance rejection control |
CN115390512A (en) * | 2022-09-08 | 2022-11-25 | 上海交通大学 | Flexible gantry double-drive system and electric-coupling decoupling motion control method thereof |
CN115390512B (en) * | 2022-09-08 | 2023-05-30 | 上海交通大学 | Flexible gantry double-drive system and electromechanical combined decoupling motion control method thereof |
CN116232282A (en) * | 2023-01-12 | 2023-06-06 | 湖南大学无锡智能控制研究院 | Time-varying time delay estimation method, device and system based on adaptive all-pass filter |
CN116232282B (en) * | 2023-01-12 | 2023-12-19 | 湖南大学无锡智能控制研究院 | Time-varying time delay estimation method, device and system based on adaptive all-pass filter |
CN116700359A (en) * | 2023-08-08 | 2023-09-05 | 兰笺(苏州)科技有限公司 | Unmanned aerial vehicle disturbance control method and device under load change condition |
Also Published As
Publication number | Publication date |
---|---|
CN110531777B (en) | 2020-11-10 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
CN110531777A (en) | Quadrotor attitude control method and system based on Auto Disturbances Rejection Control Technique | |
CN110531776B (en) | Four-rotor aircraft position control method and system based on active disturbance rejection control technology | |
Tal et al. | Accurate tracking of aggressive quadrotor trajectories using incremental nonlinear dynamic inversion and differential flatness | |
CN110119089B (en) | Immersion constant flow pattern self-adaptive quad-rotor control method based on integral sliding mode | |
Liu et al. | Modeling, autopilot design, and field tuning of a UAV with minimum control surfaces | |
CN104898429A (en) | Tri-rotor attitude control method based on auto-disturbance rejection controller | |
CN111258216B (en) | Sliding mode repetitive controller suitable for four-rotor aircraft | |
Yu et al. | Attitude tracking control of a quadrotor UAV in the exponential coordinates | |
CN108873929A (en) | A kind of fixed wing aircraft autonomous landing on the ship method and system | |
CN109507890A (en) | A kind of unmanned plane dynamic inverse generalized predictive controller based on ESO | |
CN112578805B (en) | Attitude control method of rotor craft | |
CN111522356B (en) | Strong-robustness full-envelope integrated control method for tilt rotor unmanned aerial vehicle | |
CN113778129A (en) | Hypersonic speed variable sweepback wing aircraft tracking control method with interference compensation | |
Capello et al. | Mini quadrotor UAV: design and experiment | |
CN110647160A (en) | Flight control method and device for aircraft | |
CN110673623B (en) | Quad-rotor unmanned aerial vehicle landing method based on dual-ring PD control algorithm control | |
CN109976364B (en) | Attitude decoupling control method for six-rotor aircraft | |
Xu et al. | Learning pugachev's cobra maneuver for tail-sitter uavs using acceleration model | |
Liu et al. | Application of the improved incremental nonlinear dynamic inversion in fixed-wing UAV flight tests | |
Hegde et al. | Transition flight modeling and robust control of a VTOL unmanned quad tilt-rotor aerial vehicle | |
Zhang et al. | Application of total energy control on vertical take-off and landing UAV | |
Harikumar et al. | Design and experimental validation of a robust output feedback control for the coupled dynamics of a micro air vehicle | |
CN110209179A (en) | A kind of prompt high track algorithm of hypersonic aircraft | |
Liang et al. | Tailsitter VTOL flying wing aircraft attitude control | |
González-Hernández et al. | Super-twisting control scheme for a miniature quadrotor aircraft: Application to trajectory-tracking problem |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination | ||
GR01 | Patent grant | ||
GR01 | Patent grant |