CN110161840A - A kind of mobile robot speed decoupling disturbance rejection control device based on linear active disturbance rejection - Google Patents
A kind of mobile robot speed decoupling disturbance rejection control device based on linear active disturbance rejection Download PDFInfo
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Abstract
A kind of mobile robot speed decoupling disturbance rejection control device based on linear active disturbance rejection, which comprises the steps of: step 1) establishes the mathematical model of mobile robot forward speed and turning velocity driving；Step 2) carries out the static decoupling of speed to mathematical model；The design of step 3) speed dynamic decoupling disturbance rejection control device.The present invention can effectively promote the movenent performance of wheeled mobile robot.
Description
Technical field
The invention belongs to wheeled robot movement control technology fields, are related to wheeled mobile robot forward speed and turn
Specifically how control to speed, eliminate the coupled problem of robot forward speed and turning velocity control, and eliminates system
Influence of the inside and outside disturbance to speed control, realizes a kind of wheeled mobile robot for being based on linear active disturbance rejection (LADRC)
Speed decouples disturbance rejection control device.
Background technique
Two wheel guide robot mobile robot control is simple, and movement flexibly, is widely used in the fields such as service, logistics, detection,
With extremely wide application prospect.The drive system of two wheel guide robot formula wheeled mobile robot is made of two driving wheels in left and right, often
There is independent power source on a driving wheel, robot motion is driven by controlling the speed of left and right sidesing driving wheel, so that robot
It can complete a series of movement instruction.
In practical applications, such as in the flying track conjecture of robot, positioning and motion control, the motion state one of robot
As be to be described by forward speed and turning velocity, the revolving speed of two-wheeled is by can just obtain forward speed and turn after kinematic transform
To speed.In view of the load difference of left and right two-wheeled and the elastic differentiated wheels of transmission system are engaged the factors such as difference, work as machine
The position of centre of gravity of people in center or is not in asymmetric state, forward speed and turning velocity and is coupled, and makes
The control for obtaining forward speed and turning velocity can not be separately adjustable.
Patent CN201710623784.7 gives a kind of corner of wheeled mobile robot and the PID control side of speed
Case, but there is no the decoupling regulation problems for solving forward speed and turning velocity.
Summary of the invention
It is a primary object of the present invention to overcome two wheel guide robot wheeled mobile robot forward speed in the prior art and
Coupled problem between turning velocity provides a kind of mobile robot speed decoupling disturbance rejection control based on linear active disturbance rejection
Device can effectively promote the movenent performance of wheeled mobile robot.
The present invention adopts the following technical scheme:
A kind of mobile robot speed decoupling disturbance rejection control device based on linear active disturbance rejection, which is characterized in that including as follows
Step:
Step 1) establishes the mathematical model of mobile robot forward speed and turning velocity driving；
Step 2) carries out the static decoupling of speed to mathematical model；
The design of step 3) speed dynamic decoupling disturbance rejection control device.
The mathematical model are as follows:
Wherein GwL、GwRThe respectively driving model of mobile robot left and right driving wheel, uL、uRRespectively left and right driving wheel
The voltage input of brshless DC motor, v are the forward speed of mobile robot, and w is the steering angular velocity of mobile robot.
The static decoupling of the speed is specific as follows:
The inverse matrix transformation of a speed static matrix transformation is introduced, it is as follows
Wherein uv、uwFor the forward speed of robotically-driven model and the control amount of turning velocity, after introducing inverse matrix transformation
Robot forward speed and the mathematical model of turning velocity driving become:
The speed dynamic decoupling disturbance rejection control device design is specific as follows:
3.1) extended state observer is designed,
Wherein z1,z2,z3It is the state variable of extended state observer, yzFor the output of observer, l1=3 ωo,For the benefit of extended state observer, x1=v, bL0For bLEstimated value, bLJoin for the model of left driving wheel
Number；
3.2) controller is combined using linear PD, and the form of controller is
u0=kp(v*-z1)-kdz2
Wherein,kd=2 ωcFor the gain of controller, ωcFor controller bandwidth, u0For the output of PD control device；
3.3) system disturbance estimation compensation and state feedback are constructed, obtaining Active Disturbance Rejection Control rule is
By the above-mentioned description of this invention it is found that compared with prior art, the invention has the following beneficial effects:
The present invention by establish mobile robot forward speed and turning velocity driving mathematical model, be re-introduced into a speed
The static coupling that static decoupling matrices reduce forward speed and turning velocity is spent, is then designed dynamic based on linear active disturbance rejection
Disturbance inside and outside coupling terms and system is come out simultaneously feedback compensation as total disturbance observation, realized to moving machine by state decoupling controller
The decoupling disturbance rejection control of device people's speed can effectively promote the movenent performance of wheeled mobile robot.
Detailed description of the invention
Fig. 1 is two wheel guide robot wheeled mobile robot opened loop control block diagram；
Fig. 2 is two wheel guide robot wheeled mobile robot opened loop control block diagram after static decoupling；
The second-order active disturbance rejection controller structural block diagram of Fig. 3 forward speed v；
Fig. 4 is the active disturbance rejection decoupling anti-interference structural block diagram of forward speed v and turning velocity w；
Fig. 5 open cycle system uvInfluence of the dynamic change to w；
Fig. 6 open cycle system uwInfluence of the dynamic change to v；
Fig. 7 is based on v when LADRC decoupling disturbance rejection control*Influence of the dynamic change to w；
Fig. 8 is based on w when LADRC decoupling disturbance rejection control*Influence of the dynamic change to v；
Immunity Performance of the Fig. 9 based on LADRC decoupling disturbance rejection control and PID control；
Below in conjunction with the drawings and specific embodiments, the invention will be further described.
Specific embodiment
Below by way of specific embodiment, the invention will be further described.
Fig. 1 is two wheel guide robot wheeled mobile robot opened loop control block diagram, by the electricity for controlling left and right brshless DC motor
Signal is pressed to control left and right sidesing driving wheel speed, then left and right sidesing driving wheel speed converts to obtain robot by a static matrix
Forward speed and turning velocity.
Fig. 2 is that two-wheeled is poor after introducing the inverse matrix transformation that a speed static matrix converts before the control input quantity of motor
Fast wheeled mobile robot opened loop control block diagram.
Fig. 3 is the second-order active disturbance rejection controller structural block diagram of forward speed v, by designing extended state observer (ESO),
Coupling terms are treated as into a kind of disturbance, and are come out simultaneously instead with the internal disturbance of system and external disturbance as total disturbance observation of system
Feedback compensation, realizes the decoupling disturbance rejection control to mobile robot forward speed.
Kind of the invention decouples disturbance rejection control device based on the mobile robot speed of linear active disturbance rejection, and specific implementation includes such as
Lower step:
Step 1) establishes the mathematical model of mobile robot forward speed and turning velocity driving:
The drive system for the two wheel guide robot wheeled mobile robot that the present invention considers is by two independent brushless dcs
Machine driving, consider that no-load condition motor speed Second Order state equation is respectively as follows:
In formulaWherein ω is the revolving speed of motor, RsFor electricity
The resistance of machine, LsFor the inductance of motor, J is the rotary inertia of rotor, BvFor the coefficient of viscosity, keFor back EMF coefficient, kt
For torque coefficient, u is the voltage signal of motor.
The speed Second Order state equation of so robot left and right wheels driving motor is respectively
Wherein ωL, ωRFor the revolving speed of left and right driving motor.
Robot forward speed and turning velocity are transformed by left and right sidesing driving wheel speed, and transformation matrix is
Wherein v indicates the forward speed of wheeled mobile robot, and w indicates the steering angular velocity of robot；L indicates robot
The distance between two driving wheels of left and right；vLIndicate the linear velocity of revolver；vRIndicate the linear velocity of right wheel.
The linear velocity v of wheeled mobile robot driving wheelL、vRWith the rotational speed omega of brshless DC motorL、ωRThere is only certain
Proportionate relationship
Wherein r is driving wheel radius, npFor motor number of pole-pairs, knFor the reduction ratio of retarder, kwFor wheel linear velocity and electricity
The conversion coefficient of machine angular speed.It is G by the driving model that formula (1) can write out mobile robot driving wheelw
The mathematical model of so available mobile robot forward speed and turning velocity driving:
Wherein GwL、GwRThe respectively driving model of mobile robot left and right sidesing driving wheel.uL、uRRespectively left and right sidesing driving wheel without
The voltage input of brushless motor.There is larger for the off-diagonal element of the driving model of robot forward speed and turning velocity
Coupling terms caused by coupling due to speed static matrix the reason is that converted, and couple serious.It is easily detected by two driving of control
The control amount u of motorL、uR, to control the forward speed and turning velocity of robot.
The static decoupling of step 2) speed
The inverse matrix transformation of a speed static matrix transformation is introduced before the control input quantity of motor, it is as follows
Wherein uv、uwFor the forward speed of robotically-driven model and the control amount of turning velocity, after introducing inverse matrix transformation
The driving model of robot forward speed and turning velocity becomes.
For formula (9) compared to formula (6) as can be seen that the amount of intercoupling of formula (9) is smaller, the introducing of inverse matrix transformation has reached one
The effect of a static decoupling.If wheeled mobile robot left and right sidesing driving wheel driving model GwL=GwRWhen, G12=G21=0, and G11
=G22=GwL=GwR, work as GwL≠GwRWhen, G12、G21It is not zero, the driving model of robot forward speed and turning velocity exists
Coupling terms, and model difference is bigger, couples more serious.
The design of step 3) speed dynamic decoupling disturbance rejection control device
In conjunction with the static matrix transformation and inverse matrix transformation of speed, the Second Order state equation of available v, w, as follows respectively
It is shown
A in formulaL1、aL0、bLFor the model parameter of left driving wheel, aR1、aR0、bRFor the model parameter of right driving wheel, and size
It is unknown.Define w is to the coupling of vV is to the coupling of wAnd the equivalent external disturbance d of consideration amount drive systemv、dw, then have
From the second-order model of formula (11) wheeled mobile robot forward speed v and turning velocity w, it is easy the control of discovery v and w
There is the d that intercouples between simulationvwAnd dwvIf by coupling terms treat as a kind of disturbance, and with the internal disturbance of system and
External disturbance comes out as total disturbance observation of system and feedback compensation, can be achieved with the decoupling of forward speed v and turning velocity w
Control.Specific design process is as follows
3.1) design extended state observer enables b by taking forward speed v as an exampleL0For bLEstimated value, then have
WhereinIt outer disturb, interior disturb and coupling terms for contain system
Summation disturbance.Definition status variable x1=v,x3=fv, then system is represented by
Its extended state observer is constructed for formula (13)
Wherein z1,z2,z3It is the state variable of extended state observer, yzFor the output of observer, l1=3 ωo, For the benefit of extended state observer.By designing suitable observer bandwidth parameter, expansion state can be made
The convergence of observer observation error, there is z1→ v, z3→fv。
3.2) controller is combined using linear PD, and the form of controller is
u0=kp(v*-z1)-kdz2 (15)
Wherein,kd=2 ωcFor the gain of controller, ωcFor controller bandwidth, u0For the output of PD control device.
3.3) system disturbance estimation compensation and state feedback further, are constructed, obtaining Active Disturbance Rejection Control rule is
In practical engineering applications, control output limitation must be taken into consideration in system, therefore actual control amount is
This example chooses two motor model G having differenceswLAnd GwR, as follows
System open loop is emulated, l=0.4 in emulation gives u respectivelyv、uwConstant obtains the step response of v and w, respectively
U is given at t=2s the and t=4s momentvSpline smoothing observes its influence to w, and same another group at t=2s the and t=4s moment
Given uwSpline smoothing observes its influence to v.Simulation result is as shown in Figure 5 and Figure 6.
The control block diagram of Fig. 4 is built in simulations, designs suitable LADRC parameter in simulations, is then set step and is rung
Answer the v of dynamic change*And w*, the step response of v and w are obtained, gives v at t=2s the and t=4s moment respectively*Spline smoothing is seen
Its influence to w is examined, same another group gives Spline smoothing at t=2s the and t=4s moment, observes its influence to v.Emulation knot
Fruit is as shown in Figure 7 and Figure 8.
Finally emulated for the immunity characteristic of method, in t=2s, be based respectively on LADRC decoupling disturbance rejection control and
PID control inputs u in systemvThe vulnerability to jamming based on LADRC decoupling disturbance rejection control device is analyzed in the upper disturbance that same size is added
Can, simulation result is as shown in Figure 9.
The above is only a specific embodiment of the present invention, but the design concept of the present invention is not limited to this, all to utilize this
Design makes a non-material change to the present invention, and should all belong to behavior that violates the scope of protection of the present invention.
Claims (4)
1. a kind of mobile robot speed based on linear active disturbance rejection decouples disturbance rejection control device, which is characterized in that including walking as follows
It is rapid:
Step 1) establishes the mathematical model of mobile robot forward speed and turning velocity driving；
Step 2) carries out the static decoupling of speed to mathematical model；
The design of step 3) speed dynamic decoupling disturbance rejection control device.
2. a kind of mobile robot speed based on linear active disturbance rejection as described in claim 1 decouples disturbance rejection control device, special
Sign is, the mathematical model are as follows:
Wherein GwL、GwRThe respectively driving model of mobile robot left and right driving wheel, uL、uRRespectively left and right driving wheel is brushless
The voltage input of direct current generator, v are the forward speed of mobile robot, and w is the steering angular velocity of mobile robot.
3. a kind of mobile robot speed based on linear active disturbance rejection as described in claim 1 decouples disturbance rejection control device, special
Sign is that the static decoupling of the speed is specific as follows:
The inverse matrix transformation of a speed static matrix transformation is introduced, it is as follows
Wherein uv、uwFor the forward speed of robotically-driven model and the control amount of turning velocity, machine after inverse matrix transformation is introduced
People's forward speed and the mathematical model of turning velocity driving become:
4. a kind of mobile robot speed based on linear active disturbance rejection as described in claim 1 decouples disturbance rejection control device, special
Sign is that the speed dynamic decoupling disturbance rejection control device design is specific as follows:
3.1) extended state observer is designed,
Wherein z1,z2,z3It is the state variable of extended state observer, yzFor the output of observer, l1=3 ωo,For the benefit of extended state observer, x1=v, bL0For bLEstimated value, bLJoin for the model of left driving wheel
Number；
3.2) controller is combined using linear PD, and the form of controller is
u0=kp(v*-z1)-kdz2
Wherein,kd=2 ωcFor the gain of controller, ωcFor controller bandwidth, u0For the output of PD control device；
3.3) system disturbance estimation compensation and state feedback are constructed, obtaining Active Disturbance Rejection Control rule is
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| CN111965969A (en) * | 2020-08-19 | 2020-11-20 | 华侨大学 | Double closed-loop anti-interference PID control method and system for speed and position of direct current motor |
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Cited By (2)
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| CN111965969A (en) * | 2020-08-19 | 2020-11-20 | 华侨大学 | Double closed-loop anti-interference PID control method and system for speed and position of direct current motor |
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