CN107168064A - A kind of wheel type mobile stage robot on-line optimization stabilized control method - Google Patents
A kind of wheel type mobile stage robot on-line optimization stabilized control method Download PDFInfo
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- CN107168064A CN107168064A CN201710467447.3A CN201710467447A CN107168064A CN 107168064 A CN107168064 A CN 107168064A CN 201710467447 A CN201710467447 A CN 201710467447A CN 107168064 A CN107168064 A CN 107168064A
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
- G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
- G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
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Abstract
A kind of wheel type mobile stage robot on-line optimization stabilized control method, point stabilization needs are realized under the conditions of nonholonomic constraint for wheel type mobile stage robot, pass through the rank kinetic model of discrete time three for defining wheel type mobile stage robot and randomly selected initial time finite time window control sequence first, calculate gradient of the point stabilization error sequence and error sequence in time window on control input sequence, Newton method is recycled to set up the update mechanism of each sampling instant control sequence, and combine rolling optimization control principle, calculate the control input amount in each sampling instant, realize the point stabilization of wheel type mobile stage robot.The advantage of design method of the present invention is to understand simple, few arrange parameter, highly versatile and easy in line computation, meets the requirement of real-time of the quick point stabilization of wheel type mobile stage robot.
Description
Technical field
The present invention relates to a kind of wheel type mobile stage robot on-line optimization stabilized control method.
Background technology
Stage performance art has turned into the important component of China's daily culture life, wherein wheel type mobile stage machine
People is that one of important stage property of high-quality stage performance art is presented.Generally when song is performed, stage robot needs basis
The change of performance song moves quickly into specified target location.Fitup robot quickly reaches specified location, can be considered shifting
The point stabilization problem of mobile robot.The target of point stabilization be obtain a Feedback Control Laws so that fitup robot gradually
It is near to reach target location.But there is nonholonomic constraint limitation in wheel type mobile stage robot, constant quiet when arbitrary smooth is continuous
State state feedback control law all can not driving wheel-type fitup robot reach the target location specified, this is waved to wheel type mobile
The point stabilization of platform robot proposes challenge.Pass through the inspection of the document to existing wheeled mobile robot stabilized control method
Suo Faxian, wheel type mobile stage robot stabilized control method mainly has：Discontinuous point stabilization, time-varying point stabilization, mix
Point stabilization and model prediction point stabilization, but discontinuous point stabilization, time-varying point stabilization and mix point stabilization and can not locate
Physical constraint and the moving section limitation of wheel type mobile stage robot actuating mechanism are managed, model prediction point stabilization needs online
The Hessian matrixes of object function are constructed, on-line calculation is very big, and these control methods understand complicated, control effect
Convergence rate is slow.Because wheel type mobile stage robot, which needs to be reached according to song change, specifies stage position, control on time
Requirement of real-time is high, and wheel type mobile stage robot is a typical nonholonomic constraint control system again, therefore, although
The research of wheel type mobile stage robot point stabilization achieves some achievements, but in recent years related scholar and performing art expert for this
Individual challenging important problem has still carried out a large amount of meticulously researchs and inquired into, to meet current high-quality stage performance
An urgent demand of the art to easy, the flexible point stabilization of wheel type mobile stage robot.
The content of the invention
In order to overcome the arrange parameter of existing wheel type mobile stage robot stabilized control method it is many, line computation it is complicated and
Realize difficult deficiency, the present invention, which is provided, a kind of to be understood that directly perceived, design is simple, is easy to wheel type mobile stage machine in line computation
People's on-line optimization stabilized control method.
The technical solution adopted for the present invention to solve the technical problems is：
A kind of wheel type mobile stage robot on-line optimization stabilized control method, the control method comprises the following steps：
1) the discrete time kinetic model of wheel type mobile stage robot moving process, is set up, referring to formula (1)：
Wherein, normal number TsThe sampling period is represented, variable k represents sampling instant；x1And x (k)2(k) when being illustrated respectively in k
Carve the position coordinates of wheel type mobile stage robot X-direction and Y-direction in stage rectangular coordinate system；x3(k) represent at the k moment
Azimuth of the wheel type mobile stage robot in rectangular coordinate system；u1And u (k)2(k) it is illustrated respectively in k moment wheel type mobile dance
The linear velocity and angular speed of platform robot；Consider modular form (1), define the status Bar vector x of wheel type mobile stage robot=
[x1 x2 x3]TWith control column vector u=[u1 u2]T, wherein, symbol T represents the transposition of vector；
2) modular form (1), is abbreviated as formula (2)：
X (k+1)=f (x (k), u (k)) (2)
Wherein, f (x (k), u (k))=[f1(x(k),u(k)) f2(x(k),u(k)) f3(x(k),u(k))]T, f1(x
(k), u (k))=x1(k)+Tsu1(k)cosx3(k), f2(x (k), u (k))=x2(k)+Tsu1(k)sinx3(k), f3(x(k),u
(k))=x3(k)+Tsu2(k) the discrete time forecast model of wheel type mobile stage robot, is set up, referring to formula (3)：
X (k+j+1 | k)=f (x (k+j | k), u (k+j | k)), j=0,1 ..., M-1 (3)
Wherein, x (k+j | k) represents wheel type mobile stage robot control system in moment k to future time instance k+j states
Predicted vector；Positive integer M represents to optimize time window；
3), makeu k,M=[uT(k|k)uT(k+1|k)…uT(k+M-1|k)]TRepresent what is be made up of at the k moment 2M element
One control sequence, willu k,MSubstitution formula (3) obtains the predicted state vector at k+M moment, referring to formula (4)：
X (k+M | k)=φM(x(k|k),u k,M) (4)
Wherein, symbol φMRepresent the M composite function of the pattern function f in modular form (2)；
4) x, is madedThe mobile target equilibrium point of wheel type mobile stage robot is represented, wheel type mobile stage robot is defined
Point stabilization error, referring to formula (5)：
ek,M=φM(x(k|k),u k,M)-xd (5)
And calculation error ek,MTo list entriesu k,MDerivative, referring to formula (6)：
Wherein, symbol xkRepresent measured value of state of the wheel type mobile stage robot at the k moment, and xk=x (k | k)；
5), using Newton method and formula (6), the control sequence at the k moment is updated, referring to formula (7)：
Wherein, symbolv k,M=[vT(k|k) vT(k+1|k) … vT(k+M-1|k)]T, represent after the k moment updates
Control sequence, variable ηkRepresent to update step-length, meet 0<ηk<1, symbol Dk +Represent DkGeneralized inverse matrix；
6), consider formula (7), controlled quentity controlled variable of the wheel type mobile stage robot at the k moment is defined, referring to formula (8)：
U (k)=[I2 02 … 02]2×2M v k,M (8)
Wherein, symbol I2Represent 2 rank unit matrixs, symbol 02Represent 2 rank null matrix；
7) controlled quentity controlled variable (8), is acted on into wheel type mobile stage robot, after next sampling instant k+1 arrival,
The motion state x (k+1) of wheel type mobile stage robot is detected, and updates the initial control sequence at k+1 momentWherein, symbol2 dimensional vectors of random value are represented,
Then k=k+1 and return to step 3 are made), go round and begin again, until wheel type mobile stage robot motion is to giving point target point xdPosition
It is set to only.
The present invention technical concept be：Calm control is realized under the conditions of nonholonomic constraint for wheel type mobile stage robot
System needs, when first passing through the rank kinetic model of discrete time three that defines wheel type mobile stage robot and be randomly selected initial
The point stabilization error sequence and error sequence being carved with finite window of time mouthful control sequence, calculation optimization time window are on control
The gradient of list entries, recycles Newton method to set up the update mechanism of each sampling instant control sequence, and combine rolling optimization
Control principle calculates the control input amount in each sampling instant, realizes the point stabilization of wheel type mobile stage robot.This hair
The advantage of bright design method is to understand simple, few arrange parameter, highly versatile and easy in line computation.
Main executable portion of the invention runs implementation on wheel type mobile stage motion planning and robot control computer.This method
Application process can be roughly divided into 3 stages：
1st, parameter setting：Imported in parameter in interface, with random value initialization control sequencesu 0,M, input target location
xd, sampling period Ts, optimization time window M and step-size factor ηk, after input parameter confirms, data will be set by control computer
Send into computer memory cell RAM and preserve；
2nd, offline debugging：The Debug button in configuration interface is clicked on, control system is debugged into controller off-line simulation
Step-size factor η in stage, adjustment configuration interfacek, observation wheel type mobile stage robotary variable is position and deflection
Control effect, thereby determine that can well realize a step value for wheeled mobile robot point stabilization；Optimize time window M
With step-size factor ηkValue rule：M takes limited nature number and 0<ηk<1；Optimize the regulation rule of time window and step-size factor：
Increase M can improve the stationarity of wheel type mobile stage robot kinematics, but the amount of calculation of increase on-line optimization, conversely,
The rapidity of wheel type mobile stage robot kinematics can be improved by reducing M, but easily produce wheel type mobile stage robot
The concussion of condition responsive；Increase ηkValue will shorten the adjustment time of wheel type mobile stage robotary response, but can draw
The concussion of wheel type mobile stage robotary response is played, conversely, reducing ηkValue by gentle wheel type mobile stage robot
Condition responsive speed and controlled quentity controlled variable, but the adjustment time of extension wheel type mobile stage robotary response is therefore, actual to adjust
Examination optimization time window and during step-size factor, should weigh the overshoot of wheel type mobile stage robotary response, adjustment time,
Combination property between damping effect and controlled quentity controlled variable；
3rd, on-line operation：Configuration interface " RUN " button is clicked on, starts wheel type mobile stage motion planning and robot control and calculates
The CPU of machine reads initialization control sequencesu 0,M, sampling period Ts, optimization time window M and step-size factor ηk, and perform " wheeled
Fitup robot point stabilization program ", passes through the position and azimuth of on-line measurement wheel type mobile stage robot, control
Into the linear velocity and angular speed of wheel type mobile stage robot, realize wheel type mobile stage robot to specifying target to calm
Control, when reaching in next sampling period, the physical location of on-line measurement wheel type mobile stage robot and azimuth, afterwards
Whole implementation procedure is repeated, is gone round and begun again, point stabilization of the wheel type mobile stage robot to specified target is realized.
A full set of wheel type mobile stage robot on-line optimization stabilized control method can be in the control of wheel type mobile stage robot
Completed on system configuration interface processed, this process may be referred to this specification examples provided hereinafter application.Moved with Conventional drum
Dynamic stage robot stabilized control method is compared, the on-line optimization point stabilization side of wheel type mobile stage robot that the present invention is provided
The maximum feature of method is, without solving-optimizing object function and its Hessian matrixes during Optimal Controller Design, and
Required arrange parameter only has 2, so as to substantially increase the calculating of wheel type mobile stage robot on-line optimization point stabilization
Rapidity, stability and on-line implement simplification.Implementation is with wheel type mobile stage robot target origin town in detail below
Illustrate the actual effect of the present invention exemplified by fixed control, but the application of the present invention is not waved with the wheel type mobile in the present embodiment
Platform robot origin point stabilization is limited.
Beneficial effects of the present invention are mainly manifested in：1st, design is simple, be readily appreciated that, on-line implement is simple, highly versatile；
2nd, during Optimal Controller Design without solving-optimizing object function and its Hessian matrixes, high wheel type mobile stage
The calculating rapidity and stability of robot on-line optimization point stabilization, meet the quick realtime control of fitup robot
It is required that.
Brief description of the drawings
Fig. 1 is the schematic diagram of the change of line speed curve of wheel type mobile stage robot.
Fig. 2 is the schematic diagram of the angular speed change curve of wheel type mobile stage robot.
Fig. 3 is schematic diagram of the wheel type mobile stage robot in stage plane motion geometric locus.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
1~Fig. 3 of reference picture, a kind of wheel type mobile stage robot on-line optimization stabilized control method, the control method
Comprise the following steps：
1) the discrete time kinetic model of wheel type mobile stage robot moving process, is set up, referring to formula (1)：
Wherein, normal number TsThe sampling period is represented, variable k represents sampling instant；x1And x (k)2(k) when being illustrated respectively in k
Carve the position coordinates of wheel type mobile stage robot X-direction and Y-direction in stage rectangular coordinate system；x3(k) represent at the k moment
Azimuth of the wheel type mobile stage robot in rectangular coordinate system；u1And u (k)2(k) it is illustrated respectively in k moment wheel type mobile dance
The linear velocity and angular speed of platform robot；Consider modular form (1), define the status Bar vector x of wheel type mobile stage robot=
[x1 x2 x3]TWith control column vector u=[u1 u2]T, wherein, symbol T represents the transposition of vector；
2) modular form (1), is abbreviated as formula (2)：
X (k+1)=f (x (k), u (k)) (2)
Wherein, f (x (k), u (k))=[f1(x(k),u(k)) f2(x(k),u(k)) f3(x(k),u(k))]T, f1(x
(k), u (k))=x1(k)+Tsu1(k)cosx3(k), f2(x (k), u (k))=x2(k)+Tsu1(k)sinx3(k), f3(x(k),u
(k))=x3(k)+Tsu2(k) the discrete time forecast model of wheel type mobile stage robot, is set up, referring to formula (3)：
X (k+j+1 | k)=f (x (k+j | k), u (k+j | k)), j=0,1 ..., M-1 (3)
Wherein, x (k+j | k) represents wheel type mobile stage robot control system in moment k to future time instance k+j states
Predicted vector；Positive integer M represents to optimize time window；
3), makeu k,M=[uT(k|k)uT(k+1|k)…uT(k+M-1|k)]TRepresent what is be made up of at the k moment 2M element
One control sequence, willu k,MSubstitution formula (3) obtains the predicted state vector at k+M moment, referring to formula (4)：
X (k+M | k)=φM(x(k|k),u k,M) (4)
Wherein, symbol φMRepresent the M composite function of the pattern function f in modular form (2)；
4) x, is madedThe mobile target equilibrium point of wheel type mobile stage robot is represented, wheel type mobile stage robot is defined
Point stabilization error, referring to formula (5)：
ek,M=φM(x(k|k),u k,M)-xd (5)
And calculation error ek,MTo list entriesu k,MDerivative, referring to formula (6)：
Wherein, symbol xkRepresent measured value of state of the wheel type mobile stage robot at the k moment, and xk=x (k | k)；
5), using Newton method and formula (6), the control sequence at the k moment is updated, referring to formula (7)：
Wherein, symbolv k,M=[vT(k|k) vT(k+1|k) … vT(k+M-1|k)]T, represent after the k moment updates
Control sequence, variable ηkRepresent to update step-length, meet 0<ηk<1, symbol Dk +Represent DkGeneralized inverse matrix；
6), consider formula (7), controlled quentity controlled variable of the wheel type mobile stage robot at the k moment is defined, referring to formula (8)：
U (k)=[I2 02 … 02]2×2M v k,M (8)
Wherein, symbol I2Represent 2 rank unit matrixs, symbol 02Represent 2 rank null matrix；
7) controlled quentity controlled variable (8), is acted on into wheel type mobile stage robot, reached in next sampling instant k+1
Afterwards, the motion state x (k+1) of detection wheel type mobile stage robot, and update the initial control sequence at k+1 momentWherein, symbolRepresent average be zero 2 dimension random columns to
Amount, then makes k=k+1 and return to step 3), go round and begin again, until wheel type mobile stage robot motion is to giving point target point xd
Untill position.
This example is the calm process of wheel type mobile stage robot target origin, and specific operation process is as follows：
Firstth, in parameter setting interface, target location x is inputtedd=0, sampling period Ts=0.1 second, optimization time window
M, step-size factor ηkWith with random value initialization control sequencesu 0,M；
Secondth, the Debug button is clicked on configuration interface and enters Debugging interface, starts wheel type mobile stage robot fortune
The CPU of dynamic control computer calls " the controller calculation procedure " that weaves in advance to solve controller, and specific calculating process is as follows：
According to given M and ηk, calculate and update optimal control sequence (7), define wheel type mobile stage robot in k moment linear velocity and
One optimal controller (8) of angular speed, according to M and ηkValue and regulation rule, compare wheel type mobile stage robot position
Put and obtain M=10 and η with azimuthal response results and controlled quentity controlled variable result of calculation, debuggingk=0.5, debugging result is saved in
In computer memory cell RAM；
3rd, configuration interface " RUN " button is clicked on, the CPU for starting wheel type mobile stage robot control computer is read
Target location xd, initialization control sequencesu 0,M, sampling period Ts, optimization time window M and step-size factor ηk, and perform " wheeled
Fitup robot point stabilization program ", passes through the position and azimuth of on-line measurement wheel type mobile stage robot, control
Into the linear velocity and angular speed of wheel type mobile stage robot, realize that wheel type mobile stage robot calms to target location
Control, when reaching in next sampling period, the physical location of on-line measurement wheel type mobile stage robot and azimuth, afterwards
Whole implementation procedure is repeated, goes round and begins again, realizes point stabilization of the wheel type mobile stage robot to target location.
Described above is the calm control of a wheel type mobile stage robot target origin on-line optimization that the present invention is provided
The good exercise performance that example processed is shown.It may be noted that examples detailed above is used for illustrating the present invention, rather than to this hair
Bright to be limited, in the protection domain of spirit and claims of the present invention, any modification made to the present invention is both fallen within
Protection scope of the present invention.
Claims (1)
1. a kind of wheel type mobile stage robot on-line optimization stabilized control method, it is characterised in that：The control method includes
Following steps：
1) the discrete time kinetic model of wheel type mobile stage robot moving process, is set up, referring to formula (1)：
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Wherein, normal number TsThe sampling period is represented, variable k represents sampling instant；x1And x (k)2(k) being illustrated respectively in the k moment takes turns
The position coordinates of formula fitup robot X-direction and Y-direction in stage rectangular coordinate system；x3(k) represent wheeled at the k moment
Azimuth of the fitup robot in rectangular coordinate system；u1And u (k)2(k) k moment wheel type mobile stage machines are illustrated respectively in
The linear velocity and angular speed of device people；Consider modular form (1), define the status Bar vector x of wheel type mobile stage robot=
[x1x2x3]TWith control column vector u=[u1u2]T, wherein, symbol T represents the transposition of vector；
2) modular form (1), is abbreviated as formula (2)：
X (k+1)=f (x (k), u (k)) (2)
Wherein, f (x (k), u (k))=[f1(x(k),u(k)) f2(x(k),u(k)) f3(x(k),u(k))]T, f1(x(k),u
(k))=x1(k)+Tsu1(k)cosx3(k), f2(x (k), u (k))=x2(k)+Tsu1(k)sinx3(k), f3(x (k), u (k))=
x3(k)+Tsu2(k) the discrete time forecast model of wheel type mobile stage robot, is set up, referring to formula (3)：
X (k+j+1 | k)=f (x (k+j | k), u (k+j | k)), j=0,1 ..., M-1 (3)
Wherein, x (k+j | k) represents prediction of the wheel type mobile stage robot control system in moment k to future time instance k+j states
Vector；Positive integer M represents to optimize time window；
3), makeu k,M=[uT(k|k) uT(k+1|k) … uT(k+M-1|k)]TRepresent one be made up of at the k moment 2M element
Individual control sequence, willu k,MSubstitution formula (3) obtains the predicted state vector at k+M moment, referring to formula (4)：
X (k+M | k)=φM(x(k|k),u k,M) (4)
Wherein, symbol φMRepresent the M composite function of the pattern function f in modular form (2)；
4) x, is madedThe mobile target equilibrium point of wheel type mobile stage robot is represented, the calm of wheel type mobile stage robot is defined
Error is controlled, referring to formula (5)：
ek,M=φM(x(k|k),u k,M)-xd (5)
And calculation error ek,MTo list entriesu k,MDerivative, referring to formula (6)：
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5), using Newton method and formula (6), the control sequence at the k moment is updated, referring to formula (7)：
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Wherein, symbolv k,M=[vT(k|k) vT(k+1|k) … vT(k+M-1|k)]T, represent the control sequence after being updated at the k moment
Row, variable ηkRepresent to update step-length, meet 0<ηk<1, symbolRepresent DkGeneralized inverse matrix；
6), consider formula (7), controlled quentity controlled variable of the wheel type mobile stage robot at the k moment is defined, referring to formula (8)：
U (k)=[I2 02 … 02]2×2M v k,M (8)
Wherein, symbol I2Represent 2 rank unit matrixs, symbol 02Represent 2 rank null matrix；
7) controlled quentity controlled variable (8), is acted on into wheel type mobile stage robot, after next sampling instant k+1 arrival, inspection
The motion state x (k+1) of measuring wheel formula fitup robot, and update the initial control sequence at k+1 momentWherein, symbol2 dimensional vectors of random value are represented,
Then k=k+1 and return to step 3 are made), go round and begin again, until wheel type mobile stage robot motion is to giving point target point xdPosition
It is set to only.
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| CN108107885A (en) * | 2017-11-24 | 2018-06-01 | 浙江工业大学 | A kind of wheel type mobile stage robot flat pendulum line tracking and controlling method |
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