CN103970138B - Based on active disturbance rejection and the smooth ALV crosswise joint methods of differential - Google Patents
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Abstract
The present invention proposes a kind of based on active disturbance rejection and the smooth ALV crosswise joint methods of differential, and demonstrates differential by the emulation under different condition and is smoothly combined control effect and robustness of the method to under-actuated systems with active disturbance rejection.Initially set up ground autonomous land vehicle horizontal dynamic model；Then further according to the kinetic model, design its differential and smoothly export；Smoothly exported and control law and automatic disturbance rejection controller finally according to described differential, design the composite controller of ground autonomous land vehicle crosswise joint system.Described automatic disturbance rejection controller includes Nonlinear Tracking Differentiator, extended state observer and nonlinear Feedback Control rule.
Description
Technical field
The invention belongs to ground autonomous land vehicle system crosswise joint field, it is related to a kind of flat with differential based on active disturbance rejection
Sliding ALV crosswise joint methods.
Background technology
Ground autonomous land vehicle (Autonomous Land Vehicle, ALV) is Future Combat System (FCS) and intelligence
The key components of energy traffic system (ITS), are the most active research sides in the fields such as current intelligent robot and artificial intelligence
One of to.ALV, which should not only have, the conventional locomotive function such as accelerates, slows down, advancing, falling back, turning, but also should have task
The capacity of will such as analysis, environment sensing, path planning, path trace, automatic obstacle-avoiding.Its study then be related to machinery, kinematics with
The science and technology fields such as dynamics, electronics, computer, information processing, control and artificial intelligence.
It is smoothly theoretical that Fliess M, Levine J, Martin P and Rouchon P propose differential at first.For owing drive
Dynamic ground moving platform courses, after given initial position and target location, it is possible to use the smooth theoretical solution repositioning of differential
The problem of.The smooth concept of differential features original system can be equivalent to the spy of another system after appropriate dynamic expansion
Property.The problem of smoothly exporting for Track Pick-up plays an important roll, if smooth output, it is known that if can obtain corresponding shape
State variable and control variable.But the shortcoming of this method is only effective to differential smoothing system, and smoothly output is difficult to find.It is micro-
Dividing the proposition of smoothing system makes the smooth theory of differential be widely used in control problem.Differential is smoothly used as a kind of feasible track
Generation method is applied in the research of underactuated spacecraft.
Auto Disturbances Rejection Control Technique is to absorb modern control theory achievement, develop PID thoughts marrow and (mistake is eliminated based on error
Difference), development and usage Special Nonlinear effect is the novel practical technology that develops.Auto Disturbances Rejection Control Technique is totally independent of controlled pair
The mathematical modeling of elephant, the characteristics of it is most prominent is exactly that the effect for all uncertain factors for acting on controlled device is all attributed to
" unknown disturbance " and it is estimated and recompensed in real time using the inputoutput data of object.The meaning of active disturbance rejection just exists
In this, here and disturbing effect outside direct measurement is not needed, it is not required that the action rule of disturbance is known in realization.This also disliking
Require to realize the occasion that high-speed, high precision is controlled in bad environment, Auto Disturbances Rejection Control Technique can more show its superiority.
The content of the invention
The present invention be directed to the defect of prior art, propose a kind of based on active disturbance rejection and the smooth ALV crosswise joints of differential
Method, and differential is demonstrated by the emulation under different condition be smoothly combined control of the method to under-actuated systems with active disturbance rejection
Effect and robustness.
Technical scheme is as follows：
It is a kind of based on active disturbance rejection and the smooth ALV crosswise joint methods of differential, initially set up ground autonomous land vehicle horizontal
To kinetic model；Then further according to the kinetic model, design its differential and smoothly export；Differential is smoothly exported to carry out model
Conversion obtains Affine Incentive system；Smoothly exported and automatic disturbance rejection controller finally according to described differential, design ground is independently driven
Sail the composite controller of vehicle lateral control system；Wherein, composite controller smoothly exported including differential, Nonlinear Tracking Differentiator, expansion
Open state observer and nonlinear Feedback Control rule；Differential according to designed by the kinetic model of ground autonomous land vehicle is defeated
Go out as follows
Wherein, vyIt is vehicle lateral speed, r is yaw rate, lfFor the distance between barycenter and front axle, m is whole
Car equipment quality, CafFor the cornering stiffness of front tyre, IzRepresent rotary inertia about the z axis；Stateful, the v of systemy, r and control
Input δfIt can smoothly export the function of F and its derivative to represent by differential, therefore according to the definition of differential smoothing system, owe to drive
Dynamic kinetic control system is when implementing flight tracking control, with the smooth characteristic of differential.
Described Nonlinear Tracking Differentiator is used with drag：
Wherein
And sgn is sign function,
Wherein,D=r0h0,d0=dh0,y0=v1-v0+hv2
Wherein, r0It is parameter to be adjusted, is also the velocity factor of Nonlinear Tracking Differentiator, h0It is filtering factor, h is sampling step length, Fr
For the reference locus of smooth function, andVyrAnd rrThe respectively reference of lateral velocity and body gesture angular speed
Track, v1(k) it is the input signal for tracking, v2(k) it is the approximate differential signal that obtains input signal, k represents the moment, d,
d0、a、a0、y、y0For the intermediate variable during equation solver, eliminated in iteration；Obtain approximate micro- by solving this equation
Sub-signal, i.e., while input signal is tracked, while obtaining its approximate differential signal.
Described extended state observer is used with drag：
Wherein：
Wherein, z1(k)、z2(k)、z3(k) be k moment extended state observers output, h is sampling step length, b0For control
The coefficient z of variable1(k+1)、z2(k+1)、z3(k+1) be extended state observer output, z1(k+1) tracking system state v1
(k),z2(k+1) the state v of tracking system2(k),z3(k+1) be estimating system internal disturbance and external disturbance, β01、β02、β03
It is the coefficient of observer, embodies the observing capacity of observer, e is state error, and u (k) is the controlled quentity controlled variable of system, and y is that system is defeated
Go out, δ is power function fal linearity range siding-to-siding block length, it is necessary to meet δ ∈ [0,1], takes δ=0.01, α to represent power function fal
Power, α is expressed as α in two fal functions1And α2, meet 0<α2<α1<1, take α1=0.5, α2=0.25.
Described nonlinear Feedback Control rule is used with drag：
Wherein, e1、e2It is the error and its differential between observed quantity and input signal, K respectivelyp、KDFeed back and increase for error
Benefit, embodies δ in the control ability of controller, above formula and meets δ ∈ [0,1], take the power of δ=0.01, two power function to meet 0<
αp<1<αD, take αp=0.5, αD=2；The expression formula for obtaining automatic disturbance rejection controller control law is as follows：
U (k)=u0-z3(k)/b0。 (5)
Beneficial effects of the present invention：
1st, when speed is higher, mobile platform horizontal dynamic linear model can meet wanting for its transverse movement control
Ask；
2nd, smoothly it is combined in differential with ADRC under the control of controller, mobile platform is real in 0~40m/s velocity intervals
Steady and high-precision transverse movement is showed, to changing also with very strong for inherent parameters, road conditions and lane-change time etc.
Robustness, can meet the requirement of high performance control, so as to show that differential is smoothly used at a high speed with the ADRC controllers being combined
Mobile platform transverse movement control is feasible；
3rd, the present invention can provide guidance for the Engineering Design for the high motor platform of high speed studied.
Brief description of the drawings
Fig. 1 ground autonomous land vehicle system lateral control model figure；
Fig. 2 are in controller U1Lower system S1Output response；
Fig. 3 are in controller U1Lower system S2Output response；
Fig. 4 are in controller U2Lower system S2Output response；
Fig. 5 tracks expect lateral displacement figure；
The reference locus of Fig. 6 vehicle body angles；
Fig. 7 .Vx=1m/s and platform parameters are the curve of output under nominal value；
Fig. 8 .Vx=20m/s and platform parameters are the curve of output under nominal value；
Fig. 9 .Vx=13m/s and platform parameters are the curve of output under non-nominal value；
Curve of output when Figure 10 platforms have perturbation and disturbed.
Embodiment
The present invention is described in detail below in conjunction with the accompanying drawings.
The present invention based on smooth and Auto Disturbances Rejection Control Technique the Vehicular system crosswise joint method of differential, including following step
Suddenly：
The first step, set up ground autonomous land vehicle system lateral control model and see accompanying drawing 1, be described as follows：
Wherein, lfFor the distance between barycenter and front axle, lrFor the distance between barycenter and rear axle, m is that vehicle equips matter
Amount, Cf、CrThe cornering stiffness of respectively front and rear tire, δfFor vehicle front wheel angle, IzRepresent rotary inertia about the z axis, vxRepresent
Longitudinal velocity, vyRepresent lateral velocity,Represent yaw velocity.
Second step, the Controlling model set up according to the first step, design its differential and smoothly export：
Formula (1) has differential smoothness properties, and its differential is smoothly output as：
The controlled quentity controlled variable δ of front-wheelfInput is expressed as：
Stateful, the v of systemy, r and control input δfIt can be represented by the function for smoothly exporting F and its derivative, therefore
According to the definition of differential smoothing system, drive lacking kinetic control system is when implementing flight tracking control, with the smooth characteristic of differential.
3rd step, based on smooth and ADRC the controller design of differential.
1st, ground autonomous mobile platform transverse movement smoothing system Transformation of Mathematical Model
For design platform transverse movement smoothing system ADRC controllers, smoothing system model (3) need to be converted into Affine Incentive.
Therefore, making x1=F,U=δ, formula (4) is rewritten as by formula (3).
Wherein,
In order that system turns into the system of pure integration, we will design extended state observer, to disturb in eliminating and outside
Disturb.Still formula (4) is write as to the form of expansion state spatial expression, such as formula (5)：
Wherein, g (x1,x2) it is f (x1,x2) derivative.
2nd, based on smooth and ADRC the controller design of differential
We are based on formula (5) below and Auto-disturbance-rejection Control carries out the control of autonomous mobile platform transverse movement smoothing system
The design of device.
Autonomous mobile platform transverse movement smoothing system automatic disturbance rejection controller based on formula (5) is expressed as formula (6)~(9)：
Described Nonlinear Tracking Differentiator is used with drag：
Wherein
And sgn is sign function,
Wherein,D=r0h0,d0=dh0,y0=v1(k)-Fr+hv2(k)
Wherein, r0It is parameter to be adjusted, is also the velocity factor of Nonlinear Tracking Differentiator, h0It is filtering factor, h is sampling step length, Fr
For the reference locus of smooth function, andVyrAnd rrThe respectively reference of lateral velocity and body gesture angular speed
Track, v1(k) it is the input signal for tracking, v2(k) it is the approximate differential signal that obtains input signal, d, d0、a、a0、y、y0
For the intermediate variable during equation solver, eliminated in iteration；Approximate differential signal, i.e., one are obtained by solving this equation
Side tracks input signal, while obtaining its approximate differential signal；
Described extended state observer is used with drag：
Wherein：
Wherein, z1(k)、z2(k)、z3(k) be k moment extended state observers output, h is sampling step length, b0For control
The coefficient z of variable1(k+1)、z2(k+1)、z3(k+1) be extended state observer output, z1(k+1) tracking system state v1
(k),z2(k+1) the state v of tracking system2(k),z3(k+1) be estimating system internal disturbance and external disturbance, β01,β02,β03
It is the coefficient of observer, embodies the observing capacity of observer, e is state error, and u (k) is the controlled quentity controlled variable of system, and y is that system is defeated
Go out, δ is power function fal linearity range siding-to-siding block length, it is necessary to meet δ ∈ [0,1], takes δ=0.01, α to represent power function fal
Power, α is expressed as α in two fal functions1And α2, meet 0<α2<α1<1, take α1=0.5, α2=0.25；
Described nonlinear Feedback Control rule is used with drag：
Wherein, e1、e2It is the error and its differential between observed quantity and input signal, K respectivelyp、KDFeed back and increase for error
Benefit, embodies δ in the control ability of controller, above formula and meets δ ∈ [0,1], take the power of δ=0.01, two power function to meet 0<
αp<1<αD, take αp=0.5, αD=2；The expression formula for obtaining automatic disturbance rejection controller control law is as follows：
U (k)=u0-z3(k)/b0。 (9)
3rd, the parameter tuning based on smooth and ADRC the controller of differential
By design differential smoothly export and control the track following that differential is smoothly exported realize ground autonomous put down
The underactuated system of platform transverse movement.And smoothly output is controlled the differential designed from active disturbance rejection (ADRC) herein,
Shown in controller such as formula (6)~(9).
The part of controller design most critical is parameter testing, because the smooth output system coefficient designed herein is excessive and
The regulation of the excessive parameter of time scale is difficult to carry out, and can not be directly obtained by repeatedly debugging, therefore access time method of scales is adjusted
Parameter.
First, baseline system is chosen first
Parameter is adjusted to obtain by time scale method, the time scale p of system (10)1=0.241 and its parameter is adjusted.
According to model GS1ADRC controllers U can be adjusted1For
r11=0.1, r12=0.02, h=0.01,
h1=0.02, c=100, β1=100,
β2=200, β3=30000.
Systematic parameter is substituted into system (3) to obtain
Parameter is adjusted to obtain by time scale method, the time scale p of system (11)2=2.83.First, ADRC controllers are utilized
U1To the nonlinear model, i.e. system S1And S2, emulation is controlled, gained output F is shown in accompanying drawing 2,3.
Accompanying drawing 2,3 results show, controller U1Although can be preferably to S1Implement steady control；But, to S2Control
Process does not catch up with trajectory divergence and gone out completely, it is seen that now U1It has not been suitable for S2。
By S1And S2Time scale ratio m=p2/p1≈ 10, further according to the ADRC parameter tunings of controlled system time scale
Method, can be obtained according to controller U1Controller U is obtained after parameter adjustment2：
r11=0.1, r12=0.2, h=0.001,
h1=0.002, c=200, β1=1000,
β2=2800, β3=30000000.
Then it is utilized respectively controller U1And U2To system S2It is controlled emulation, gained output y accompanying drawings 4.It is shown.
Accompanying drawing 4 shows, compared to controller U1, controller U2To S2Obtain satisfied control effect, it is seen that controller U2It is
Suitable for S2's.
In order to verify that being smoothly combined based on differential with active disturbance rejection for above-mentioned design realizes ground autonomous land vehicle system
The method of Lateral Controller design, and control of the differential smoothing method to under-actuated systems is demonstrated by the emulation under different condition
Effect and robustness processed.
The kinetics equation for the ground autonomous land vehicle system crosswise joint set up in the present invention is as follows：
Wherein, lfFor the distance between barycenter and front axle 1.05m, lrFor the distance between barycenter and rear axle 1.63m, m is whole
Car equipment quality 1480Kg, CfFor the cornering stiffness 67500N/rad, C of front tyrerFor the cornering stiffness 47500N/ of rear tyre
Rad, δfFor vehicle front wheel angle, IzRepresent rotary inertia 2350Kgm about the z axis2, vxRepresent longitudinal velocity, vyRepresent laterally
Speed,Represent yaw velocity.
The present invention is by taking above-mentioned model as an example, and specific simulation implementation step is as follows：
Simulated environment
Moved assuming that platform makees two-track line with a certain fixed longitudinal velocity, lane-change track (transient process of arrangement) is shown in accompanying drawing
5.The track is produced using SIN function planning algorithm, shown in planning formula such as formula (12).In formula, v0(t)：Expect horizontal position
Move；w：Lane width；t1：At the time of left-lane being turned to from right lane；t2：At the time of being started running on left-lane；t3：From a left side
At the time of track turns to right road；t4：At the time of coming back to right lane.Assuming that the ideal pose of vehicle body is the tangent line of transverse path
Direction, then the reference locus of vehicle body angle then see accompanying drawing 6.
During emulation, change the parameter and longitudinal velocity V of platform and steering mechanismx, to examine or check the robustness of ADRC controllers
Wherein, tire angular rigidity Csf,CsrChange can both represent the perturbation of tire parameter itself, may also indicate that road ground condition
Change (disturbance)；The change of platform barycenter to axle distance can then represent the longitudinal unevenness of Mass Distribution and road simultaneously
Change (disturbance) therefore, the setting of above-mentioned simulation parameter can examine or check designed ADRC controllers to " inside " and " outside "
Probabilistic adaptability.
Simulation result
It is V respectively to see accompanying drawing 7~8x=1m/s, 40m/s and platform parameters are the simulation result under nominal value；Accompanying drawing 9
Be following parameter simulation result：Vx=35m/s, m=2220kg (1.5 times of nominal value), Iz=3290kgm2It is (nominal
1.4 times of value), lf=1.2m (moves 0.15m) after barycenter, lr=1.48m, Csf=40500N/rad (the 60% of nominal value), Csr
=28500N/rad (the 60% of nominal value).Accompanying drawing 10 is in Csf=[0.85+0.15 (2U (0,1) -1)] Csf_nom、Csr=
[0.85+0.15(2U(0,1)-1)]Csr_nom, result when other specification is identical with the simulated conditions of accompanying drawing 9, wherein U (0,1) is
Unit uniformly distributed function.
The result of accompanying drawing 7~8 shows, with neutral net with the method that fuzzy control is combined compare differential smoothly with ADRC phases
With reference to controller to platform speed change have good adaptability, be successfully realized and system transverse movement put down
Surely, high-precision control.The result of accompanying drawing 9~10 shows, even if road switching time shortens, platform parameters and road conditions occur compared with
Big to change, platform still has preferable transverse movement performance under the control of ADRC controllers.
Claims (1)
1. it is a kind of based on active disturbance rejection and the smooth ALV crosswise joint methods of differential, it is characterised in that：Ground is initially set up independently to drive
Sail lateral direction of car kinetic model；Then further according to the kinetic model, design its differential and smoothly export；Differential is smoothly exported
Carry out model conversion and obtain Affine Incentive system；Smoothly exported and automatic disturbance rejection controller finally according to described differential, design ground
The composite controller of face autonomous land vehicle crosswise joint system；Wherein, composite controller smoothly exported including differential, track it is micro-
Divide device, extended state observer and nonlinear Feedback Control rule；According to designed by the kinetic model of ground autonomous land vehicle
Differential output it is as follows
Wherein, vyIt is vehicle lateral speed, r is yaw rate, lfFor the distance between barycenter and front axle, m fills for vehicle
Standby quality, CafFor the cornering stiffness of front tyre, IzRepresent rotary inertia about the z axis；Stateful, the v of systemy, r and control input
δfIt can smoothly export the function of F and its derivative to represent by differential, therefore according to the definition of differential smoothing system, drive lacking fortune
Autocontrol system is when implementing flight tracking control, with the smooth characteristic of differential；
Described Nonlinear Tracking Differentiator is used with drag：
Wherein
And sgn is sign function,
Wherein,D=r0h0,d0=dh0,y0=v1(k)-Fr+hv2(k)
Wherein, r0It is parameter to be adjusted, is also the velocity factor of Nonlinear Tracking Differentiator, h0It is filtering factor, h is sampling step length, FrIt is flat
The reference locus of sliding function, andVyrAnd rrThe respectively reference rail of lateral velocity and body gesture angular speed
Mark, v1(k) it is the input signal for tracking, v2(k) it is the approximate differential signal that obtains input signal, k represents moment, d, d0、
a、a0、y0For the intermediate variable during equation solver, eliminated in iteration；Approximate differential letter is obtained by solving this equation
Number, i.e., while input signal is tracked, while obtaining its approximate differential signal；
Described extended state observer is used with drag：
Wherein：
Wherein, z1(k)、z2(k)、z3(k) be k moment extended state observers output, h is sampling step length, b0For control variable
Coefficient z1(k+1)、z2(k+1)、z3(k+1) be extended state observer output, z1(k+1) tracking system state v1(k),z2
(k+1) the state v of tracking system2(k),z3(k+1) be estimating system internal disturbance and external disturbance, β01,β02,β03It is observation
The coefficient of device, embodies the observing capacity of observer, and e is state error, and u (k) is the controlled quentity controlled variable of system, and y exports for system, and δ is
Power function fal linearity range siding-to-siding block length takes δ=0.01, α to represent power function fal power, α, it is necessary to meet δ ∈ [0,1]
α is expressed as in two fal functions1And α2, meet 0<α2<α1<1, take α1=0.5, α2=0.25；
Described nonlinear Feedback Control rule is used with drag：
Wherein, e1、e2It is the error and its differential between observed quantity and input signal, K respectivelyp、KDFor error feedback oscillator, embody
δ meets δ ∈ [0,1] in the control ability of controller, above formula, takes the power of δ=0.01, two power function to meet 0<αp<1<αD,
Take αp=0.5, αD=2；The expression formula for obtaining automatic disturbance rejection controller control law is as follows：
U (k)=u0-z3(k)/b0 (5)。
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| CN105137968A (en) * | 2015-07-20 | 2015-12-09 | 柳州一健科技有限公司 | Agricultural vehicle automatic steering control method based on disturbance observation |
| CN105467996B (en) * | 2015-12-21 | 2018-07-03 | 北京理工大学 | Four-wheel steering automobile Trajectory Tracking Control method based on differential flat and active disturbance rejection |
| CN105676643B (en) * | 2016-03-02 | 2018-06-26 | 厦门大学 | A kind of intelligent automobile turns to and braking self-adaptive wavelet base method |
| CN106168758B (en) * | 2016-05-24 | 2019-12-06 | 中国人民解放军空军第一航空学院 | course tracking control method of four-wheel independent drive electric vehicle |
| CN106527139B (en) * | 2016-11-29 | 2019-07-26 | 桂林航天工业学院 | Communicate the vehicle yaw motion robust Controller Design method under limited situation |
| CN107272692A (en) * | 2017-07-18 | 2017-10-20 | 北京理工大学 | Unmanned vehicle path planning and tracking and controlling method based on differential flat and active disturbance rejection |
| CN107272707B (en) * | 2017-08-03 | 2020-11-27 | 郑州轻工业学院 | IPV 6-based automatic unmanned vehicle track fuzzy PID following control method |
| CN108196545B (en) * | 2018-01-03 | 2021-06-25 | 浙江同筑科技有限公司 | AGV magnetic navigation control method adopting active disturbance rejection control technology |
| CN108646756B (en) * | 2018-07-05 | 2021-01-19 | 合肥工业大学 | Intelligent automobile transverse control method and system based on segmented affine fuzzy sliding mode |
| CN109164699A (en) * | 2018-08-29 | 2019-01-08 | 浙江工业大学 | A kind of chip mounter head running position accuracy control method |
| CN110212514B (en) * | 2019-06-27 | 2023-04-28 | 上海电力学院 | Nonlinear control method of direct-current power spring based on differential smoothing theory |
| CN110825095B (en) * | 2019-12-06 | 2022-11-08 | 苏州智加科技有限公司 | Transverse control method for automatic driving vehicle |
| CN111949036B (en) * | 2020-08-25 | 2022-08-02 | 重庆邮电大学 | Trajectory tracking control method and system and two-wheeled differential mobile robot |
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