CN111949038A - Decoupling control method for mobile robot considering iteration sliding mode - Google Patents

Decoupling control method for mobile robot considering iteration sliding mode Download PDF

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CN111949038A
CN111949038A CN202010873333.0A CN202010873333A CN111949038A CN 111949038 A CN111949038 A CN 111949038A CN 202010873333 A CN202010873333 A CN 202010873333A CN 111949038 A CN111949038 A CN 111949038A
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wheel
sliding mode
decoupling
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control method
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CN111949038B (en
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蒋立泉
王书亭
谢远龙
孟杰
刘伦洪
李鹏程
孙浩东
吴天豪
章小龙
吴昊
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Huazhong University of Science and Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course, altitude or attitude of land, water, air or space vehicles, e.g. using automatic pilots
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle

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Abstract

The invention belongs to the technical field related to robot control, and discloses a decoupling control method for a mobile robot considering an iterative sliding mode, which comprises the following steps: s1, constructing a theoretical dynamic model about the yaw inertia moment generated by the driving wheel and the wheel rotation angle; calculating the inertia moment and the wheel rotation angle, and substituting the calculation result into a theoretical dynamic model to obtain an actual dynamic model; s2, decoupling the actual dynamic model to obtain a decoupled inverse system model; and constructing an iterative fuzzy sliding mode controller, and controlling the decoupled inverse system model by using the fuzzy sliding mode controller so as to realize decoupling control of the wheeled robot to be processed. By the method, linear mapping decoupling is realized, and the control coordination degree and tracking precision of the system are improved.

Description

Decoupling control method for mobile robot considering iteration sliding mode
Technical Field
The invention belongs to the technical field related to robot control, and particularly relates to a decoupling control method for a mobile robot considering an iterative sliding mode.
Background
The mobile robot control means sending appropriate control to enable the mobile platform to operate according to a formulated track or a formulated mode, and the main evaluation indexes comprise track tracking precision, tracking operation efficiency, stability of a tracking process and the like.
The traditional mobile robot motion control method is to control a kinematic model, and the method has many defects: 1) the yaw moment of the platform cannot be considered, and the moment easily causes serious shaking of the platform and even overturning of the platform; 2) the general control method is often accompanied by multivariable coupling, so that the control is not coordinated and even multi-constraint is brought; 3) for multivariable controllers, it is difficult to balance convergence speed and stability.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a decoupling control method of a mobile robot considering an iterative sliding mode.
To achieve the above object, according to the present invention, there is provided a control method including the steps of:
s1, constructing a theoretical dynamic model about yaw inertia moment and wheel rotation angle generated by a driving wheel according to the motion mode of the wheeled robot; calculating inertia force and wheel rotation angle by using the geometric relation in the wheeled robot to be processed under the condition of considering the wheel slip angle, and substituting the calculation result into the theoretical dynamic model so as to obtain an actual dynamic model of the wheeled robot to be processed;
s2, for the actual dynamic model, decoupling the actual dynamic model according to a decoupling control method of an inverse system so as to obtain a decoupled inverse system model; and constructing an iterative fuzzy sliding mode controller according to the decoupled inverse system model, and controlling the decoupled inverse system model by using the fuzzy sliding mode controller so as to realize the decoupling control of the wheeled robot to be processed.
Further preferably, in step S2, in the fuzzy sliding mode controller, the adaptation rate ψ is constructedadapt，
ψadapt＝λ1z1+λ2z2
Figure BDA0002651840610000021
Wherein the content of the first and second substances,
Figure BDA0002651840610000022
λ1and λ2Are all self-adaptive parameters, s is a designed sliding mode surface,
Figure BDA00026518406100000211
is the coefficient matrix, e is the tracking error,
Figure BDA0002651840610000023
is the number of the iteration variables,
Figure BDA0002651840610000024
is as follows
Figure BDA0002651840610000025
The error of the secondary iteration, n is the number of sliding mode surface iterations.
Further preferably, in order to ensure the stability of the inverse control system, the adaptive rate further needs to satisfy the following equation:
ψadapt≤pm
wherein p ismIs an adaptive parameter of the arrival rate.
Further preferably, in step S2, for the fuzzy sliding-mode controller, in order to obtain its iterative adaptive sliding-mode control rate, a fitted control quantity rate is obtained according to the following steps:
Figure BDA0002651840610000026
Figure BDA0002651840610000027
wherein the content of the first and second substances,
Figure BDA0002651840610000028
for adaptive control of rate
Figure BDA0002651840610000029
The fitting value of (a) is determined,
Figure BDA00026518406100000210
in order to decouple the control variable of the inverse system,
Figure BDA0002651840610000031
and
Figure BDA0002651840610000032
are respectively a parameter matrix F (u)1,u2,...,un) And G (u)1,u2,..,un) Fitting value of u1,u2,..,unIn order to output the signals discretely,
Figure BDA0002651840610000033
is a coefficient matrix, e is a tracking error, pmIs a variable parameter, s is a designed sliding mode variable,
Figure BDA0002651840610000034
is an adaptive function with respect to lambda, which is an adaptive variable,
Figure BDA0002651840610000035
is an iteration variable, n is the number of iterations of the sliding mode surface, λψIs composed of
Figure BDA0002651840610000036
Adaptive parameter of (2), zψ＝[z1,z2]TIs an intermediate variable, wherein
Figure BDA0002651840610000037
Figure BDA0002651840610000038
Is the reference value for the nth iteration of the state quantity u.
Further preferably, the parameter matrix equation of the fuzzy sliding-mode controller is obtained by fitting in the following way:
Figure BDA0002651840610000039
Figure BDA00026518406100000310
wherein the content of the first and second substances,
Figure BDA00026518406100000311
is the fitted value of the parameter matrix f (u),
Figure BDA00026518406100000312
is moment of parameterFitting value of matrix G (u), λFAnd λgAdaptive parameters for F (u) and G (u), respectively,
Figure BDA00026518406100000325
f (u) and G (u), respectively, are fuzzy basis vectors.
Further preferably, said λF，λgAnd λψObtained in the following way:
Figure BDA00026518406100000313
Figure BDA00026518406100000314
Figure BDA00026518406100000315
τ1,τ2,τ3is a constant number of times, and is,
Figure BDA00026518406100000316
and
Figure BDA00026518406100000317
are each lambdaF，λgAnd λψFirst order inverse of (a) (-)ψIs composed of
Figure BDA00026518406100000318
The adaptive parameters of (a) are set,
Figure BDA00026518406100000326
is psiadaptS is the sliding mode surface and lambda is the fuzzy basis vector ofF,λg,λψThe following equation is also satisfied:
Figure BDA00026518406100000319
Figure BDA00026518406100000320
Figure BDA00026518406100000321
Figure BDA00026518406100000322
is λF,λg,λψA set of values of (a) is selected,
Figure BDA00026518406100000323
and
Figure BDA00026518406100000324
for optimized lambdaF,λg,λψSup denotes the infimum limit of the set,
Figure BDA0002651840610000041
is an n-dimensional real space and z is a variable with respect to s.
Further preferably, in step S2, the decoupled inverse system model is performed according to the following relation:
Figure BDA0002651840610000042
wherein u is the output of the inverse system after decoupling, and [ theta ]f,M]T，θfFor virtual front wheel turning, M is the yaw moment of inertia generated by the drive wheel, dfAnd drTransverse stiffness of the front and rear wheels, respectively, /)fAnd lrDistances from the central point of the chassis of the wheeled robot to the front virtual wheel and the rear virtual wheel, IzIs yaw moment of inertia of the platform, v is longitudinal speed of the wheeled robot to be processed, m is mass of the wheeled robot to be processed, x is system state quantity before decoupling, u1＝fAnd u2M is the state quantity of the inverse system after decoupling,
Figure BDA0002651840610000043
in order to decouple the control variable of the inverse system,
Figure BDA0002651840610000044
is the derivative order of the inverse system observations y after decoupling,
Figure BDA0002651840610000045
is a positive integer.
Further preferably, in step S1, the theoretical kinetic model is performed according to the following relationship:
Figure BDA0002651840610000046
Figure BDA0002651840610000047
ay＝a2β+b2vγ
wherein
Figure BDA0002651840610000048
Figure BDA0002651840610000049
Figure BDA00026518406100000410
Wherein beta is a sideslip angle, a0，a1，a2，b0，b1，b2，c0And c1Is an intermediate variable, gamma is the yaw angle of the chassis of the wheeled robot, dfAnd drRespectively a front wheel andtransverse stiffness of the rear wheels, /)fAnd lrRespectively the distance theta from the central point of the chassis of the wheeled robot to the front virtual wheel and the rear virtual wheelfAnd thetarRespectively the corners of a virtual front wheel and a virtual rear wheel, and the mass of the platform is m and IzThe yaw moment of inertia of the platform, M is the yaw moment of inertia generated by the driving wheels, and v is the longitudinal speed of the wheeled robot to be processed.
Further preferably, in step S1, the inertia moment and the wheel rotation angle are calculated according to the following relationship:
for the moment of inertia M, the relationship is as follows:
M＝My+Mx
My＝[lf lr][Fyf Fyr]T
Mx＝h(Fxf+Fxr)
Figure BDA0002651840610000051
Figure BDA0002651840610000052
where i represents the indicia of the wheel, i ═ f, r, f are the front wheels, r are the rear wheels, M is the moment of inertia, M represents the wheel's weightyIs a partial moment in the transverse direction, MxIs the component moment in the longitudinal direction,/fAnd lrDistances from the central point of the chassis of the wheeled robot to the front virtual wheel and the rear virtual wheel respectively, FyfTo simulate the transverse forces of the front wheels of the wheel, FyrTo simulate the transverse forces of the rear wheels of the wheels, FxfAnd FxrLongitudinal forces, theta, of the front and rear wheels, respectivelyLiAnd thetaRiRespectively the angle of rotation, alpha, of the actual left-hand wheel and the actual right-hand wheelLiAnd alphaRiThe slip angles of the actual left and right side wheels,
Figure BDA0002651840610000053
and
Figure BDA0002651840610000054
is an intermediate variable, fLiAnd fRiThe friction force of the actual left wheel and the actual right wheel respectively, and h is the width between the left wheel and the right wheel;
for wheel angle thetaLiAnd thetaRiThe method is carried out according to the following relations:
Figure BDA0002651840610000061
Figure BDA0002651840610000062
wherein, thetafkAnd thetarkActual front and rear wheel angles, θiWhere i is f, r, f is the front wheel, r is the rear wheel, θ is the virtual wheel anglefAnd thetarRespectively the angle of rotation, g, of the virtual front wheel and the virtual rear wheeliAnd lmIs an intermediate variable.
Further preferably, the lateral force F of the front wheel of the virtual wheelyfAnd the lateral force F of the rear wheel of the virtual wheelyrCalculating the yaw force of the actual wheels according to the following formula:
Fyj(αj)＝pjsin{qjarctan[(1-j)ρjαj+jarctan(ρjαj)]}
Figure BDA0002651840610000063
the parameter expression is as follows:
Figure BDA0002651840610000064
wherein j isThe number of wheels, for a four-wheeled robot, j ═ 1,2,3,4, piIs a peak value, qiAs a curve shape parameter, piIn order to be a factor of the curve,iin order to be a coefficient of stiffness of the tire,i(i ═ 1, 2.., 5) is an environmental parameter, Fy1,Fy2Transverse force of front side No. 1,2 actual wheel, Fy3And Fy4The lateral forces of the rear side No. 3 and No. 4 actual wheels, respectively.
In general, the above technical solutions contemplated by the present invention are compared with the prior art:
1. according to the method, the slip angle of the wheel is considered in the calculation of the inertia moment and the wheel rotation angle, compared with the prior art, each calculated amount in calculation is fully considered, the physical amount is not ignored due to small influence, the calculation precision is improved, and the system error is reduced;
2. according to the invention, the existing coupling dynamics model is decoupled, a fuzzy sliding mode controller is constructed for the decoupled subsystem, the adaptive rate is constructed in the fuzzy sliding mode controller, a parameter matrix equation is obtained through fitting calculation, and finally, the model parameters and the adaptive quantity are adjusted on line in real time by using a fuzzy logic rule, so that the latest output control rate is obtained, and the control precision and the robustness of the system are improved.
Drawings
FIG. 1 is a flow chart of a mobile robot decoupling control method constructed in accordance with a preferred embodiment of the present invention;
FIG. 2 is a process diagram of a process for performing a configuration constructed in accordance with a preferred embodiment of the present invention;
fig. 3 is a schematic view showing the structure of the yaw force and the lateral force of the four-wheeled robot constructed according to the preferred embodiment of the present invention;
fig. 4 is a virtual wheel model of a four-wheeled robot constructed in accordance with a preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, a decoupling control method for a mobile robot considering an iterative sliding mode includes the following steps:
s1, firstly, building a yaw dynamic model according to the inherent attributes of the mobile robot;
since the yaw rate of the system tends to be substantially constant, it is set to a constant v, and its nonlinear yaw dynamics model is represented as follows:
Figure BDA0002651840610000071
Figure BDA0002651840610000072
ay＝a2β+b2vγ
wherein
Figure BDA0002651840610000081
Figure BDA0002651840610000082
Figure BDA0002651840610000083
Wherein beta is the sideslip angle, gamma is the yaw angle of the platform, dfAnd drTransverse stiffness of the front and rear wheels, respectively, /)fAnd lrThe distances from the platform center point to the front virtual wheel and the rear virtual wheel, theta, respectivelyfAnd thetarRespectively the corner of the virtual front wheel and the virtual rear wheel and the platform qualityIs m, IzIs the yaw moment of inertia of the platform and M is the yaw moment of inertia generated by the drive wheels.
S2 estimates expressions of driving torque and wheel turning angle as system inputs, as shown in fig. 3 and 4;
the drive torque of the drive wheels is expressed as follows:
M＝My+Mx
My＝[lf lr][Fyf Fyr]T
Mx＝h(Fxf+Fxr)
Figure BDA0002651840610000084
Figure BDA0002651840610000085
wherein i ═ F, r, FyfTo simulate the longitudinal force of the front wheel of the wheel, FyrTo simulate the longitudinal force of the rear wheel of the wheel, FxfAnd FxrTransverse forces, θ, of the front and rear wheels, respectivelyLiAnd thetaRiRespectively the actual left and right wheel turning angles, alphaLiAnd alphaRiThe actual slip angles of the left and right wheels.
The wheel corner is:
Figure BDA0002651840610000091
Figure BDA0002651840610000092
s3 is an expression for solving the transverse moment, and the yaw acting force of the wheel needs to be solved according to a magic formula:
the magic formula is as follows:
Fyj(αj)＝pjsin{qjarctan[(1-j)ρjαj+jarctan(ρjαj)]}
the parameter expression is as follows:
Figure BDA0002651840610000093
wherein p isiIs a peak value, qiAs a curve shape parameter, piIn order to be a factor of the curve,iin order to be a coefficient of stiffness of the tire,i(i ═ 1, 2.., 5) is an environmental parameter.
S4 as shown in fig. 2, decoupling the coupled system according to the decoupling control method of the inverse system:
the system model of the decoupled system is as follows:
Figure BDA0002651840610000094
x(t0)＝x0
wherein x ═ β γ]TX and y are the output and observed quantities of the inverse system before decoupling, u ═ θf θr M]TThe system control rate.
Constructing a non-linear inverse system
Figure BDA0002651840610000101
Redefining the mapping input as
Figure BDA0002651840610000102
And the output is u ═ θf θr M]TWherein the input order is
Figure BDA0002651840610000103
Simultaneous parameter factor satisfaction
Figure BDA0002651840610000104
Through the above formula, the decoupling of the system is realized, and the decoupled input of the inverse system is:
Figure BDA0002651840610000105
Figure BDA0002651840610000106
defining system outputs
Figure BDA0002651840610000107
Is provided with
Figure BDA0002651840610000108
Definition of thetaf＝-θr，un＝[θ M]TWherein theta isT＝[θf -θf]TTherefore u isnCan be simplified to un＝[θf,M]T。
The system equation can be expressed as:
Figure BDA0002651840610000109
x(t0)＝x0
coefficient matrix:
Figure BDA00026518406100001010
because of the fact that
Figure BDA00026518406100001011
The inverse system presence system input can be expressed as:
Figure BDA00026518406100001012
Figure BDA0002651840610000111
thus through input
Figure BDA0002651840610000112
A decoupled inversion system can be obtained.
S5, aiming at the decoupled single-input single-output system, an iterative fuzzy sliding mode controller is provided:
a discrete system defining a single input and a single output is:
Figure BDA0002651840610000113
Figure BDA0002651840610000114
Figure BDA0002651840610000115
Figure BDA0002651840610000116
y＝x
wherein F (u, t) and G (u, t) are bounded nonlinear functions,
Figure BDA0002651840610000117
is a state vector of ydFor reference tracking, the tracking error is defined as:
Figure BDA0002651840610000118
we therefore obtain a slip form face of
Figure BDA0002651840610000119
Design arrival rate of-pmsat(s)，pmThe parameters of the variables are set to be,
Figure BDA00026518406100001110
for system parameters, the adaptation rate psi is designed in the system due to model and parameter uncertaintiesadaptThus, the control rate is defined as follows:
Figure BDA00026518406100001111
wherein the adaptation rate psiadaptThe following conditions are satisfied:
ψadapt＝λ1z1+λ2z2
wherein z is1＝s,
Figure BDA00026518406100001112
λ1,λ2For adaptive parameters and defining lambdaψ＝[λ1,λ2]TIn order to obtain the iterative adaptive sliding mode control rate, fuzzy logic is adopted to fit F (u), G (u), and the control rate after fitting is obtained is as follows
Figure BDA0002651840610000121
Figure BDA0002651840610000122
Figure BDA0002651840610000123
Figure BDA0002651840610000124
Wherein
Figure BDA0002651840610000125
For adaptive control of rate
Figure BDA0002651840610000126
The fitting value of (a) is determined,
Figure BDA0002651840610000127
as fitting values of a parameter matrix, u1,u2,..,unFor discrete output, e is the error value of the tracking quantity, pmThe parameters of the variables are set to be,
Figure BDA0002651840610000128
as parameters, s is a designed sliding mode variable,
Figure BDA0002651840610000129
is an adaptive function with respect to λ, λ being an adaptive variable, λFAnd λgAdaptive parameters of F (u) and G (u), respectively, lambdaψ＝[λ1,λ2]TIs composed of
Figure BDA00026518406100001210
Adaptive parameter of (2), zψ＝[z1,z2]TIs an intermediate variable, wherein z1＝s,
Figure BDA00026518406100001211
Respectively is F (u), G (u),
Figure BDA00026518406100001212
Of a membership function of λF,λg,λψObtained from the following adaptation rate.
Figure BDA00026518406100001213
Figure BDA00026518406100001214
Figure BDA00026518406100001215
τ1,τ2,τ3Is constant, s is the slip form face, and λF,λg,λψThe optimization parameters satisfy the following equation:
Figure BDA00026518406100001216
Figure BDA00026518406100001217
Figure BDA00026518406100001218
Figure BDA00026518406100001219
is λF,λg,λψThe value set sup represents the infimum limit of the set, and meanwhile, in order to ensure the smoothness and stability of the system, the value of the adaptive quantity is obtained when argmin is the minimum value. Adaptive rate psiadaptThe following equation is satisfied:
Figure BDA0002651840610000131
i.e.. psiadapt≤pm。
In order to eliminate chattering in sliding mode control, the gradient coefficient of the switching surface is planned on line by using elements of a fuzzy logic system so as to obtain the optimal switching gain, the sliding surface and the differential of the sliding surface are input, and a parameter p is usedmAs output, a fuzzy set is chosen { negative large,small negative value, small zero positive number and large positive number, and processing by adopting a T-S fuzzy model to obtain the final system output pmAnd finishing the design of the subsystem.
The invention realizes the modeling of the dynamic model of the mobile robot, realizes the linear mapping decoupling of the model by adopting an inverse system method, and provides the self-adaptive fuzzy sliding mode controller for the decoupled subsystem, thereby improving the control coordination degree and the tracking precision of the system.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A decoupling control method for a mobile robot considering an iterative sliding mode is characterized by comprising the following steps:
s1, constructing a theoretical dynamic model about yaw inertia moment and wheel rotation angle generated by a driving wheel according to the motion mode of the wheeled robot; calculating inertia force and wheel rotation angle by using the geometric relation in the wheeled robot to be processed under the condition of considering the wheel slip angle, and substituting the calculation result into the theoretical dynamic model so as to obtain an actual dynamic model of the wheeled robot to be processed;
s2, for the actual dynamic model, decoupling the actual dynamic model according to a decoupling control method of an inverse system so as to obtain a decoupled inverse system model; and constructing an iterative fuzzy sliding mode controller according to the decoupled inverse system model, and controlling the decoupled inverse system model by using the fuzzy sliding mode controller so as to realize the decoupling control of the wheeled robot to be processed.
2. The decoupling control method for mobile robot considering iteration sliding mode according to claim 1, characterized in that in step S2, in the fuzzy sliding mode controller, an adaptive rate ψ is constructedadapt，
ψadapt＝λ1z1+λ2z2
Figure FDA0002651840600000011
Wherein z is1＝s,
Figure FDA0002651840600000012
λ1And λ2Are all self-adaptive parameters, s is a designed sliding mode surface,
Figure FDA0002651840600000013
is the coefficient matrix, e is the tracking error,
Figure FDA0002651840600000014
is the number of the iteration variables,
Figure FDA0002651840600000015
is as follows
Figure FDA0002651840600000016
The error of the secondary iteration, n is the number of sliding mode surface iterations.
3. The decoupling control method for the mobile robot considering the iterative sliding mode according to claim 2, wherein in order to ensure the stability of the inverse control system, the adaptive rate further needs to satisfy the following equation:
ψadapt≤pm
wherein p ismIs an adaptive parameter of the arrival rate.
4. The decoupling control method for the mobile robot considering the iterative sliding mode according to claim 1, wherein in step S2, for the fuzzy sliding mode controller, in order to obtain the iterative adaptive sliding mode control rate thereof, the fitted control quantity rate is obtained according to the following steps:
Figure FDA0002651840600000021
Figure FDA0002651840600000022
wherein the content of the first and second substances,
Figure FDA0002651840600000023
for adaptive control of rate
Figure FDA0002651840600000024
The fitting value of (a) is determined,
Figure FDA0002651840600000025
in order to decouple the control variable of the inverse system,
Figure FDA0002651840600000026
and
Figure FDA0002651840600000027
are respectively a parameter matrix F (u)1,u2,...,un) And G (u)1,u2,..,un) Fitting value of u1,u2,..,unIn order to output the signals discretely,
Figure FDA00026518406000000221
is a coefficient matrix, e is a tracking error, pmIs a variable parameter, s is a designed sliding mode variable,
Figure FDA0002651840600000028
is an adaptive function with respect to lambda, which is an adaptive variable,
Figure FDA0002651840600000029
is an iteration variable, n is the number of iterations of the sliding mode surface, λψIs composed of
Figure FDA00026518406000000210
Adaptive parameter of (2), zψ＝[z1,z2]TIs an intermediate variable, wherein z1＝s,
Figure FDA00026518406000000211
Figure FDA00026518406000000212
Is the reference value for the nth iteration of the state quantity u.
5. The decoupling control method for the mobile robot considering the iterative sliding mode according to claim 4, wherein the parameter matrix equation of the fuzzy sliding mode controller is obtained by fitting in the following way:
Figure FDA00026518406000000213
Figure FDA00026518406000000214
wherein the content of the first and second substances,
Figure FDA00026518406000000215
is the fitted value of the parameter matrix f (u),
Figure FDA00026518406000000216
is the fitting value, λ, of the parameter matrix G (u)FAnd λgAdaptive parameters for F (u) and G (u), respectively,
Figure FDA00026518406000000217
f (u) and G (u), respectively, are fuzzy basis vectors.
6. The decoupling control method of the mobile robot considering the iterative sliding mode according to claim 5, wherein λ isF，λgAnd λψObtained in the following way:
Figure FDA00026518406000000218
Figure FDA00026518406000000219
Figure FDA00026518406000000220
τ1,τ2,τ3is a constant number of times, and is,
Figure FDA0002651840600000031
and
Figure FDA0002651840600000032
are each lambdaF，λgAnd λψFirst order inverse of (a) (-)ψIs composed of
Figure FDA0002651840600000033
The adaptive parameters of (a) are set,
Figure FDA0002651840600000034
is psiadaptS is the sliding mode surface and lambda is the fuzzy basis vector ofF,λg,λψThe following equation is also satisfied:
Figure FDA0002651840600000035
Figure FDA0002651840600000036
Figure FDA0002651840600000037
Figure FDA0002651840600000038
is λF,λg,λψA set of values of (a) is selected,
Figure FDA0002651840600000039
and
Figure FDA00026518406000000310
for optimized lambdaF,λg,λψSup denotes the infimum limit of the set,
Figure FDA00026518406000000311
is an n-dimensional real space and z is a variable with respect to s.
7. The decoupling control method for the mobile robot considering the iterative sliding mode according to claim 1, wherein in step S2, the decoupled inverse system model is performed according to the following relation:
Figure FDA00026518406000000312
wherein u is the output of the inverse system after decoupling, and [ theta ]f,M]T，θfFor virtual front wheel turning, M is the yaw moment of inertia generated by the drive wheel, dfAnd drTransverse stiffness of the front and rear wheels, respectively, /)fAnd lrRespectively the distance from the central point of the chassis of the wheeled robot to the front virtual wheel and the rear virtual wheelFrom, IzIs yaw moment of inertia of the platform, v is longitudinal speed of the wheeled robot to be processed, m is mass of the wheeled robot to be processed, x is system state quantity before decoupling, u1＝fAnd u2M is the state quantity of the inverse system after decoupling,
Figure FDA00026518406000000313
in order to decouple the control variable of the inverse system,
Figure FDA00026518406000000314
is the derivative order of the inverse system observations y after decoupling,
Figure FDA00026518406000000315
is a positive integer.
8. A decoupling control method for a mobile robot considering iterative sliding mode according to claim 1, characterized in that in step S1, the theoretical dynamic model is performed according to the following relation:
Figure FDA0002651840600000041
Figure FDA0002651840600000042
ay＝a2β+b2vγ
wherein
Figure FDA0002651840600000043
Figure FDA0002651840600000044
Figure FDA0002651840600000045
Wherein beta is a sideslip angle, a0，a1，a2，b0，b1，b2，c0And c1Is an intermediate variable, gamma is the yaw angle of the chassis of the wheeled robot, dfAnd drTransverse stiffness of the front and rear wheels, respectively, /)fAnd lrRespectively the distance theta from the central point of the chassis of the wheeled robot to the front virtual wheel and the rear virtual wheelfAnd thetarRespectively the corners of the virtual front wheel and the virtual rear wheel, m is the platform mass, IzThe yaw moment of inertia of the platform, M is the yaw moment of inertia generated by the driving wheels, and v is the longitudinal speed of the wheeled robot to be processed.
9. A decoupling control method of a mobile robot considering iterative sliding mode according to claim 1, characterized in that in step S1, the inertia moment and the wheel rotation angle are calculated according to the following relation:
for the moment of inertia M, the relationship is as follows:
M＝My+Mx
My＝[lf lr][Fyf Fyr]T
Mx＝h(Fxf+Fxr)
Figure FDA0002651840600000046
Figure FDA0002651840600000047
where i represents the indicia of the wheel, i ═ f, r, f are the front wheels, r are the rear wheels, M is the moment of inertia, M represents the wheel's weightyIs a partial moment in the transverse direction, MxIs a partial moment in the longitudinal direction，lfAnd lrDistances from the central point of the chassis of the wheeled robot to the front virtual wheel and the rear virtual wheel respectively, FyfTo simulate the transverse forces of the front wheels of the wheel, FyrTo simulate the transverse forces of the rear wheels of the wheels, FxfAnd FxrLongitudinal forces, theta, of the front and rear wheels, respectivelyLiAnd thetaRiRespectively the angle of rotation, alpha, of the actual left-hand wheel and the actual right-hand wheelLiAnd alphaRiThe slip angles of the actual left and right side wheels,
Figure FDA0002651840600000051
and
Figure FDA0002651840600000052
is an intermediate variable, fLiAnd fRiThe friction force of the actual left wheel and the actual right wheel respectively, and h is the width between the left wheel and the right wheel;
for wheel angle thetaLiAnd thetaRiThe method is carried out according to the following relations:
Figure FDA0002651840600000053
Figure FDA0002651840600000054
wherein, thetaiWhere i is f, r, f is the front wheel, r is the rear wheel, θ is the virtual wheel anglefAnd thetarRespectively the angle of rotation, g, of the virtual front wheel and the virtual rear wheeliAnd lmIs an intermediate variable.
10. The decoupling control method for the mobile robot considering the iterative sliding mode according to claim 9, wherein the lateral force F of the front wheel of the virtual wheel isyfAnd the lateral force F of the rear wheel of the virtual wheelyrCalculated from the yaw forces of the actual wheels according to the following formulaAnd (3) calculating:
Fyj(αj)＝pjsin{qjarctan[(1-j)ρjαj+jarctan(ρjαj)]}
Figure FDA0002651840600000055
the parameter expression is as follows:
Figure FDA0002651840600000056
where j is the number of the wheel, and for a four-wheel wheeled robot, j is 1,2,3,4, piIs a peak value, qiAs a curve shape parameter, piIn order to be a factor of the curve,iin order to be a coefficient of stiffness of the tire,i(i ═ 1, 2.., 5) is an environmental parameter, Fy1,Fy2Transverse force of front side No. 1,2 actual wheel, Fy3And Fy4The lateral forces of the rear side No. 3 and No. 4 actual wheels, respectively.
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