CN103433924A - High-accuracy position control method for serial robot - Google Patents

Abstract

The invention provides an improved serial robot control method. According to the improved serial robot control method, a specific mathematical model of a controlled object does not need to be known; the improved serial robot control method has strong robustness and high tracking precision; and moreover, the problems of moment jump and velocity jump, which are caused by deviation of an original pose in a large range, are improved. Strong robustness in the control is ensured by adopting a slip form method on the basis of a torque calculation method; the buffeting problem in the slip form control is eliminated by introducing an exponential approach law; a self-adaptive fuzzy controller is adopted to carry out estimation on a slip form switching gain according to slip form arrival conditions so as to reinforce adaptive capacity of the controlled object for uncertain factors and eliminate the buffeting phenomenon of output torque in the slip form control; and another fuzzy self-adaptive controller is adopted to correct a coefficient of the exponential approach law so as to improve the problems of large moment and velocity jumps, which are caused by deviation of the original pose in a large range.

Description

Serial machine people high precision position control method

Technical field

The present invention relates to serial machine people's Position Control field, specifically refer to and a kind ofly realize serial machine people's high precision position is followed the tracks of and the improvement method of robot moment and velocity jump problem while starting by the fuzzy self-adaption sliding-mode control.

Background technology

Robotics is that collecting mechanism, electronic technology, computer technology, sensing technology, cybernetics, artificial intelligence and bionics etc. are multidisciplinary in the new and high technology of one.

It is a key areas of Robotics that the robot location controls.Industrial robot is the nonlinear system of the multiple-input and multiple-output of a complexity, has close coupling, time and becomes and the dynamics such as non-linear, its control procedure complexity.Inaccuracy due to robot parameter measurement and modeling, add the uncertainty of robot load and industrial external disturbance, can't obtain complete, the accurate object model of robot in reality, the specific application environment of industrial robot, determine that it must be in the face of the existence of various uncertain factors.

For robot, its controller design is divided into two classes: a class is to carry out negative feedback control according to the deviation between robot actual path and desired trajectory.These class methods are called " motion control ", and major advantage is that control law is simple, are easy to realize.But, for controlling high-speed high-accuracy robot, these class methods have two obvious shortcomings: the one, be difficult to guarantee that the controlled machine people has good dynamic and static performance; The 2nd, control energy that need to be larger.Another kind of controller design is called " dynamically controlling ".These class methods are to design meticulousr Nonlinear control law according to the character of Dynamic Models of Robot Manipulators, so often be called again " take model as basic control ".Can make to be there is good dynamic and static performance by man-controlled mobile robot with the controller of dynamic control method design, overcome the shortcoming of motion control method.

Sliding formwork is controlled the Mathematical Modeling that does not need to know controlled device, but the problem of shaking that struggles against easily appears in controlling, control effect in order further to improve sliding formwork, can adopt Adaptive Fuzzy Sliding Mode Control, self adaptation is regulated the gain that sliding formwork is controlled, enhancing, to random probabilistic adaptive capacity, is eliminated the input chattering phenomenon in sliding formwork is controlled.But it is worth noting, in high-torque and the velocity jump problem of tracking error sudden change Time Controller, control to actual robot and bring very large drawback, be very easy to damage the servomotor in each joint.

Summary of the invention

The object of the invention is to based on Double Fuzzy adaptive sliding mode control technology, design that a kind of tracking effect is good, robot location's control algolithm of speed output smoothing.Improve well high-torque that the deviation that produces due to large initial pose causes and the saltus step problem of speed.

For reaching this purpose, technical scheme of the present invention is as follows: the sliding formwork control technology based on the computing power moments method, set up the link rod coordinate system of robot, and obtain its D-H parameter, obtain the kinetics equation of robot.Inertia item, coriolis force item and gravity item according to each joint of D-H parameter estimation, finally draw the moment estimation equation in each joint.Site error by each joint is set up sliding-mode surface, and the sliding formwork control technology of utilization based on the computing power moments method carried out the Position Control in each joint.In order to reduce the chattering phenomenon in sliding formwork control, added the exponential approach rule, for sliding formwork handoff gain K employing Adaptive Fuzzy Control wherein, estimated online.Moment saltus step and the velocity jump problem in order to weaken large initial deviation, brought, adopt another fuzzy control to estimate the coefficient A of exponential approach rule, determines optimized parameter.Whole flow process comprises: the dynamics estimation block, set up sliding-mode surface module, sliding formwork handoff gain estimation block, exponential approach rule estimation block, control moment computing module.

The first step, set up each link rod coordinate system of robot, determines the D-H parameter (a of each connecting rod _i, α _i, d _i, θ _i).By Lagrange's equation:

i=1,2 ..., n, derive kinetics equation: $T_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{D}_{\mathrm{ij}}{\stackrel{\·\·}{q}}_j+I_{\mathrm{ai}}{\stackrel{\·\·}{q}}_i+\underset{j=1}{\overset{6}{\mathrm{\Σ}}}\underset{k=1}{\overset{6}{\mathrm{\Σ}}}{D}_{\mathrm{ijk}}{\stackrel{\·}{q}}_j{\stackrel{\·}{q}}_k+D_i$

Estimate inertia item, coriolis force item and gravity item according to kinetics equation finally draw the moment estimation equation of each axle: $\widehat{\mathrm{\τ}}=\hat{H}{\stackrel{\·\·}{q}}_r+\hat{C}{\stackrel{\·}{q}}_r+\hat{G}.$

Second step, by site error e and the error rate that calculates each joint

set up sliding-mode surface

Λ=diag[λ wherein ₁... λ _lλ _n], λ _l>0.

And definition: ${\stackrel{\·}{q}}_r=\stackrel{\·}{q}-s={\stackrel{\·}{q}}_d-\mathrm{\Λe},{\stackrel{\·\·}{q}}_r=\stackrel{\·\·}{q}-\stackrel{\·}{s}={\stackrel{\·\·}{q}}_d-\mathrm{\Λ}\stackrel{\·}{e}$

Design control law is: $\mathrm{\τ}=\widehat{\mathrm{\τ}}-\mathrm{As}-\mathrm{Ksgns},$ $\widehat{\mathrm{\τ}}=\hat{H}{\stackrel{\·\·}{q}}_r+\hat{C}{\stackrel{\·}{q}}_r+\hat{G}$

Wherein,

for equivalent control, As is the exponential approach rule, and K sgns is switching controls.

be respectively H, C, the estimated value of G, K=diag[K ₁₁... K _ii... K _nn], A=diag[a ₁..., a _i..., a _n] be positive definite matrix.

The 3rd step, approach the gain K of sliding formwork control law by the fuzzy control self adaptation.Adopt product inference machine, the average defuzzifier of monodrome fuzzy device and center to design Fuzzy control system, the control of system is output as:

$k_i=\frac{\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_{k_i}^m{\mathrm{\μ}}_{A^m}\left(S_i\right)}{\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\μ}}_{A^m}\left(S_i\right)}={\mathrm{\ϵ}}_{k_i}^T{\mathrm{\Ψ}}_{k_i}\left(S_i\right),$

For meaning that the membership function of fuzzy set is designed to:

${\mathrm{\μ}}_A\left(x_i\right)=\exp [-{\left(\frac{x_i-\mathrm{\α}}{\mathrm{\σ}}\right)}^2]$

Choosing adaptive law is:

The 4th step, the index control item coefficient that sliding formwork is controlled carries out fuzzy control, by regulating A, reaches: when error and error rate reduce controlled quentity controlled variable large the time as far as possible; Otherwise, increase controlled quentity controlled variable.Thereby retain the tracking effect that former control algolithm is good, high-torque and velocity jump problem while improving the robot startup simultaneously.

The 5th step, by top a few part combinations, the Torque Control in joint is input as:

$\mathrm{\τ}=\widehat{\mathrm{\τ}}-\mathrm{As}-\mathrm{Ksgns},\widehat{\mathrm{\τ}}=\hat{H}{\stackrel{\·\·}{q}}_r+\hat{C}{\stackrel{\·}{q}}_r+\hat{G}.$

Wherein,

be respectively H, C, the estimated value of G, s is sliding-mode surface, by the adaptive sliding mode control method of the 3rd step, estimates parameter K, utilizes the sliding-mode control of the 4th step to estimate parameter A.

Beneficial effect of the present invention: provide a kind of robot location's control method based on the Double Fuzzy adaptive sliding mode, for improving serial machine people tracking accuracy and improving moment, velocity jump problem.It is the special nonlinear Control of a class in essence that sliding formwork is controlled, and because having strong robustness, becomes a kind of effective control method; Introduce the exponential approach rule on the basis of controlling at sliding formwork, effectively eliminate the buffeting problem; Adopt an adaptive fuzzy controller, arrive condition according to sliding formwork the sliding formwork handoff gain is estimated, strengthen its adaptive capacity to uncertain factor, eliminated the chattering phenomenon of output torque in sliding formwork is controlled; Adopt another fuzzy adaptive controller to be revised the coefficient of exponential approach rule, improve the high-torque and the velocity jump problem that cause due on a large scale initial pose change of error.

The accompanying drawing explanation

Fig. 1 link rod coordinate system schematic diagram;

Fig. 2 overall schematic of the present invention.

The specific embodiment

For making the purpose, technical solutions and advantages of the present invention clearer, below in conjunction with specific embodiment, and, with reference to accompanying drawing, the present invention is described in further detail.

Basic ideas of the present invention are: the control method that a kind of improved robot is provided: it does not need to know the concrete mathematical model of controlled device; And there is strong robustness, high tracking accuracy; And improve the moment saltus step and the velocity jump problem that cause due on a large scale initial pose deviation.At first the present invention carries out its kinetic model of modeling estimation to robot, adopts the sliding formwork nonlinear control method based on the computing power moments method, the strong robustness in guaranteeing to control; The robot sliding formwork is controlled and be there will be chattering phenomenon, so the present invention introduces the exponential approach rule, effectively eliminates the buffeting problem.Simultaneously, the present invention adopts an adaptive fuzzy controller, arrives condition according to sliding formwork the sliding formwork handoff gain is estimated, strengthens its adaptive capacity to uncertain factor, eliminates the chattering phenomenon of output torque in sliding formwork is controlled; Adopt another fuzzy adaptive controller to be revised the coefficient of exponential approach rule, improve the high-torque and the velocity jump problem that cause due on a large scale initial pose change of error.

Accompanying drawing 2 is whole control block diagram of the present invention.Dynamics estimation block 1 is by setting up the link rod coordinate system of robot, obtain its D-H parameter, obtain the kinetics equation of robot, inertia item, coriolis force item and gravity item according to each joint of D-H parameter estimation, finally draw the moment estimation equation in each joint.Set up sliding-mode surface module 2 and set up sliding-mode surface by the site error in each joint, the sliding formwork control technology of utilization based on the computing power moments method carried out the Position Control in each joint.Sliding formwork handoff gain estimation block 3, for reducing the chattering phenomenon of sliding formwork in controlling, adds the exponential approach rule, for sliding formwork handoff gain K wherein, adopts Adaptive Fuzzy Control to be estimated online.Exponential approach rule estimation block 4, for to weaken high-torque and the velocity jump problem that large initial deviation brings, adopts another fuzzy control to estimate exponential approach rule coefficient, determines optimized parameter.Control moment computing module 5 is finally calculated the control inputs τ in each joint _icomplete the Position Control of robot.

Further, described dynamics estimation block 1 is specially:

(1.1) acquisition of D-H parameter:

An affixed coordinate system respectively on each connecting rod, the coordinate system affixed with pedestal is designated as that { 0}, the coordinate system affixed with connecting rod i is designated as { i}, two parameter connecting rod torsional angle α for the D-H method _iwith length of connecting rod α _idescribe any connecting rod i, use connecting rod offset d _iwith joint angle θ _ithe relation of adjacent connecting rod is described.4 link parameters can be defined as respectively: α _i--around X _iaxle, Z _i-1axle is to Z _ithe angle of axle; a _i--along X _iaxle, Z _i-1axle is to Z _ithe distance of axle; d _i--along Z _i-1axle, X _i-1axle is to X _ithe distance of axle; θ _i--around Z _i-1axle, X _i-1axle is to X _ithe angle of axle.As Fig. 1.

(1.2) ask for kinematical equation:

After having determined the D-H parameter, by two translational motions and two, rotatablely move to set up the relativeness between adjacent connecting rod i-1 and i, the connecting rod conversion ^i-1t _imean link rod coordinate system i} with respect to coordinate system the conversion of i-1} can be decomposed into four steps:

A) around Z _i-1axle rotation θ _iangle, make X _i-1axle forwards to and X _iin same plane;

B) along axle Z _i-1translation one distance, d _i, X _i-1move to and X _ion same straight line;

C) along axle X _i-1translation distance a _i, make the initial point of two coordinate systems overlapping;

D) around axle X _i-1rotation alpha _iangle, make two coordinate systems fully overlapping.

So, { with respect to link rod coordinate system, { pose of i-1} can be used the homogeneous transformation matrix to i} to link rod coordinate system ^i-1t _ibe expressed as:

$T_i^{i-1}=T_{\mathrm{rot}}(Z_{i-1},{\mathrm{\θ}}_i)T_{\mathrm{tran}}(Z_{i-1},d_i)T_{\mathrm{tran}}(X_{i-1},a_i)T_{\mathrm{rot}}(X_{i-1},{\mathrm{\α}}_i)$

$=\left[\begin{array}{cccc}{\cos \mathrm{\θ}}_i& -{\sin \mathrm{\θ}}_i{\cos \mathrm{\α}}_i& {\sin \mathrm{\θ}}_i{\sin \mathrm{\α}}_i& a_i{\cos \mathrm{\θ}}_i\\ {\sin \mathrm{\θ}}_i& {\cos \mathrm{\θ}}_i{\cos \mathrm{\α}}_i& {-\cos \mathrm{\θ}}_i{\sin \mathrm{\α}}_i& a_i{\sin \mathrm{\θ}}_i\\ 0& {\sin \mathrm{\α}}_i& {\cos \mathrm{\α}}_i& d_i\\ 0& 0& 0& 1\end{array}\right]$

Kinematical equation is:

⁰T ₆＝ ⁰T ₁? ¹T ₂? ²T ₃? ³T ₄? ⁴T ₅? ⁵T ₆

(1.3) system dynamics equation, Lagrange's equation is as follows:

i=1,2 ..., the accurate kinetic model of n mechanical arm is:

${\mathrm{\τ}}_i=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{D}_{\mathrm{ij}}{\stackrel{\·\·}{q}}_j+I_{\mathrm{ai}}{\stackrel{\·\·}{q}}_i+\underset{j=1}{\overset{6}{\mathrm{\Σ}}}\underset{k=1}{\overset{6}{\mathrm{\Σ}}}{D}_{\mathrm{ijk}}{\stackrel{\·}{q}}_j{\stackrel{\·}{q}}_k+D_i$

For three joint mechanical arms:

$D_{\mathrm{ij}}=\underset{p=\max i,j}{\overset{3}{\mathrm{\Σ}}}\mathrm{Trace}\left(\frac{{\∂T}_p}{{\∂q}_j}{I}_p\frac{{\∂T}_p^T}{{\∂q}_i}\right)$

$D_{\mathrm{ijk}}=\underset{p=\max i,j,k}{\overset{3}{\mathrm{\Σ}}}\mathrm{Trace}\left(\frac{{\∂}^2{T}_p}{{\∂q}_j{\∂q}_k}{I}_i\frac{{\∂T}_p^T}{{\∂q}_i}\right)$

$D_i=\underset{p=i}{\overset{3}{\mathrm{\Σ}}}{-m}_p{g}^T\frac{{\∂T}_p}{{\∂q}_i}r_p^p$

I _aifor the equivalent moment of inertia of transmission device, generally can ignore.Estimate each joint inertia item, coriolis force item and gravity item according to kinetics equation

finally draw the moment estimation equation of each axle: $\widehat{\mathrm{\τ}}=\hat{H}{\stackrel{\·\·}{q}}_r+\hat{C}{\stackrel{\·}{q}}_r+\hat{G}.$

Described sliding formwork control module 2 is specially:

(2.1) design of sliding-mode surface

The position tracking error of definition mechanical arm is e=q _d-q, wherein q _dfor the joint desired locations, q is physical location.The definition error function is: Λ=diag[λ wherein ₁..., λ _i..., λ _n], λ _i>0.

(2.2) design of sliding formwork control law

Definition: ${\stackrel{\·}{q}}_r=\stackrel{\·}{q}-s={\stackrel{\·}{q}}_d-\mathrm{\Λe},{\stackrel{\·\·}{q}}_r=\stackrel{\·\·}{q}-\stackrel{\·}{s}={\stackrel{\·\·}{q}}_d-\mathrm{\Λ}\stackrel{\·}{e}$

Design control law is: $\mathrm{\τ}=\widehat{\mathrm{\τ}}-\mathrm{As}-\mathrm{Ksgns},\widehat{\mathrm{\τ}}=\hat{H}{\stackrel{\·\·}{q}}_r+\hat{C}{\stackrel{\·}{q}}_r+\hat{G}$

Wherein,

for equivalent control, As is the exponential approach rule, and Ksgns is switching controls.

be respectively H, C, the estimated value of G, K=diag[K ₁₁..., K _ii... K _nn], A=diag[a ₁..., a _i..., a _n] be positive definite matrix.

Described sliding formwork handoff gain estimation block 3 is specially:

(3.1) design of fuzzy rule

Design of control law based on the Fuzzy Gain adjustment is: k=[k wherein ₁..., k _i..., k _n], k _ibe the output of i fuzzy system.

If gain K adopts fuzzy control to be approached, and definition Lyapunov function:

$\stackrel{\·}{V}=\frac{1}{2}[{\stackrel{\·}{s}}^T\mathrm{Hs}+s^T\stackrel{\·}{H}s+s^{T}H\stackrel{\·}{s}]=\frac{1}{2}[{2s}^{T}H\stackrel{\·}{s}+s^T\stackrel{\·}{H}s]=s^T[-(C+A)s+\mathrm{\Δf}-K+\mathrm{Cs}]=$ $s^T[-\mathrm{As}+\mathrm{\Δf}-K]=s^T[\mathrm{\Δf}-K]-s^T\mathrm{As}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[s_i{\mathrm{\Δf}}_i-s_i{k}_i]-s^T\mathrm{As}$

As can be seen here, for guaranteeing

for negative, should make s _ik _i>=O, guarantee s _iwith k _isymbol is identical.Simultaneously, consider s _iΔ f _i-s _ik _i, when | s _i| when larger, for guaranteeing

for larger negative, wish | k _i| larger; When | s _i| hour, | k _i| keep less value, just can guarantee

for negative.

(3.2) Design of Fuzzy Systems

For meaning that the membership function of fuzzy set is designed to:

${\mathrm{\μ}}_A\left(x_i\right)=\exp [-{\left(\frac{x_i-\mathrm{\α}}{\mathrm{\σ}}\right)}^2]$

Adopt product inference machine, the average defuzzifier of monodrome fuzzy device and center to design Fuzzy control system, the control of system is output as: fuzzy system is output as:

$k_i=\frac{\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\ϵ}}_{k_i}^m{\mathrm{\μ}}_{A^m}\left(s_i\right)}{\underset{m=1}{\overset{M}{\mathrm{\Σ}}}{\mathrm{\μ}}_{A^m}\left(s_i\right)}={\mathrm{\ϵ}}_{k_i}^T{\mathrm{\Ψ}}_{k_i}\left(s_i\right)$

Wherein: ${\mathrm{\&epsiv;}}_{k_i}={[{\mathrm{\&epsiv;}}_{k_{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HSA0000093138170000011.png"\; state="\{\{state\}\}">i</figure-callout>}}}^1,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&epsiv;}}_{k_i}^m,\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&epsiv;}}_{k_i}^M]}^T,{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)={[{\mathrm{\&phi;}}_{k_i}^1\left(s_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&phi;}}_{k_i}^m\left(s_i\right),\&CenterDot;\&CenterDot;\&CenterDot;,{\mathrm{\&phi;}}_{k_i}^M\left(s_i\right)]}^T,$

${\mathrm{\&phi;}}^m\left(x\right)=\frac{\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}{\mathrm{\&mu;}}_{A_i^m}\left(x_i^{*}\right)}{\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}{\mathrm{\&mu;}}_{A_i^m}\left(x_i^{*}\right)},$

(3.3) design of Adaptive Fuzzy Control rule

The above obtains: $H\stackrel{\&CenterDot;}{s}=-(C+A)s+\mathrm{\&Delta;f}-k---\left(1\right)$

Get

for desirable Δ f _iapproach, according to omnipotent approximation theorem, have ω _i>0, have:

$|{\mathrm{\&Delta;f}}_i-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)|\&le;{\mathrm{\&omega;}}_i---\left(2\right)$

Definition Lyapunov function: $V=\frac{1}{2}{s}^T\mathrm{Hs}+\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left({\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\widetilde{\mathrm{\&theta;}}}_{k_i}\right).$ Wherein ${\widetilde{\mathrm{\&theta;}}}_{k_i}={\mathrm{\&theta;}}_{k_i}-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}.$ ?

$\stackrel{\&CenterDot;}{V}=\frac{1}{2}[{\stackrel{\&CenterDot;}{s}}^T\mathrm{Hs}+s^T\stackrel{\&CenterDot;}{H}s+s^{T}H\stackrel{\&CenterDot;}{s}]+\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}({\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}^T{\widetilde{\mathrm{\&theta;}}}_{k_i}+{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i})$

$=\frac{1}{2}[{2s}^{T}H\stackrel{\&CenterDot;}{s}+s^T\stackrel{\&CenterDot;}{H}s]+\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}2{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}=s^T[H\stackrel{\&CenterDot;}{s}+\mathrm{Cs}]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}$

$=s^T[-(C+A)s+\mathrm{\&Delta;f}-k+\mathrm{Cs}]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}$

$=s^T[-\mathrm{As}+\mathrm{\&Delta;f}-k]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}=-s^T\mathrm{As}+s^T[\mathrm{\&Delta;f}-k]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}$

$=-s^T\mathrm{As}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{s}_i[\mathrm{\&Delta;f}-k_i]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}$

Due to $k_i={\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)+{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right),$ :

$\stackrel{\&CenterDot;}{V}={-s}^T\mathrm{As}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{s}_i[{\mathrm{\&Delta;f}}_i-({\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)+{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right))]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}$

$=-s^T\mathrm{As}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{s}_i[{\mathrm{\&Delta;f}}_i-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left({-s}_i{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)\right)+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i}$

$=-s^T\mathrm{As}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{s}_i[{\mathrm{\&Delta;f}}_i-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}({-s}_i{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)+{\widetilde{\mathrm{\&theta;}}}_{k_i}^T{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i})---\left(3\right)$

$={-s}^T\mathrm{As}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{s}_i[{\mathrm{\&Delta;f}}_i-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)]+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\widetilde{\mathrm{\&theta;}}}_{k_i}^T({-s}_i{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)+{\stackrel{\&CenterDot;}{\widetilde{\mathrm{\&theta;}}}}_{k_i})$

Choosing adaptive law is: ${\stackrel{\stackrel{\&CenterDot;}{~}}{\mathrm{\&theta;}}}_{k_i}=s_i{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)---\left(4\right)$

And substitution (3) formula obtains: $\stackrel{\&CenterDot;}{V}=-s^T\mathrm{As}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{s}_i[{\mathrm{\&Delta;f}}_i-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right)]$

There is arithmetic number γ _i, make (2) formula meet:

0<γ wherein _i<1.: $s_i|{\mathrm{\&Delta;f}}_i-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}^T{\mathrm{\&Psi;}}_{k_i}\left(s_i\right){|\&le;{\mathrm{\&gamma;}}_i|s_i|}^2={\mathrm{\&gamma;}}_i{s}_i^2$

$\stackrel{\&CenterDot;}{V}\&le;-s^T\mathrm{As}+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_i{s}_i^2=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(-a_i{s}_i^2+{\mathrm{\&gamma;}}_i{s}_i^2)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}({\mathrm{\&gamma;}}_i-a_i)s_i^2\&le;0---\left(5\right)$

γ=diag[γ wherein ₁..., γ _i... γ _n], a _i>γ _i.From formula (5), only when s=0,

adaptive law (4) asymptotic convergence.Reach a conclusion for:

?

$\underset{t\&RightArrow;\&infin;}{\lim }\stackrel{\&CenterDot;}{q}={\stackrel{\&CenterDot;}{q}}_d.$

Described exponential approach rule estimation block 4 is specially:

(4.1) controller at this moment can produce a larger error and error rate while just having started due to robot, so can produce a larger output.In order to reduce this situation, on the basis of controlling at sliding formwork, the index control item coefficient that sliding formwork is controlled carries out fuzzy control, by regulating A, reaches: when error and error rate reduce controlled quentity controlled variable large the time as far as possible; Otherwise, increase controlled quentity controlled variable.Thereby high-torque and velocity jump problem while improving the robot startup.

(4.2) realization that control law can self-regulating fuzzy controller:

The quality of a fuzzy controller performance depends on its fuzzy control rule to a great extent, if adopt fixing fuzzy control rule, once fuzzy controller forms, language rule and compositional rule of inference are exactly definite, nonadjustable.But control in scene at some, in order to make existing fuzzy controller, there is stronger compliance, to be adapted to different control objects, just require control law to there is certain self-regulating function.

For the fuzzy controller of a two dimension, when the domain divided rank of its input variable E, EC and output quantity U is identical, the description control law expression formula of introducing is:

$U=[\mathrm{\&alpha;E}+(1-\mathrm{\&alpha;})\mathrm{EC}],\mathrm{\&alpha;}\&Exists;\&Element;\left(\mathrm{0,1}\right)$

By regulating the α value, just can be regulated control law.

Described control moment computing module 5 is specially:

(5) by top a few part combinations, the Torque Control in joint is input as:

wherein,

be respectively H, C, the estimated value of G, s is sliding-mode surface, by the adaptive sliding mode control method of the 3rd step, estimates parameter K, utilizes the sliding-mode control of the 4th step to estimate parameter A.Control inputs using the τ of calculating as joint.

Claims (6)

1. a kind of improved serial machine people control method is provided: it does not need to know the concrete mathematical model of controlled device; And there is strong robustness, high tracking accuracy; And improve the moment saltus step and the velocity jump problem that cause due on a large scale initial pose deviation; At first the present invention carries out modeling to robot, estimates its kinetic model, adopts the sliding formwork nonlinear control method based on the computing power moments method, the strong robustness in guaranteeing to control; The robot sliding formwork is controlled and be there will be chattering phenomenon, so the present invention introduces the exponential approach rule, effectively eliminates the buffeting problem; Simultaneously, the present invention adopts an adaptive fuzzy controller, arrives condition according to sliding formwork the sliding formwork handoff gain is estimated, strengthens its adaptive capacity to uncertain factor, eliminates the chattering phenomenon of output torque in sliding formwork is controlled; Adopt another fuzzy adaptive controller to be revised the coefficient of exponential approach rule, improve the high-torque and the velocity jump problem that cause due on a large scale initial pose change of error;

Dynamics estimation block 1 is by setting up the link rod coordinate system of robot, obtain its D-H parameter, obtain the kinetics equation of robot, inertia item, coriolis force item and gravity item according to each joint of D-H parameter estimation, finally draw the moment estimation equation in each joint;

Set up sliding-mode surface module 2 and set up sliding-mode surface by the site error in each joint, the sliding formwork control technology of utilization based on the computing power moments method carried out the Position Control in each joint;

Sliding formwork handoff gain estimation block 3, in order to reduce the chattering phenomenon in sliding formwork control, has added the exponential approach rule, for constant speed convergence item coefficient K employing Adaptive Fuzzy Control wherein, is estimated online;

Exponential approach rule estimation block 4, for to weaken high-torque and the velocity jump that large initial deviation brings, adopts another fuzzy control to estimate exponential approach rule coefficient, determines optimized parameter;

Control moment computing module 5 is finally calculated the control inputs τ in each joint _icomplete the Position Control of robot; Realize robot location's high precision tracking and improve the moment saltus step and the velocity jump problem.

2. the Double Fuzzy adaptive sliding mode control method based on the computing power moments method according to claim 1, it is characterized in that: described D-H ginseng is asked for and the dynamics estimation block, sets up each link rod coordinate system of robot, determines the D-H parameter (a in each joint _i, α _i, d _i, θ _i); By Lagrange's equation:

i=1,2 ..., n, derive kinetics equation:

estimate inertia item, coriolis force item and gravity item according to kinetics equation

finally draw the moment estimation equation in each joint:

3. the Double Fuzzy adaptive sliding mode control method based on the computing power moments method according to claim 1 is characterized in that: the described sliding-mode surface module of setting up, and by site error e and the error rate that calculates each joint

set up sliding-mode surface

Λ=diag[λ wherein ₁..., λ _i..., λ _n], λ _i>0;

And definition:

Design control law is:

wherein,

for equivalent control, As is the exponential approach rule, and Ksgns is switching controls;

be respectively H, C, the estimated value of G, K=diag[K ₁₁..., K _ii... K _nn], A=diag[a ₁..., a _i..., a _n] be positive definite matrix.

4. the Double Fuzzy adaptive sliding mode control method based on the computing power moments method according to claim 1 is characterized in that: described sliding formwork handoff gain estimation block, approach the gain K of sliding formwork control law by the fuzzy control self adaptation; Adopt product inference machine, the average defuzzifier of monodrome fuzzy device and center to design Fuzzy control system, the control of system is output as:

For meaning that the membership function of fuzzy set is designed to:

Choosing adaptive law is:

5. the Double Fuzzy adaptive sliding mode control method based on the computing power moments method according to claim 1, it is characterized in that: described exponential approach rule estimation block, the index control item coefficient that sliding formwork is controlled carries out fuzzy control, by regulating A, reaches: when error and error rate reduce controlled quentity controlled variable large the time as far as possible; Otherwise, increase controlled quentity controlled variable, thereby retained the good tracking effect of former control algolithm, improved high-torque problem when robot starts simultaneously.

6. the Double Fuzzy adaptive sliding mode control method based on the computing power moments method according to claim 1 is characterized in that: described control moment computing module, and by top several parts combinations, the Torque Control in joint is input as:

wherein, be respectively H, C, the estimated value of G, s is sliding-mode surface, by the adaptive sliding mode control method of the 3rd step, estimates parameter K, utilizes the sliding-mode control of the 4th step to estimate parameter A; Control inputs using the τ of calculating as joint.

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