CN104216403A - Multi-model adaptive control method in visual servo robot - Google Patents

Abstract

The invention provides a multi-model adaptive control method in a visual servo robot. The multi-model adaptive control method comprises the following steps of taking center point values in subsets of models; applying the center point values to error models so as to obtain a first system identification error; estimating objective position parameters of the subsets of the models so as to obtain estimated values; applying the estimated values in the error models so as to obtain a second system identification error; comparing the first system identification error and the second system identification error so as to judge whether the objective position parameters are changed or not; controlling a controlled object through a hybrid controller by using a mixed strategy if a judgment result is not changed; and reconstructing the corresponding estimated values into the center point values of the subsets of the models if the judgment result is changed and controlling the controlled objects by using secondary controllers corresponding to the subsets of the models.

Description

Multi-model Adaptive Control method in Visual Servo Robot

Technical field

The present invention relates to automation field, particularly relate to a kind of multi-model Adaptive Control method in Visual Servo Robot.

Background technology

In actual industrial process, under different working condition, model structure or parameter are often different.In this case, the effect of the adaptive controller of single model is unsatisfactory, may cause larger transient error.Multi-model Adaptive Control is the powerful solving control of complex systems problem, more effectively improves the transient process of system.

Based on the multi-model Adaptive Control device switched, can the sudden change of response model rapidly, but when switching between sub-controller, transient response is bad, and when Systematical control exists delayed, likely can cause frequently switching between sub-controller, initiating system shakes.Multi-model Adaptive Control device based on mixing avoids the generation switched between sub-controller, and within submodel collection occurs simultaneously, mixture control is better than the control effects of single sub-controller.The controlled device of constant or slow change when mixture control is applicable to parameter, but in industrial processes, some incidents, as environmental change, external interference etc., change a lot making the model parameter of controlled device, mixture control can not be responded in time, larger error can be caused.

Specific to Visual Servo Robot field, Visual Servo Robot, in the process of Tracking Maneuvering Targets, first will find the accurate location of target in image sequence.If all searched for target in whole image range at every turn, the calculated amount of system will inevitably be increased, the real-time of influential system .-individual effective solution is exactly filtering.Namely according to the target location obtained before and movable information, reliable prediction is carried out to the motion of target, in relatively little region, complete the search to target, but because be difficult to set up an accurate maneuvering target model, so more difficult to the prediction of maneuvering target.Go to approach maneuvering target model based on the multi-model switched or mix although scholar proposes, achieve good control effects.But based on the easy initiating system concussion of the multi-model mechanism switched, transient effects is poor.Multi-model mechanism based on mixing can not responding system parameter saltus step in time, and control effects is undesirable.

Summary of the invention

The technical problem to be solved in the present invention is that how to avoid can not the problem of responding system parameter saltus step in time based on the multi-model mechanism of mixing in Visual Servo Robot.

In order to solve this and a technical matters, the invention provides a kind of multi-model Adaptive Control method in Visual Servo Robot, comprising the steps:

S100: according to position and the movable information of acquired maneuvering target before, set up the system parameter model collection of related ends location parameter, this system parameter model collection is divided into the model subset that several have union each other;

S200: for each described model subset designs a corresponding sub-controller;

S300: set up an error model;

S400: get the centerpoint value in each described model subset, applies it in the error model that step S300 obtains, obtains the first system Identification Errors;

Estimate the target location parameter of Visual Servo Robot motion model, obtain estimated value, the error model obtained by step S300 is applied in this estimated value, obtains second system Identification Errors;

S500: more described the first system Identification Errors and second system Identification Errors, thus judge whether target location parameter saltus step occurs; If judged result is not for saltus step to occur, then mixture control is adopted to carry out Hybrid mode to all described sub-controllers; If generation saltus step, then corresponding estimated value is reconstructed into the centerpoint value of described model subset, the sub-controller corresponding by described model subset controls.

In described step S400, also comprise the process adopting the adaptive algorithm with constraint projection algorithm to upgrade target location parameter.

In described step S100, controlled system is described to:

y(t)＝G(s；θ ^*)u(t)+d(t) (1)

G(s；θ ^*)＝G ₀(s；θ ^*)(1+△ _m(s)) (2)

$G_0(s;{\mathrm{\θ}}^{*})=\frac{N_0\left(s\right)}{D_0\left(s\right)}=\frac{{{\mathrm{\θ}}_b}^{*T}{\mathrm{\α}}_{n-1}\left(s\right)}{s^n+{{\mathrm{\θ}}_{\mathrm{\α}}}^{*T}{\mathrm{\α}}_{n-1}\left(s\right)}---\left(3\right)$

y _m(t)＝y(t)+v(t) (4)

In formula, u (t), y (t) represent the input and output of controlled device, and d (t) is the interference of bounded, meet g (s; θ ^*) be actual controlled device; G ₀(s; θ ^*) describe for the model of controlled device; △ _ms () represents unmodelled dynamics; Vector represent G ₀(s; θ ^*) unknown parameter; a _n-1(s)=[s ^n-1, s ^n-2... s, 1] ^t; y _mt measured value that () is y (t); V (t) represents the sensor noise of bounded, meets

Wherein:

A1:D ₀(s) to be leading coefficient be 1 polynomial expression, and order n is known;

A2:N ₀order be less than n.

A3: △ _ms () is canonical, Re [s]>=-δ ₀/ 2, δ ₀it is known constant.

A4: θ ^*∈ Ω, Ω ∈ R ²ⁿit is known parameter model collection

System parameter model collection is divided into the model subset Ω that n has union each other _i(i=1,2 ... n.). and Ω _imeet:

1) non-NULL, i=1,2 ... n.;

2) $\∀{\mathrm{\θ}}^{*}\∈{\mathrm{\Ω}}_i,i=\mathrm{1,2}...n,\∃\underset{i}{{\mathrm{\θ}}^{*}}\∈{\mathrm{\Ω}}_i$ With $0\≤\underset{i}{r}\≤\∞,$ Meet $\left|\right|{\mathrm{\θ}}^{*}-\underset{i}{{\mathrm{\θ}}^{*}}\left|\right|\≤\underset{i}{r},\underset{i}{{\mathrm{\θ}}^{*}}$ For model subset Ω _icenter, for radius;

3) Ω _i∩ Ω _i+1=δ, i=1,2 ... n, δ are constant.

Described step S200 comprises the steps:

2.1 design mixed signals

As estimates of parameters θ (t) ∈ Ω _i(i=1,2 ... n; ) time, Ω _ifor active subset of parameters, be expressed as the set enlivening subset of parameters, definition β (θ ^*)=[β ₁(θ ^*) ... β _i(θ ^*)] ^tfor Hybrid mode signal, determine the degree of participation of each sub-controller, it has following character:

B1: β ₁(θ ^*)+β ₂(θ ^*)+... β _i(θ ^*)=1; β ₁(θ ^*), β ₂(θ ^*) ... β _i(θ ^*)>=0; When or time,

β _i(θ ^*)＝0；i＝1,2,…n；

B2: β (θ ^*) be continuously differentiable function.

2.2 Controller gain variations

Mixture control is described as following formula:

$\begin{array}{c}{\stackrel{\·}{x}}_c=A_c[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]x_c+B_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]y_m\left(t\right)\\ u\left(t\right)=-C_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]x_c\end{array}---\left(5\right)$

In formula, x _c∈ R ⁿthe state variable of controller, to each fixed value beta (θ ^*) and θ ^*: u (t)=K [s; β (θ ^*), θ ^*] y _mt () has following transport function:

$K[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]=C_c[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]{\{\mathrm{sI}-A_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}\left]\right\}}^{-1}\×B_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]$

$=\frac{N_k(s;b,q)}{D_k(s;b,q)}---\left(6\right)$

Wherein:

C1:A _c[β (θ ^*), θ ^*], B _c[β (θ ^*), θ ^*] and C _c[β (θ ^*), θ ^*] be about β (θ ^*), θ ^*continuously differentiable function.C2:K [s; e _i, θ (t)] and=K _i(s), wherein θ (t) ∈ Ω _i, e _i∈ R ^pi-th standard base vector.

C3: to all θ ^*∈ Ω, K [s; β (θ ^*), θ ^*] controlled device can be made to keep stable.

Further to sub-controller k _is () carries out stable coprime factorization: be defined as follows formula:

$\begin{array}{c}{Q}_i(s;{\mathrm{\θ}}^{*})=[\tilde{Y}(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{V}}_i\left(s\right)-\tilde{X}(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{U}}_i\left(s\right)]\×{[{\tilde{N}}_0(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{U}}_i\left(s\right)+{\tilde{G}}_0(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{V}}_i\left(s\right)]}^{-1}\\ U_i(s;{\mathrm{\θ}}^{*})=D_0(s;{\mathrm{\θ}}^{*})Q_i(s;{\mathrm{\θ}}^{*})-Y(s;{\mathrm{\θ}}^{*})\\ V_i(s;{\mathrm{\θ}}^{*})=N_0(s;{\mathrm{\θ}}^{*})Q_i(s;{\mathrm{\θ}}^{*})-X(s;{\mathrm{\θ}}^{*})\end{array}---\left(7\right)$

In formula, $G_0(s;{\mathrm{\θ}}^{*})=N_0(s;{\mathrm{\θ}}^{*}){D_0}^{-1}(s;{\mathrm{\θ}}^{*})={\tilde{M}}^{-1}(s;{\mathrm{\θ}}^{*})\tilde{N}(s;{\mathrm{\θ}}^{*})$ Based on θ ^*change and the transport function of smooth change.X (s; θ ^*), also be based on θ ^*change and the function of smooth change. there is following equation:

$\begin{array}{c}\left(\begin{array}{cc}1& 0\\ 1& 0\end{array}\right)=\left(\begin{array}{cc}\tilde{X}& \tilde{Y}\\ {\widetilde{-N}}_0& {\tilde{D}}_0\end{array}\right)\left(\begin{array}{cc}{D}_0& -Y\\ N_0& X\end{array}\right)\\ =\left(\begin{array}{cc}{D}_0& -Y\\ N_0& X\end{array}\right)\left(\begin{array}{cc}\tilde{X}& \tilde{Y}\\ {\widetilde{-N}}_0& {\tilde{D}}_0\end{array}\right)\end{array}---\left(8\right)$

The expression formula obtaining control law is:

$\begin{array}{c}K[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]=U[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]V^{-1}[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]\\ U[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\β}}_i\left({\mathrm{\θ}}^{*}\right)U_i(s;{\mathrm{\θ}}^{*})\\ V\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\β}}_i\left({\mathrm{\θ}}^{*}\right)V_i(s;{\mathrm{\θ}}^{*})\end{array}---\left(9\right)$

Error model in step S300 is obtained by following process:

Linear parametric model can be expressed as: z=θ ^*t φ, wherein:

z＝s ⁿF(s)y _m(t) (10)

$\mathrm{\φ}={[{\mathrm{\α}}_{n-1}^T\left(s\right)F\left(s\right)u-{\mathrm{\α}}_{n-1}^T\left(s\right)F\left(s\right)y_m]}^T---\left(11\right)$

$\begin{array}{c}F\left(s\right)=\frac{{\mathrm{\λ}}^n}{{(s+\mathrm{\λ})}^n}{F}_{\mathrm{\η}}\left(s\right)\\ F_{\mathrm{\η}}\left(s\right)=\frac{N_F\left(s\right)}{D_F\left(s\right)}\end{array}---\left(12\right)$

In formula, λ be greater than zero constant, F _ηs () represents the wave filter of minimum phase.When we replace parameter actual value θ with estimates of parameters θ (t) ^*can error e (t) be produced, we define an error model, and its u (t) and y (t) that is input as exports as e (t), can describe with state-space expression below:

$\begin{array}{c}x=A_{E}x+B_{E}u\left(t\right)+G_E{y}_m\left(t\right);\\ z=C_{z}x+D_Z{y}_m\left(t\right),\hat{z}=\mathrm{\θ}{\left(t\right)}^T\mathrm{\φ},\mathrm{\φ}=C_{E}x;---\left(13\right)\\ e\left(t\right)=(C_Z-{\mathrm{\θ}}^{*T}{C}_E)x+D_Z{y}_m\left(t\right)\end{array}$

In formula, x is the state vector of error.

Due to actual controlled process G (s; θ ^*) there is unmodelled dynamics, △ _m(s), interference d (t), and sensor noise v (t), then

z＝θ ^*Tφ+η，

Wherein:

η＝N ₀(s)△ _m(s)F(s)u(t)+D ₀(s)F(s)(d(t)+v(t))

We claim η to be the error term of modeling, and when we calculate the estimated value of unknown parameter, η can bring interference.From the expression formula of η, we can find out, by reasonably designing wave filter F (s), can alleviate this interference, reduce △ _m(s), interference d (t), and the impact that sensor noise v (t) brings.

Described have constraint projection algorithm adaptive algorithm as follows:

$\mathrm{\θ}\left(t\right)=P_r\{\mathrm{\θ}(t-1)+\mathrm{\γ}\frac{e(t-1)\mathrm{\φ}(t-1)}{c+{\mathrm{\φ}}^T(t-1)\mathrm{\φ}(t-1)}\}---\left(14\right)$

In formula, γ is adaptive gain, and c is constant, P _r{ } is projection operator, is constrained in by θ (t) in parameter model collection Ω.

Step S500 comprises the steps:

Known for the center of each model subset, work as estimates of parameters controller K (s)=K _i(s), bring in formula (13), can error e be obtained _i(t), (i=1,2 ... n).

If δ >0, i=1,2 ... n; Then have:

J _min=j _q, q=1,2 ... n. (15) obtain according to estimates of parameters θ (t)

$J\left(\mathrm{\θ}\right)={\left|\right|e\left(t\right)\left|\right|}_{2\mathrm{\δ}}^2,\mathrm{\δ}>0---\left(16\right)$

If

(1+h)J(θ)>J _min (17)

In formula, h is system delay time, and now we think that parameter there occurs saltus step, and jump to subset Ω _qin, so be directly reconstructed estimates of parameters:

θ(t)＝θ ^* _q,q＝1,2,…n.(18)

Thus the sub-controller achieving employing corresponding controls.

The present invention is confirmed whether to undergo mutation by judgement, and then converts between two kinds of control modes, can control with changeable corresponding sub-controller by Hybrid mode.Compare with multi-model switching control technology with existing multi-model Hybrid mode, the present invention has both advantage simultaneously, avoids respective defect.System, most of time, adopts Hybrid mode.But when systematic parameter is undergone mutation, by being reconstructed estimates of parameters, be switched to corresponding sub-controller fast, timely response parameter change.

Accompanying drawing explanation

The actual input-output curve of system in the process that Fig. 1 (a), Fig. 1 (b) are system employing multi-model self-adapting Hybrid mode;

Fig. 2 (a), Fig. 2 (b) are for have employed the actual input-output curve based on system in the multi-model Adaptive Control process switched and mix in one embodiment of the invention;

Fig. 3 is the schematic flow sheet of the multi-model Adaptive Control method in one embodiment of the invention in Visual Servo Robot.

Embodiment

The invention provides a kind of multi-model Adaptive Control method in Visual Servo Robot, comprise the steps:

S100: according to position and the movable information of acquired maneuvering target before, set up the system parameter model collection of related ends location parameter, this system parameter model collection is divided into the model subset that several have union each other;

S200: for each described model subset designs a corresponding sub-controller;

S300: set up an error model;

S400: get the centerpoint value in each described model subset, applies it in the error model that step S300 obtains, obtains the first system Identification Errors;

Estimate the target location parameter of Visual Servo Robot motion model, obtain estimated value, the error model obtained by step S300 is applied in this estimated value, obtains second system Identification Errors;

S500: more described the first system Identification Errors and second system Identification Errors, thus judge whether target location parameter saltus step occurs; If judged result is not for saltus step to occur, then adopt mixture control to carry out Hybrid mode to all described sub-controllers, namely mixture control adopts mixed strategy to control controlled device; If generation saltus step, then corresponding estimated value is reconstructed into the centerpoint value of described model subset, the sub-controller corresponding by described model subset controls.

In described step S400, also comprise the process adopting the adaptive algorithm with constraint projection algorithm to upgrade target location parameter.

The method that the present embodiment adopts is contemplated that: first utilize the centerpoint value of each model subset to replace unknown parameters ' value to obtain least error, and compare with the error that parameter current estimated value obtains, judge whether parameter saltus step occurs.If parameter saltus step does not occur, adopt Hybrid mode; If parameter generation saltus step, be then reconstructed into estimates of parameters the centerpoint value of subset, controller is just switched to corresponding sub-controller, timely response parameter change.

The technical scheme that this method adopts comprises the following steps:

1: according to priori, system parameter model collection is divided into the model subset that n has union each other.

2: each model subset designs a corresponding Robust adaptive controller, based on the Hybrid mode signal deciding degree of participation of each sub-controller of estimates of parameters.

3: set up a parameter error model, obtain the Identification Errors of system, then adopt the adaptive algorithm with constraint projection algorithm to upgrade parameter.

4: the System Discrimination error obtained based on estimates of parameters with compare based on the System Discrimination error that model subset central value obtains and judge whether parameter saltus step occurs, thus determine to control to select mixing or switching control strategy.

Specific description is done to technical solution of the present invention step below:

Step 1: set up multi-model collection.

Controlled system describes

Consider following continuous linear system:

y(t)＝G(s；θ ^*)u(t)+d(t) (1)

G(s；θ ^*)＝G ₀(s；θ ^*)(1+△ _m(s)) (2)

$G_0(s;{\mathrm{\θ}}^{*})=\frac{N_0\left(s\right)}{D_0\left(s\right)}=\frac{{{\mathrm{\θ}}_b}^{*T}{\mathrm{\α}}_{n-1}\left(s\right)}{s^n+{{\mathrm{\θ}}_{\mathrm{\α}}}^{*T}{\mathrm{\α}}_{n-1}\left(s\right)}---\left(3\right)$

y _m(t)＝y(t)+v(t) (4)

In formula, u (t), y (t) represent the input and output of controlled device, and d (t) is the interference of bounded, meet g (s; θ ^*) be actual controlled device; G ₀(s; θ ^*) describe for the model of controlled device; △ _ms () represents unmodelled dynamics; Vector represent G ₀(s; θ ^*) unknown parameter; a _n-1(s)=[s ^n-1, s ^n-2... s, 1] ^t; y _mt measured value that () is y (t); V (t) represents the sensor noise of bounded, meets control objectives selects input u (t) of controlled device to make output y (t) trend towards 0, and for this reason, we make the following assumptions system:

A1 D ₀(s) to be leading coefficient be 1 polynomial expression, and order n is known.

A2 N ₀order be less than n.

A3 △ _ms () is canonical, Re [s]>=-δ ₀/ 2, δ ₀it is known constant.

A4 θ ^*∈ Ω, Ω ∈ R ²ⁿit is known parameter model collection.

According to priori, system parameter model collection is divided into n model subset Ω _i(i=1,2 ... n.). and Ω _imeet:

(1) non-NULL, i=1,2 ... n.

(2) $\∀{\mathrm{\θ}}^{*}\∈{\mathrm{\Ω}}_i,i=\mathrm{1,2}...n,\∃\underset{i}{{\mathrm{\θ}}^{*}}\∈{\mathrm{\Ω}}_i$ With $0\≤\underset{i}{r}\≤\∞,$ Meet $\left|\right|{\mathrm{\θ}}^{*}-\underset{i}{{\mathrm{\θ}}^{*}}\left|\right|\≤\underset{i}{r},\underset{i}{{\mathrm{\θ}}^{*}}$ For model subset Ω _icenter, for radius.

(3) Ω _i∩ Ω _i+1=δ, i=1,2 ... n, δ are constant.

Step 2: design mixed signal and Robust adaptive controller.

2.1 design mixed signals

As estimates of parameters θ (t) ∈ Ω _i(i=1,2 ... n; ) time, we claim Ω _ifor active subset of parameters, be expressed as the set enlivening subset of parameters, definition β (θ ^*)=[β ₁(θ ^*) ... β _i(θ ^*)] ^tfor Hybrid mode signal, determine the degree of participation of each sub-controller, it has following character:

B1: β ₁(θ ^*)+β ₂(θ ^*)+... β _i(θ ^*)=1; β ₁(θ ^*), β ₂(θ ^*) ... β _i(θ ^*)>=0; When or time, β _i(θ ^*)=0; I=1,2, in;

B2: β (θ ^*) be continuously differentiable function.

2.2 Controller gain variations

Mixture control can describe by following formula:

$\begin{array}{c}{\stackrel{\·}{x}}_c=A_c[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]x_c+B_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]y_m\left(t\right)\\ u\left(t\right)=-C_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]x_c\end{array}---\left(5\right)$

In formula, x _c∈ R ⁿthe state variable of controller, to each fixed value beta (θ ^*) and θ ^*: u (t)=K [s; β (θ ^*), θ ^*] y _mt () has following transport function:

$\begin{array}{c}K[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]=C_c[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]{\{\mathrm{sI}-A_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}\left]\right\}}^{-1}\×B_C[\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]\\ =\frac{N_K(s;b,q)}{D_K(s;b,q)}\end{array}---\left(6\right)$

And make the following assumptions:

C1:A _c[β (θ ^*), θ ^*], B _c[β (θ ^*), θ ^*] and C _c[β (θ ^*), θ ^*] be about β (θ ^*), θ ^*continuously differentiable function.

C2:K [s; e _i, θ (t)] and=K _i(s), wherein θ (t) ∈ Ω _i, e _i∈ R ^pi-th standard base vector.

C3: to all θ ^*∈ Ω, K [s; β (θ ^*), θ ^*] controlled device can be made to keep stable.

We can further to sub-controller k _is () carries out stable coprime factorization: be defined as follows formula:

$\begin{array}{c}{Q}_i(s;{\mathrm{\θ}}^{*})=[\tilde{Y}(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{V}}_i\left(s\right)-\tilde{X}(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{U}}_i\left(s\right)]\×{[{\tilde{N}}_0(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{U}}_i\left(s\right)+{\tilde{G}}_0(s;{\mathrm{\θ}}^{*}){\stackrel{\‾}{V}}_i\left(s\right)]}^{-1}\\ U_i(s;{\mathrm{\θ}}^{*})=D_0(s;{\mathrm{\θ}}^{*})Q_i(s;{\mathrm{\θ}}^{*})-Y(s;{\mathrm{\θ}}^{*})\\ V_i(s;{\mathrm{\θ}}^{*})=N_0(s;{\mathrm{\θ}}^{*})Q_i(s;{\mathrm{\θ}}^{*})-X(s;{\mathrm{\θ}}^{*})\end{array}---\left(7\right)$

In formula, $G_0(s;{\mathrm{\θ}}^{*})=N_0(s;{\mathrm{\θ}}^{*}){D_0}^{-1}(s;{\mathrm{\θ}}^{*})={\tilde{M}}^{-1}(s;{\mathrm{\θ}}^{*})\tilde{N}(s;{\mathrm{\θ}}^{*})$ Based on θ ^*change and the transport function of smooth change.X (s; θ ^*), with also be based on θ ^*change and the function of smooth change. there is following equation:

$\begin{array}{c}\left(\begin{array}{cc}1& 0\\ 1& 0\end{array}\right)=\left(\begin{array}{cc}\tilde{X}& \tilde{Y}\\ {\widetilde{-N}}_0& {\tilde{D}}_0\end{array}\right)\left(\begin{array}{cc}{D}_0& -Y\\ N_0& X\end{array}\right)\\ =\left(\begin{array}{cc}{D}_0& -Y\\ N_0& X\end{array}\right)\left(\begin{array}{cc}\tilde{X}& \tilde{Y}\\ {\widetilde{-N}}_0& {\tilde{D}}_0\end{array}\right)\end{array}---\left(8\right)$

The expression formula that we can obtain control law is like this:

$\begin{array}{c}K[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]=U[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]V^{-1}[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]\\ U[s;\mathrm{\β}\left({\mathrm{\θ}}^{*}\right),{\mathrm{\θ}}^{*}]=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\β}}_i\left({\mathrm{\θ}}^{*}\right)U_i(s;{\mathrm{\θ}}^{*})\\ V\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\β}}_i\left({\mathrm{\θ}}^{*}\right)V_i(s;{\mathrm{\θ}}^{*})\end{array}---\left(9\right)$

Step 3: set up error model, design adaptive law, according to the input and output of controlled process, online calculate the estimated value of parameter.

3.1 error model

The linear parametric model of system (3) can be expressed as: z=θ ^{* T}φ, wherein:

z＝s ⁿF(s)y _m(t) (10)

$\mathrm{\φ}={[{\mathrm{\α}}_{n-1}^T\left(s\right)F\left(s\right)u-{\mathrm{\α}}_{n-1}^T\left(s\right)F\left(s\right)y_m]}^T---\left(11\right)$

$\begin{array}{c}F\left(s\right)=\frac{{\mathrm{\λ}}^n}{{(s+\mathrm{\λ})}^n}{F}_{\mathrm{\η}}\left(s\right)\\ F_{\mathrm{\η}}\left(s\right)=\frac{N_F\left(s\right)}{D_F\left(s\right)}\end{array}---\left(12\right)$

In formula, λ be greater than zero constant, F _ηs () represents the wave filter of minimum phase.When we replace parameter actual value θ with estimates of parameters θ (t) ^*can error e (t) be produced, we define an error model, and its u (t) and y (t) that is input as exports as e (t), can describe with state-space expression below:

$\begin{array}{c}x=A_{E}x+B_{E}u\left(t\right)+G_E{y}_m\left(t\right);\\ z=C_{z}x+D_Z{y}_m\left(t\right),\hat{z}=\mathrm{\θ}{\left(t\right)}^T\mathrm{\φ},\mathrm{\φ}=C_{E}x;---\left(13\right)\\ e\left(t\right)=(C_Z-{\mathrm{\θ}}^{*T}{C}_E)x+D_Z{y}_m\left(t\right)\end{array}$

In formula, x is the state vector of error.

Due to actual controlled process G (s; θ ^*) there is unmodelled dynamics, △ _m(s), interference d (t), and sensor noise v (t), then

z＝θ ^*Tφ+η，

Wherein:

η＝N ₀(s)△ _m(s)F(s)u(t)+D ₀(s)F(s)(d(t)+v(t))

We claim η to be the error term of modeling, and when we calculate the estimated value of unknown parameter, η can bring interference.From the expression formula of η, we can find out, by reasonably designing wave filter F (s), can alleviate this interference, reduce △ _m(s), interference d (t), and the impact that sensor noise v (t) brings.

3.2 adaptive algorithm

Adopt the adaptive algorithm as follows with constraint projection algorithm:

$\mathrm{\θ}\left(t\right)=P_r\{\mathrm{\θ}(t-1)+\mathrm{\γ}\frac{e(t-1)\mathrm{\φ}(t-1)}{c+{\mathrm{\φ}}^T(t-1)\mathrm{\φ}(t-1)}\}---\left(14\right)$

In formula, γ is adaptive gain, and c is constant, P _r{ } is projection operator, is constrained in by θ (t) in parameter model collection Ω.

Step 4: set up a judgment criterion to judge whether parameter saltus step occurs, thus determine that controller adopts mixing or the control strategy switched.

Known for the center of each model subset, work as estimates of parameters controller K (s)=K _i(s), bring in formula (13), can error e be obtained _i(t), (i=1,2 ... n).

If δ >0, i=1,2 ... n; Then have:

J _min=j _q, q=1,2 ... n. (15) obtain according to estimates of parameters θ (t)

$J\left(\mathrm{\θ}\right)={\left|\right|e\left(t\right)\left|\right|}_{2\mathrm{\δ}}^2,\mathrm{\δ}>0---\left(16\right)$

If

(1+h)J(θ)>J _min (17)

In formula, h is system delay time, and now we think that parameter there occurs saltus step, and jump to subset Ω _qin, so be directly reconstructed estimates of parameters:

θ (t)=θ ^* _q, q=1,2 ... n. (18) such controller will be directly switch to corresponding sub-controller, avoids mixture control parameter and slowly changes tracking actual parameter value, take in time to control.

Compare with multi-model switching control technology with existing multi-model Hybrid mode, the present invention has both advantage simultaneously, avoids respective defect.System, most of time, adopts Hybrid mode.But when systematic parameter is undergone mutation, by being reconstructed estimates of parameters, be switched to corresponding sub-controller fast, timely response parameter change.

Specific in the present embodiment, the tracker of maneuvering target can be described as:

$y=\frac{1}{s-\mathrm{\θ}}[1+{\mathrm{\Δ}}_m\left(s\right)](u+d)$

The target location parameter of system $\mathrm{\&theta;}=\left\{\begin{array}{c}2.3;0\&le;k<40;\\ -2;40\&le;k\&le;100;\end{array}\right.$ θ ∈ [-2.5,2.5], unmodelled dynamics d=0; When K=40, θ jumps to-2. methods proposed according to this patent from 2.3, and first we set up multi-model collection in the variation range of θ, Ω ₁=[0.5,2.5], Ω ₂=[-1,1], Ω ₃=[-2.5 ,-0.5], approaches the tracker of maneuvering target, designing filter γ=100, then according to formula (13), (15) we can pick out the estimated values theta of location parameter ^*, and based on parameter θ ^*design mixed signal

${\mathrm{\&beta;}}_1=\mathrm{\&psi;}\left(\frac{{\mathrm{\&theta;}}^{*}-1.75}{1.25}\right),{\mathrm{\&beta;}}_2=\mathrm{\&psi;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&beta;}}_3=\mathrm{\&psi;}\left(\frac{{\mathrm{\&theta;}}^{*}+1.75}{1.25}\right)$

From contrast, we can see, when saltus step does not occur parameter, method herein has the same control effects with Hybrid mode, but works as k=40, and during systematic parameter generation saltus step, the control effects under context of methods is better than Hybrid mode.This is because when parameter is from subset Ω ₁jump to subset Ω ₃in, because mixture control slowly changes, estimates of parameters will first through subset Ω ₂, then just enter subset Ω ₃tracking parameter actual value.But adopt proposed method, when judging that parameter jumps to subset Ω ₃time middle, estimates of parameters directly can be reconstructed into Ω ₃central value 1.5, such controller will be switched to Ω ₃corresponding sub-controller, the saltus step of timely response parameter.

Claims (7)

1. the multi-model Adaptive Control method in Visual Servo Robot, is characterized in that: comprise the steps:

S100: according to position and the movable information of acquired maneuvering target before, set up the system parameter model collection of related ends location parameter, this system parameter model collection is divided into the model subset that several have union each other;

S200: for each described model subset designs a corresponding sub-controller;

S300: set up an error model;

S400: get the centerpoint value in each described model subset, applies it in the error model that step S300 obtains, obtains the first system Identification Errors;

The target location parameter of Visual Servo Robot motion model is estimated, obtains estimated value, apply it in the error model that step S300 obtains, obtain second system Identification Errors;

S500: more described the first system Identification Errors and second system Identification Errors, thus judge whether target location parameter saltus step occurs; If judged result is not for saltus step to occur, then mixture control is adopted to carry out Hybrid mode to all described sub-controllers; If generation saltus step, then corresponding estimated value is reconstructed into the centerpoint value of described model subset, the sub-controller corresponding by described model subset controls.

2. the multi-model Adaptive Control method in Visual Servo Robot as claimed in claim 1, is characterized in that: in described step S400, also comprises the process adopting the adaptive algorithm with constraint projection algorithm to upgrade target location parameter.

3. the multi-model Adaptive Control method in Visual Servo Robot as claimed in claim 1, is characterized in that: in described step S100, controlled system is described to:

y(t)＝G(s；θ ^*)u(t)+d(t) (1)

G(s；θ ^*)＝G ₀(s；θ ^*)(1+△ _m(s)) (2)

$G_0(s;{\mathrm{\&theta;}}^{*})=\frac{N_0\left(s\right)}{D_0\left(s\right)}=\frac{{{\mathrm{\&theta;}}_b}^{*T}{\mathrm{\&alpha;}}_{n-1}\left(s\right)}{s^n+{{\mathrm{\&theta;}}_{\mathrm{\&alpha;}}}^{*T}{\mathrm{\&alpha;}}_{n-1}\left(s\right)}---\left(3\right)$

y _m(t)＝y(t)+v(t) (4)

In formula, u (t), y (t) represent the input and output of controlled device, and d (t) is the interference of bounded, meet g (s; θ ^*) be actual controlled device; G ₀(s; θ ^*) describe for the model of controlled device; △ _ms () represents unmodelled dynamics; Vector represent G ₀(s; θ ^*) unknown parameter; a _n-1(s)=[s ^n-1, s ^n-2... s, 1] ^t; y _mt measured value that () is y (t); V (t) represents the sensor noise of bounded, meets

Wherein:

A1:D ₀(s) to be leading coefficient be 1 polynomial expression, and order n is known;

A2:N ₀order be less than n.

A3: △ _ms () is canonical, Re [s]>=-δ ₀/ 2, δ ₀it is known constant.

A4: θ ^*∈ Ω, Ω ∈ R ²ⁿit is known parameter model collection

System parameter model collection is divided into the model subset Ω that n has union each other _i(i=1,2 ... n.). and Ω _imeet:

1) non-NULL, i=1,2 ... n.;

2) $\&ForAll;{\mathrm{\&theta;}}^{*}\&Element;{\mathrm{\&Omega;}}_i,i=\mathrm{1,2}...n,\&Exists;\underset{i}{{\mathrm{\&theta;}}^{*}}\&Element;{\mathrm{\&Omega;}}_i$ With $0\&le;\underset{i}{r}\&le;\&infin;,$ Meet $\left|\right|{\mathrm{\&theta;}}^{*}-\underset{i}{{\mathrm{\&theta;}}^{*}}\left|\right|\&le;\underset{i}{r},\underset{i}{{\mathrm{\&theta;}}^{*}}$ For model subset Ω _i

Center, for radius;

3) Ω _i∩ Ω _i+1=δ, i=1,2 ... n, δ are constant.

4. the multi-model Adaptive Control method in Visual Servo Robot as claimed in claim 1, is characterized in that: described step S200 comprises the steps:

2.1 design mixed signals

As estimates of parameters θ (t) ∈ Ω _i(i=1,2 ... n; ) time, Ω _ifor active subset of parameters, be expressed as the set enlivening subset of parameters, definition β (θ ^*)=[β ₁(θ ^*) ... β _i(θ ^*)] ^tfor Hybrid mode signal, determine the degree of participation of each sub-controller, it has following character:

B1: β ₁(θ ^*)+β ₂(θ ^*)+... β _i(θ ^*)=1; β ₁(θ ^*), β ₂(θ ^*), 1 β _i(θ ^*)>=0; When or time,

β _i(θ ^*)＝0；i＝1,2,…n；

B2: β (θ ^*) be continuously differentiable function.

2.2 Controller gain variations

Mixture control is described as following formula:

$\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_c=A_c[\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]x_c+B_C[\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]y_m\left(t\right)\\ u\left(t\right)=-C_C[\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]x_c\end{array}---\left(5\right)$

In formula, x _c∈ R ⁿthe state variable of controller, to each fixed value beta (θ ^*) and θ ^*: u (t)=K [s; β (θ ^*), θ ^*] y _mt () has following transport function:

$\begin{array}{c}K[s;\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]=C_c[\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]{\{\mathrm{sI}-A_C[\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}\left]\right\}}^{-1}\&times;B_C[\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]\\ =\frac{N_K(s;b,q)}{D_K(s;b,q)}\end{array}---\left(6\right)$

Wherein:

C1:A _c[β (θ ^*), θ ^*], B _c[β (θ ^*), θ ^*] and C _c[β (θ ^*), θ ^*] be about β (θ ^*), θ ^*continuously differentiable function.

C2:K [s; e _i, θ (t)] and=K _i(s), wherein θ (t) ∈ Ω _i, e _i∈ R ^pi-th standard base vector.

C3: to all θ ^*∈ Ω, K [s; β (θ ^*), θ ^*] controlled device can be made to keep stable.

Further to sub-controller k _is () carries out stable coprime factorization: be defined as follows formula:

$\begin{array}{c}{Q}_i(s;{\mathrm{\&theta;}}^{*})=[\tilde{Y}(s;{\mathrm{\&theta;}}^{*}){\stackrel{\&OverBar;}{V}}_i\left(s\right)-\tilde{X}(s;{\mathrm{\&theta;}}^{*}){\stackrel{\&OverBar;}{U}}_i\left(s\right)]\&times;{[{\tilde{N}}_0(s;{\mathrm{\&theta;}}^{*}){\stackrel{\&OverBar;}{U}}_i\left(s\right)+{\tilde{G}}_0(s;{\mathrm{\&theta;}}^{*}){\stackrel{\&OverBar;}{V}}_i\left(s\right)]}^{-1}\\ U_i(s;{\mathrm{\&theta;}}^{*})=D_0(s;{\mathrm{\&theta;}}^{*})Q_i(s;{\mathrm{\&theta;}}^{*})-Y(s;{\mathrm{\&theta;}}^{*})\\ V_i(s;{\mathrm{\&theta;}}^{*})=N_0(s;{\mathrm{\&theta;}}^{*})Q_i(s;{\mathrm{\&theta;}}^{*})-X(s;{\mathrm{\&theta;}}^{*})\end{array}---\left(7\right)$

In formula, $G_0(s;{\mathrm{\&theta;}}^{*})=N_0(s;{\mathrm{\&theta;}}^{*}){D_0}^{-1}(s;{\mathrm{\&theta;}}^{*})={\tilde{M}}^{-1}(s;{\mathrm{\&theta;}}^{*})\tilde{N}(s;{\mathrm{\&theta;}}^{*})$ Based on θ ^*change and the transport function of smooth change. with also be based on θ ^*change and the function of smooth change. there is following equation:

$\begin{array}{c}\left(\begin{array}{cc}1& 0\\ 1& 0\end{array}\right)=\left(\begin{array}{cc}\tilde{X}& \tilde{Y}\\ {\widetilde{-N}}_0& {\tilde{D}}_0\end{array}\right)\left(\begin{array}{cc}{D}_0& -Y\\ N_0& X\end{array}\right)\\ =\left(\begin{array}{cc}{D}_0& -Y\\ N_0& X\end{array}\right)\left(\begin{array}{cc}\tilde{X}& \tilde{Y}\\ {\widetilde{-N}}_0& {\tilde{D}}_0\end{array}\right)\end{array}---\left(8\right)$

The expression formula obtaining control law is:

$\begin{array}{c}K[s;\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]=U[s;\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]V^{-1}[s;\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]\\ U[s;\mathrm{\&beta;}\left({\mathrm{\&theta;}}^{*}\right),{\mathrm{\&theta;}}^{*}]=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_i\left({\mathrm{\&theta;}}^{*}\right)U_i(s;{\mathrm{\&theta;}}^{*})\\ V\left(s\right)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&beta;}}_i\left({\mathrm{\&theta;}}^{*}\right)V_i(s;{\mathrm{\&theta;}}^{*})\end{array}---\left(9\right)$

5. the multi-model Adaptive Control method in Visual Servo Robot as claimed in claim 1, is characterized in that: the error model in step S300 is obtained by following process:

Linear parametric model can be expressed as: z=θ ^*t φ, wherein:

z＝s ⁿF(s)y _m(t) (10)

$\mathrm{\&phi;}={[{\mathrm{\&alpha;}}_{n-1}^T\left(s\right)F\left(s\right)u-{\mathrm{\&alpha;}}_{n-1}^T\left(s\right)F\left(s\right)y_m]}^T---\left(11\right)$

$\begin{array}{c}F\left(s\right)=\frac{{\mathrm{\&lambda;}}^n}{{(s+\mathrm{\&lambda;})}^n}{F}_{\mathrm{\&eta;}}\left(s\right)\\ F_{\mathrm{\&eta;}}\left(s\right)=\frac{N_F\left(s\right)}{D_F\left(s\right)}\end{array}---\left(12\right)$

In formula, λ be greater than zero constant, F _ηs () represents the wave filter of minimum phase.When we replace parameter actual value θ with estimates of parameters θ (t) ^*can error e (t) be produced, we define an error model, and its u (t) and y (t) that is input as exports as e (t), can describe with state-space expression below:

$\begin{array}{c}x=A_{E}x+B_{E}u\left(t\right)+G_E{y}_m\left(t\right);\\ z=C_{z}x+D_Z{y}_m\left(t\right),\hat{z}=\mathrm{\&theta;}{\left(t\right)}^T\mathrm{\&phi;},\mathrm{\&phi;}=C_{E}x;---\left(13\right)\\ e\left(t\right)=(C_Z-{\mathrm{\&theta;}}^{*T}{C}_E)x+D_Z{y}_m\left(t\right)\end{array}$

In formula, x is the state vector of error.

Due to actual controlled process G (s; θ ^*) there is unmodelled dynamics, △ _m(s), interference d (t), and sensor noise v (t), then

z＝θ ^*Tφ+η，

Wherein:

η＝N ₀(s)△ _m(s)F(s)u(t)+D ₀(s)F(s)(d(t)+v(t))

We claim η to be the error term of modeling, and when we calculate the estimated value of unknown parameter, η can bring interference.From the expression formula of η, we can find out, by reasonably designing wave filter F (s), can alleviate this interference, reduce △ _m(s), interference d (t), and the impact that sensor noise v (t) brings.

6. the multi-model Adaptive Control method in Visual Servo Robot as claimed in claim 2, is characterized in that: described in have the adaptive algorithm of constraint projection algorithm as follows:

$\mathrm{\&theta;}\left(t\right)=P_r\{\mathrm{\&theta;}(t-1)+\mathrm{\&gamma;}\frac{e(t-1)\mathrm{\&phi;}(t-1)}{c+{\mathrm{\&phi;}}^T(t-1)\mathrm{\&phi;}(t-1)}\}---\left(14\right)$

In formula, γ is adaptive gain, and c is constant, P _r{ } is projection operator, is constrained in by θ (t) in parameter model collection Ω.

7. the multi-model Adaptive Control method in Visual Servo Robot as claimed in claim 1, is characterized in that: step S500 comprises the steps:

Known for the center of each model subset, work as estimates of parameters controller K (s)=K _i(s), bring in formula (13), can error e be obtained _i(t), (i=1,2 ... n).

If δ >0, i=1,2 ... n; Then have:

J _min=j _q, q=1,2 ... n. (15) obtain according to estimates of parameters θ (t)

$J\left(\mathrm{\&theta;}\right)={\left|\right|e\left(t\right)\left|\right|}_{2\mathrm{\&delta;}}^2,\mathrm{\&delta;}>0---\left(16\right)$ If

(1+h)J(θ)>J _min (17)

In formula, h is system delay time, and now we think that parameter there occurs saltus step, and jump to subset Ω _qin, so be directly reconstructed estimates of parameters:

θ(t)＝θ ^* _q,q＝1,2,…n. (18)

Thus the sub-controller achieving employing corresponding controls.