CN103612267A - Self-adaptive controller used for parallel robot - Google Patents

Abstract

The invention relates to a non-linear self-adaptive controller used for a two-freedom-degree planar parallel robot. A control Lyapunov method is used for achieving task space self-adaptive control of the parallel robot. Due to the fact that the characteristics of parameters in an inertial matrix are fully considered, changes of undetermined parameter linearity of a model are not adopted any more in the design, and designing of a control law and a self-adaptive law becomes simpler because part of the parameters do not need to be estimated. According to the method, global asymptotic stability of the terminal position and speed of a system can be guaranteed.

Description

A kind of adaptive controller for parallel robot

Technical field

The invention belongs to robot and control control technology field, relate to a kind of method for designing of adaptive controller of parallel robot.

Background technology

Parallel robot be by many independently kinematic chain connect end effector and fixed system and many close loop mechanisms of forming.It has the series of advantages such as rigidity is large, bearing capacity is strong, error is little, precision is high, deadweight duty ratio is little, power performance is good, becomes the motion platform of a potential high-speed, high precision.But because parallel manipulator human occupant dynamic model is complicated, and exist strong nonlinearity coupling, therefore parallel robot Dynamic Modeling, control strategy research and system emulation thereof are one of challenging fields of tool of parallel robot research, are also one of difficult points of research.

Control for parallel robot can be divided into Linkspace control and task space control.Linkspace control generally supposes that each joint of parallel robot is independent non-coupling.Based on this hypothesis, a comparatively complicated parallel robot system with the chain of doing more physical exercises just can be broken down into several independently single-input single-output systems, thereby design the controller of each single-input single-output subsystem, just can complete the controller design of whole parallel robot system.But because parallel robot is non-linear a, strongly coupled system, Linkspace control effect when height track following is poor.Task space has been considered the dynamics of robot, so Nonlinear Dynamic can well be compensated, controls effect better when following the tracks of at a high speed.

When setting up the dynamic model of robot, the dynamic parameter of system is difficult to accurately definite, and therefore, design adaptive controller has very large meaning to improving control accuracy.In robot control system, self-adaptation control method is own through having obtained application comparatively widely.But due to the complexity of parallel manipulator human occupant dynamic model, also seldom, and great majority are to be based upon joint space in the at present research of relevant parallel robot Self Adaptive Control.

Therefore design a kind of rational adaptive controller for parallel robot, especially the adaptive controller at task space has important using value.

Summary of the invention

Technical problem to be solved by this invention is to design a kind of adaptive controller for parallel robot, the control problem of the parallel robot of solution under the inaccurate condition of parameter Estimation.

The present invention mainly comprises following content:

(1) foundation of parallel robot dynamic model;

(2) design of adaptive controller;

(3) selection of controller parameter.

Accompanying drawing explanation

Fig. 1 robot task space structure figure.

The specific embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

The present invention is with the artificial research object of two degrees of freedom redundantly driven parallel device (as shown in Figure 1).

(1) model description.

In the structure of task space as shown in Figure 1, wherein robot is by three driven by servomotor that are positioned at A1, A2, A3, q for the parallel robot with redundant drive _a1, q _a2, q _a3be respectively three the diarthrodial active of master angles, q _b1, q _b2, q _b3be respectively the driven angle of three driven joints.This device has comprised three independently two degrees of freedom devices, and each device has following dynamical equation:

$M_i{\stackrel{..}{q}}_i+C_i{\stackrel{.}{q}}_i+f_i={\mathrm{\τ}}_i(i=\mathrm{1,2,3}),---\left(1\right)$

Wherein, q _i=[q _aiq _bi ^t, M _iwith C _ithe inertial matrix and the centrifugal force matrix that are respectively each separate branches, be expressed as:

$M_i=\left[\begin{array}{cc}{\mathrm{\α}}_i& {\mathrm{\γ}}_i\cos (q_{\mathrm{ai}}-q_{\mathrm{bi}})\\ {\mathrm{\γ}}_i\cos (q_{\mathrm{ai}}-q_{\mathrm{bi}})& {\mathrm{\β}}_i\end{array}\right],C_i=\left[\begin{array}{cc}0& {\mathrm{\γ}}_i\sin (q_{\mathrm{ai}}-q_{\mathrm{bi}}){\stackrel{.}{q}}_{\mathrm{bi}}\\ {\mathrm{\γ}}_i\sin (q_{\mathrm{ai}}-q_{\mathrm{bi}}){\stackrel{.}{q}}_{\mathrm{ai}}& 0\end{array}\right].---\left(2\right)$

M _ifor positive definite matrix, α _i, β _i, γ _i, i=1,2,3 is dynamic parameter.These parameters are relevant by physical parameters such as the quality to system, barycenter, inertia, and are subject to the impact of certainty of measurement.τ _i=[τ _aiτ _bi ^tfor joint moment vector, due to B _ifor driven joint, so τ _bi=0.F _i=[f _aif _bi] ^tfor moment of friction vector,

with f _aicompare f _bivery I is to be left in the basket.

The dynamic model of parallel robot is three the independently combinations of serial mechanism under certain constraint, sets up following form:

$W^T\mathrm{MW}{\stackrel{\·\·}{q}}_e+W^T(M\stackrel{\·}{W}+\mathrm{CW}){\stackrel{\·}{q}}_e+S^T{f}_a=S^T{\mathrm{\τ}}_a,---\left(3\right)$

Wherein M is positive definite symmetry.Q wherein _e=(x y) ^tfor terminal location coordinate, W is the Jacobian matrix between node speed and terminal velocity, and S is the Jacobin matrix in terminal velocity and three joints

If X _l=q _e

$X={\left[\begin{array}{cc}{X}_1^T& X_2^T\end{array}\right]}^T,$ According to (3) formula, the kinetic model of having set up parallel robot is as follows:

$\begin{array}{c}\stackrel{.}{X_1}=X_2\\ W^T\mathrm{MW}{\stackrel{.}{X}}_2=-W^{T}M\stackrel{.}{W}{X}_2-W^T\mathrm{CW}{X}_2-S^T{f}_a+S^T{\mathrm{\τ}}_a\end{array}.---\left(4\right)$

(2) design of controller

Order $f\left(X\right)=\left(\begin{array}{cc}0& I_{2\×2}\\ 0& 0\end{array}\right)\left(\begin{array}{c}{X}_1\\ X_2\end{array}\right)-\left(\begin{array}{c}0\\ S^T{f}_a\end{array}\right),g=\left(\begin{array}{c}{0}_{2\×3}\\ S^T\end{array}\right),F_1=\left(\begin{array}{c}{0}_{2\×6}\\ W^T\end{array}\right)\mathrm{\Θ}=\mathrm{diag}\left(\begin{array}{cccccc}{\mathrm{\γ}}_1& {\mathrm{\γ}}_2& {\mathrm{\γ}}_3& {\mathrm{\γ}}_1& {\mathrm{\γ}}_2& {\mathrm{\γ}}_3\end{array}\right),$ F ₂=M′WX ₂， $M^{\′}=\left[\begin{array}{cc}{0}_{3\×3}& M^{*}\\ -M^{*}& 0_{3\×3}\end{array}\right],$ $M^{*}=\mathrm{diag}\left(\frac{1}{2}{r}_1{s}_{\mathrm{ab}1}({\stackrel{.}{q}}_{a1}+{\stackrel{.}{q}}_{b1})\frac{1}{2}{r}_2{s}_{\mathrm{ab}2}({\stackrel{.}{q}}_{a2}+{\stackrel{.}{q}}_{b2})\frac{1}{2}{r}_3{s}_{\mathrm{ab}3}({\stackrel{.}{q}}_{a3}+{\stackrel{.}{q}}_{b3})\right)$ g _n=(I _4×4 F _l)， $K_{\mathrm{\Θ}}=\left(\begin{array}{cc}{0}_{4\×4}& 0\\ 0& {\mathrm{\Θ}}_{6\×6}\end{array}\right),$ h=((f ^*) ^T F ₂ ^T) ^T, $\tilde{M}=\left(\begin{array}{cc}{I}_{2\×2}& 0\\ 0& W^T\mathrm{MW}\end{array}\right).$

If wherein P is positive definite symmetrical matrix, for system (3), if set up exist at R ⁴/ { 0} * R ^{10 * 10}smooth controller

τ _a=-p _s[X ^TPg] ^T， (5)

$p_s\left(X\right)=\left\{\begin{array}{cc}0& B=0\\ \frac{A+\sqrt{A^2+B^2}}{B}& B\≠0\end{array}\right.,---\left(6\right)$

And adaptive law

${\stackrel{.}{K}}_{\widehat{\mathrm{\Θ}}}\left(t\right)={\left({\mathrm{hX}}^{T}P{g}_n\right)}^T,---\left(7\right)$

Make all state Existence of Global Stables of system closed-loop system, and have

wherein,

for matrix estimates of parameters, B=X ^tpg (X ^tpg) ^t,

(3) selection of parameter

The key that controller is selected is to select to satisfy condition

controller.Selection matrix $P=\left(\begin{array}{cc}14I& 3I\\ 3I& 5I\end{array}\right),$ Due to $X^T{\mathrm{Pg}}_n{K}_{\mathrm{\Θ}}h=X^{T}P(f+F_1\mathrm{\ΘF}+\mathrm{BX})=X^{T}P\left(\begin{array}{c}{X}_2\\ \frac{1}{2}{W}^T\stackrel{.}{M}{\mathrm{WX}}_2-W^T{\mathrm{CWX}}_2-S^T{f}_a\end{array}\right)+X^T\mathrm{PBX},$ Can obtain:

$X^T\mathrm{Pg}=0\&DoubleRightArrow;\left(\begin{array}{cc}{X}_1& X_2\end{array}\right)\left(\begin{array}{cc}14I& 3I\\ 3I& 5I\end{array}\right)\left(\begin{array}{c}{0}_{2\&times;3}\\ S^T\end{array}\right)=0\&DoubleRightArrow;5X_1^T+{3X}_2^T=0\&DoubleRightArrow;X^{T}P{g}_n{K}_{\mathrm{\&Theta;}}h=-(17/3)X_1^T{X}_1<0.---\left(8\right)$

The present invention makes full use of the feature of parallel robot model structure, for the task space of parallel robot, has designed a kind of adaptive controller.Owing to having taken into full account parameter in inertial matrix, in design, no longer take the conversion of the uncertain linear-in-the-parameter of model, the design of control law and adaptive law is also become comparatively simple because estimating the minimizing of parameter.The method can guarantee the terminal location of system and the asymptotically stable in the large of speed.

Claims (5)

1. the adaptive controller design method for planar parallel robot, it is characterized in that controlling Lyapunov function is design tool, the design feature of system model of take is breach, has realized when model parameter can not accurately be determined the design problem of parallel robot controller.

2. according to the adaptive controller design method of the planar parallel robot described in right 1, it is characterized in that the dynamical equation of system has following form:

$\begin{array}{c}\stackrel{.}{X_1}=X_2\\ W^T\mathrm{MW}{\stackrel{.}{X}}_2=-W^{T}M\stackrel{.}{W}{X}_2-W^T\mathrm{CW}{X}_2-S^T{f}_a+S^T{\mathrm{\&tau;}}_a\end{array}.$

3. according to the adaptive controller design method of the planar parallel robot described in right 1, it is characterized in that taking full advantage of M positive definite symmetry and in parameter characteristic.

4. according to the adaptive controller design method of the planar parallel robot described in right 1, its feature is uncertain parameter alpha ₁, β ₁can not carry out parameter Estimation and direct CONTROLLER DESIGN.

5. according to the adaptive controller design method of the planar parallel robot described in right 1, it is characterized in that having utilized control Lyapunov method for designing to carry out CONTROLLER DESIGN.

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