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

High-precision position control method for series robot

Technical Field

The invention relates to the field of position control of a series robot, in particular to a method for improving the problems of high-precision position tracking of the series robot and moment and speed jump when the robot is started by a fuzzy self-adaptive sliding mode control method.

Background

The robot technology is a high and new technology integrating multiple disciplines such as mechanics, electronics, computer technology, sensing technology, cybernetics, artificial intelligence and bionics.

Robot position control is an important area of robotics. The industrial robot is a complex multi-input multi-output nonlinear system, has dynamics characteristics such as strong coupling, time variation and nonlinearity, and is complex in control process. Due to the inaccuracy of the measurement and modeling of the number of robot parameters and the uncertainty of the robot load and the external interference of the industry, a complete and accurate object model of the robot cannot be obtained in practice, and the specific application environment of the industrial robot determines that the industrial robot must face the existence of various uncertain factors.

For robots, their controller designs fall into two categories: one is to perform negative feedback control according to a deviation between an actual trajectory and a desired trajectory of the robot. The method is called 'motion control', and has the main advantages of simple control law and easy realization. However, for controlling high-speed and high-precision robots, this type of method has two significant disadvantages: firstly, the controlled robot is difficult to ensure to have good dynamic and static quality; secondly, a larger control energy is required. Another type of controller design is referred to as "dynamic control". Such methods are also commonly referred to as "model-based control" because they design a more refined nonlinear control law based on the properties of the robot dynamics model. The controller designed by the dynamic control method can ensure that the controlled robot has good dynamic and static quality, and overcomes the defects of the motion control method.

In order to further improve the sliding mode control effect, self-adaptive fuzzy sliding mode control can be adopted, the gain of the sliding mode control is adjusted in a self-adaptive mode, the adaptive capacity to random uncertainty is enhanced, and the input buffeting phenomenon in the sliding mode control is eliminated. However, it is worth paying attention to the problem that when the tracking error suddenly changes, the large moment and the speed jump of the controller bring great disadvantages to the actual robot control, and the servo motors of all joints are very easy to damage.

Disclosure of Invention

The invention aims to design a robot position control algorithm with good tracking effect and smooth speed output based on a dual-fuzzy self-adaptive sliding mode control technology. The problem of large moment and speed jump caused by deviation generated by a large initial pose is well solved.

In order to achieve the purpose, the technical scheme of the invention is as follows: and establishing a connecting rod coordinate system of the robot based on a sliding mode control technology of a moment calculation method, and acquiring D-H parameters of the connecting rod coordinate system to obtain a kinetic equation of the robot. And estimating an inertia force term, a Coriolis force term and a gravity term of each joint according to the D-H parameters, and finally obtaining a moment estimation formula of each joint. And establishing a sliding mode surface through the position error of each joint, and performing position control on each joint by using a sliding mode control technology based on a moment calculation method. In order to reduce the buffeting phenomenon in the sliding mode control, an exponential approximation law is added, and the sliding mode switching gain K is estimated on line by adopting self-adaptive fuzzy control. In order to weaken the problems of moment jump and speed jump caused by large initial deviation, another fuzzy control is adopted to estimate a coefficient A of an exponential approximation law and determine an optimal parameter. The whole process comprises the following steps: the system comprises a dynamics estimation module, a sliding mode surface establishing module, a sliding mode switching gain estimation module, an index approach law estimation module and a control moment calculation module.

Firstly, establishing a coordinate system of each connecting rod of the robot, and determining D-H parameters (a) of each connecting rod_i，α_i，d_i，θ_i). From the lagrange equation:

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

estimating an inertial force term, a Coriolis force term and a gravity term according to a kinetic equationFinally, obtaining a moment estimation formula of each axis: $\widehat{\mathrm{\τ}}=\hat{H}{\stackrel{\·\·}{q}}_r+\hat{C}{\stackrel{\·}{q}}_r+\hat{G}.$

second, calculating the position error e and error change rate of each joint

Establishing a slip form surface

Wherein lambda is diag lambda₁，…λ_l…λ_n]，λ_l＞0。

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

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

wherein,

for equivalent control, As is exponential approximation law, and K sgns is switching control.

Estimated values for H, C, G, K ═ diag [ K₁₁，…K_ii，…K_nn]、A＝diag[a₁，…，a_i，…，a_n]Is a positive definite matrix.

And thirdly, adaptively approaching the gain K of the sliding mode control law by using fuzzy control. A product inference engine, a single-value fuzzifier and a center average defuzzifier are adopted to design a fuzzy control system, and the control output of the system is as follows:

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

membership functions used to represent fuzzy sets are designed as:

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

the self-adaptive law is selected as follows:

fourthly, fuzzy control is carried out on the index control item coefficient of the sliding mode control, and the following steps are achieved by adjusting A: when the error and the error change rate are large, the control quantity is reduced as much as possible; otherwise, the control amount is increased. Therefore, the good tracking effect of the original control algorithm is kept, and the problems of large moment and speed jump when the robot is started are solved.

Fifthly, combining the above parts, and inputting the moment control of the joint as follows:

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

wherein,

and respectively H, C and G, and s is a sliding mode surface, the parameter K is estimated by the self-adaptive sliding mode control method in the third step, and the parameter A is estimated by the sliding mode control method in the fourth step.

The invention has the beneficial effects that: the robot position control method based on the dual-fuzzy self-adaptive sliding mode is used for improving the tracking precision of the series robot and improving the problems of moment jump and speed jump. Sliding mode control is essentially a special nonlinear control, and is an effective control method due to strong robustness; an index approach law is introduced on the basis of sliding mode control, so that the problem of buffeting is effectively solved; an adaptive fuzzy controller is adopted to estimate the sliding mode switching gain according to the sliding mode arrival condition, so that the adaptive capacity of the sliding mode switching gain to uncertainty factors is enhanced, and the buffeting phenomenon of output torque in sliding mode control is eliminated; and the other fuzzy adaptive controller is adopted to correct the coefficient of the exponential approximation law so as to solve the problems of large moment and speed jump caused by the variation of the large-range initial pose deviation.

Drawings

FIG. 1 is a schematic view of a link coordinate system;

FIG. 2 is a general schematic of the present invention.

Detailed Description

In order that the objects, technical solutions and advantages of the present invention will become more apparent, the present invention will be further described in detail with reference to the accompanying drawings in conjunction with the following specific embodiments.

The basic idea of the invention is as follows: an improved control method of a robot is provided: it does not require knowledge of the specific mathematical model of the controlled object; the method has strong robustness and high tracking precision; and the problems of moment jump and speed jump caused by large-range initial pose deviation are solved. Firstly, modeling is carried out on a robot to estimate a dynamic model of the robot, and a sliding mode nonlinear control method based on a moment calculation method is adopted to ensure strong robustness in control; the phenomenon of buffeting can occur in sliding mode control of the robot, so that the buffeting method introduces an index approach law and effectively eliminates the buffeting problem. Meanwhile, the self-adaptive fuzzy controller is adopted to estimate the sliding mode switching gain according to the sliding mode arrival condition, so that the adaptability of the sliding mode switching gain to uncertain factors is enhanced, and the buffeting phenomenon of output torque in sliding mode control is eliminated; and the other fuzzy adaptive controller is adopted to correct the coefficient of the exponential approximation law so as to solve the problems of large moment and speed jump caused by the variation of the large-range initial pose deviation.

Fig. 2 is an overall control block diagram of the present invention. The dynamics estimation module 1 acquires the D-H parameters of the robot by establishing a connecting rod coordinate system of the robot to obtain a dynamics equation of the robot, estimates an inertia force term, a Coriolis force term and a gravity term of each joint according to the D-H parameters, and finally obtains a moment estimation formula of each joint. The sliding mode surface establishing module 2 establishes a sliding mode surface according to the position error of each joint, and performs position control of each joint by using a sliding mode control technology based on a moment calculation method. The sliding mode switching gain estimation module 3 adds an exponential approximation law for reducing buffeting in sliding mode control, and estimates the sliding mode switching gain K on line by adopting self-adaptive fuzzy control. The index approach law estimation module 4 adopts another fuzzy control to estimate an index approach law coefficient and determine an optimal parameter in order to weaken the problem of large moment and speed jump caused by large initial deviation. The control moment calculation module 5 calculates the control input tau of each joint finally_iTo accomplish the position control of the robot.

Further, the dynamics estimation module 1 specifically includes:

(1.1) obtaining of D-H parameter:

a coordinate system is fixed on each connecting rod, the coordinate system fixed with the base is marked as {0}, and the connecting rod is fixed with the connecting rod iThe coordinate system is marked as { i }, and the D-H method uses two parameters of the torsion angle alpha of the connecting rod_iAnd link length alpha_iTo describe any link i, with link offset d_iAnd joint angle theta_iThe relationship of adjacent links is described. The 4 link parameters can be defined as: alpha is alpha_i- -around X_iAxis, Z_i-1Axis to Z_iThe angle of the shaft; a is_i- -along X_iAxis, Z_i-1Axis to Z_iDistance of the shaft; d_i-. along Z_i-1Axis, X_i-1Axis to X_iDistance of the shaft; theta_i- - (Y- -O) - -around Z_i-1Axis, X_i-1Axis to X_iThe angle of the shaft. As in fig. 1.

(1.2) solving a kinematic equation:

after the D-H parameters are determined, the relative relation between the adjacent connecting rods i-1 and i is established through two translation motions and two rotation motions, and the connecting rods are transformed^i-1T_iThe transformation representing the link coordinate system { i } relative to the coordinate system { i-1} can be decomposed into four steps:

a) around Z_i-1Axis of rotation theta_iAngle, X_i-1The shaft is rotated to and X_iIn the same plane;

b) along axis Z_i-1Is translated by a distance d_iA handle X_i-1Move to and with X_iOn the same straight line;

c) along axis X_i-1Translation distance a_iSo that the origins of the two coordinate systems overlap;

d) about axis X_i-1Rotation alpha_iAngle such that the two coordinate systems completely overlap.

Thus, the pose of the link coordinate system { i } relative to the link coordinate system { i-1} can be transformed using the homogeneous transformation matrix^i-1T_iExpressed as:

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

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

the kinematic equation is:

⁰T₆＝⁰T₁ ¹T₂ ²T₃ ³T₄ ⁴T₅ ⁵T₆

(1.3) the system dynamics equation, Lagrangian equation, is as follows:

the exact kinetic model for a mechanical arm, i-1, 2, …, n, 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 a three joint robotic arm:

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

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

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

I_aiis generally negligible for the equivalent moment of inertia of the transmission. Estimating the inertia force term, the Coriolis force term and the gravity term of each joint according to a kinetic equation

Finally, obtaining a moment estimation formula of each axis: $\widehat{\mathrm{\τ}}=\hat{H}{\stackrel{\·\·}{q}}_r+\hat{C}{\stackrel{\·}{q}}_r+\hat{G}.$

the sliding mode control module 2 specifically comprises:

(2.1) design of slip form faces

Defining the position tracking error of the mechanical arm as e-q_dQ, wherein q_dThe desired position of the joint and q the actual position. The error function is defined as:wherein lambda is diag lambda₁，…，λ_i，…，λ_n]，λ_i＞0。

(2.2) design of sliding mode control law

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

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

wherein,

for equivalent control, As is exponential approximation law, Ksgns is switching control.

Estimated values for H, C, G, K ═ diag [ K₁₁，…，K_ii，…K_nn]、A＝diag[a₁，…，a_i，…，a_n]Is a positive definite matrix.

The sliding mode switching gain estimation module 3 specifically comprises:

(3.1) design of fuzzy rules

The control law based on fuzzy gain adjustment is designed as follows:wherein K is [ K ]₁，…，k_i，…，k_n]，k_iIs the output of the ith fuzzy system.

If the gain K is approximated using fuzzy control and the Lyapunov function is defined:

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

it follows that, to ensure

To be negative, should make s_ik_iNot less than O, i.e. ensuring s_iAnd k is_iThe symbols are the same. At the same time, consider s_iΔf_i-s_ik_iWhen s_iWhen | is larger, to ensure

For larger negative numbers, | k is desired_iI is larger; when s_iIf | is smaller, | k_iKeeping the value of | small, it can be guaranteed

Is a negative number.

(3.2) fuzzy System design

Membership functions used to represent fuzzy sets are designed as:

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

a product inference engine, a single-value fuzzifier and a center average defuzzifier are adopted to design a fuzzy control system, and the control output of the system is as follows: the output of the fuzzy system is:

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

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 law

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

get

Is an ideal Δ f_iThe approximation of (1) exists according to the universal approximation theorem of (omega)_i> 0, there are:

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

defining the 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 ${\widetilde{\mathrm{\&theta;}}}_{k_i}={\mathrm{\&theta;}}_{k_i}-{\mathrm{\&theta;}}_{k_{\mathrm{id}}}.$ Then

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

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

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

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

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

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

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

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

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

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

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

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

presence of positive real numbers gamma_iSo that equation (2) satisfies:

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

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

wherein γ is diag [ γ ]₁，…，γ_i，…γ_n]，a_i＞γ_i. As can be seen from formula (5), only when s ═ 0,

the adaptation law (4) converges progressively. The conclusion is that:

namely, it is

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

The exponential approximation law estimation module 4 specifically comprises:

(4.1) since a relatively large error and error change rate are generated when the robot is just started, the controller generates a relatively large output. In order to reduce the situation, on the basis of sliding mode control, the coefficient of exponential control term of the sliding mode control is subjected to fuzzy control, and the following steps are achieved by adjusting A: when the error and the error change rate are large, the control quantity is reduced as much as possible; otherwise, the control amount is increased. Therefore, the problems of large moment and speed jump when the robot is started are solved.

(4.2) implementation of fuzzy controller with self-adjustable control rule:

the performance of a fuzzy controller depends greatly on its fuzzy control rules, and if fixed fuzzy control rules are adopted, once the fuzzy controller is formed, the linguistic rules and the synthetic reasoning are determined and are not adjustable. However, in some control scenarios, in order to make the existing fuzzy controller have stronger adaptability to adapt to different control objects, the control rule is required to have a certain self-adjusting function.

For a two-dimensional fuzzy controller, when the domain of discourse degree of the input variable E, EC and the output variable U is the same, the introduced expression describing the control rule is as follows:

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

the control law can be adjusted by adjusting the value of alpha.

The control torque calculation module 5 specifically includes:

(5) combining the above parts, the moment control input of the joint is:

wherein,

and respectively H, C and G, and s is a sliding mode surface, the parameter K is estimated by the self-adaptive sliding mode control method in the third step, and the parameter A is estimated by the sliding mode control method in the fourth step. And taking the calculated tau as the control input of the joint.

Claims (6)

1. An improved tandem robot control method is provided: it does not require knowledge of the specific mathematical model of the controlled object; the method has strong robustness and high tracking precision; the problems of moment jump and speed jump caused by large-range initial pose deviation are solved; firstly, modeling is carried out on a robot, a dynamic model of the robot is estimated, and a sliding mode nonlinear control method based on a moment calculation method is adopted to ensure strong robustness in control; the phenomenon of buffeting can occur in sliding mode control of the robot, so that the buffeting method introduces an index approach law and effectively eliminates the buffeting problem; meanwhile, the self-adaptive fuzzy controller is adopted to estimate the sliding mode switching gain according to the sliding mode arrival condition, so that the adaptability of the sliding mode switching gain to uncertain factors is enhanced, and the buffeting phenomenon of output torque in sliding mode control is eliminated; correcting the coefficient of the exponential approximation law by adopting another fuzzy adaptive controller to solve the problems of large moment and speed jump caused by the variation of the large-range initial pose deviation;

the dynamics estimation module 1 acquires D-H parameters of the robot by establishing a connecting rod coordinate system of the robot to obtain a dynamics equation of the robot, estimates an inertia force item, a Coriolis force item and a gravity item of each joint according to the D-H parameters, and finally obtains a moment estimation formula of each joint;

the sliding mode surface building module 2 builds a sliding mode surface through the position error of each joint, and performs position control on each joint by using a sliding mode control technology based on a moment calculation method;

in order to reduce buffeting in sliding mode control, the sliding mode switching gain estimation module 3 adds an exponential approximation law, and estimates a constant speed approximation term coefficient K in the sliding mode switching gain estimation module on line by adopting self-adaptive fuzzy control;

the index approach law estimation module 4 adopts another fuzzy control to estimate an index approach law coefficient and determine an optimal parameter for weakening large moment and speed jump caused by large initial deviation;

the control moment calculation module 5 calculates the control input tau of each joint finally_iTo complete the position control of the robot; the robot position high-precision tracking and the problems of torque jump and speed jump are solved.

2. The dual-fuzzy adaptive sliding-mode control method based on the calculation moment method of claim 1, which is characterized in that: the D-H parameter obtaining and dynamics estimating module establishes coordinate systems of all connecting rods of the robot and determines D-H parameters (a) of all joints_i，α_i，d_i，θ_i) (ii) a From the lagrange equation:

and (3) deriving a kinetic equation of i-1, 2, … and n:

estimating an inertial force term, a Coriolis force term and a gravity term according to a kinetic equation

Finally, obtaining a moment estimation formula of each joint:

3. the dual-fuzzy adaptive sliding-mode control method based on the calculation moment method of claim 1, which is characterized in that: the sliding mode surface building module is used for calculating the position error e and the error change rate of each joint

Establishing a slip form surface

Wherein lambda is diag lambda₁，…，λ_i，…，λ_n]，λ_i＞0；

And defines:

the design control law is as follows:

wherein,

for equivalent control, As is exponential approximation law, Ksgns is switching control;

estimated values for H, C, G, K ═ diag [ K₁₁，…，K_ii，…K_nn]、A＝diag[a₁，…，a_i，…，a_n]Is a positive definite matrix.

4. The dual-fuzzy adaptive sliding-mode control method based on the calculation moment method of claim 1, which is characterized in that: the sliding mode switching gain estimation module is used for adaptively approaching the gain K of the sliding mode control law by using fuzzy control; a product inference engine, a single-value fuzzifier and a center average defuzzifier are adopted to design a fuzzy control system, and the control output of the system is as follows:

membership functions used to represent fuzzy sets are designed as:

the self-adaptive law is selected as follows:

5. the dual-fuzzy adaptive sliding-mode control method based on the calculation moment method of claim 1, which is characterized in that: the index approaching law estimation module carries out fuzzy control on the index control item coefficient of the sliding mode control, and achieves the following effects by adjusting A: when the error and the error change rate are large, the control quantity is reduced as much as possible; otherwise, the control quantity is increased, so that the good tracking effect of the original control algorithm is kept, and the problem of large moment when the robot is started is solved.

6. The dual-fuzzy adaptive sliding-mode control method based on the calculation moment method of claim 1, which is characterized in that: the control moment calculation module combines the above parts, and the moment control input of the joint is as follows:

wherein,respectively H, C and G, and s is a sliding mode surface, estimating a parameter K by using the self-adaptive sliding mode control method in the third step, and estimating a parameter A by using the sliding mode control method in the fourth step; and taking the calculated tau as the control input of the joint.

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