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Procedía Engineering 38 (2012) 1984 - 1993

ANFIS TECHNIQUE APPLIED TO THE CONTROL OF A ROBOT MANIPULATOR WITH DISTURBANCES

M.P.Flower Queena ,Dr. M.Sasi KumarbP.Babu Aurthersona*

aAssistant Professor,Noorul Islam University,Kumaracoil, Tamilnadu,India. bProfessor, Noorul Islam University,Kumaracoil, Tamilnadu,India. a*Professor,M.E.TEngineering College,Chenbagaramanputhoor.

Abstract

The objective of this paper is to propose an ANFIS (Adaptive Network based Fuzzy Interference System) technique, which enables the controller to obtain different combinations of gain (Kp and Kd) with disturbance signals to reflect the real time performance of the manipulator. The outputs of these controllers are used to produce the final actuation signal based on current position errors. Numerical simulation using PD, Fuzzy+PD and ANFIS+PD is also determined and compared. Finally, the results of simulations indicates that, ANFIS based controllers reduce the position tracking error in a more effective manner. Thus the proposed ANFIS based controller works effectively in the tracking control of a robot manipulator

© 2012 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Noorul Islam Centre for Higher Education

Keywords: ANFIS based controller,Conventional controller, Robot manipulator,Positional error.

1 .Introduction:

Design of controlling the robot manipulator is presented in this paper. The controlling of the robot manipulator has always been considered as an important problem. They are required to perform tasks with higher precision, speed and accuracy than the human beings. These manipulators are widely used in many applications such as in industries for handling heavy mechanical parts and in nuclear power plants to handle the radioactive elements. But they are highly nonlinear, hardly coupled and time varying systems. Therefore an accurate mathematical model which requires high degree of speed and accuracy is needed. Many conventional methods such as proportional-integral(PI), proportional-derivative(PD) and proportional-derivative-integral(PID) controllers are used for controlling the robot manipulator. The main drawbacks of these conventional controllers are they will not provide the accurate results for non-linear systems and they are only applicable for linear time invariant systems. Nowadays many intelligent controllers are used for controlling the robot manipulator. In robot manipulator position control is defined as a command signal to move its end-effector to a specified position in order to perform a task. The work of the positional controller is to reduce the positional error to the minimum limit as possible. Positional error is defined as the difference between actual and desired position for the end effecter, when the manipulator moves its arms to the commanded position. In this paper position control has to be performed

1877-7058 © 2012 Published by Elsevier Ltd. doi: 10. 1016/j .proeng .2012.06.240

on the robot manipulator with uncertainties and disturbances. In recent literature lot of studies are available related to the design of controllers for robot manipulators employing PID, adaptive, neural network, artificial intelligence and adaptive fuzzy logic algorithms[l],[2],[4-8].

Kazuo and Toshio[9] proposed a fuzzy vector method which enables the controller to deal efficiently with force sensor signals which include noise and/or unknown vibration caused by the working tool to search the direction of the constraint surface of an unknown object.In [10] the practical implementation of a neural network (NN) tracking controller on a single flexible link and its performance is compared to that of PD and PID standard controllers. In[3] a scara robot manipulator is simulated under PD and its learning based controllers. Subudhi and A.S.Mooris[ll] introduced the control of flexible manipulator using soft computing methods such as fuzzy logic and neural network techniques. A complete mathematical model of SCARA robot and the PD controller for each robot joint is presented in[12], In[13] B.K.Rout and R.K.Mittal illustrated the simulation approach for optimizing the parametric design and performance of 2-DOF R-R Planar manipulator is explained. This proposed work illustrates the procedure to apply ANFIS technique to control the robot manipulator by minimizing the tracking error.Since it is considered to be superior than other other methods.

The paper is organized as follows:-The structure and explanation of ANFIS related robot manipulator are formulated in section 2. Section 3 explains the dynamics of robot manipulator. Section 4 introduces the design of ANFIS+PD controller. Section 5 presents simulation results. Discussion and final conclusion with future works are outlined in section 6.

2.ADAPTIVE NETWORK BASED FUZZY INFERENCE SYSTEMS (ANFIS)

It combines the advantages of fuzzy logic (FL) and neural networks(NN).It starts with an initial FL structure and uses NN for adapting the FL membership function parameters and the rule base to the training data. ANFIS technique was originally presented by Jang, [15] in the year 1992. The model uses neuro-adaptive learning techniques, which are similar to those of neural networks. Given an input/output data set, the ANFIS can construct a fuzzy inference system (FIS) whose membership function parameters were adjusted using back-propagation algorithm or other similar optimization techniques. This allows fuzzy systems to learn from the data and they are modeled, this is illustrated in fig.l. For simplicity, assume the fuzzy inference system with two inputs X and Y with one response F. From the first-order Sugeno fuzzy model, a typical rule set with two fuzzy if-then rules can be expressed as

I jqifT I I f JFUf-TS I jqn~4 IxjM'.l

Fig. 1 An ANFIS architecture for a two rule Sugeno system A two Rule Sugeno ANFIS has rules of the form:

Rule 1: if x is Ai and y is B! then fx = pxx + qxy + rx Rule 2: if x is A2 and y is B2 then f2 = p2x + q2y + r2

For the training of the network, there is a forward pass and a backward passbook at each layer in turn for the forward pass. The forward pass propagates the input vector through the network layer by layer. In the backward pass, the error is sent back through the network in a similar manner to backpropagation.The operations of the different layers are described as follows. Layer 1: Every node i in this layer is a square node with a node function

o] =M(*)

Where x is the input node to i and Aj is the linguistic label (small,large,etc.,) associated with this node function. O) is the membership function of Ai.

Usually fjAl (x) is to be chosen as bell shaped with maximum equal to 1 and minimum equal to zero,such as

¿/4(x)=exp{-

f \2 x-c,

where {a;, ty, cj is the parameter set. As the values of these parameter change, the bell sha;ped functions vary accordingly. These parameters in this layer are referred to as premise parameters. Layer 2: Every node in this layer is a circle node labeled with II which multiplies the in coming signals and send the product for instance.

C0i =juAi(x) x fiBt{y) i= 1,2......

Each node output represents the firing strength of a rule. Layer 3: Every node in this layer is a circle node labeled N.The i"1 node calculates the

ratio of i"1 rules firing strength to sum of all rules firing strength.

=----i= 1,2.......s

(Ox +0)2

For convenience, output of this stage will be called normalized firing strength. Layer 4: Every node i in this layer is an adaptive node with a node function

04J = a J, = wi (ptx + qiy + ri)

Where G)i is a normalized firing strength from layer 3 and {pi5 qi; r;} is the

parameter set of this node. Parameters in this layer are referred to as consequent parameters.

Layer 5: The single node in this layer is a fixed node labeled E , which computes the Overall output as the summation of all incoming signals:

^ „ „ ^ _ , X aift

Overall output: U51 = -

3 .DYNAMICS OF ROBOT MANIPULATOR

The robot manipulator dynamics for a 6-axis industrial robot modeled as the following fourth order SISO is given by [15],[16] is considered for simulation

'0 1 0 0 "0

K K K 0 1 1

X = Jm 0 Jm 0 Jm 0 x+ Jm 0

K 0 K Bl

7i T Jt. 0

where Jm and J\ are the inertia of the mass connected to the motor and the link respectively, K is the torsional spring constant, Bm and Bi are the rotary damping constants for the motor and the link respectively, shows the system parameters, fig.2 shows the simulation diagram of dynamics of robot manipulator.

System Parameters

Jm 0.0108

Jl 0.0108

Bm 0.007

Bl 0.001

K 1.37

Table 1

4.Design of ANFIS+PD controller :

ANFIS is a hybrid neuro-fuzzy technique that brings learning capabilities of neural networks to fuzzy inference systems. The learning algorithm tunes the membership functions of a Sugeno-type Fuzzy Inference System using the training input/output data. The most common conventional control technique for manipulator control is PD controller. The PD controller is a conventional controller which combines the characteristics of proportional and derivative gain.In this paper ANFIS+PD controller combines the ANFIS technique and PD controller technique to form the ybrid controller. The main features of these controllers are that the final control output applied to the plant is summation of individual output of these controllers. The simulation diagram of ANFIS+PD controller is shown in fig.3

Fig.3 ANFIS +PD control of Robot Manipulator

5. SIMULATION RESULTS OF ROBOT MANIPULATOR WITH VARIOUS CONTROLLERS:

Dynamics of the six axis robot manipulator and three types of controller with uncertainity and disturbances that is PD,Fuzzy+PD and ANFIS+PD are simulated in matlab simulink.The values for the Kp and IQ are selected for the simulation were [0.0685 0.0967].Position qd is chosen as the desired variable.

The desired trajectory is given as

qd (t) = - 0.5 + (-1 + tanh(lOcosOO)) Where (0= \rad / s

The function given here is for pick and place task that is widely used in industrial application.All verification process is carried out by simulation. Six axis robot manipulator is used for this simulation.Uncertainities and disturbances are given by the equation

Tc = 0.3^+0.38111(3^) Td= qd +sin(2 qd)

All the simulations are carried out under uncertainties and disturbances.Fig.4 represents the desired trajectory of the six axis robot manipulator fig(5-7)indicates the position tracking error under variety of controllers.fig.5(a,b) shows the position tracking error using PD controller. Link angle error for PD controller is 0.1403 rad, greater value of Kp and lesser value of Kd gives the steady state performance and reduce oscillation.fig6(c,d) shows the position tracking error under fuzzy controller along with the conventional controller. Link angle error for Fuzzy+PD controller is 0. 09412rad. Fig7(e,f) shows the position tracking error under ANFIS controller along with the conventional controller. Link angle error for fuzzy+ PD controller is 0. 08029rad.lt can be seen that ANFIS+PD controller gives better reduction in error when compared to both PD and Fuzzy+PD controller. Finally the error of the link angle is drawn, error angle is maximum in PD controller, the error angle is reduced in Fuzzy+PD controller The results shows that the ANFIS +PD controller is better one when compared to other controllers such as PD and Fuzzy+PD and it is a good choice for controlling the robot manipulator. The parameters are taken from [16] and the desired trajectory is adapted from [3].

Fig.4 desired trajectory

Fig 5(a) .Desired and actual link angles when PD controller is used

Fig 6(a) .Desired and actual link angles when Fuzzy + PD controller is used

Fig 7(a) .Desired and actual link angles when ANFIS + PD controller is used

6. CONCLUSION:

Thus the present work illustrates the controller of robot manipulator with minimum position error. Simulation studies were performed by using PD, FUZZY+PD and ANFIS+PD controllers and they are compared. It is concluded that ANFIS+PD controller is most suitable for controlling the robot manipulator. Future studies are relatedto tune the controller by optimization technique such as genetic algorithm and particle swarm optimization to ANFIS technique applied for the control of robot manipulator.

REFERENCES

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[10] L. B. Guti'errez,, F. L. Lewis,, and J. Andy Lowe "Implementation of a Neural Network Tracking Controller for a Single Flexible Link: Comparison with PD and PID Controllers" IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 45,NO. 2, APRIL 1998.

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[13] B.K. Rout, RK. Mittal "Parametric design optimization of 2-DOF R-R planar manipulator A design of experiment approach"Robotics and Computer-Integrated Manufacturing 24 (2008) 239-248.

[14]Spong M, Vidyasagar M. Robot dynamics and control. New York: Wiley; 1989.

[15] Jang JSR. ANFIS: Adaptive-network-based fuzzy inference systems. IEEE Transactions on Systems, Man, and Cybernetics 1993;23(03):665-85.

[16] S. G. Anavatti and S. A. Salman J. Y. Choi "Fuzzy + PID Controller for Robot Manipulator" International Conference on Computational Intelligence for Modelling Control and Automation,and International Conference on Intelligent Agents,Web Technologies and Internet Commerce (CIMCA-IAWTIC'06) 2006,IEEE.