dynamic control three links car a manipulator an f is

Dynamic Control of Three-Link SCARA Manipulator using AdaptiveNeuro Fuzzy Inference System

Prabu D, Member, IEEE., Surendra Kumar and Rajendra Prasad

Abstract- In this work the Adaptive Neuro-Fuzzy InferenceSystem (ANFIS) controller is designed for the dynamic control(continuous path control) of the three-link Selective CompliantAssembly Robot Arm (SCARA) manipulator. This ANFIScontroller is designed to overcome the unmodeled dynamics andin the presence of structured and unstructured uncertainties ofSCARA. The proposed controller-building technique combinesartificial neural networks with fuzzy logic. The ANFIS controlcombines the advantages of neural networks (learning andadaptability) with the advantages of fuzzy logic (use of expertknowledge) to achieve the goal of robust control of robotdynamic systems. The fuzzy sets are used to formalize thelevel of human perception of the physical system. The neuralnetwork on the other hand performs all the necessarycomputations and regarding their learning capabilities, theyenable an adaptation of the existing controller through itslearning to the changes in the system behavior. Theexperimental ANFIS simulation results show very good SCARAtracking performance.

I. INTRODUCTION

TH E very precise control of robot manipulator to track thedesired trajectory is a very tedious job and almost

unachievable to certain limit with the help of adaptivecontrollers. This task is achievable to certain limit with thehelp of adaptive controllers but these controllers also havetheir own limitation of assuming that the system parametersbeing controlled change relatively very slow. With referenceto the tasks assigned to an industrial robot, one importantissue is to determine the motion of the joints and the endeffectors of the robot. Therefore, the purpose of the robotarm control, as Fu et al [1] wrote in one classical works onrobotics, is to maintain the dynamic response of themanipulator in accordance with some prespecifiedperformance criterion. Among the early robots of the firstgeneration, non-servo control techniques, such as bang-bangcontrol and sequence control were used.

Manuscript received on October 15, 2007Prabu D was a Master of Technology (M.Tech ) graduate studentin the Department of Electrical Engineering ( with Specializationof System Engineering and Operations Research) of Indian Instituteof Technology (IIT) Roorkee, Uttarakhand, 247667, India. This workwas done during 2002 through 2004. He is now with the WiproTechnologies, PTG Lab (R&D), Electronic city, Bangalore, India. Hecan be reached for any correspondence of this paper by E-mail:.prabud.trLagmaJ1com. He is a member of IEEE, ACM and CMG.Dr Surendra Kumar is a faculty with the Department of ElectricalEngineering, IIT Roorkee, Uttarakhand, 247667, India. E-mail:

Dr Rajendra Prasad is a faculty with the Department of ElectricalEngineering, IIT Roorkee, Uttarakhand, 247667, India. E-mail:,

These robots move from one position to another under thecontrol or limit switches, relays, or mechanical stops.During the 1970s, a great deal of work was focused onincluding such internal state sensors as encoders,potentiometers, tachogenerators, etc., into the robotcontroller to facilitate manipulative operation [2, 3]. Sincethen, feedback control techniques have been applied forservoing robot manipulators. Up till now, the majority ofpractical approaches to the industrial robot arm controllerdesign use traditional techniques, such as Proportional andDerivative (PD) or Proportional-Integral-Derivative (PID)controllers, by treating each joint of the manipulator as asimple linear servomechanism. In designing these kinds ofcontrollers, the non-linear, coupled and time-varyingdynamics of the mechanical part of the robot manipulatorsystem are completely ignored, or dealt with as disturbances.These methods generally give satisfactory performancewhen the robot operates at a low speed. However, when thelinks are moving simultaneously and at a high speed, thenon-linear coupling effects and the interaction forcesbetween the manipulator links may degrade the performanceof the overall system and increase the tracking errors. Thedisturbances and uncertainties in a task cycle may alsoreduce the tracking quality of robot manipulators. Thus,these methods are only suitable for relatively slowmanipulator motion and for limited-precision tasks [4]. TheComputed Torque Control (CTC) is commonly used in theresearch community. The CTC law has the ability to makethe error asymptotically stable if the dynamics of the robotare exactly known [5] However, manipulators are subject tostructured and/or unstructured uncertainty. Structureduncertainty is defined as the case of a correct dynamic modelbut with parameter uncertainty due to tolerance variances inthe manipulator link properties, unknown loads, inaccuraciesin the torque constants of the actuators, and others.Unstructured uncertainty describes the case of unmodeleddynamics, which result from the presence of high-frequencymodes in the manipulator, neglected time-delays and non-linear friction. It has been widely recognized that thetracking performance of the CTC method in high-speedoperations is severely affected by the structured andunstructured uncertainties. To cope with the problem, someadaptive approaches have been proposed to maintain thetracking performance of the robotic manipulator in thepresence of structured uncertainty [6]. In this paper, wehave proposed ANFIS controller for SCARA manipulator toovercome the above-discussed problem. Present paper isorganized in the following manner. Section 2 Overview ofSCARA robot control system. Section 3 describes theproposed Adaptive Neuro Fuzzy Inference System and

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Section 4 presents the ANFIS architecture and learningalgorithm and simulation of Continuous Path Motion (CPM)of real-world applications of SCARA Robot Manipulator.Finally, conclusions are summarized in Section5.

II. OVERVIEW OF SCARA ROBOT CONTROL SYSTEM

The SCARA acronym stands for Selective CompliantAssembly Robot Arm or Selective Compliant ArticulatedRobot Arm. SCARA is normally used in industries for pickand place operation, etc.

Fig. 1. Shows the SCARA Robot

The figurel shows the model picture of SCARA with twovertical revolute joint and one vertical prismatic joint used inthis experiment. In this experiment, the dynamical model ofSCARA robot is derived using Newton Euler formulation isused for simulating the CPM control using ANFIS and PDController. Due to maximum of 6 pages restriction in theregular paper of IEEE ICNSCO8, It becomes difficult toaddress the dynamical model of the SCARA in this paper.Moreover, the dynamical model of the SCARA is given inmany robotics books and papers. The figure 2 shows thebasic ANFIS feed back control system for the CPM controlofSCARA Manipulator used in this experiment.

e

Trajectory (DT) generator to achieve minimum trackingerror. The ANFIS controller is designed for the two controlinput viz, error (e) and change in error (ce) and one output asa control signal (u). In order to achieve the feedback controldesign, the output of the SCARA joint torque angles (o) isfedback to the system. As a result the error and change errorobtained at the adder of the feedback control system is givenas the input to ANFIS controller for the SCARA CPMcontrol. The ANFIS output control signals (u) are usuallyweak signals, which cannot able to drive the SCARA jointsdirectly, so the signal (u) is amplified and actuated by theservo control system for SCARA manipulator joints. Theoutputs (t) of the servo system are given to individualmanipulator links of the SCARA. The simulation model ofANFIS controller architecture is described elaborately in thesection 3.

III. ADAPTIVE NEURO FUZZY INFERENCE SYSTEM

This paper investigates Adaptive Neuro Fuzzy InferenceSystem (ANFIS) structures with fuzzy IF-THEN-rule basedmodels whose consequent constituents are constants,membership functions, and linear functions as shown infigure 3. The Fuzzy logic can also be used to map complexnonlinear relations by a set of IF-THEN rules. Themembership functions are designed by intuitive humanreasoning. This causes three different problems. One, fordifferent control applications, a new set of membershipfunctions have to be developed, second, latent stabilityproblem[7] and third, once these membership functions aredeveloped and implemented there is no means of changingthem. This means fuzzy logic lacks a learning function. Inthe past decades, there is a growing interest in Neural-FuzzySystems (NFS) as they continue to find success in a widerange of applications. Unfortunately, it has broaden theapplication spectrum, this paved the way to discover thatmost existing neural-fuzzy systems [8,9,10] exhibit severalmajor drawbacks that may eventually lead to performancedlevrnmIltion

u

-4ce

*00.

Fig. 2. Shows the ANFIS feedback control system ofSCARA

The feedback control system consists of ANFIS controller,servo actuating system for the SCARA Robot manipulatorsystem and the SCARA robot manipulator system. Thewhole feedback system is simulated using Desired

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Fig. 3. The architecture of sugeno Adaptive Neuro Fuzzy Inference System(ANFIS)

It


One of the drawbacks is the curse of dimensionality or fuzzyrule explosion. This is an inherent problem in fuzzy logiccontrol systems; that is, too many fuzzy rules are used toapproximate the input-output function of the system becausethe number of rules grows exponentially with the number ofinput and output variables. Another drawback is their lack ofability to extract input-output knowledge from a given set oftraining data. Since neural-fuzzy systems are trained bynumerical input output data, the cause-effect knowledge ishidden in the training data and is difficult to be extracted.Another drawback is their inability to re-structure theinternal structure. i.e. the fuzzy term sets and the fuzzy rulesin their hidden layers. In addition, this work proposes asystematic approach for establishing a concise ANFIS that iscapable of online self-organizing and self-adapting itsinternal structure for learning the required controlknowledge that satisfies the desired system performance.The initial structure of the proposed ANFIS has no rule orterm set node. The rule nodes and the term-set nodes arecreated adaptively and dynamically via simultaneous self-organizing learning and parameter learning procedures. Inorder to optimize the existing structure, the established rulesand term sets are re-examined based on a significance indexand similarity measure [11]. Thus, the rules with the indexvalues below a prespecified threshold are pruned and thehighly similar input term sets are combined. The backpropagation algorithm and/or the recursive least squareestimate are incorporated into the ANFIS to optimally adjustthe parameters. This pruning of rule nodes and term-setnodes will result in a more concise ANFIS structure withoutsacrificing the system performance

the hybrid learning rule, a computational speedup may bepossible by using variants of the gradient method or otheroptimization techniques on the premise parameters. SinceANFIS and radial basis function networks (RBFNs) arefunctionally equivalent, a variety of learning methods can beused for both ofthem. Figure 4 and 5 shows the membershipfunction of the input before training and after training.

IV. DESIGN OF ANFIS CONTROLLER FOR SCARA

In this section, the tracking and adaptability features ofthe ANFIS control applied to a three-link SCARAmanipulator are tested using simulation. Figure 5 shows thearchitecture of the fuzzy system with the ANFIS approach.The ANFIS methodology is used to estimate the parametersof the membership functions and the consequent functions.In this experiment, ANFIS network is implemented withhelp of MATLAB, ANFIS toolbox. ANFIS Input variableconsist of error (e) and change in error (ce), which has beendescribes by low, medium and high membership function inthe ANFIS network. The training data (control signal data) isobtained from the dynamic model of SCARA. The designedANFIS network is trained for SCARA control signal. Theback propagation algorithm and/or the recursive least squareestimate are incorporated into the ANFIS to optimally adjustthe parameters (linguistic variables) of the membershipfunction. It is found that there is a significant differencebetween the ANFIS membership functions before and aftertraining as shown in the figures 4 and 5 respectively.

Fig. 4. Membership functions before ANFIS learning

Fig. 5. Membership functions after ANFIS learning

Fig. 6. Generated rule base ofthe ANFIS structure.

This show the membership functions learns the training dataand adjusts its shapes according to the dynamics of thesystem. The nine rules are used to model the fuzzy part ofthe ANFIS controller as shown in figure 6 and three

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membership functions for each linguistic input variable. Thefuzzy rules generated by the ANFIS method are shown infigure 6. Figure 7 and 8 shows the loading and training ofANFIS structure using the SCARA dynamic data. TheANFIS structure is trained for 50 epochs and theperformance Mean Square Error (MSE) is found to be0.0064759. Figure 9 shows the fuzzy rule viewer ofMATLAB, which is used for predetermine the output of themodel for specific input values.

Fig. 9. Rule viewer ofANFIS structure

A. Continuous Path Control & Experimental Results.

The Continuous Path Motion (CPM), sometimes calledcontrolled-path motion [12]. Normally SCARA is used forpick and place applications. CPM has become a morechallenging control problem Robot work. The figure 10shows the simulation model of a three-link SCARAmanipulator with PD controller for the given joint angletrajectories.

Fig. 7. Loading Training data for ANFIS structure.

Step Ilplt of0.3 Alipthide

SCARA stemr

co0lsta1i

Fig. 8. Training when error tolerance is chosen to be 0 and number ofepochs is limited to 50.

Fig. 10. Simulation model ofthe step/sinusoidal trajectories tracking ofthree-link SCARA manipulator with PD controller for joint angles

(q I (t) = 0.8sin(t), q 2 (t) = 0.5sin(t) ) and joint distance

(q3(t) = 0.3m )

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This SCARA dynamic model is constructed using MATLABSimulink software. SCARA is initially tuned for PD valuesas per the dynamics of the system and its environment. Thedesigned model is experimented with desired trajectories(qd,(t) = 0.8sin(t), q 2(t) = 0.5sin(t)) and joint distance

(q3(t) =0.3m) as shown in figure 10. The figure 11 showsgood trajectory characteristics at the joint distance, but sometracking error for the sinusoidal trajectories.

controller gave the best results when compare toconventional PD controller. It is very clear from figure 11,

ct7~

a).

*

Time(s)

Fig. 11. The step/ sinusoidal trajectories tracking of three-link SCARAmanipulator with PD controller forjoint angles viz,


(q3(t) = 0.3m)The figure 12 depicts the simulation model of three-linkSCARA Manipulator with ANFIS controller for joint angles(q ,(t) = 0.8sin(t), q 2(t) = 0.5sin(t)) and joint distance( q3 (t) = 0.3m ). The ANFIS model for SCARA is designedas per the design discussed in section 4 of this paper. Thetrained ANFIS network model is shown in figure 12 ismodeled by using ANFIS tool and Simulink software. Fromthe figure 13 it shows ANFIS controller is able to cope withthe uncertainty and model deficiency of the system. Theactual trajectories and desired trajectories in ANFIS networkalmost overlaid each other. Figure 11 and figure 13 togetherreveal the tracking performance of PD and ANFIScontroller. The results are compared with a classical PDcontroller and with an ANFIS (sugeno) [13] controller, tomeasure how much the adaptive neuron fuzzy approach canimprove the performance. Of course, the neuro-fuzzycontroller (designed with ANFIS) was better in tracking andadaptability than the other controllers. Another advantage ofthis method over classical quantitative controllers is that, itdoes not require a fixed sampling time. Therefore, theproposed design confirms the fact that ANFIS control isrelevant to the control fast of non-linear processes such asrobot manipulator controls where quantitative methods arenot always appropriate. From the response shown in figure13 is very clear that ANFIS controller gives no trackingerror,i.e the response of the desired trajectories is almostsuperimposed with the actual one, Thus the ANFIS

SCARA sstem

coEIltStap Input of0.3 Amphlitud

Fig. 12. Simulation model ofthe step/sinusoidal trajectories tracking ofthree-link SCARA manipulator with ANFIS Controller


(q3(t) = 0.3m)the tracking performance of the conventional PD controlleris not that appreciable since it is not able cope up withsudden change in the state this leads to some tracking errorin its response and also it is not able to follow faithfully asthe ANFIS controller does.

Time(s)

Fig. 13. The step/ sinusoidal trajectories tracking of three-link SCARAmanipulator with ANFIS controller for joint angles. With


(q3(t) = 0.3m ).

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11

1-

ct7.ct

(D7.4-

C).E


The figure 13 shows the ANFIS controller response of theSCARA for the given desired joint angle trajectories. It isfound that actual trajectories of the SCARA are almostmerged with the desired trajectories. From this inference, itis concluded that the ANFIS training is completely satisfiedand SCARA tracking error is almost nearly zero.

V. CONCLUSIONS

In this paper, the feasibility of ANFIS control for a three-link SCARA manipulator has been proved and illustrated bysimulation. The best parameters for the fuzzy controller weredetermined by using the ANFIS methodology and by usingsimulations of the SCARA manipulator dynamics. Asimulation tool (i.e., Fuzzy logic toolbox (ANFIS)) was usedto validate experimentally the tracking ability and theinsensibility to plant parameter changes. The ANFIScontroller presented very interesting tracking features andwas able to respond to different dynamic conditions. Inaddition, the fuzzy control computation is very inexpensive,and this regulator could be used for the control of machinetools and robotics manipulators [11] without significantlyincreasing the cost of the drive. The proposed designconfirms the fact that fuzzy control is relevant to the fastcontrol of non-linear processes such as SCARA manipulatorcontrol where quantitative methods are not alwaysappropriate. Thus, the results obtained using the ANFIScontrollers are encouraging when compared to conventionalPD controller.

[10] C. T. Lin and C. S. G. Lee, Neural Fuzzy Systems: A Neuro-FuzzySynergism to Intelligent Systems, Prentice Hall PTR, 393 Pages, 1996.

[11] J. S. Wang, C. S. G. Lee, and C. H. Juang, "Structure and Learning inSelf-Adaptive Neural Fuzzy Inference Systems", Proc. of the Eighth Int'7Fuzzy Syst. Association World Conf., Taipei, Taiwan, 935-980, August 13-20, 1999.

[12]. R.J. Schilling, Fundamentals ofRobotics, Prentice-Hall, 1990

[13] M. Sugeno, "On Stability of Fuzzy Systems Expressed by Fuzzy Ruleswith Singleton Consequents," IEEE Trans. on Fuzzy Systems, vol.3, no.2,pp 201-222, April 1999.

REFERENCES

[1]. Fu, K.S., Gonzalez, R.C., and Lee, C.S.G., Robotics: Control, Sensing,Vision, and Intelligence. McGraw Hill, New York, 1987

[2]. Inoue, H., Force Feedback in Precise Assembly Tasks, MIT ArtificialIntelligence Laboratory Memo 308, MIT, Cambridge, Mass., 1974

[3]. Will. P. and Grossnlan. D, "An Experimental System for ComputerControlled Mechanical Assembly". IEEE Trans. EICYY Devices, Vol 29,42-48, 1975

[4]. Sciavicco. L. and Siciliano. B., Modelling and Control of RobotManipulators. McGraw-Hill Companies. Inc., 1996

[5]. Paul, R.C, Modellings, trajectory, Cancellation and Servoing ofcomputer Controlled Arm, A.I.Memo 177, Stanford Artificial IntelligenceLab., Stanford University. California. 1972

[6]. Dubowsky. S. and Desforges, D.T. "The application of ModelReferenced Adaptive control to Robotic Manipulators", Transactions ofASME, Journal ofDynamic System. Vol 101, 193-200, 1979

[7] Rong-Jong Wai, "Tracking control based on neural network strategy forrobot manipulator", Elsevier, Journal of Neuro computing. Vol.51, 425-445, 2003.

[8] H. R. Berenji and P. Khedkar, "Learning and Tuning Fuzzy LogicControllers through Reinforcements," IEEE Trans. Neural Networks, vol.3,no.5, pp.322-320, September 1992.

[9] J. R. Jang, "ANFIS: Adaptive-Network-Based Fuzzy Inference System,"IEEE Trans. Syst. Man Cybern., vol.23, no.3, pp.665-685, 1993.

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