Research Article. Adaptive Neuro-Fuzzy Inference System based control of six DOF robot manipulator. Srinivasan Alavandar * and M. J.

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1 Jestr Journal of Engneerng Scence and Technology Revew (8) 6- Research Artcle Adaptve Neuro-Fuzzy Inference System based control of sx DOF robot manpulator Srnvasan Alavandar * and M. J. Ngam JOURNAL OF Engneerng Scence and Technology Revew Department of Electroncs & Computer Engneerng, Indan Insttute of Technology Roorkee, Inda-7667 Receved 3 October 8; Accepted 7 December 8 Abstract The dynamcs of robot manpulators are hghly nonlnear wth strong couplngs exstng between onts and are frequently subected to structured and unstructured uncertantes. Fuzzy Logc Controller can very well descrbe the desred system behavor wth smple f-then relatons owng the desgner to derve f-then rules manually by tral and error. On the other hand, Neural Networks perform functon approxmaton of a system but cannot nterpret the soluton obtaned nether check f ts soluton s plausble. The two approaches are complementary. Combnng them, Neural Networks wll allow learnng capablty whle Fuzzy-Logc wll brng knowledge representaton (Neuro-Fuzzy). Ths paper presents the control of sx degrees of freedom robot arm (PUMA Robot) usng Adaptve Neuro Fuzzy Inference System (ANFIS) based PD plus I controller. Numercal smulaton usng the dynamc model of sx DOF robot arm shows the effectveness of the approach n traectory trackng problems. Comparatve evaluaton wth respect to PID, Fuzzy PD+I controls are presented to valdate the controller desgn. The results presented emphasze that a satsfactory trackng precson could be acheved usng ANFIS controller than PID and Fuzzy PD+I controllers Keywords: ANFIS, Fuzzy PD+I, PUMA robot, Degree of Freedom (DOF), manpulator control... Introducton Industral robot manpulators are manly postonng and handlng devces. The essental problem n controllng robots s to make the manpulator follow a desred traectory. In general an N-degree of freedom (DOF) rgd robot manpulator s characterzed by N nonlnear, dynamc, coupled dfferental equatons [ 3]. The problem of controllng robot manpulators stll offers many practcal and theoretcal challenges due to the complextes of the robot dynamcs and the requrement to acheve hgh precson traectory trackng n the cases of hgh-velocty movement and hghly varyng loads. Conventonal robot control methods depend heavly upon accurate mathematcal modelng, analyss, and synthess. These approaches are sutable for the control of robots that operate n structured envronments. However, operatons n unstructured envronments requre robots to perform much more complex tasks wthout an adequate analytcal model. The most challengng problem n ths feld s that there are always * E-mal address: seenu.phd@gmal.com ISSN: Kavala Insttute of Technology. All rghts reserved. uncertantes n the unstructured envronments. These uncertantes are prmarly due to sensor mprecson and unpredctablty of the envronment characterstcs and ts dynamcs. [] [5] [6]. On the other hand, the advent of fuzzy set technques provdes us wth a powerful tool for solvng demandng realworld problems wth uncertan and unpredctable envronments. Fuzzy controller can characterze better behavor comparng wth classcal lnear PID controller because of ts non lnear characterstcs [7] [9]. Recently, fuzzy-logc and conventonal-technques have been combned (hybrd) to desgn FL controllers whch pave to approprate soluton for controllng the robot manpulators [-].The research on the fuzzy controller has been focused on the twonput fuzzy system [l3].the general structure of the two-nput fuzzy controller that uses error and change n error as the nput varables []. Wth PD type controller, elmnaton of steady state error s not possble. And PI type has lmtaton n enhancng the transent response. However, three-nput and one-output fuzzy system s too complex to construct the PID controller. It s very dffcult to decde the fuzzy control rules ntutvely. The fuzzy PID controllers that use multple two-nput fuzzy 6

2 Srnvasan Alavandar and M. J. Ngam / Journal of Engneerng Scence and Technology Revew (8) 6- controller or partally fuzzy modfed lnear PID controllers are emergng to overcome these problems. The fuzzy PID controllers that use multple two-nput fuzzy controller or partally fuzzy modfed lnear PID controllers are emergng to overcome these problems [5-6]. Fuzzy PD+I Controller [6] suffers the dffculty of tunng a partcular nference system to model a complex dynamcal system based on the tranng data. It works well wth mprecse dynamcs or even wth no knowledge about the model the system dynamcs, but they do not have a learnng capablty of ther own. Hence, n that work a learnng mechansm s created f neural networks, whch have good learnng attrbutes, are hybrdzed wth fuzzy systems. Neuro-Fuzzy technques [7] have emerged from the fuson of Neural Networks (ANN) and Fuzzy Inference Systems (FIS) and form a popular framework for solvng real world problems. Jang et al., [8], propose an Adaptve Neuro Fuzzy Inference System, n whch a polynomal s used as the defuzzfer. Ths structure s commonly referred to as ANFS. ANFIS dstngushes tself from normal fuzzy logc systems by the adaptve parameters,.e., both the premse and consequent parameters are adustable. Recent studes [-3] have shown that the use of a controller that utlzes neural networks and fuzzy logc can be attractve. Takag and Sugeno change the defuzzfcaton procedure where dynamc systems are ntroduced as defuzzfcaton subsystems. The potental advantage of the method s that under certan constrants, the stablty of the system can be studed. In ths paper, an Adaptve Neuro Fuzzy Inference System (ANFIS) based PD plus conventonal I controller s appled to the dynamc model of sx DOF robot arm presented. Two nputs had been used, error (e), change of error ( e& ) that wll be fed to ANFIS controller whle ntegral error ( Δ e ) wll be used as conventonal ntegral acton. Ths s due to dffculty of desgnng the rules for the ntegral acton. The proposed controller s manly focused on enhancement of the transent response. The proportonal sgnal and the dervatve sgnal are domnant to decde the transent response. But the ntegral sgnal whose maor roll s to elmnate the steady state error has fxed gan. The ANFIS structure wth frst order Sugeno model, Gaussan membershp functons wth product nference rule are used at the fuzzfcaton level. Hybrd learnng algorthm that combnes least square method wth gradent descent method s used to adust the parameter of membershp functon. To valdate the performance, a comparson wth the fuzzy PD+I and the lnear PID s performed under same tunng. Organzaton of the paper s as follows. Secton ntroduces the sx degrees of freedom robot arm Puma 56 and ts dynamc model. Secton 3 descrbes the scheme of the hybrd Adaptve Neuro Fuzzy Inference System (ANFIS) based PD plus conventonal I controller. Secton provdes numercal smulaton results to demonstrate the effectveness of ths hybrd controller and comparatve evaluaton of the ANFIS control method wth that of fuzzy PD+I and the conventonal PID s performed. And Secton 5 dscusses the benefts of the studed adaptve neuro fuzzy control law and conclusons are presented.. Dynamcs of Sx DOF Puma robot The dynamcs of a seral n-lnk rgd robot can be wrtten as, M ( q ) q & + c ( q, q & ) + g ( q ) = τ & () where q s the n x vector of ont dsplacements, q s the n x vector of ont veloctes, τ s the n x vector of actuators appled torques, s the n x n symmetrc M (q) postve defnte manpulator nerta matrx, & c ( q, q&) g (q ) s the n x l vector of centrpetal and Corols torques and s the n x vector of gravtatonal torques obtaned as the gradent of the potental energy U(q) due to gravty. We assume the robot onts are oned together wth revolute onts. Let the desred ont poston q d be a twce dfferentable vector functon. We defne a control problem to determne the actuator torques n such a way that the followng control am be acheved. lm q ( t ) = q t d Fg. PUMA robot ( t ) A sx-degrees-of-freedom PUMA-56 robot s consdered for the smulaton, the knematcal and dynamcal parameters of the arm are adopted from the work of Armstrong [9]. The electrcal parameters of the motors are assumed by comparng the sze and power of the PUMA motors wth well-documented commercally-avalable DC motors, and then nterpolatng the correspondng parameters of nterest are taken from our prevous work [6]. Fgure shows the structure of PUMA robot. The overall block dagram of the system under control s shown n Fgure. () Fg.. The overall block dagram of the system 7

3 Srnvasan Alavandar and M. J. Ngam / Journal of Engneerng Scence and Technology Revew (8) 6-3. Adaptve Neuro Fuzzy Inference System (ANFIS based controller desgn Ths secton ntroduces the bascs of ANFIS network archtecture and ts hybrd learnng rule. Inspred by the dea of basng the fuzzy logc nference procedure on a feedforward network structure, Jang [8] proposed a fuzzy neural network model - the Adaptve Neural Fuzzy Inference System or semantcally equvalently, Adaptve Network-based Fuzzy Inference System (ANFIS), whose archtecture s shown n Fgure 3. He reported that the ANFIS archtecture can be employed to model nonlnear functons, dentfy nonlnear components on-lne n a control system, and predct a chaotc tme seres. It s a hybrd neuro-fuzzy technque that brngs learnng capabltes of neural networks to fuzzy nference systems. The learnng algorthm tunes the membershp functons of a Sugeno-type Fuzzy Inference System usng the tranng nputoutput data. The ANFIS s, from the topology pont of vew, an mplementaton of a representatve fuzzy nference system usng a BP neural network-lke structure. It conssts of fve layers. The role of each layer s brefly presented as follows: l let O denote the output of node n layer l, and x s the th nput of the ANFIS, =,,...,p. In layer, there s a node functon M assocated wth every node: O = M ( x ) (3) Gaussan shape functons are the typcal choces. The adustable parameters that determne the postons and shapes of these node functons are referred to as the premse parameters. The output of every node n layer s the product of all the ncomng sgnals: O = M ( x ) ANDM ( x Each node output represents the frng strength of the reasonng rule. In layer 3, each of these frng strengths of the rules s compared wth the sum of all the frng strengths. Therefore, the normalzed frng strengths are computed n ths layer as: 3 O O = O Layer mplements the Sugeno-type nference system,.e., a lnear combnaton of the nput varables of ANFIS, x,x,...x p plus a constant term, c,c,...,c p, form the output of each IF THEN rule. The output of the node s a weghted sum of these ntermedate outputs: ) () (5) O = O 3 p = P x + c (6) where parameters P,P,...,P p and c,c,...,c p, n ths layer are referred to as the consequent parameters. The node n layer 5 produces the sum of ts nputs,.e., defuzzfcaton process of fuzzy system (usng weghted average method) s obtaned: 5 O O (7) = Fg. 3. Structure of ANFIS The role of the node functons M, M...Mq here s equal to that of the membershp functons μ(x) used n the regular fuzzy systems, and q s the number of nodes for each nput. The flowchart of ANFIS procedure s shown n Fgure. ANFIS dstngushes tself from normal fuzzy logc systems by the adaptve parameters,.e., both the premse and consequent parameters are adustable. The most remarkable feature of the ANFIS s ts hybrd learnng algorthm. The adaptaton process of the parameters of the ANFIS s dvded nto two steps. For the frst step of the consequent parameters tranng, the Least Squares method (LS) s used, because the output of the ANFIS s a lnear combnaton of the consequent parameters. The premse parameters are fxed at ths step. After the consequent parameters have been adusted, the approxmaton error s back-propagated through every layer to update the premse parameters as the second step. Ths part of the adaptaton procedure s based on the gradent descent prncple, whch s the same as n the tranng of the BP neural network. The consequence parameters dentfed by the LS method are optmal n the sense of least squares under the condton that the premse parameters are fxed. 8

4 Srnvasan Alavandar and M. J. Ngam / Journal of Engneerng Scence and Technology Revew (8) 6- factors, because these are the global tunng parameters that affect the overall control performance. In adustng these, consderaton s gven to rse tme (t r ), overshoot (M P ) and the steady state error (e ss). When the response s far away from the desred value, the nput scalng factors (SF) are adusted to reduce the rse tme, and s later readusted to prevent overshoot as the response approaches the desred value. The output scalng factors s tuned to lmt the FLC output to a reasonable value and to reduce the steady state error basc manual tunng procedure that can be used for the nput and output scalng factors s gven n Table. Table. Tunng of Scalng factors of Fuzzy PD controller Increase n SF Effect on t r Effect on M P Effect on e ss K P Decrease Increase Decrease K D Increase Decrease Small change K U Decrease Increase Decrease Fg.. ANFIS procedure In the proposed structure, the adaptve neuro fuzzy system s normalzed wth respect to the maxmum range of the sgnal. Usng ths characterstc, the smulaton and comparson between the ANFIS based PD plus conventonal I controller, Fuzzy PD conventonal I controller and the lnear PID s done. Therefore, ths hybrd learnng algorthm s more effectve than the pure gradent decent approach, because t reduces the search space dmensons of the orgnal back propagaton method. The pure BP learnng process could easly be trapped nto local mnma. When compared wth employng ether one of the above two methods ndvdually, the ANFIS converges wth a smaller number of teraton steps wth ths hybrd learnng algorthm. Ths paper consders the ANFIS structure wth frst order Sugeno model contanng 36 rules. Gaussan membershp functons wth product nference rule are used at the fuzzfcaton level. Hybrd learnng algorthm that combnes least square method wth gradent descent method s used to adust the parameter of membershp functon. In ths structure, the Adaptve neuro fuzzy system s appled only to the proportonal and dervatve sgnal of the lnear PID controller. The ntegral sgnal uses conventonal lnear method. The maor roll of the ntegral sgnal s to elmnate the steady state error. The transent response s affected mostly by the proportonal sgnal and the dervatve sgnal. For the enhancement of the transent response, the varyng gans are mplemented on the proportonal and dervatve parts usng two-nput fuzzy system. The nonlneartes emphasze the proportonal gan when the trackng error s relatvely large and accelerates decreasng speed of the trackng error. The nonlneartes n the dervatve gan suppress overshoot and ncrease dampng from the begnnng of the settlng. The control wll take place n the ont space. Each ont has ts own PID controller. The control acton of the fuzzy controller was scaled to a torque control acton appled to the PUMA dynamc model. The frst prorty s to tune the scalng 3. Conventonal ntegral control The conventonal ntegral control has the smple purpose of elmnatng the steady state error and mantanng some control constant output when the system that s been controlled requres t.. Smulaton and Results In ths secton, the smulaton was run under MATLAB 7. wth Fuzzy Logc Toolbox. (RSP). To demonstrate the effectveness of the proposed Adaptve Neuro Fuzzy based PD plus conventonal I controller, the dynamc model of sxdegrees-of-freedom PUMA-56 robot s consdered. Knematcal and dynamcal parameters of the arm are adopted from the work of Armstrong [9] and the electrcal parameters are taken from [6]. Numercal smulatons of conventonal PID controller, Fuzzy PID and Fuzzy PD+I s performed under same manual tunng procedure as shown n Table for a sx degree of freedom robot arm. The same values of PID control gans are used for conventonal PID controller, FPD+I controller and Adaptve Neuro Fuzzy based PD plus conventonal I controller to examne the performance. The trackng response of varous controllers and error profle are shown n the Fgure 7 to. 9

5 Srnvasan Alavandar and M. J. Ngam / Journal of Engneerng Scence and Technology Revew (8) 6-8 Response of PID controller for varous onts Error Profle of Fuzzy PD+I Controller for varous Jonts 6... desred ont postons actual ont postons.8.6. Jont Postons q (rads) - Jont Poston Error Tme(secs) Tme (secs) Fg.. Error profle of Fuzzy PD+I controller for varous onts Fg. 7. Response of PID controller for varous onts Error profle of PID controller for varous onts 8 Response of ANFIS based PD + I controller for varous onts actual ont postons desred ont postons.6. Jont Poston Error. -. Jont Postons q (rads) Tme (secs) Tme(secs) Fg. 8. Error profle of PID controller for varous onts Fg.. Response of ANFIS based PD+I controller for varous onts Error profle of ANFIS based PD+I controller for varous onts Response of FPD+I controller for varous onts desred ont postons actual ont postons.6.5. Jont Postons q (rads) - Jont Poston Error Tme (secs) Tme (secs) Fg. 9. Response of Fuzzy PD+I controller for varous onts Fg.. Error profle of ANFIS based PD+I controller for varous onts

6 Srnvasan Alavandar and M. J. Ngam / Journal of Engneerng Scence and Technology Revew (8) 6-5. Conclusons Due to the strong nonlnear characterstcs and parameter varatons n real envronments, trackng control of a robot arm system s dffcult. Proposed ANFIS based PD+I controller s manly focused on enhancement of the transent response. Complexty of the three nput fuzzy PID controller s mnmzed as possble and only two desgn varables are used to adust the rate of varatons of the proportonal gan and dervatve gan. Also the ANFIS converges wth a smaller number of teraton steps wth the hybrd learnng algorthm. The ANFIS based PD+I controller developed n ths paper provdes a practcal approach for such tasks. It s seen that the performance of ANFIS based PD+I controller mproves apprecably compared to ther respectve fuzzy PD+I only or conventonal PID counterparts. The results presented emphasze that a satsfactory trackng precson could be acheved usng ANFIS based PD+I controller combnaton than fuzzy PD+I only or conventonal PID only. Automatc tunng of the fuzzy system usng neuro-fuzzy or genetc algorthm can be further studed. References. Spong M, Vdyasagar M, (989) Robot dynamcs and control. Wley, New York.. Crag JJ (993) Adaptve control of manpulators through repeated trals. In: Spong MW, Lews FL, Abdallah CT (eds) Robot control: dynamcs, moton plannng, and analyss. IEEE, IEEE Control Systems Socety, pp Crag JJ, Hsu P, Sastry SS (987) Adaptve control of mechancal manpulators. Int Journal of Robotc Research 6():6 8. J. J. Crag, Introducton to Robotcs: Mechancs and control, nd edton, Readng, A: Addson-Wesley, Lews, F. L., Abdallah, C. T. and Dawson, D. M.: Control of Robot Manpulators. USA: Macmllan Publshng Company, a dvson of Macmllan, Inc., O. Castllo, P. Meln, Intellgent adaptve model-based control of robotc dynamc systems wth a new hybrd neuro-fuzzy-fractal approach, n: Proceedngs of FLINS, World Scentfc, Bruges, Belgum,, pp H. R. Beren, Fuzzy logc controllers, n An Introducton to Fuzzy Logc Applcaton n Intellgent Systems, R. R. Yager and L. A. Zadeh, Eds. Boston, MA: Kluwer, H.-J. Zmmermann, Fuzzy Sets Theory and Its Applcatons. Norwell, MA: Kluwer-Nhoff, E. H. Mamdan, Applcaton of fuzzy algorthm for control of smple dynamc plant, Proc. Inst. Elect. Eng., vol., pp , 97.. We L, Desgn of a Hybrd Fuzzy Logc Proportonal Plus Conventonal Integral-Dervatve Controller, IEEE trans. on Fuzzy Systems, Vol. 6, No.. 998, pp L, W. et al, Trackng Control of a Manpulator under Uncertanty by FUZZY P + ID Controller, Fuzzy Sets and Systems, vol.,, pp W. L, X. G. Chang, J. Farrell, and F. M. Wahl, Desgn of an enhanced hybrd fuzzy p+d controller for a mechancal manpulator, IEEE Transactons on Systems, Man, and Cybernetcs Part B: Cybernetcs, vol. 3, December. 3. G. K. I. Mann, B. G. Hu and R. G. Gosne, "Analyss of drect acton fuzzy PID controller structures", IEEE Trans. Syst., Man, Cybern., vol. 9, no. 3, pp , H. Yng, "Theory and applcaton of a novel fuzzy PID controller usng a smplfed Takag-Sugeno rule scheme", Informaton Scences, vol 3, pp. 8-93,. 5. Msr, D., Malk, H. A. and Chen, G Desgn and Analyss of a Fuzzy Proportonal-ntegral- Dervatve Controller, Fuzzy Sets and Systems, 79, Srnvasan Alavandar, M.J. Ngam Fuzzy PD+I Control of a Sx DOF Robot Manpulator, Industral Robot: An Internatonal Journal, vol. 35, ssue, pp. 5-3, Jang, J. S. R., C. T. Sun, E. Mzutan, Neuro-Fuzzy and Soft Computng, PTR Prentce Hall, J. S. R. Jang, ANFIS: Adaptve-Network-based Fuzzy Inference Systems, IEEE Transactons on Systems, Man, and Cybernetcs, Vol. 3, No. 3, pp , Bran Armstrong, Oussama Khatb, Joel Burdck, The Explct Dynamc Model and Inertal Parameters of the PUMA 56 Arm, Stanford Artfcal Intellgence Laboratory Stanford Unversty, IEEE Transactons and Systems Tberu Vesseleny, Smona Dztac, Ioan Dztac, Msu-Jan Manolescu, Fuzzy and Neural Controllers for a Pneumatc Actuator, Internatonal Journal of Computers, Communcatons and Control, Vol., No., pp , 7.. Y. L. Sun and M. J. Er, Hybrd fuzzy control of robotcs systems, IEEE Transactons on Fuzzy Systems, vol., no. 6, pp ,.. Hong-Ru Wang L Yang L-Xn We Fuzzy-neuro poston/force control for robotc manpulators wth uncertantes Soft Computng (7) : Durasamy, N. Devaraan, D. Somasundareswar, A. Antony Mara Vasanth, S.N. Svanandam, Neuro fuzzy schemes for fault detecton n power transformer, Appled Soft Computng 7 (7) Peter I.corke, The Unmaton Puma Servo System, CSIRO Dvson of Manufacturng Technology, AUSTRALIA July Peter I. Corke, A Search for Consensus among Model Parameters Reported for the PUMA 56 Robot, CSIRO Dvson of Manufacturng Technology, Australa. Bran Armstrong-Helouvry Unversty of Wsconsn Mlwaukee, USA. July 99.