Design of Fuzzy Logic Controller for Inverted Pendulum-type Mobile Robot Using Smart In-Wheel Motor

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1 Indian Jounal of Science and Technology, Vol 8(S5), 87 96, Mach 5 ISSN (Pint) : ISSN (Online) : DOI:.7485/ijst/5/v8iS5/7 Design of Fuzzy Logic Contolle fo Inveted Pendulum-tye Mobile Robot Using Smat In-heel Moto Kwak Sangfeel, Song Eunji, Kim KyungSik and Song ByungSeo * Rovitek Co.,, Daegudae-o, Gyeongsan, Gyeongsangbuk-do Povince, Koea Deatment of Rehabilitation, Science & Technology, Daegu Univesity,, Daegudae-o, Gyeongsan, Gyeongsangbuk-do Povince, Koea; bssong@daegu.ac.k Abstact Some eseaches fo inveted endulum-tye mobile obots have been esented in many aticles. In this ae we esent the design of a Fuzzy Logic Contolle (FLC) fo an inveted endulum-tye mobile obot. Its mathematical model is fistly analyzed, and then we get its aametes though some maniulations. The FLC is good fo some nonlinea lants. e design a conventional FLC fo inveted endulum-tye mobile obot and show some simulation esults. Keywod: Fuzzy Logic Contolle (FLC), Inveted Pendulum, Mobile Robot. Intoduction Many eseaches have ecently studied inveted endulum-tye mobile obot including develoment of inveted endulum-tye mobile two-wheeled vehicle at home and aboad. The inveted endulum-tye twowheeled vehicleis a system that added mobility by using dynamic function to balance the inveted endulum. The balancing system is simila to the contolling mechanism fo a bied obot modeled afte a eson keeing balance with two feet while moving 3. The inveted endulum system has been fequently used as a contol model fo contolle veification in many studies that coveed the theoy on non-linea contolle 4. The study designed a fuzzy logic contolle fo non-linea dynamics model of the inveted endulum-tye mobile obot and veified its function though simulation.. Design & Analysis The inveted endulum-tye mobile obot consists of two wheels and a ole in between. The system measues tilting of this ole using tilting senso, acceleation and gyo senso and maintains the tilted angle at. This system is geneally called ZMP (Zeo Moment Point) contol system.. Dynamics Model fo the Inveted Pendulum-Tye Mobile Robot Designing the contolle fist needs motion equation of the inveted endulum-tye mobile obot and identification of system model. The following is hysical aametes of the inveted endulum-tye mobile obot. : obotdislacement (m) M : wheel weight (kg) J : wheel moment of inetia (kg m ) : wheel adius (m) l : ole length (m) M : weight fo the ole s cente of gavity (kg) J : moment of inetia fo the ole s cente of gavity (kg m ) g : gavity acceleation (m/s ) q : tilted angle of the ole (ad) φ : otation angle of wheel (ad) V : eaction foce of ole fo vetical diection *Autho fo coesondence

2 Design of Fuzzy Logic Contolle fo Inveted Pendulum-tye Mobile Robot Using Smat In-heel Moto H : eaction foce of ole fo hoizontal diection H : eaction foce of wheel fo hoizontal diection f : unknown inut fo wheel f : unknown inut fo ole t : wheel toque : ole dislacement foais y : ole dislacement foais y ) heel Dynamics Equation The inveted endulum-tye mobile obot can be divided into two ats: wheels and moto and body ole that suots the body and kees balance with the wheels. The model can be descibed with sum of the wheel dynamics equation fo the dive shaft, eaction foce of the ole s vetical and hoizontal ais and wheel moment of inetia. M = H + f + H () J f = H + t () Equation () and () showed the elation between wheel moment of inetia and eaction foce fom the ole. Robot dislacement and wheel otation angle φ had the following elation: f = (3-) Figue heel dynamics. ḟ. = (3-) Figue 3. Pole dynamics. hen Equation () and (3) wee combined, H could be descibed as the following equation fo t and : H t J = (4) The following was Equation () combined with Equation (4): M J + t H f = + + (5) Figue. Dynamics model of the inveted endulum-tye mobile obot. ) Pole Dynamics Equation The illustation below showed the foce given to the body that consisted of the moto and ole ecet fo the wheels. 88 Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology

3 Kwak Sangfeel, Song Eunji, Kim KyungSik and Song ByungSeo Dislacement of the ole s cente of gavity fo hoizontal diection was: = + lsinq (6) hen Equation (6) went though two sets of diffeential fo, it could be shown as:. = + lqcosq lq sinq (7) Equation (7) could be descibed as dynamics equation fo ais fo the ole s cente of gavity as: M = f H (8). H = ( M + M l( qcosq q sin q)) + f (9) y, which was ole dislacement fo ais y could be descibed as: y = lcosq () Two sets of diffeentials fo fo Equation () bought about:. y = l( q cosq+ qsin q) () ith Equation (), the dynamics equation fo ais y fo ole s cente of gavity could be: M y = V M g () V = M l( q cosq+ qsin q) + M g. Equation (9) and (5) could be esented as: M M J M lcosqq M lsinqq. (3) = f + f + t (4) whee acceleation was ẋ., angula acceleation was q and toque was t. Moment of inetia fo the ole s cente of gavity was: Jq = Vlsinq Hl cosq t (5) Combining Equation (9) and (3) showed: J + M l q M l cos q M gl sin q ( ) + = lcos qf t (6) hee angula acceleation was q, acceleation was ẋ. and toque was t.. State Equation of Linea Model hen it was assumed that tilted angle of the ole q was vey small, sinq q (7) cosq = (8) it could be aoimated like Equation (7) and (8) and aoimated to q =. M M J + + Ml f f + q = + + t (9) ( J + Ml ) q+ Ml Mglq = lf t () To establish state equation, Equation (9) and () could be changed to the equation about ẋ. and q as below: Al q = A l () hen it was ut as unknown inuts at Equation () Equation (3) was oduced like: f = f = () Al q = A l (3) It could be eessed as state equation based on Equation (3): T s = ( 3 4), =, =, = q, = q (4) 3 4 = A + B (5) s s = = = A = q = = A State Equation of Non-Linea Model (6) If the constant of Equation (4) and (6) could be ut as: = ( M M J + + ) (7) Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology 89

4 Design of Fuzzy Logic Contolle fo Inveted Pendulum-tye Mobile Robot Using Smat In-heel Moto P = J + Ml the following could come u: (8) Q= Ml (9) Qcosqq + Qsin qq = t (3) P q + Qcosq Qsin qg = t (3) hen Equation (3) and (3) wee eessed as those fo ẋ. and q, An q = A n (3) Equation (3) above was oduced. ith this, state equation was induced as: = = = An 3 = q = 4 = A (33) 4 n.4 Linea Contolle Design and Simulation fo Linea Model The hysical aametes of the inveted endulum-tye obot to be simulated fo the study wee as below4: M :.76 (kg) J : 3.4E-5 (kg m ) :.3 (m) l :.5 (m) M :.6 (kg) J :.34E- (kg m ) g : 9.8 (m/s ) The following showed coefficient of each mati fo Equation (5): A = (34) hen contollability fo the system was distinguished, it became ank baba ba 3 b = 4 and n is 4. Theefoe, the system had contollability. hen abitay ole was assumed as (36) to design a contolle, following could be gained: Figue 4. Contolle block diagam..5 P = 4 3 (36) K = T (37) Contolle block diagam fo Equation (37) could be illustated as below: The simulation esults of the linea contolle fo the linea system wee shown fom Figue 5 though Figue 9 whee dislacement of the inveted endulumtye mobile obot was, velocity was, ole s tilting angle was 3, ole s angula velocity was 4 and toque. If the initial value of 3 was ut, it was found the system stabilized with the contol inut toque fo the contolle..5 B = (35) Figue 5. Gah on dislacement. 9 Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology

5 Kwak Sangfeel, Song Eunji, Kim KyungSik and Song ByungSeo 3 d d Figue 6 Gah on taveling velocity. Figue 7. Gah onole s tilting angle Figue 8. Gah on ole s angula velocity 4. toque Figue. Fuzzy logic contolle. Hee, the study could achieve the following when q value was maintained and feedback contolle was stuctued so that osition could be contolled fo dislacement..5. Fuzzy Membeshi Function This contolle comised Distance FLC to contol moved osition and Balance FLC to balance the ole. Distance FLC inut was the eo between the cuent osition and set osition and the diffeence while its outut was angula weight of the ole eo to contol the obot s movement. In the mean, Balance FLC inut was the sum of the cuent ole angle q and angula weight of the ole eo, the outut of Distance FLC, and the outut was toque to contol the moto..5. Distance FLC s Membeshi Function and Infeence Rule The following showed the membeshi function fo the inut and outut of Distance FLC Figue 9. Gah on toque..5 Design of Fuzzy Logic Contolle fo Linea Model Imotant aametes that decide stability of the inveted endulum-tye mobile obot wee q and q. ith the linea contolle, contolling size can be checked as below: q = q q = 3 q 3 Toque :.5 Toque.5 Figue. Membeshi function fo inut aamete edist. edist : Distance Eo inut NBED : Negative Big Eo Distance NSED : Negative Small Eo Distance ZED : Zeo Eo Distance PSED : Positive Small Eo Distance PBED : Positive Big Eo Distance Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology 9

6 Design of Fuzzy Logic Contolle fo Inveted Pendulum-tye Mobile Robot Using Smat In-heel Moto.5.3 Balance FLC s Membeshi Function and Infeence Rule The following esented the membeshi function fo the inut and outut of Balance FLC. Figue. dedist. Membeshi function fo inut aamete dedist : Diff Distance Eo inut NBD : Negative Big Diff Eo Distance NSD : Negative Small Diff Eo Distance ZDD : Zeo Eo Diff Eo Distance PSD : Positive Small Diff Eo Distance PBD : Positive Big Diff Eo Distance Figue 3. Add Angle. Membeshi function fo outut aamete AddAngle : Add Angle NBA : Negative Big Angle NSA : Negative Small Angle ZA : Zeo Angle PSA : Positive Small Angle PBA : Positive Big Angle Figue 4. e. e : Eo Angle Theta NL : Negative Lage NM : Negative Medium NS : Negative Small Z : Zeo PS : Positive Small PM : Positive Medium Membeshi function fo inut aamete.5 Imlication: If edist is A and dedist is B then Add Angle is C Table. Rule table fo Distance FLC ed NBD NSD ZDD PSD PBD ed NBED PBA PBA PBA PSA ZA NSED PBA PBA PSA ZA NSA ZED PBA PSA ZA NSA NBA PSED PSA ZA NSA NBA NBA PBED ZA NSA NBA NBA NBA Figue 5. de. Membeshi function fo inut aamete de : Diff Eo Angle Theta NLD : Negative Lage Diff Eo NMD : Negative Medium Diff Eo NSD : Negative Small Diff Eo ZD : Zeo Diff Eo PSD : Positive Small Diff Eo PMD : Positive Medium Diff Eo PLD : Positive Lage Diff Eo 9 Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology

7 Kwak Sangfeel, Song Eunji, Kim KyungSik and Song ByungSeo Figue 6. toque. Membeshi function fo outut aamete Toque : Toque Outut NLO : Negative Lage Outut NMO : Negative Medium Outut NSO : Negative Small Outut ZO : Zeo Outut PSO : Positive Small Outut PMO : Positive Medium Outut PLO : Positive Lage Outut ZO Membeshi of toque outut was wide oen and it became naowe towads NLO and PLO. ith this fom, vibation of the outut was educed and nomal condition was ket stably Imlication : If e is A and de is B then Toque is C In comosing the two FLCs, AND comutation had minimum value, OR comutation had maimum value and infeence used Mamdani method. Defuzzification used cente of gavity method to obtain sensible esults..5.4 Simulation Result of FLC fo Linea Model The simulation esult could be eessed as the following figues with Add Angle, toque, dislacement, velocity, ole s tilting angle q, ole s angula velocity q. As the initial condition of the obot, the ole tilted adian ositive and the taget distance was set at m fo simulation. Fo the m given above, AddAngle of Distance FLC outut was authoized as Balance FLC inut. The above gah showed AddAngle outut. Figue 8 was Balance FLC outut, which was the moto toque inut fo the inveted endulum-tye mobile obot linea model. Toque was authoized fo initial movement and ket as fine value. hen it eached taget osition, it was found that the obot ole s angle was stabilized and toque was geneated to halt. Figue 9 showed dislacement. The obot stoed afte eaching the taget osition by taveling m. Figue 7. AddAngle toque Gah on AddAngle..5 AddAngle Table. e e Rule table fo Balance FLC NLD NMD NSD ZD PSD PMD PLD NL NLO NLO NLO NMO NMO NMO NSO Figue Gah on toque. NM NLO NLO NMO NMO NSO NSO PSO NS NLO NMO NSO NSO ZO PSO PSO Z NMO NSO NSO ZO PSO PSO PMO PS NSO NSO ZO PSO PSO PMO PLO PM NSO PSO PSO PMO PMO PLO PLO PL PSO PMO PMO PMO PLO PLO PLO Figue 9. Gah on dislacement. Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology 93

8 Design of Fuzzy Logic Contolle fo Inveted Pendulum-tye Mobile Robot Using Smat In-heel Moto Figue dislayed the obot s velocity of about.7m/s befoe it stoed. Figue esented the ole s tilting angle with the obot s movement. It was found the obot moved while maintaining balance of the ole. hen the weight gah of AddAngle was comaed, AddAngle and tilting angle eacted against each othe duing acceleation and deceleation of the obot. Figue Coveed the ole s angula velocity..5.5 Simulation Result fo Non-Linea Model Leaving the contolle comosition as it was, the study changed the state equation of the contol system fom linea to non-linea model to eecute simulation. Figue 3 showed changing Distance FLC outut AddAngle. The obot began to move using the initial ole tilting and eaction foce fom the moment it eached its taget osition caused AddAngle to sto it with contolling owe. Figue 4 showed moto toque to oeate the inveted endulum-tye mobile obot. Big toque was geneated fo initial obot acceleation and fine toque was maintained when it was in motion. hen it eached its taget osition, toque was geneated fo evese acceleation fom the moment oveshoot occued. Figue 5 showed the obot dislacement and Figue 6 showing its changing movement velocity. As Figue 6 and Figue 7 showed, the dislacement conveged towad the m taget osition. It was also found the obot ole balance also conveged towad ecet fo the change of eaction foce size occuing when the obot acceleated o deceleated. Figue. d Gah on taveling velocity..5.5 d.5.6 Smat In-heel Moto Smat In-heel Moto efes to the moto that contains moto, deceleato, moto dive, contolle, encode and cuent senso inside the wheel. This tye is aoiate fo the diving system like a obot as the stuctue is simle. The study alied Smat In-heel moto. toque Figue. Gah on ole s tilting angle. Figue 4. Gah on toque fo non-linea model Figue. AddAngle Gah on ole s angula velocity AddAngle Figue Gah on dislacement fo non-linea model. d 4 3 d Figue 3. Gah on AddAngle fo non-linea model. Figue 6. Gah on obot velocity fo non-linea model. 94 Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology

Kwak Sangfeel, Song Eunji, Kim KyungSik and Song ByungSeo.5.5 -.5 5 5 5 3 Figue 7. Gah on ole angle 3 fo non-linea model. Figue 3. Stuctue of smat In-heel moto. Figue 8.

Conclusion The study confimed the dynamics model of the non-linea inveted endulum-tye mobile obot, induced the linea contolle using linea model to stuctue non-linea contolle fo it and efomed

9 Kwak Sangfeel, Song Eunji, Kim KyungSik and Song ByungSeo Figue 7. Gah on ole angle 3 fo non-linea model. Figue 3. Stuctue of smat In-heel moto. Figue 8. Gah on ole angula velocity 4 fo nonlinea model. Figue Conclusion The study confimed the dynamics model of the non-linea inveted endulum-tye mobile obot, induced the linea contolle using linea model to stuctue non-linea contolle fo it and efomed simulation, allowing obtaining aoimate size fo the inut and outut. It also designed Distance FLC that contolled taveling distance based on the scoe of the acquied inut and outut as well as Balance FLC that maintained balance of the ole angle and contolled the linea and non-linea model esectively though simulation. It was found fom the study that comle non-linea system could be aoiately contolled with a elatively simle FLC design. Following this, it will educe the amount of calculation with modified design of a simle stuctued FLC though futhe study on its contol featue and constuct the system as the embedded system based on this. ith the embedded system, the imoved FLC contolle will be oeated to veify efomance. 4. Acknowledgement This wok (Gants No. C38638) was suoted by Business fo Academic-industial Cooeative establishments funded Koea Small and Medium Business Administation in 4. Figue 3. Smat In-heel Moto. 5. Refeences. Segway. Available fom: htt:// Pak JH. Fuzzy-logic zeo-moment-oint tajectoy geneation fo educed tunk motion of bied obots. Fuzzy Set Techniques fo Intelligent Robotic Systems. 3 Feb 6; 34():89 3. Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology 95

10 Design of Fuzzy Logic Contolle fo Inveted Pendulum-tye Mobile Robot Using Smat In-heel Moto 3. Yoon JH, Pak JH. Locomotion contol of bied obots with seially-linked aallel legs. Tansaction of the Koean Soc Mech Eng A. ; 34(6): Lee S-H, Rhee S-Y. Dynamic modeling of a wheeled inveted endulum fo inclined oad and changing its cente of gavity. Koean Institute of Intelligent Systems. ; (): Lee S-H, Pak J-K. Simulation fo imlementing attitude contolle of wheeled inveted endulum. Confeence on the Koean Society of Mechanical Enginees Gyungnam Region; Ha H-U, Lee J-M. A contol of mobile inveted endulum using single acceleomete. Institute of Contol Robotics and Systems. ; 6(5): Nawawi S, Ahmad MN, Osman JHS. Contoll of two-wheels inveted endlum mobile obot using full ode sliding mode contol. Poceedings of Intenational Confeence on Man-Mahcine System. Lankawi, Malaysia; 6 Se Aelsson P, Jung Y. Lego Segway Poject Reot. Technical eot fom Automatic Contol at Linkoings Univesitet. Devision of Automatic Contol;. 96 Vol 8 (S5) Mach 5 Indian Jounal of Science and Technology

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