Discussion on Fuzzy Logic Operation of Impedance Control for Upper Limb Rehabilitation Robot 1,a Zhai Yan

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1 Intenational Confeence on Automation, Mechanical Contol an Computational Engineeing (AMCCE 05) Discussion on Fuzzy Logic Opeation of Impeance Contol fo Uppe Limb Rehabilitation Robot,a Zhai Yan,b Guo Xiaobo Mechanical Engineeing College of Anyang Institute of Technology, Anyang, Henan , P.R. China Anyang Institute of Technology College of compute science an Engineeing, Anyang, Henan , P.R. China a,b Keywos: Rehabilitation obot; impeance contol; fuzzy logic; simulation. Abstact. Fo the influence cause by illness conition of suffee limb on system stability when obot maes ehabilitation taining on assiste suffee limb, on the basis of the taitional impeance contol metho, this pape puts fowa one in of impeance contol metho base on fuzzy neual netwo. This metho aopts mechanical impeance paamete of suffee limb which can coectly eflect illness chaacteistics of suffee limb as contolle input, the impeance contol paamete base on position is applie in obot fo uppe limb ehabilitation. It maes simulation by simulin an maes analysis on influence of taget impeance paamete on contol ability of system. The analysis an simulation esult inicate that metho afte impovement can effectively aapt to illness change of patient than the taitional impeance contol metho, an it has bette smoothness an stability. Intouction With the evelopment of obot technology, applying auxiliay teatment technology by obot into ehabilitation taining of patients has aleay been emphasize by eseaches both in China an aboa, an it has gaually become to be the impotant topic an hot point[,,3] in the eseach fiel of ehabilitation poject. Rehabilitation obot technology is one in of new moto neve teatment technology. In the pocess of maing ehabilitation movement by obot, one of the impotant aspects is that ehabilitation obot can timely peceive illness conition of patients an aopt coesponing contol measues, so that system can eep stable when illness conition of suffee limb changes. In ecent yeas, thee ae many eseaches have mae eseach on this poblem, of which those have univesal application ae as follows: foce contol stategy [4], contol metho base on foce fiel an biological signal etc [5]. As one in of effective foce contol metho by obot foce, impeance contol has been univesally applie in movement contol of ehabilitation obot [6,7]. With the evelopment of intelligent contol technology, taitional impeance contol metho combines with intelligent contol metho, which has mae up the shotages in taitional methos an enhance effect [8,9] of ehabilitation taining. Howeve, in the above mentione impeance contol stategy by obot, most of them ae mae esign on contolle accoing to foce signal peceive by senso, an in the esign pocess of intelligent contolle, stuy algoithms iectly aopts the taitional an optimal BP algoithm to mae optimization easily to fall into local. Fo the above poblems, this pape is base on obot on uppe limb ehabilitation an aopts myoelectic signal to ealize ehabilitation taining base on boy movement intention contol. In aition, on the basis of moeling of pneumatic muscle it espectively puts fowa contol algoithm of slie moel an ynamic suface contol algoithm base on non-linea istubance obseve to ealize contol of high pecision by pneumatic muscle. Consieing complication on moeling of pneumatic muscle an iffeence in people on obot ynamics moel fo uppe limb ehabilitation, fo the unnown conitions of moel, it puts fowa impeance contol metho base on fuzzy neual netwo. This metho aopts mechanical impeance paamete of suffee limb which can coectly eflect illness chaacteistics of suffee limb as contolle input. Though 05. The authos - Publishe by Atlantis Pess 434

2 theoetical analysis an test emonstation, this algoithm can enhance esponse spee, taget tace tacing an simultaneous pecision of ehabilitation taining obot on uppe extenal bone to ive joint. EMG intention ientification on suffee mechanical impeance paamete Impeance contol as eo input signal of foce contol to the input en of position contol, it ealizes contol by ajustment of position loop, impeance contol theoy is iffeent fom mixe contol stategy, it is one in of contol metho on iniect foce, impeance contol by contact envionment to eceive an input is the ynamic elations by ajusting teminal stiffness foce an position of obot, an it integates foce contol an position contol into one fame, an it uses the same contol stategy to ealize it, it has stonge obustness fo unefine intefeence factos, so it gets univesal application in ealizing foce an position contol of obot. The taget impeance moel aopte by this pape is inicate by the following fomula: M ( X ( t) + C ( X ( t) + K ( X ( t) = F F () t Of which, X (t), (t) espectively inicates position, spee an vecto of acceleate spee of X, X (t) X, (t) X obot en limb, X (t), (t) espectively inicates taget position, spee an vecto of acceleate spee of obot limb en, M inicates expecte inetia matix of obot limb, it will have geat impact when thee is movement of high spee o movement poucing impact foce, C inicates taget inetia matix of obot limb, it has geat impact on movement at mile spee o stonge intefeence foce K inicates the ieal stiffness matix of obot, it will have geat impact by neaby movement of low spee, Ft inicates the expecte contact foce of obot, F inicates foce vecto of obot limb by estaint envionment.. Because the collecte signals ae typical ispese oe, it uses ispese wavelet pacage to analyze an eal with EMG signal. Analysis algoithm of multi-esolution atio, which can get paamete of small wavelet pacage: of which, j is scale facto, is time-lapse facto an n is fequency facto. n j / n j ω j, n, =< f, W j, >=< f, W ( t > () If each (j, n) inicates one small wavelet pacage, then its noe enegy can be efine as follows: accoing to each couple of iffeent j an n, it can inicate etaile signal enegy of cetain fequency ange. e j, n = ω j, n, (3) Define this chaacteistic choice metho as PWMFS an non-paamete weight chaacteistic to extact chaacteistic eflection to ealize chaacteistic choice an imensionality euction. Suppose these ae L ins of ientifying objects, imension of oiginal chaacteistic space is n, it uses PWMFS chaacteistic to choose algoithm. Impeance contol stategy base on fuzzy neutal netwo Contol stuctue of impeance: With changes in illness conition of suffee limb, stiffness an amp of mechanical impeance paamete ae gaually changing. Accoing to the above analysis, this pape consie aopting mechanical impeance paamete of uppe limb of patients as contolle input, contol paamete of taget impeance is contolle input. Accoing to the online mechanical impeance paamete of patients, this pape uses fuzzy neutal netwo to iectly ajust taget impeance contol paamete. Impeance contolle base on fuzzy neutal netwo is to incease contolles of online stuy taget impeance contol paamete on the basis of taitional contolle, espectively efines it as stiffness contolle of fuzzy neutal netwo an amp contolle of evolution fuzzy netwo. Diagam gives self-aaptation impeance contol stuctue of uppe limb ehabilitation by obot base on evolution fuzzy neutal netwo. It uses stiffness contolle of evolution fuzzy neutal 435

3 netwo to mae analysis, its stuctue is inicate by iagam, an it is simila to analysis metho of amp contolle. This contolle aopts netwo stuctue of 5 layes, mechanical impeance paamete of suffee limb bˆe,ˆe espectively egae as contolle input, K is contolle put. The input an put fuzzy set iscouse omains ae efine as [-6, 6]. In this iscouse omain, espectively efines 7 fuzzy language vaiables, negative lage, negative meium, negative small, zeo, positive small, positive meium, positive lage. Diagam. : Impeance contol stuctue of evolution fuzzy neutal netwo of uppe limb ehabilitation obot The suboinate function of each language viable uses Kosi function ( x b) u( x = exp( ) (3) c Diagam. :Stiffness contolle stuctue of evolution fuzzy neutal netwo Stuy an contol algoithm of impeance contolle:esn is one in of ynamic ecusion neutal netwo; it is much moe suitable fo esciption of ynamic chaacteistic of complicate non-linea system. This pape combines ESN an PLS to ealize online self-aaptation ientification of ESN. ESN of combining RLS algoithm online stuy can be egae as RLSESN. ESN just only nees to ajust put weight value, if put unit of ESN is linea unit, this in of ESN stuctue maes stuy pocess of ESN aopt RLS algoithm simila to pocess of self-aaptation filtation to use RLS algoithm. If expecte put of EXN in step is y(,w( is the put weight value in step, v is unit state vecto connecte with put weight value in ESN. Then all the eos befoe step can be inicate as follows: e( i = y ( i) W ( i (4) ESN aopts RLS algoithm, which can mae netwo iteative to minimum taget function of the step. J = γ i= i e ( i (5) 436

4 Of which, Г is euction facto; its usual value is appoximately o less than. :Accoing to pinciple of minimum mean squae eo, RLS algoithm can be inicate as follows: P( ) λ( = (6) T v ( P( ) + γ ( ) = T P γ P( ) λ( v ( P( ) (7) y( = W ( ) (8) e( = y ( y( (9) W ( = W ( ) + λ( e( (0) Of which, λ is the gain matix of Kalman filte; v is vecto of intenal neutal cell state. Y is vecto of taget value, y ( is put vecto of ESN, e is the pio eo of each iteation. P is invese matix of elevant matix in intenal activate vecto. P is iagonal matix in initialization, an its value is elatively lage, it is inicate as follows: p (0) = δ I( δ > 0) ( ) Of which, δ is one smalle positive numbe, I is one unit matix. Consieing matix P will easily cause instability of RLS algoithm une long-time an non-ynamic signal. In oe to solve this poblem, this pape aopts self-elevant matix eset to avoi this poblem. If tace of matix P is locate in one elatively smalle positive numbe, then est as pimay state. The etaile algoithm pocess is inicate by iagam3. Diagam. 3: Algoithm pocess Online ajustment:in the online stuy stage, put offline taget impeance contol netwo afte optimization into system fo opeation, netwo can mae small ajustment online accoing to ynamic algoithm, so that it can futhe optimize taget impeance contol paamete, of which, taget function of FNN stiffness contolle an amp contolle ae espectively efine as follows: M ( X ( t) + C ( X ( t) + K ( X ( t) = ( F F ) () Though RLSESN, it can constuct ESN evese contolle to ealize fee fowa contol. As fo object of moel position, it can use contolle to ealize fee bac contol. The contol fame base on fee fowa an fee bac, it is constucte by ESN evese contolle base on RLSESN paallel contol. Of which, ESN evese contolle ealizes most contol put by fee fowa, meanwhile, it ealizes one in of contol compensation accoing to tacing eo. It can ealize system stability by choosing suitable contol paamete an fee bac contol. Fo the unnown object of moel, contolle base on RLSESN combines with meits of fee fowa an fee bac contol to ealize tacing an contol with high pecision on contol objects. Simulation of example emonstation t 437

5 In oe to emonstate effectiveness of algoithm put fowa by this pape, now it gives simulation test of ehabilitation obot. In the obot contol on uppe limb ehabilitation, the contact foce between obot an patients becomes inceasingly impotant; contol capacity on contol ability can iectly eflect system stability an safety pefomance. In the joint space impeance contol base on position, the mechanical limb of uppe limb ehabilitation an contact foce of patient ae measue by foce senso, it is eplace by sping flexibility in the simulation, its fomula is as follows: (3) Of which, Ke is envionment stiffness; X e is the pimay envionment position. The impeance contol algoithm Simulin moel fo uppe limb ehabilitation obot is inicate by iagam 4. Fom zeo to ten, thee is one estaint plane in space position of ϴ=5, suppose thee is no faction between mechanical limb an envionment, envionment stiffness K e=,the stess conition completely aopts sping to eplace it. When it equies obot to contact with envionment, thee contact stess shoul be ept at 0N Diagam.4: Simulin simulation moel base on impeance contol algoithm Keep amp B =0,stiffness K =0,envionment stiffness K e= has no change,inetia of ajustment taget is 0.5, an 5,simulation time is 0S,the pefomance cuve of esistance contol is inicate by iagam 5. Diagam. 5: Pefomance cuve of esistance contol Diagam.6 :Pefomance cuve of esistance contol When taget inetia changes, pefomance inex of each one is inicate by the following table. Table : Contol pefomance inex table of iffeent taget inetia M M pea( N m) Stable value( N m) Stable time( S ) Fom table we can see when inetia paamete inceases, pea of contact stess gaually inceases, but the change fluctuation is vey small, an it can stabilize above 0N in the en, this is because ehabilitation obot of uppe limb moves at low spee, the spee change is vey little an taget 438

6 inetia has effect on change of acceleate spee, so on inetia joint M has little effect on esistance contol of uppe limb obot. Keep inetia M =,stiffness K =0,envionment stiffness K e= has no change,inetia of ajustment taget is 0, 0 an 40, simulation time is 0S,when taget stiffness changes, the pefomance cuve of esistance contol is inicate by table. Table : Contol pefomance inex table of iffeent taget inetia K esistance K pea( N m) Stable value( N m) stable time( S ) Taget stiffness K eflects stiffness of mechanical limb, it iectly eflects whethe mechanical limb pesents stiffness o flexibility when contacts with envionment, when taget stiffness K gaually inceases, pea value of contact stess gaually becomes lage, but its stable time gaually becomes shot. Fom the simulation esult base on position impeance contol stategy we now: though ajustment on taget impeance paamete, foce contol of obot is iffeent, the setting of taget impeance paamete will iectly affects system contol pefomance an safety pefomance. Conclusion When ehabilitation obot contacts with patients, in oe to guaantee safety an comfot in the taining pocess, at the same time of maing tace tacing, we must consie the mutual foce between contol obot an patient, because suffee limb of patients is vey wea, if the mutual stess is too lage, it will possibly pull suffee limb of patient, this is not absolutely allowe. By using impeance contol, an position contol to get effect of iniect contol foce, although the position eo is lage, foce contol is much moe impotant as fo foce contol. Fom cetain meaning, impeance contol is to incease foce contol pefomance at the cost of position pecision. When ehabilitation obot maes taining with patients, it will choose easonable impeance paamete accoing to iffeent envionment, an it contols acting foce between ehabilitation obot an patients within the ange that one patient can bea, so that it guaantees the safety an stability in the whole ehabilitation taining pocess. (Fun numbe: Natual Science Fun Poject No. U0463 Henan joint fun: U0463) Refeences [] Zhang Xiufeng. Stuy on Rehabilitation Robot Technology of Auxiliay Uppe Limb Movement [J].Jounal of Tsinghua Univesity (natual science vesion), 006, 48(): [] Li Qingling. Analysis an Stuy on Development State of Uppe Limb Rehabilitation Robot [J].Mechanical Design, 008, 5(9): -3. [3] Dong Yan etc. Stuy on Uppe Limb Rehabilitation Robot of Extenal Bone an Its Contol Metho. Jounal of Habin Engineeing Univesity, 007, 8(9): [4] Fatouechi M, Bashashati A, Wa R K, et al. EMG an EOG Atifacts in Bain Compute Inteface Systems: A Suvey. Clinical Neuophysiology, 007, 8(3): [5] Usali A B, Guan S. Design of a Novel Efficient Human compute Inteface: An Electooculagam base Vitual Keyboa. IEEE Tansactions on Instumentation an Measuement, 00, 59(8): [6] Luo Zhizeng. Font Limb Multi-movement Moel Ientification Base on Suface Electomyogam Signal [J]. Appliance an Instument Jounal, 006, 7(9):

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