APPLICATION OF NEURAL NETWORKS TO ACCELERATION CONTROL OF ELECTRIC WHEELCHAIR

Transcription

1 Potr BOJARCZAK Zbgnew GORYCA APPLICATION OF NEURAL NETWORKS TO ACCELERATION CONTROL OF ELECTRIC WHEELCHAIR ABTRACT In ths paper the acceleraton block of controllng software of electrc wheelchar has been presented. Ths acceleraton block was mplemented wth the use of MLP and neurofuzzy networks. For the sake of moderate throughput of mcrocontroller beng used to mplementaton of ths software, the network of smaller structure (neurofuzzy) has been chosen to realzaton. Keywords: electrc wheelchar, neural networks, acceleraton control. INTRODUCTION Contemporary electrc wheelchars are ftted wth brushless DC motors, ts controllng system and oystck beng used to determne the speed and drecton of the movement. Hgh power to mass rato and noseless operaton of brushless Potr BOJARCZAK, Ph.D. e-mal: Prof. Zbgnew GORYCA, Ph.D. e-mal: Radom Unversty of Technology, Malczewskego 29, Radom, POLAND phone. +(48-48) PROCEEDINGS OF ELECTROTECHNICAL INSTITUTE, Issue 229, 2006

2 88 P. Boarczak, Z. Goryca DC motors make desgners go over to them. Presented here drvng system of wheelchar conssts of two brushless DC motors mounted separately n each wheel and correspondng controllng crcuts. The controllng crcut n turn conssts of crcut drectly steerng motors beng called drver crcut and the mcrocontroller. The task of mcrocontroller s an assgnment of the deflecton of the oystck to the drecton and the speed of the vehcle movement. Fg. presents the workflow dagram of mcrocontroller. The mcrocontroller s program conssts of three maor parts. Fg.. Structure of controllng system of electrc wheelchar The frst part s responsble for convertng the deflecton of the oystck (n X and Y axes) nto ts bnary representaton. It s acheved wth the use of mcrocontroller s mult-channel AD converter. The converter s resoluton allows obtanng two numbers frst for X-axs and the second for Y n the range of 28 to 28. In the second part beng called velocty block, on the bass of prevously determned bnary representaton of X and Y deflecton, approprate speed and the drecton of the revoluton for each wheel are calculated. The acceleraton block havng already estmated speed and drecton of each wheel determnes acceleraton needng to smoothly change the vehcle speed and drecton. The last two parts deserve attenton. Let x and y be a bnary representatons of nstantaneous oystck s deflecton n X and Y axes respectvely, then the rght wheel velocty s equal to y x and the left wheel velocty s equal to y + x. Thanks to t, the oystck s deflecton to the rght corresponds to ncreasng the left wheel velocty and decreasng the

3 Applcaton of neural networks to acceleraton control of electrc wheelchar 89 rght wheel velocty turnng to the rght. In the case of the oystck s deflecton to the left, the left wheel velocty s decreasng and the rght wheel velocty s ncreasng, what corresponds to turnng to the left. In the thrd part of the program beng called an acceleraton block, on the bass of veloctes obtaned form velocty block and an actual nstantaneous veloctes the approprate value of acceleraton s calculated. The acceleraton cannot be a constant. The value of acceleraton should be dependent on the oystck s deflecton. In the case of vehcle movement n the straght drecton, the acceleraton should be low at the begnnng and ncreases successvely n the further stage of the movement. It prevents from abrupt erks durng startng process. On the other hand the acceleraton n turnng phase should be much hgher than n the straght drecton phase, otherwse the vehcle wll be unable to avod the collson wth obstacles. Each acceleraton block s assgned to every wheel. Therefore the value of acceleraton should be the functon of two varables actual speed and the turnng gauge beng the dfference between veloctes of rght and left wheels. On the bass of ther experence and [], authors decded to present the acceleraton n the form shown n Fg. 2. Fg. 2. Dependence of acceleraton on velocty and turnng gauge

4 90 P. Boarczak, Z. Goryca 2. IMPLEMENTATION OF ACCELERATION BLOCK IN THE FORM OF MLP NETWORK In order to present the acceleraton from Fg. 2 n the algebracally form the MLP (Mult- Layer Perceptron) network has been used. Accordng to [2], on the bass of provded learnng data, MLP s able to descrbe any relatonshp wth any accuracy. Fg. 3 shows the structure of MLP network. Fg. 3. Structure of MLP network It conssts of layers havng neurons. The network of Fg. 3 has three layers beng called nput, hdden and output layers respectvely. Only hdden and output layers have neurons. The task of nput layer elements s the dstrbuton of nput vector components to the hdden layer s neurons. Both nput layer elements and neurons of two last layers are connected through weghts. Let X = [x, x 2,..., x n ] be an nput vector gven to the network s nput and D = [d, d 2,..., d m ] be the destnaton vector gven to the network s output, then the learnng process conssts n weghts adaptaton whch leads to mnmzaton of square error defned n followng manner: p m k = = ( ) 2 ( k ) ( k ) y d E = () where p means the number of pars of vectors X and D.

5 Applcaton of neural networks to acceleraton control of electrc wheelchar 9 There exst several methods beng used to weghts adaptaton [ 2]. Authors resolved to choose backpropagaton wth momentum algorthm. After many experments the network havng 2 neurons n the nput layer, 20 neurons n the hdden layer and neuron n the output layer has been chosen. Neurons of the hdden layer have sgmod actvaton functon and neuron of the output layer has lnear actvaton functon. The structure of learnng data conssts of two vectors X and D. Vector X gven to the nput has two components, frst correspondng to the velocty value and the second correspondng to turnng gauge. Vector D gven to the output has only one component correspondng to desred value of acceleraton. The learnng data havng 250 pars of X and D vectors have been dvded randomly nto two groups, frst consstng of 75 pars and second consstng of 75 pars. The frst group was used to tranng the network and the second group to testng learned network. The network was constructed and learned wth the use of NeuroSoluton developng software. Fg. 4 shows the chart of acceleraton produced by learned neural network. If we compare Fg. and Fg. 4 we notce only slght dfference between them. The man drawback of the soluton beng based on MLP network s a sgnfcant number of neurons needng to descrbe the acceleraton relatonshp. Such large neural network structure makes ts mplementaton n AVR mcrocontroller qute dffcult. Fg. 4. Acceleraton relatonshp generated by learned MLP network

6 92 P. Boarczak, Z. Goryca 3. IMPLEMENTATION OF ACCELERATION BLOCK IN THE FORM OF NEUROFUZZY NETWORK As t can be notced the structure of MLP network s large. In the second approach to the mplementaton of acceleraton block, the neurofuzzy network has been used. The operaton of ths network s based on fuzzy set theory. In fuzzy sets, the degree of membershp of element x n approprate set A s determned on the bass of membershp functon μ A (x). The value of membershp functon s of range (0, ). If value of membershp functon μ A (x) s equal to 0, the element x s not a member of the set A. If value of membershp functon μ A (x) s equal to, the element x s a member of the set A. When the membershp functon μ A (x) has values between 0 and, element x s partally contaned n the set A. In fuzzy sets, x s called the lngustc varable. In our case there are two lngustc varables velocty x and turnng gauge x 2. Frst lngustc varable velocty x can take followng lngustc values: low and hgh and second lngustc varable turnng gauge x 2 can take: straght drecton and turnng. Therefore we have two fuzzy sets: low and hgh for the velocty varable and addtonal two fuzzy sets: straght drecton and turnng for the turnng gauge varable. Each of these fuzzy sets has the own membershp functon. The relatonshp between acceleraton and lngustc varables are descrbed wth the use of f-then rules. In the case of the neurofuzzy network beng used n acceleraton block ths relatonshp s based on Takag-Sugeno-Kanga (TSK) nference rules havng the exemplary form: If velocty x s low and turnng gauge x 2 s straght drecton then acceleraton y = p0 + px + p2 x2 where: p 0, p, p 2, are coeffcents whose values are adapted durng the learnng process. In the case of M nference rules the acceleraton formula takes the form: where: y = y M y = M = = w = w M p0 + p x + p2 x2 w' y (2) = (3) s the acceleraton relatonshp for the -th nference rule. As we can see the overall acceleraton relatonshp s equal to a weghted sum of all rules. The

7 Applcaton of neural networks to acceleraton control of electrc wheelchar 93 meanng of w are gven n (5). Accordng to [3, 4], the structure of the neurofuzzy network can be presented n the form of Fg.5. It conssts of fve layers. Fg. 5. Structure of the pneurofuzzy network Frst layer contans the set of membershp functon of gaussan form: b A c x x 2 ) ( + = σ μ (4) where: b c σ,, are parameters whose values are adapted durng the learnng process. Second layer calculates the weght w accordng to (5) correspondng to the approprate nference rule: = + = N b c x w 2 σ (5) where N s equal to the number of lngustc varables, n our case N = 2.

8 94 P. Boarczak, Z. Goryca For every nference rule thrd layer calculates the y accordng to (3). Parameters p 0, p, p2 are adapted durng the learnng process. Fourth layer contans two neurons. Frst calculates the weghted sum of y M and the second the sum of weghts w k. k = The task of ffth layer (the last) s a smple dvson the value of f generated by the frst neuron of fourth layer by the value of f2 generated by the second neuron of the fourth layer. The structure and the number of learnng data are the same as n the MLP network. After many experments, neurons of second layer have been chosen. NeuroSoluton developng software has been used to construct and learn the network. The chart of acceleraton beng generated by neurofuzzy network s dentcal wth ths generated by MLP network (Fg. 4). Despte to ts smaller structure, t s able to generate the acceleraton relatonshp of the same accuracy as n MLP network. 4. CONCLUSIONS The complexty of the acceleraton block s a crucal topc when the controllng software s mplemented on typcal mcrocontroller havng moderate throughput such as Atmel AVR. As t has been shown the complexty of structure of neurofuzzy network s much less than MLP network. The whole controllng software ncludng acceleraton block basng on neurofuzzy network has been wrtten wth the use of GNU C compler for Atmel AVR mcrocontroller. The software was successfully tested n actual wheelchar prototype whose mage s shown n Fg. 6. Fg. 6. The wheelchar prototype

9 Applcaton of neural networks to acceleraton control of electrc wheelchar 95 LITERATURE. Fręchowcz A.: Use of fuzzy logc n control speed crcut of a powered wheelchar, Conference of Electrc Tracton, Zakopane, October, 2002 (n polsh) 2. Haykn S.: Neural networks, a comprehensve foundaton, Prentce Hall, New Jersey, Nguyen H.T, Prasad N.R, Walker C.L, Walker E.A : A frst course n fuzzy and neural control, CRC Press, Florda, Ross T. J.: Fuzzy logc wth engneerng applcatons, McGraw-Hll, USA, 995 Manuscrpt submtted Revewed by Jerzy Zadrożny ZASTOSOWANIE SIECI NEURONOWYCH DO STEROWANIA PRZYSPIESZENIA ELEKTRYCZNYCH WÓZKÓW DLA INWALIDÓW P. BOJARCZAK, Z. GORYCA STRESZCZENIE Artykuł omawa oprogramowane bloku sterowana przyspeszena wózka nwaldzkego. Blok ten wdrożono przy użycu MLP sec neuronowe rozmyte. Dla moderac przepustowośc użytego mkrosterownka do wdrożena tego oprogramowana wybrano do realzac seć o mnesze konstrukc (neurorozmytą).