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ãRQ l q® n ejS UT­â æ à Ï

weight vector

pattern vector

WV

6 YX

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a. b.

çWV 6

V

ç 6

îï ýÖðûòñ<óZ\dZ]1eñöùhñ û'÷<ïRüTïbü_ý ùñNþLïRü üZñ û­ïRüq(÷]øTñöùmï ùmï úñq ñ û'üïRü_ý üZñöùÿþTûsr,tuk1û4ñjñküTû'÷3i¤ï õ^ñ ú ñöù<û õvtkMZñfùfûòñjñfúñöùTû õw_úïbü_ýIùfZñfõx ÷ñq ïRû4ñöùaï üZõ_õfïbü?tygv ð_ùþLï ùfw ï oñ û4ñ ü_ùn ñ üZýùZõz ütygú ñöù<û õç ü WV û4ñ üZñ ûòñöõùGù<ñ,q ùfZñ û'g|ü ùfZñïbûl i ùøûmi "ðöù ç WV ~ ç ~R~ V ~ §c ï õD û ýTñ ûù, ü<ùfZñ i ùLø û-t ðöù ç ü 6 Mz üwvtygzþ%ñú ñ û'g"ùfZñfø,ZùXùhñ û'ü ü fþñï ýG_ù ú ñöù<û õh û4ñfü ùüTû'÷3i¤ï õ^ñ g ü IïbüùfTï õM_õ^ñ 6 õð vTñü_õöï ñ û4ñ ùñw þïRüüñ û'þ"Zñ ü ç ï õ1ø ø ï ñ "jþñúñ ûsg>ùfZñ( ù.ø û-t ðöù ç WVï õ õùaï û ýTñ ûùf ü ç 6 ÕÿlÔZI y2ÖÕÓ>(.y:Õlt"«BÕ?Ö"y Mw?M"7x2ex2MMwVzMvxE-Y2Mv|__MçÄx2|zewV~vge2wV§32(b ew?MwU|2(yx2MwVz^UM|~OMv_wMv_wdx2§MExEM|Ò|P§M|b~2wV|y|bwNxEM| !Ã*¤B~2wV8xb·1P2~§?x2Px2MPwê M_M|^*#|b´~_MwÃBAbbMv_*A|rv_ Mv_wx2~22(Mv -Pz¨:x2e||_2Nyx23wVz¨2wV§32(-w?(w3&wMwVz^2UxEM_(x2|_w-Pz2w3x2§?§yzxE3w¦Mv_wx2~22NMv Ò2||_2(x23wVz¨|_P_OzxEMxÇu>©MvtwV|z^BMv_wc|||_~t|_wV_M|E73wVwV§3wVz¦cMvM-ewV~vd2wV§32 # Óx+òÔ=Êf&83Mv_wO|P_"xE33w?(|ç-M|_~tMv_w

ÃE lmâ n äã s bT åMqvæ â s æ Uprq s--§?z_wVx2|¦z3Mx2|§wOwVx2MMw

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# IH @ *¤ # IHM¤ @ ´\ íç7 IHM¤ = # IHM¤3¤=Å !ÃFäßA~x2|º|Mv_wOewV~vM2BMv_wOc||_w?dxEMw¢_^zxE3wVzIßÎ&|28xE33wV|M||¥MvwV3wt(wV§?_(M2wt§?33w?(|_~y3wV§(vP|N_wVAMv_wb|Mx2MxEM|^-"MYwV§?x2eMv_w|_P_52wV§32(xEMwz_(x*c|¨ÒMæx©xEM~2wy2v~v $ zwV|(|x2B|_P_OMPx2§w2¢O|2¢&w?2|zxE~|xEM|rMvxExNx2|z_y¨|Mx23wVzÄewV~vg2wV§32n ì A"|w?2w?Yw§(v_MwV| x2Mv_wA||_w?x2|z¦AYMvPc|_w?2w?&wO 2wVz©x2|Pz¥|_w?2w?c&wOMwVz^8uv_w?Mw?Ò2Mw2Pd§?33yxE(3|Mx23wU-wV~v2wV§32(3¯x3w?2O|_P_PxE33w?N|açz_(x*c| ÒM Mv_wÇ|_Py3w?xE(x2|z_ºßU|_2Mv_w?2MwMv_2(_~vºxEMx2§NvºMvxEx*2zdMv_wVMw¢x2|z¦2Mv_w?PM2PwVy7|¦§&w?MM2wOwVxE(||~b7§?x2wVz7+ÊP)*a+ÊP)èNûúû\BucvddyPwVwV|3wVz¦¦w¡Px2|z|_~tMvwO-wV~vgc&zPxE3wU~2wV||¦wNxEM| !ÃFädcMv

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−0.5 0 0.5 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

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¢ øZ£ â û ü ý"¤ä㥧¦Gý T åúp¤væ â ÿhþ ¦ þÿ æ ÿ ý ü¨ úp¤(©.¦

: input pattern : weight vector

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x1

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UWV XWYZ"[#"]\ &%c]c'[,'c'[!1ceZ+0[Z"X]Vÿ'X1[$c]Y1-#Y1ct1cgf/+0[Z7fg\F N[ >YE*] VY[ F V AG@BA W ADFP W· F J FU I8JfI8V/W A dTãÇVW > I S EZF=AGA J FU I ^ W > I F¶gA I EGU I8MXH F [_N,W @%F V FP W > I F¶ Ü`I8[!W,~ñ:N PF=]E î[ F J C6F VI8VW U I8[!W FE ó @BA@ V C] WbW F W > IqVI_W· FE gd`1 A · @ W > W > I + F=>F VI8VcVI_W· FE ^ W > IqVI ]EGF V · @ W >c>@ S > I A W?N[!W @%U N,W @%F V U NH ] I @KA(A I8H%I8[!W`I8MXN A · @ VVI E^/¶ I8[_N ]A I @ W A ·TI @ S > W U I8[!W FEQ¡p¢m@BA VI8N E I A W?W F,¯d ¼?> I(VI ]EGF V A_^ · >@ [ > N E IQN EZE NV S I8M @ VfN¡îM @ JfI8V AG@%F VNHhHKN,W`W @ [!I ^ [ FEGE I AGC6F VM @ VN\6ùX P N AG>@%F V· @ W >AG]¶E I S @%F V A¯FP W > IQ¡· FE AGC N[!I FP W > I EGF¶LF W ^@ dId ^ W > IQVI ]EZF VNHHBN,W`W @ [!I @BA N õhB!GT ' *6£RFP W > Im· FE A`C N[!Id @ W > I8N[ > VI ]EZF VON U I8[!W FE ÝNVM£=N[ F¶g@ NVOJ\N,W E*@ À¥¤vN E ImN AGAGF [ @ N,W`I8Md2 ]EZ@ V SS EGF=AZA J FU IOÝ ¢@BA2P I8M9W F W > I EGF¶LF Wq· >@ [ > J\N,I A#@ W A J FU I ^E I AG] HBW @ V S @ V E I_W @ VNHt[ FhFE M @ VN,W`I A ,§¦ FPW > IfI8VMî£I I8[!W FE d ¼F [ FEGE I8[!W PFE W > IM @KA [ E I_W @BA N,W @BF V FP W > I\· FE @ V S A`C N[!I ^ NVNMM @ W @BF VNHJ FU I @BA

u )¨]) P¦w¦w#r©0P0ª Ãr«ty¬¬ªOÆ8o& TJ\NMIm· >@ [ >9@BA MI C I8VMI8V/W FP W > IfM @BA WGNV[!I ¶ I_W·TI_I8V9W > IfVI ]EGF V9NVMW > I F¶ ÜaI8[!W @ V A`C N[!I ¡p¢ ù., W >@KAQA J\NHKHM @BA`C HBN[!I8JfI8V/W @ VZþDN E W`I AG@ NV A`C N[!I @BA W E NV A HBN,W`I8MçW F NVçNV S HBIm[ > NV S I ]AG@ V S W > IrN[ F¶@ NV¤ ¢ i

Ý*­ Ù_Ô ® 9 Ý ¢ D ¤ ¢ ñ,cù ¡h¢ ó ñdShd°¯ó· >@ [ >c@BA N#Ñ EZA Waî FE MI E(¼ N8lH FE I!À C NV AG@%F V FP ÝA­ Ù_Ô ® d ¼?> IjÑgVNH E I_W @ VNH6[ FhFE M @ VN,W`I ADFP W > I2I8VMî£I I8[!W FEN P W`I E W >@BA ÑgVI¦J FU IN E I @ V±,³²d´ I8N E V @ V S CEGF [!I_I8M A N A¦PF HBH F · A i¦· > I8VNV @ J CEGFU I8M9I A W @ J\N,W`I9ñaÝ n ¤2ó µ > N A¦¶ I_I8V PRF=] VM ^ W > I PF HæîH F · @ V S NMN C WGN,W @%F V A N E ImJ\NMI5¶ j,öBöeg·¸ i¡ I Ù׺¹ 9 ¡ Ig» ®Ú Dh¼ ñ7½`ó#¾ I ¢ ñ7½Gó±¿ ,cù ¡ I» ®ÚÀ n

ñaÝ n ¤2ó Ù!×d¹I 9 ñaÝ n ¤¦ó » ®ÚI Dh¼ ÷ ñ7½Gó#¾ ÷I ¢ ñ7½Gó ¿ ñaÝ n ¤¦ó µI ùñaÝ n ¤2ó » ®ÚI À ßã P ¾ I ¢ ñ7½Gó 9 ¾÷I ¢ ñ7½`ó 9 B I ¢^ W >@BA@KAAG@ J @ HBN E W FC I E [!I C W EGF VH%I8N E V @ V S dôjI E I ^ N A · @ W > W > I + F=>F VI8VH%I8N E V @ V S EZ] H%I ^ NM @BA WGNV[!I P] V[!W @%F V @BAT]A I8M AG] [ > W > N,W¾ I ¢ ñ7½GóNVM±¾ ÷I ¢ ñ7½`ókN E I¦µ2N ]AGAG@ NV A MI C I8VM @ V S F VW > IM @BA WGNV[!I ¶ I_W·I_I8VOVI ]EGF V A¸ NVM · @ W > NfJ\NÀ @ J ] JÒN,W ¸ 9 ñ:[ P dI8idñnhd¢n=ó`ó*d1qV @ J CEGFU I8MI A W @ J\N,W`IcñaÝ n ¤¦ó µ @BADF¶ WGN @ VI8MXN A?PF HBH F · A d

Ý µ 9 Ý ¢ D ¤ ¢ ñ,ù£,³²ó n ñdShdOS=ó¤ µ 9 ¤ ¢ D ¤ ¢ ñ,Yù ¡h¢ ù£,³² D ,Á¦ó ñ,ò2ù£,A¦óºÄÅ ,Ʋqù£,§¦ Å > ñdShdOT=ó9 ¤ ¢ D ñ Ýùh¤ ¢ ,ó ,*ÄÅ , Å > ß

ãaVI8id¯ñdShdOS=ó ^ W > I2ÑgVNHLI EGEGFE ,cùÇ,Ʋ @ V'þDN E W`I AG@ NV A`C N[!I @BA W E NV A HBN,W`I8MW F NVXI EGEGFEQ@ VmÜ F=@ V/W A`C N[!I U@ NJ ] H%W @%C H @ [_N,W @%F V ¶ l¤ ¢ d ¼?>@BA I EZEGFEm@BA W > I8VNMMI8MW F Ý ¢ W F [ F V A W @ W ] W`IW > I @ J CEGFU I8MI A W @ J\N,W`IÝ µñ A W`I_I C I A WjMI A [!I8V/WQJ @ V @ J @BA N,W @%F V FP I EGEGFE ó*d

ãaVI8idñdShdOT=ó ^] , 9 ,³²eù:,A¦ ^=@ dId ^ W > I[ > NV S I @ V E I_W @ VNH/[ FhFE M @ VN,W`I AFP W > IDI8VMî£I I8[!W FE M ] IW F W > IÑgVIQJ FU I8J\I8VW ^ NVM Ý 9 ¤ ¢ ñ,mù ¡h¢ ó ^@ dId ^ W > I E I8HKN,W`I8M¦Ü F=@ V/WkNV S H%I A M ]EZ@ V S ÑgVIQJ FU I8JfI8V/W_d ¼?>h]AI8igdñdShdOT=ó[_NV ¶ I E I8[ F S V @KA I8MN A NVI EZEGFE î[ FEGE I8[!W @BF V EZ] H%I FP W > I @ M EGF ·?îô F, Wl C I PFE =N[ F¶@ NV A ¤md

ãÇWN CC I8N EZA W > N,WbN P W`I E n ^ (( @ W`I E N,W @BF V A W > I A l A W`I8J N CCEGF N[ > I A [ FEGE I8[!W ¶ I > N Uh@BF=]E8^ NVMW > N,WbN P W`I E¡ ^ ((H%I8N E V @ V S A W`I CA V F V F W`I_· FE W > lYMI U@ N,W @%F V @BADCE I A I8V/W_d¤¦¥ÉÈ Ê °¬Ëc°(®Ì(±ÆÍ ªrÎm¨rÌQÍ¿²G­EÏ>@ H%I¦I8VMî£I I8[!W FE¦CLF=AG@ W @%F V @ V S U@ N A I8V A`FE ÐEGF¶LF Wq[ F/FE M @ VN,W @%F V @KA NV @ J CLFE WGNV/W CEGF¶ H%I8J´W FA`F H U I ^W > I EZF¶6F W @ W A I8H P · @ HBH6V F WQJ FU I#· @ W >F=] W(MlVNJ @ [2[ F V/W EGF H FP@ W A H @ J ¶A d1 S N @ V ^ N[_[ ]E N,W`I[ F V/W EGF HL· @ W > V F VîNMN C W @%U I¦[ F V/W EGF HBH%I EZAD@BATCLF=AGAG@%¶ H%I F VH%lf· > I8VN[_[ ]E N,W`IJ F MI8H AFP W > I EZF¶6F WN E ITN U N @ HKN ¶ H%I ^ NVMW > I EZF¶6F W @BA V F WW F/FQAZ]A [!I C W @%¶ H%IW F ·I8N E îNVMî£W`I8N E d ¼Q>@BALE I8i ]@%E I8J\I8VW> N A H%I8McW F W > I¦[ ]EGE I8VWaîMNl EGF¶LF W A W > N,W(N E I ]A I8M @ VJ\NV/l P N[!W FEZ@ I A d ] WDW > I¦N CC H @ [_N,W @BF V FP VI ]E NHVI_W· FE Aj@ VW >@BA ÑI8HKMY[ > NV S I A W > I A I E I8i ]@BE I8JfI8V/W A d

ï VI FP W > IÑ EZA W2VI ]E NH¯VI_W· FE A · >@ [ >9AG] [_[!I_I8MI8M @ VM F=@ V S MlhVNJ @ [[ F VW EGF H FP N EGF¶LF W¦N E J·DN A¦CE I A I8VW`I8M ¶ l + N8·DN,W F^ ]EZ] ,N8·DN ^ NVM Ü ]@8] @ ñ + N·N,W F^ ]E*] N·N ^tò Ü ]W8] @^ gT(Se¯ó*d ¼?> I_lMI A [ EZ@%¶ ImNVI ]E NHVI_W· FE ç· >@ [ > S I8VI E N,W`I A J F W FE [ F J\J\NVM A2PEGF J NMI AG@%E I8MOW E NÜ`I8[!W FE l @ VÜ F=@ VWNV S HBI A d ¼?> I @%E?A l A W`I8J M F I A V F W @ V[_H ] MIqW > IW E NÜ`I8[!W FE l S I8VI E N,W @%F V FE W > IW E NV A`PFE J\N,W @%F V FP¯U@BAG] NH[ FhFE M @ VN,W`I A W F\¶LF Ml[ FhFE M @ VN,W`I A d

¼Q> IXVI_W· FE @KA I!ÀhW E I8JfI8H%l AG@ J C H%IdãaV P N[!W ^ W > I A l A W`I8J @BA N P I_I8Mî PFE ·DN E MVI_W· FE ^(¶g] W ¶ l[_N E I P:] HBHBl[ >FhF=AG@ V S W > I ¶ N AG@BA?P:] V[!W @BF V A_^ W > IVI_W· FE O[_NV ¶ I E I A W EZ@ [!W`I8MOW FcF VIH%I8N E V @ V S HBN8lI E¦AG] [ >W > N,WQÑgVM @ V S W > I FC W @ J\NH @BA NW EZ@%U@ NHWGN A gdjãÇVOW >@BA [_N A I ^ W > I ¶ N AZ@BA?P:] V[!W @%F V A N E IW >/]A [ >F=A I8VW > N,WW > I P:] V[!W @%F VW > N,W @BA N CCEGF À @ J\N,W`I8M @BA NqH @ VI8N E [ F J ¶@ VN,W @%F V FP W >F=A I ¶ N AG@BAP] V[!W @%F V A d ¼?>@BA N CCEGF N[ >@BA(AZ@ J @ HBN E W F W > N,W CE I A I8V/W`I8M @ V A I8[!W @%F V / dONhd

Tâ oE0qpqrtsPvu ) Pwwrxo?wDyfrPwDz| ~ R<Oe¯7¸ ¼?> I\J\NV @%C] HBN,W FE]A I8MÞ[ F V AZ@BA W A¦FP W >E I_I2Ü F=@ V/W A N A W > IJ\NV @%C] HBN,W FE¦@ VÑ S î]E IShdBq· @ W >F=] WT· EZ@BA WÜ F=@ V/W_d ¼?> I2MI AG@BE I8MW E NÜaI8[!W FE l9ݧÑ=ñ7½`ó ^ · >@ [ >c@BA S I8VI E N,W`I8M ¶ lNV F W > I E?AG]¶A l A îW`I8J ^¯@BA¦P I8M @ V/W F W > I @ V U I EZA I!îMlhVNJ @ [ A J F MI8H?ñRÑ S ]E IShdON=ó*d ¼?> IfI EGEGFE#¶ I_W·TI_I8VݧÑñ7½Gó2NVMÝñ7½Gó @BAP I8M @ V/W F W > IVI ]E NHeJ F MI8Hd

manipulator

model

inverse dynamics

d

f

i(t)θ

-+

++

K

(t)θ(t) (t)T T

T (t)

θ θ

UWV XWY#Z"[m"]\Ò&`_Q['[YZÓf/.g+¬c[,.-Z"c-ecb[0Ôf`f1 cÖÕ×`Ø(Ù°Ú¼Q> IVI ]E NHqJ F MI8H ^ · >@ [ >@BAAG>F ·jV @ VÑ S ]E IÛShd¢n ^ [ F V AG@KA W AFP W >E I_I C I E [!I C W EZF V A_^ I8N[ >þF VI

P I_I8M @ V S @ V F VITÜ F=@ VW FP W > I¦J\NV @%Cg] HBN,W FE d ¼?> I¦MI AG@BE I8McW E NÜaI8[!W FE lÝ³Ñ 9 ñ L Ñ Û n L Ñ > n L ÑbÜó @BAP I8M @ V/W F 8¡V F VH @ VI8N E(AG]¶gA l A W`I8J A d ¼?> I E I AZ] H%W @ V S AG@ S VNH A N E I¦·I @ S > W`I8MONVM AZ] J\JfI8M ^AG] [ > W > N,WÝ m ¢ ñ7½Gó 9 Û Ül Þ°ßÛ*à Þ ¢ = Þ ¢ n ñ 9 n â n ¡=ó n ñdShdBó

· @ W > = Þ Û 9<; Þ ñ L Ñ Û ñ7½`ó n L Ñ > ñ7½Gó n L ÑáÜ=ñ7½`ó`ó n= Þ > 9 = Þ Ü 9 ¾ Þ ñ L Ñ Û ñ7½Gó n L Ñ > ñ7½Gó n L ÑbÜ=ñ7½Gó`ó nNVM ; Þ NVMâ¾ Þ N A?@ VWGN ¶ H%IãShdB,d

(t)

(t)

(t)

(t)

(t)

(t)

x

x

13,1

1,1

i3

i2

i1(t)

(t)

(t)T

T

T

TT

T

32

1

(t)(t)

(t)

Σ

Σ

Σ

θθθ

(t)

(t)

(t)d3

d2

d1

f

f

g

g

1

13

1

13

x1,2

1,3x

x13,3

13,2x

U@V XWY#ZÓ["]\ä&`_Q[f'[YZÓf/.'[!1Ec#ZºYb[O0Ö ff1 cÖÕ×`Ø(Ù°ÚE_Q[Z"[5fZÓ[¦1Z"[[f'[Y#Z"c'Ac'[\-e[ZåæcçVÿ'1¬V3'#1[Z"c0ec,1¬fZ£+ã\rèWfY'[YZ"c'd[[e¬æZÓc+v1#V°ZB1 [[,'Y'c'/.Vÿ'[gfZEY0 `1 [,+2g\¬_Q[Y/--e[ZD'[YZ"c'ÖV c''[!1æ[1 c1[Z"c,1ÉfZc0fb[`åæcçVÿ'10éºÉ\åæcçVÿ'12$Vÿ'$WXWYZ"["]\%$êg1[:c,1[Z1cX'[YZ"c'Q1æcQåæcçVÿ'1ë¬f'^]\

u )¨]) P¦w¦w#r©0P0ª Ãr«ty¬¬ªOÆ8o& T¡ì íbîï!ðñ òºðáóòºðbôbõ öîÓï!ðñÉòºðáóáòðbôÉõ÷ øðñ øðáóù øð ñúdûü ó ð ó øð ôý øðñþ ÿ ú ó ðáó øðáó(þ ÿ ú ðbô øðñ údûü ó ï!ðáóðbôÉõ øðbôeþ ÿ ú ðbô øð ñ þ ÿ ú ó ï!ð ó ð ô õ ð ó ñ údûü ð ó þ ÿ ú ð ó øðñ údûü ðáó údûü ï!ðáó±ðbôÉõ ð ó ñ údûü ï!ðáóðbôÉõgþ ÿ ú ï!ðáóðbôÉõ ð ñð ó(údûü ð ó þ ÿ ú ð ó ð ó ñ údûü ð ó þ ÿ ú ï!ð ó ±ð ô õ ðñ ðáó údûü ï!ðáó±ðbôÉõþæÿ ú ï!ðáó±ðbôbõ ð ó ñ þ ÿ ú ðáó údûü ï!ðó±ðáô õ ð ñð ó(údûü ð ó þ ÿ ú ï!ð ó ð ô õ ð óó údûü ð ô÷ ðñ ðáó(þ ÿ ú ðó údûü ï!ðáóðbôÉõ ð óô údûü ðbô÷÷ ðñ ðbô údûü ï!ðáó±ðbôÉõþæÿ ú ï!ðáó±ðbôbõ ðáó ðbô údûOü ðbô÷Éù ð ñð ôeúdûü ð ó þ ÿ ú ï!ð ó ð ô õ ð ó÷ ý ðñ ðbô

¼ N ¶ H%I5ShdBi F VH @ VI8N E W E NV AGPRFE JN,W @%F V A?]A I8M @ VW > I + N·N,W F J F MI8Hd¼Q> I P I_I8M ¶ N[GW FE i ] I²ñ7½Gó @ VcÑ S ]E I5ShdON\[ F V AZ@BA W A(FPÝ ² ¢ ñ7½Gó 9 ¢ ñ L Ñ ¢ ñ7½`ótù L ¢ ñ7½`ó`ó D ¢ L ¢ ñ7½`ó ½ n ñ 9 n â n ¡=ó n

¢ 9 ] VH%I AZA ý L ¢ ñ7½`ó¯ù L Ñ ¢ ñ F¶ Ü`I8[!W @%U I CLF=@ V/WZó_ý/ß¼?> I P I_I8M ¶ N[Z S N @ V A NVM ·I E I#[ F J Cg] W`I8MXN A ñdN¯/ߢâ n ¯ / nhß n gT,ß / ó Ä NVMña8nhߢâ n ¡e¯/ߢâ n Shß / ó Ä d jI!ÀW ^ W > I·I @ S > W A NMN C W ]AG@ V S W > IMI8HBWGN EZ] H%I

¼ à m ¢ ½ 9 = m ¢gÝ 9 = m ¢ ñ Ý ² ¢ ù Ý m ¢ ó n ñ 9 n â n ¡=ó*ß ñdShdBó1´MI AG@%E I8MJ FU I C N,W`W`I E V @BAmAG>F ·QV @ VÞÑ S ]E IÔShd°¯/dÛ1 P W`I E âçJ @ V ] W`I A#FP H%I8N E V @ V S W > I P I_I8M ¶ N[GW FE i ] I A N E IVI8N E HBl I EGFçAG] [ > W > N,WW > I A l A W`I8J > N AmAG] [_[!I AGA`P:] HBHBlOH%I8N E VI8MW > I\W E NV AGPRFE JN,W @%F Ved1qHæîW >F=] S > W > IqN CC H @ I8M C N,W`W`I E V A N E I U I E l\MI8M @ [_N,W`I8M ^ W E N @ V @ V S · @ W > N E I C I_W @ W @%U I C N,W`W`I E V AZ@ Veñ"! ¢ ½`ó ^ · @ W >! i#!>i#! Ü 9 :i$ âri$ ¡ @BA NH A`FAG] [_[!I AZA`P] Hd

1θ

302010−π

0

π

t/sU@V XWYZ"["]\&%&`_2[$[V°Z"[¬åëcçV3'12-f1Ç1æ[Z'$dceZçåæcçV3'1æ$(\('cçV3'1æ0f/'Ô^âf*)[V3+$V3. fZ1Vÿ+¬[-f1Ç1æ[Z£'g\¼?> I ]A I P:] HBVI AGADFP VI ]E NHeNH S FEZ@ W > J A?@BA MI8J F V A W E N,W`I8M ¶ lW > I P N[!WjW > N,WQV FU I8H EGF¶LF WQN E [ >@ W`I8[!W ]E I A_^· >@ [ > V F H F V S I E VI_I8MXN U I E l EZ@ S @ M A W E*] [!W ]E I2W FAG@ J C H @%P lW > I[ F V/W EGF HBH%I E8^ N E IV F ·x[ F V A W EZ] [!W`I8Med FEI!ÀNJ C H%I ^A I U I E NH S EGF=]CA ñ + N,WGN8l=NJ\N ò + N8·DN,W F^ gT(TâçDôjI AGA I8H EGF W >^,+ N E N E^,+ J\N S W ^kò-+ [ >h] H%W`I8V ^gT(T / ó E I CLFE W F V9· FE O· @ W > N C VI ] J\N,W @ [J ]A [ ] H F î A I8H%I_WGNH EGF¶LF W¦N E J ^ · @ W >çE*]¶¶ I E N[!W ] N,W FE*A¦E I!îC HKN[ @ V S W > I.J F W FEZA d ¼Q> I U I E l[ F J C H%I!À#MlVNJ @ [ A NVM#I8V Uh@BEGF VJfI8V/WGNH=W`I8J C I E N,W ]E ITMI C I8VMI8V[!lFP W >@BA N E JåJN,IjW > I ]A I FP V F VîNMN C W @%U IjNH S FEZ@ W > J Ak@ J CLF=AGAZ@%¶ H%I ^ · > I E IQVI ]E NHVI_W· FE AAZ] [_[!I_I8Med

T / oE0qpqrtsPvu ) Pwwrxo?wDyfrPwDz¤¦¥/ 0 °0Ëf²21G«Ò±e°¬Ëc°(®ÁÏãaVW > I CE I U@%F=]A(A I8[!W @%F V A?A`F J\I#N CC H @ [_N,W @%F V AFP VI ]E NHeVI_W· FE AQF V EGF¶LF W?N E J A ·I E IM @KA [ ]AGA I8Md¯ãaVW >@KAA I8[!W @%F V·TI PRF [ ]A#F VJ F¶g@ H%I EGF¶LF W A d N AG@ [_NHKH%l ^ W > I[ F V/W EGF H FP N EGF¶LF W#N E J NVMW > I[ F V/W EGF HFP NJ F¶@ H%I EGF¶LF W @BAU I E l AZ@ J @ HBN E ifW > Iñ >@ I E N E [ >@ [_NHó[ F V/W EGF HBH%I E Ñ EZA W C HBNV A N C N,W >e^ W > I C N,W >@BAW E NV A`PRFE JfI8M PREGF J3.DN E W`I AG@ NVvñ· FE HBMgóM F J\N @ VW F W > IÜ F=@ VW FE · > I_I8H2M F JN @ V ]AG@ V S W > I @ V U I EZA I @ VI8J\N,W @ [ AjFP W > I A l A W`I8J NVMçÑgVNHBHBlXNYMlhVNJ @ [#[ F V/W EGF HBHBI E WGN,I A [_N E I FP W > I\J\N CC@ V S PEGF J A I_WaîCLF=@ V/W Ak@ VW >@BA M F J\N @ VW F N[!W ] N,W FE?AG@ S VNH A d¯ô F ·I U I E8^@ V CE N[!W @ [!IqW > I CEGF¶ HBI8J A · @ W > J F¶@ H%I EGF¶LF W AF [_[ ]E J FE IY· @ W >©C N,W > î C HBNVV @ V S NVMVN U@ S N,W @%F VW > NV· @ W > W > IçMlhVNJ @ [ AFP W > I A l A W`I8JYd ¼ · FI!ÀNJ C H%I A · @ HBH ¶ I S @%U I8Ved

ÈtÉ54tÉ76 8:9<;,=>qÌ(?A@B=; Í(?C,D7E ?FGD79Í FE S I8V A I8Vñd FE S I8V A I8V ^ gT(Se¯óMI A [ EZ@%¶ I A N?VI ]E NHN CCEZF N[ >¦PFEC N,W > î C HBNVV @ V S d F¶LF W C N,W > î C HBNVV @ V SW`I8[ > V @ i ] I A [_NV ¶ I2M @%U@ MI8M @ VW F W· F [_N,W`I S FEZ@ I A d ¼?> I?Ñ EZA W ^ [_NHBH%I8M öR*,ö ' öR,BE I8H @ I AbF V @ V PFE J\NîW @%F VçN U N @ HBN ¶ HBI PREZF J W > I[ ]EGE I8V/W¦ú U@ I_· CLF=@ V/W_û FP W > I EGF¶LF W_d ¼?>@BA?C HBNVV @ V S @BAQ@ J C6FE WGNVW ^6AG@ V[!I @ W @BAN ¶ HBIW F MI8NH· @ W >P N A Wk[ > NV S I AT@ VW > I?I8V Uh@BEGF VJfI8V/W_d<HjV PFE W ] VN,W`I8H%l ^=¶ l @ W A I8H P H F [_NHMN,WGN @BA S I8VI E NHBHBlV F WNMI8i ] N,W`I AG@ V[!I F [_[_H ]AG@BF V @ V9W > I\H @ VI FPDAG@ S > W[_NV[_N ]A IfW > I EGF¶LF W¦W F ·DNVMI Em@ VW F MI8NMÞI8VM[ FEGE*@ M FEZAFE [ >F/F=A IçV F Vî FC W @ JNH EZF=] W`I AfFP W E N U I8Hd ¼?> I A I8[ F VM AG@ W ] N,W @%F V @BA [_NHBH%I8M öR],ö ' JI Ä' öR,B^e@ V9· >@ [ > [_N A I\W > I A l A W`I8J ]A I A S H F¶ NHV F ·QHBI8M S I PREZF J¾NYW FCLF S E N C>@ [fJ\N CCE I Uh@%F=]A H%lA W FE I8M @ VW F JfI8J FE ld1qH%W >F=] S > S H F¶ NH C HKNVV @ V S C I E J @ W AkFC W @ J\NH C N,W >A W F¶ I S I8VI E N,W`I8M ^@ W > N AD@ W A·I8N,hVI AGA d @BAGAG@ V S hV F ·QH%I8M S I FE@ V[ FEGE I8[!WGH%l A I8HBI8[!W`I8McJN CA [_NV @ V U NH @ MN,W`IQN S H F¶ NH C N,W > W F NVI!ÀhîW`I8V/WTW > N,W @ W ¶ I8[ F JfI AD]A I8H%I AGA d 1 CLF=AGAZ@%¶ H%I(W >@BE M ^ ú¢NV/W @ [ @%C N,W FE lgû C HBNVV @ V S [ F J ¶@ VI8M ¶6F W >cA W E N,W`I S @ I A iW > IH F [_NH @ V PRFE JN,W @%F V @BA [ F V A WGNV/WGH%l ]A I8MOW F S @%U IN ¶ I A W S ] I AGA · > N,WqW > I S H F¶ NH;I8V U@%EGF VJ\I8VW2J\N8l[ F V/WGN @ Ved FE S I8V A I8V @ V U I A W @ S N,W`I A W· F2@BAGAG] I A N AGAGF [ @ N,W`I8M· @ W > VI ]E NHVI_W· FE mN CC H @ [_N,W @BF V A;@ V ] V A W E*] [!W ]E I8MFE [ > NV S @ V S I8V Uh@BEGF VJfI8V/W A d @%EZA W ^ [_NVYVI ]E NHLVI_W· FE A(¶ I ]A I8M @ V[ F VÜ ] V[!W @%F Vc· @ W > M @%E I8[!W A I8V A`FEE I8NM @ V S A W F N AGA`F [ @ N,W @%U I8HBlN CCEZF À @ J\N,W`I S H F¶ NHLW`I EZE N @ V P I8N,W ]E I A V F W F¶gA I EGU N ¶ H%I PREZF J´N AG@ V S H%I EGF¶LF WC I EZA`C I8[!W @%U Id + I8[ F VMH%l ^@BA NVI ]E NHLVI_W· FE P N A W(I8V F=] S > W Ff¶ I ]A I P:] H @ V C N,W >E I8HKNÀN,W @%F V C HBNVV @ V S ^· > I E I2W > I EGF¶LF W @BA(E I8i ]@BE I8McW F\FC W @ J @KA I¦J F W @%F VONVM AG@ W ] N,W @%F V A I8V AG@ W @BU I2[ F V A W E N @ V/W A d

FE W > IXÑ EZA W CEGF¶ H%I8J ^ W > I A l A W`I8J > NMW F©A W FE I9NV ] J ¶ I EFPCLF=AGAG@%¶ HBI A I8V A`FE J\N CAFP W > II8V Uh@BEGF VJfI8V/W_d ¼?> I EGF¶LF W·N A#CLF=AG@ W @%F VI8M @ VÞI @ S > W CLF=AG@ W @%F V A¦@ VÞI8N[ >EGFhF J NVMgSGK A`F VN E#A [_NV A·I E IjJNMI PEGF J I8N[ >cCLF=AG@ W @%F Ved N A I8M F VW > I A IjMN,WGN ^PFE I8N[ >EZF/F J³N#J\N C ·DN A J\NMId ¼;Fm¶ IqN ¶ H%IW FYE I CE I A I8V/WqW > I A IfJ\N CA¦@ V9NYVI ]E NH¯VI_W· FE ^ W > IfJ\N C ·N A M @%U@ MI8M @ VW F ¡âÂÞ¡â S EZ@ MI8H%I8JfI8V/W A_^· >@ [ > [ F=] HBM ¶ I CEGF ÜaI8[!W`I8M F V/W F W > IX¡âÖÂ~¡âçV F MI A VI ]E NHTVI_W· FE gd ¼?> IJ\N CAFP W > IM @ML I E I8VWEGFhF J A ·I E Ifú A W FE I8Meû @ VYN\ô FC ÑI8HKMWl C I FP VI_W· FE 6dkãaVW > I FC I E N,W @BF VNH C> N A I ^ W > I EGF¶LF W(·NVMI EZAN EGF=] VM ^ NVMI8VW`I EZA NV ] VhV F ·QV EZF/F JYd¯ãÇWtJN,I AtF VI A [_NVm· @ W > W > I A`F VN E8^ · >@ [ >#CEGFU@ MI A N C N E W @ NHE I CE I A I8V/WGN,W @%F V FP W > I EGF/F J J\N C ñ A I_IÑ S ]E IShdOS=ó*d ¼?>@KAC N,W`W`I E V @BA [_HBNJ C I8M F VW F W > IDVI_W· FE ^ · >@ [ >· @ HBH E I S I8VI E N,W`I(W > I ¶ I A W;ÑW`W @ V S C N,W`W`I E VedON @ W > W >@BA@ V PRFE J\N,W @%F VN S H F¶ NH C N,W > î C HBNVVI E [_NV ¶ I ]A I8Med¼?> I E I AG] H%W A · >@ [ > N E I CE I A I8VW`I8M @ VmW > I C N C I E N E IV F W U I E l#I8V[ F=]E N S @ V S dPN @ W > N2VI_W· FE FP ¡âEÂq¡âVI ]EGF V A_^ W > IjW F WGNHLV ] J ¶ I ETFP ·TI @ S > W AD@BA =â /fA i ] N E I8M ^ · >@ [ > [ F=A W A J FE IQW > NVç O¶ lhW`I FP;A W FE N S I@%PkF VH%l F VI ¶ lhW`I C I E ·TI @ S > W @BA¦]A I8Medr1jH AGF W > I A`C I_I8M FP W > I E I8[_NHBH @BA H F ·$i$ FE S I8V A I8VJfI8V/W @%F V A NE I8[_NHKHkW @ J\I FP J FE IW > NVW· F NVMN > NH P?>F=]EmF V©NV~ã 1 ¼¦^ · >@ [ >@BA]A I8M F V ¶LF N E M FP W > IEGF¶LF W_d1qH A`F W > I ]A I FP N AG@ J ] HKN,W`I8MÞNVVI8NH @ V S C N E NM @ S J PFEC N,W >C HBNVV @ V S @KA V F W CEZFU@ V S W FO¶ IfNVI L I8[!W @%U IN CCEGF N[ > d ¼?> IHKN E S IV ] J ¶ I EmFP?A I_W`WGH @ V S W EZ@ NH A ñRQ ((ó @BAP N E W F/FA H F · PRFEE I8NHkW @ JfI ^· > I8VW > I A NJfI P:] V[!W @BF V A [ F=] HBM ¶ I ¶ I_W`W`I EcA I EZU I8M ¶ lW > I ]A I FP N CLF W`I8V/W @ NHQÑI8HBMN CCEGF N[ >FEM @KA WGNV[!I¦W E NV AGPRFE JXd

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units

units45 output

29 hidden

sharp left sharp right

30x32 video input retina

8x32 range finderinput retina

straight ahead

66

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Nexus

32

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sequencersequencer

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16,384 Processors

Connection Machine

16,384 Processors

Connection Machine

16,384 Processors

Connection MachineConnection Machine

16,384 Processors

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