Manipulador o brazo

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∆αj,q=b0+b1RSqP+b2RqS−1P+b3RIndq +b4RIndq−1+b5RF irmq +b6RF irmq−1 +ϵj,q U9XjXRV

r?2`2 ∆αj,q = αj,q −αj,q−1 Bb i?2 +?M;2 i?2 2biBKi2/ KBbr2B;?iBM; T`K2i2` 7Q` }`K j 7`QK [m`i2` q−1 iQ qc RSP

q Bb i?2 iQiH `2im`M QM i?2 i?2 aS 8yy BM/2t BM [m`i2`qc RIndq Bb i?2

QmiT2`7Q`KM+2 Q7 }`KǶb BM/mbi`v b +QKT`2/ iQ i?2 iQiH `2im`M QM i?2 aS 8yy BM/2t BM [m`i2`

qc M/- RF irm

q Bb i?2 QmiT2`7Q`KM+2 Q7 }`KǶb biQ+F T`B+2 b +QKT`2/ iQ Bib BM/mbi`v BM [m`i2`

qX A7b2>0-b4>0- Q`b6 >0- i?i rQmH/ #2 +QMbBbi2Mi rBi? BMp2biQ`bǶ KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM `2~2+iBM; b2H7@ii`B#miBQM #BbX

a2+QM/- A 2tKBM2 ?Qr i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM KQM; i?2 ?QH/BM;b BM BMbiBimiBQMH BMp2biQ`bǶ TQ`i7QHBQb +Qp`B2b rBi? i?2b2 BMp2biQ`bǶ Tbi TQ`i7QHBQ `2im`MbX A7 i?2 TQ`i7QHBQ KM;2` Q7 M BMp2biK2Mi 7mM/ Bb bm#D2+i iQ b2H7@ii`B#miBQM #Bb- ?2 Bb HBF2Hv iQ Qp2`2biBKi2 ?Bb BM7Q`KiBQM T`Q+2bbBM; #BHBiv 7QHHQrBM; TQbBiBp2 TQ`i7QHBQ `2im`MbX A7 bQ- BMbiBimiBQMH BMp2biQ`b b?QmH/ 2t?B#Bi +?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM KQM; i?2B` ?QH/BM;b i?i +Qp`v TQbBiBp2Hv rBi? H;;2/ TQ`i7QHBQ `2im`MbX

lbBM; h?QKbQM@_2mi2`b Rj@6 }HBM;b /i M/ *_aS biQ+F M/ BM/2t T`B+2 /i- A /2+QKTQb2 +?M;2b BM i?2 M2i bb2i pHm2 Q7 M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ BMiQ +?M;2b BM i?2 K`F2i pHm2 Q7 Bib BMBiBH ?QH/BM;b M/ M2i BM~Qrb 7`QK BMp2biQ`bX A 7m`i?2` #`2F /QrM i?2 +?M;2b BM i?2 K`F2i pHm2 Q7 Bib BMBiBH ?QH/BM;b BMiQ K`F2i@rB/2 `2im`Mb- BM/mbi`v QmiT2`7Q`KM+2- M/ }`K QmiT2`7Q`KM+2 +QKTQM2MibX

A HbQ K2bm`2 +?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM KQM; i?2 ?QH/BM;b BM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQX h?i Bb- B7 }`K j BM [m`i2` q 2t?B#Bib KBbr2B;?iBM; Q7

`2/mM/Mi BM7Q`KiBQMαj,q- A K2bm`2 BMbiBimiBQMH BMp2biQ`iǶb p2`;2 ?QH/BM;b BM i?2 KBbr2B;?iBM;

Q7 `2/mM/Mi BM7Q`KiBQM bα¯i,q =!jwi,j,qαj,q- r?2`2wi,j,q Bb i?2 r2B;?i Q7 }`Kj BM BMp2biQ`iǶb

TQ`i7QHBQ b Q7 i?2 2M/ Q7 [m`i2`qXj A b2T`i2 +?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi

BM7Q`KiBQM KQM; M BMbiBimiBQMH BMp2biQ`Ƕb ?QH/BM;b BMiQ +?M;2b BM i?2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM KQM; Bib 2tBbiBM; ?QH/BM;b- H#2H2/∆α¯Organic_i,q - M/ +?M;2b BM i?2 BMp2biQ`Ƕb ?QH/BM;b- j<sub>A +H+mHi2 i?2b2 r2B;?ib KQM; 7mM/Ƕb ?QH/BM;b 7Q` r?B+? i?2αT`K2i2`b r2`2 2biBKi2/X AM 2z2+i- A bbmK2</sub>

i?i i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM KQM; i?2 ?QH/BM;b BM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ 7Q` ?QH/BM;b 7Q` r?B+? i?2αT`K2i2`b r2`2 MQi 2biBKi2/ 2[mHb i?i 7Q` ?QH/BM;b 7Q` r?B+? i?2αT`K2i2` r2`2

2biBKi2/X

H#2H2/∆α¯T radingi,q X9

A 2biBKi2 i?2 7QHHQrBM; `2;`2bbBQMb,

∆α¯T rading_i,q =b0+b1RqSP+b2RSq−1P+b3RIndi,q +b4RIndi,q−1+b5RF irmi,q +b6RF irmi,q−1

+b5N etInf lowi,q+b6N etInf lowi,q−1 U9XjXkV

∆α¯_i,qOrganic=b0+b1RqSP+b2RSq−1P+b3RIndi,q +b4RIndi,q−1+b5RF irmi,q +b6RF irmi,q−1

+b5N etInf lowi,q+b6N etInf lowi,q−1 U9XjXjV

r?2`2∆α¯T rading<sub>i,q</sub> /2MQi2b +?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM BMbiBim@

iBQMH BMp2biQ`iǶb TQ`i7QHBQ /m2 iQ +?M;2b BM Bib ?QH/BM;b 7`QK [m`i2`q₋1iQqc∆α¯Organic_i,q /2MQi2b

+?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM BMbiBimiBQMH BMp2biQ`iǶb TQ`i7QHBQ

/m2 iQ +?M;2b BM α7`QK [m`i2` q₋1 iQ q KQM; Bib BMBiBH ?QH/BM;bc RSP

q Bb i?2 iQiH `2im`M

QM i?2 i?2 aS 8yy BM/2t BM [m`i2` qc RInd

i,q Bb i?2 `2im`M QM BMbiBimiBQMH BMp2biQ` iǶb TQ`i7QHBQ BM

[m`i2`q/m2 iQ i?2 QmiT2`7Q`KM+2 Q7 i?2 7mM/Ƕb BM/mbi`v 2tTQbm`2 b +QKT`2/ iQ i?2 `2im`M QM

i?2 aS 8yy BM/2tc RF irm

i,q Bb i?2 i?2 `2im`M QM BMbiBimiBQMH BMp2biQ`iǶb TQ`i7QHBQ BM [m`i2` q /m2

iQ }`K@bT2+B}+ QmiT2`7Q`KM+2 b +QKT`2/ iQ }`KǶb BM/mbi`vc M/-N etInf lowi,q Bb BMbiBimiBQMH

BMp2biQ`iǶb M2i BM~Qrb 7`QK QmibB/2 BMp2biQ`b BM [m`i2`qX A MQ`KHBx2 i?2b2 p`B#H2b iQ ?p2 K2Mb

2[mH iQ x2`Q M/ biM/`/ /2pBiBQMb 2[mH iQ QM2X

A7b2>0-b4>0- Q`b6>0BM 1[miBQM U9XjXkV- i?i rQmH/ #2 +QMbBbi2Mi rBi? BMp2biQ`bǶ KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM `2~2+iBM; b2H7@ii`B#miBQM #Bb KQM; BMbiBimiBQMH BMp2biQ`bX A7 b2 > 0-

b4 > 0- Q` b6 > 0 BM 1[miBQM U9XjXjV- i?i rQmH/ #2 +QMbBbi2Mi rBi? BMp2biQ`bǶ KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM `2~2+iBM; b2H7@ii`B#miBQM #Bb KQM; MQM@BMbiBimiBQMH BMp2biQ`bX

9_{h?i Bb-}

∆α¯i,q= ¯αi,q−α¯i,q−1=

! j wi,j,qαj,q− ! j wi,j,q−1αj,q−1 =! j wi,j,qαj,q− ! j wi,j,q−1αj,q+ ! j wi,j,q−1αj,q− ! j wi,j,q−1αj,q−1 =! j (wi,j,q−wi,j,q−1)αj,q+ ! j w_i,j,q−1(αj,q−αj,q−1)

A /2}M2∆α¯Organic_i,q ≡"jwi,j,q−1(αj,q−αj,q−1)M/∆α¯T radingi,q ≡ "

j(wi,j,q−wi,j,q−1)αj,qX

9XjXkX _2bmHib

h#H2 Ry b?Qrb i?2 2biBKiBQM Q7 1[miBQM U9XjXRVX lbBM; i?2αT`K2i2`b 2biBKi2/ QM }p2@KBMmi2

`2im`Mb- QM2 biM/`/ /2pBiBQM `2im`M QM i?2 aS 8yy BM/2t Bb bbQ+Bi2/ rBi? yXkN biM/`/ /2@ pBiBQM BM+`2b2 BM }`K@[m`i2`αT`K2i2`b +QMi2KTQ`M2QmbHvX lbBM; i?2αT`K2i2`b 2biBKi2/

QM jy@KBMmi2 `2im`Mb- QM2 biM/`/ /2pBiBQM QmiT2`7Q`KM+2 Q7 }`KǶb BM/mbi`v b +QKT`2/ iQ i?2 aS 8yy BM/2t Bb bbQ+Bi2/ rBi? yXye biM/`/ /2pBiBQM BM+`2b2 BM }`K@[m`i2`αT`K2i2`b

+QMi2KTQ`M2QmbHvX QM2 biM/`/ /2pBiBQM QmiT2`7Q`KM+2 Q7 }`K b +QKT`2/ Bib BM/mbi`v Bb bbQ+Bi2/ rBi? yXy9 biM/`/ /2pBiBQM BM+`2b2 BM }`K@[m`i2`αT`K2i2`b +QMi2KTQ`M2QmbHv

M/ yXy9 biM/`/ /2pBiBQM BM+`2b2 BM }`K@[m`i2`αT`K2i2`b BM i?2 bm#b2[m2Mi [m`i2`X h?Bb

`2HiBQMb?BT #2ir22M #2ir22M +?M;2b BM i?2αT`K2i2`b M/ H;;2/ `2im`Mb Bb +QMbBbi2Mi rBi? i?2 αT`K2i2`b `2~2+iBM; b2H7@ii`B#miBQM #BbX h?2b2 `2bmHib /Q MQi +?M;2 Ki2`BHHv 7i2` +QMi`QHHBM;

7Q` +H2M/` [m`i2` }t2/ 2z2+ibX

h#H2 RR b?Qr /2b+`BTiBp2 biiBbiB+b 7Q` i?2 K2bm`2b Q7 BMbiBimiBQMH BMp2biQ`bǶ TQ`i7QHBQ `2im`Mb M/ +?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM KQM; i?2 ?QH/BM;b BM BMbiBimiBQMH BMp2biQ`bǶ TQ`i7QHBQbX h?2 K2M M/ K2/BM +?M;2 BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM@ 7Q`KiBQM BM BMbiBimiBQMH BMp2biQ`bǶ TQ`i7QHBQb `2 +HQb2 iQ x2`Q- #b2/ QM i?2 T`K2i2`b 2biBKi2/ mbBM; }p2@KBMmi2 `2im`Mb M/ i?Qb2 2biBKi2/ mbBM; jy@KBMmi2 `2im`MbX *?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM BMbiBimiBQMH BMp2biQ`bǶ TQ`i7QHBQb /m2 iQ +?M;2b BM ?QH/@ BM;b M/ i?Qb2 /m2 iQ +?M;2b BM αHbQ 2t?B#Bi K2Mb M/ K2/BMb +HQb2 iQ x2`QX *?M;2b BM i?2

p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM BMbiBimiBQMH BMp2biQ`bǶ TQ`i7QHBQb /m2 iQ +?M;2b BM ?QH/BM;b 2t?B#Bi HQr2` p`BiBQM i?M i?Qb2 /m2 iQ +?M;2b BMαX h?Bb `2bmHi KB;?i bm;;2bi i?i

p`BiBQM BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM BMbiBimiBQMH BMp2biQ`bǶ TQ`i7QHBQb Bb H`;2Hv ii`B#mi#H2 iQ KBbr2B;?iBM; #v MQM@BMbiBimiBQMH BMp2biQ`bX

h#H2 Rk b?Qrb i?2 2biBKiBQM Q7 1[miBQM U9XjXkVX lbBM; i?2αT`K2i2`b 2biBKi2/ QM }p2@KBMmi2

`2im`Mb- QM2 biM/`/ /2pBiBQM `2im`M QM i?2 aS 8yy BM/2t Bb bbQ+Bi2/ rBi? yXjk biM/`/ /2pBiBQM BM+`2b2 BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ /m2 iQ +?M;2b BM Bib ?QH/BM;b +QMi2KTQ`M2QmbHvX lbBM; i?2αT`K2i2`b 2biBKi2/ QM jy@

KBMmi2 `2im`Mb- QM2 biM/`/ /2pBiBQM BM/mbi`v QmiT2`7Q`KM+2 Bb bbQ+Bi2/ rBi? yXRk biM/`/ /2pBiBQM BM+`2b2 BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ /m2 iQ +?M;2b BM Bib ?QH/BM;b +QMi2KTQ`M2QmbHvX h?2b2 bbQ+BiBQMb `2 MQi biiBbiB+HHv bB;MB}+Mi 7i2` +QMi`QHHBM; 7Q` +H2M/` [m`i2` }t2/ 2z2+ibX h?2b2 +QMi2KTQ`M2Qmb `2HiBQMb?BTb

#2ir22M `2im`Mb M/ M BMbiBimiBQMH BMp2biQ`Ƕb +?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM Bib TQ`i7QHBQ `2 MQi +QMbBbi2Mi rBi? i?2αT`K2i2`b `2~2+iBM; b2H7@ii`B#miBQM #BbX

h#H2 Rj b?Qrb i?2 2biBKiBQM Q7 1[miBQM U9XjXjVX lbBM; i?2αT`K2i2`b 2biBKi2/ QM }p2@KBMmi2

`2im`Mb- QM2 biM/`/ /2pBiBQM `2im`M QM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ /m2 iQ BM/mbi`v QmiT2`7Q`KM+2 Bb bbQ+Bi2/ rBi? yXyk biM/`/ /2pBiBQM /2+`2b2 BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ BM i?2 bm#b2[m2Mi [m`i2`X QM2 biM/`/ /2pBiBQM `2im`M QM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ /m2 iQ }`K@bT2+B}+ QmiT2`7Q`KM+2 Bb bbQ+Bi2/ rBi? yXyj biM/`/ /2pBiBQM BM+`2b2 BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ +QMi2KTQ`M2QmbHvX aBKBH` `2bmHib TT2` 7i2` +QMi`QHHBM; 7Q` +H2M/` [m`i2` }t2/ 2z2+ib M/ mbBM; i?2 α T`K2i2`b 2biBKi2/ QM jy@KBMmi2

`2im`MbX h?2b2 `2HiBQMb?BTb #2ir22M `2im`Mb M/ +?M;2b BM i?2 p2`;2 KBbr2B;?iBM; Q7 `2/mM/Mi BM7Q`KiBQM BM M BMbiBimiBQMH BMp2biQ`Ƕb TQ`i7QHBQ `2 MQi +QMbBbi2Mi rBi? i?2αT`K2i2`b `2~2+iBM;

b2H7@ii`B#miBQM #BbX

Pp2`HH- i?Bb 2pB/2M+2 Bb MQi +QMbBbi2Mi rBi? i?2 2biBKi2/α T`K2i2`b `2~2+iBM; b2H7@ii`B#miBQM

#BbX AM QMHv QM2 `2;`2bbBQM bT2+B}+iBQM /Q i?2 2biBKi2/αT`K2i2`b BM+`2b2 rBi? H;;2/ `2im`MbX

6m`i?2`- BM QM2 `2;`2bbBQM bT2+B}+iBQM- i?2 2biBKi2/ αT`K2i2`b /2+`2b2 rBi? H;;2/ `2im`MbX

h?Bb KBt2/ 2pB/2M+2 Bb MQi +QMbBbi2Mi rBi? BMp2biQ`b BM+`2bBM;Hv Qp2`2biBKiBM; i?2 MQp2Hiv M/ 2t+HmbBpBiv Q7 i?2B` T`Bpi2 bB;MHb 7i2` 2tT2`B2M+BM; TQbBiBp2 TQ`i7QHBQ `2im`MbX