Springer Tracts in Advanced Robotics
Volume 29
Editors: Bruno Siciliano · Oussama Khatib · Frans Groen
Cristian Secchi Stefano Stramigioli Cesare Fantuzzi
Control of Interactive Robotic Interfaces
A Port-Hamiltonian Approach
With 86 Figures
Professor Bruno Siciliano, Dipartimento di Informatica e Sistemistica, Universit`a degli Studi di Napoli Fede- rico II, Via Claudio 21, 80125 Napoli, Italy, email: siciliano@unina.it
Professor Oussama Khatib, Robotics Laboratory, Department of Computer Science, Stanford University, Stanford, CA 94305-9010, USA, email: khatib@cs.stanford.edu
Professor Frans Groen, Department of Computer Science, Universiteit van Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands, email: groen@science.uva.nl
Authors
Dr. Cristian Secchi Prof. Dr. Cesare Fantuzzi
DISMI – University of Modena and Reggio Emilia Morselli Building
Via G. Amendola 2 42100 Reggio Emilia Italy
secchi.christian@unimore.it cesare.fantuzzi@unimore.it
Prof. Dr. Stefano Stramigioli Universiteit Twente EL/CE
Postbus 217 7500 EAE Enschede The Netherlands S.Stramigioli@ieee.org
ISSN print edition: 1610-7438 ISSN electronic edition: 1610-742X
ISBN-10 3-540-49712-9 Springer Berlin Heidelberg New York ISBN-13 978-3-540-49712-7 Springer Berlin Heidelberg New York
Library of Congress Control Number: 2006937681
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Springer is a part of Springer Science+Business Media springer.com
© Springer-Verlag Berlin Heidelberg 2007 Printed in Germany
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Typesetting: Digital data supplied by authors.
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Printed on acid-free paper 89/3141/Yu - 5 4 3 2 1 0
Editorial Advisory Board
EUROPE
Herman Bruyninckx, KU Leuven, Belgium Raja Chatila, LAAS, France
Henrik Christensen, KTH, Sweden
Paolo Dario, Scuola Superiore Sant’Anna Pisa, Italy R¨udiger Dillmann, Universit¨at Karlsruhe, Germany AMERICA
Ken Goldberg, UC Berkeley, USA John Hollerbach, University of Utah, USA Lydia Kavraki, Rice University, USA
Tim Salcudean, University of British Columbia, Canada Sebastian Thrun, Stanford University, USA
ASIA/OCEANIA
Peter Corke, CSIRO, Australia
Makoto Kaneko, Hiroshima University, Japan Sukhan Lee, Sungkyunkwan University, Korea
Yangsheng Xu, Chinese University of Hong Kong, PRC Shin’ichi Yuta, Tsukuba University, Japan
STAR (Springer Tracts in Advanced Robotics) has been promoted under the auspices of EURON (European Robotics Research Network)
ROBOTICSResearch
Network European
EUR ON
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;$# Q3&K&+=K&# .KLQ LQ&? Q=WK$L Q3& =;QK=8 =+ 5;Q&K Q5=; 5L Q= &X?85 5Q8Y 9=$&8 Q3& &;&K2&Q5 ?K=?&KQ5&L =+ ?3YL5 8 LYLQ&9LC
5KLQ =+ 88#G)B += /B)/B+. /2. +0 (0<.: &Q ?3&;=9&;=;
Q= 9=$&8 & 25V&;C 3& ?3&;=9&;=; ?K=$U &L2EB2/=@F0B=A ;$ Q3& 9=4
$&8 3L Q= K&?K&L&;Q Q3& =UQ =9&L Q3Q ; = UKC =K &X9?8&# Q3& ?K5; 5?8&L
=+ Q3&K9=$Y;95 L 8595Q Q3& 9=U;Q =+ 3&Q Q3Q ; & QK;L+=K9&$ 5;Q=
9& 3;5 8 W=K7 ;$ K&8Q5V5QY Q3&=KY Q&88L Q3Q =$Y ;;=Q QKV&8 +LQ&K Q3; Q3& L?&&$ =+ 8523QC ; 2&;&K8# 9Q3&9Q5 8 9=$&8 L&8& QL &KQ5;
LUL&Q +K=9 U;5V&KL& =+ ?=LL5585Q5&LM Q35L LUL&Q =;Q5;L Q3& =UQ =9&L Q3Q K& $& 8K&$ ?=LL58& Y Q3& 9=$&8# Q3&)F+2< =+ Q3& 9=$&8C EUQ5=;L K&
V&KY LU5Q8& Q==8 Q= L&8& Q &KQ5; LUL&Q +K=9 U;5V&KL& =+ ?=LL5585Q5&L"
&KQ5; = UKK&; & =+ Q3& ?3&;=9&;=; 5L +=K5$$&; 5+ &KQ5; =;LQ5QUQ5V&
&EUQ5=; 5L ;=Q LQ5L.&$C 3& &3V5=K =+ Q3& 9=$&8# Q3UL# 5L 25V&; Y Q3=L& = 4 UKK&; &L Q3Q LQ5L+Y &KQ5; L&Q =+ =;LQ5QUQ5V& &EUQ5=;L# 88&$)F+2<.
9EB+20=C 9=$&8 3L Q= K&?K&L&;Q &KQ5; VK58&L =+ 95; 5;Q&K&LQ W35 3 K& 88&$/0+!=B F<+.=C ; Q3& =Q3&K 3;$# V&KY =+Q&; 9Q3&9Q5 8 9=$&8 5;V=8V&L Q3& UL& =+ =Q3&K UX585KY VK58&L# 88&$.B0B F<+.= Q=
9=$&8 Q3& &3V5=K =+ Q3& ?3&;=9&;=;C
&3V5=K# &3V5=K8 &EUQ5=;L# 9;5+&LQ ;$ 8Q&;Q VK58&L K& Q3& Q3K&&
95; 5;2K&$5&;QL =+ 9=$&85;2 8;2U2& 88&$)F+2<. 44<2) Q3Q 3L
&&; 5;QK=$U &$ 5; RR[# T1RC 35L ??K= 3 88=WL Q= $&L K5& ?3&;=9&; 5;
V&KY 2&;&K8 WY W5Q3=UQ ;Y ;& &LLKY ?K5=K5 $5LQ5; Q5=; &QW&&; 5;?UQL
;$ =UQ?UQL @W35 3 5L ;=Q 8WYL 8&K" W3&; 9=$&85;2 85;&K K&L5LQ=K# Q3&
V=8Q2& 3L Q= & =;L5$&K&$ L ; 5;?UQ ;$ Q3& UKK&;Q L ; =UQ?UQ =K V5 & V&KLFA W35 3 5L 5;LQ&$ V&KY =99=; W3&; UL5;2 LQ;$K$ 9=$&85;2 Q& 3;5EU&L L# +=K &X9?8&# QK;L+&K +U; Q5=;L =K QK;L+&K 9QK5X&LC
& UL& =+ 5QL 2&;&K85QY# Q3& &3V5=K8 ??K= 3 5L LU5Q8& +K9&W=K7 +=K $&L K55;2 ?3YL5 8 LYLQ&9LM Q3&L& LYLQ&9L 3V& V&KY ?KQ5 U8K LQKU QUK&
L ; 0QE25 :"$528/ 8" :DJ1625J:828 QEJ$6E
Q3Q Y5&8$L 8=Q =+ 5;+=K9Q5=; Q3Q ; & UL&$ 5; Q3& 9=$&85;2 ?K= &LLC ;
?KQ5 U8K 5Q 5L ?=LL58& Q= $&.;& &;&K2Y ;$ Q= 9=$&8 LYLQ&9 Y 9&;L =+
VK58&L Q3Q K& K&8Q&$ Q= &;&K2Y LQ=K2& ;$ Y Q3& WY &;&K2Y 5L &X 3;2&$
9=;2 Q3& =;LQ5QUQ5V& ?KQL =+ Q3& LYLQ&9C UKQ3&K9=K& 5Q 5L ?=LL58& Q= $&.;&
Q3& =; &?Q =+ ?=W&K ?=KQ# ;9&8Y Q3& 9&$5U9 Q3K=U23 W35 3 Q3& LYLQ&9
&X 3;2&L &;&K2Y W5Q3 Q3& K&LQ =+ Q3& W=K8$C
; Q35L 3?Q&K W& W588 L3=W 3=W 5Q 5L ?=LL58& Q= &9&$ Q3& ?3YL5 8 ;4 QUK& =+ Q3& LYLQ&9 5;Q= Q3& &3V5=K8 +K9&W=K7C & W588 .KLQ ?K=V5$& ; 5;QK=$U Q5=;# L&$ =; RR[# T1R# T</# =+ Q3& &3V5=K8 ??K= 3 +=K 9=4
$&85;2 $Y;95 8 LYLQ&9C ; & W& 3V& 2&;&K8 +K9&W=K7 +=K 9=$&85;2
;Y ?3&;=9&;=;# W& W588 += UL =; ?3YL5 8 LYLQ&9 ;$ W& W588 5;QK=$U &
Q3& =; &?QL =+ &;&K2Y# &;&K2Y VK58& ;$ ?=W&K ?=KQ Q3Q K& +U;$9&;Q8 +=K $&L K55;2 Q3& ?3&;=9&; =+ &;&K2Y LQ=K2& ;$ =+ &;&K2Y &X 3;2&C &
W588 Q3&; ?K&L&;Q Q3& 42<B*/+.B20+0 !2</.+=/ Q3Q 3L &&; 5;QK=$U &$
5; >'<# RTR# RTT# R>'# R>< ;$ Q3Q 88=WL Q= 9=$&8 ;Y ?3YL5 8 LYLQ&9 Y Q75;2 &X?85 5Q8Y 5;Q= =U;Q 5QL &;&K2&Q5 &3V5=K ;$ 5QL 5;Q&K;8 5;Q&K4 =;;& Q5=; LQKU QUK& ;$ W& W588 L3=W 3=W ?3YL5 L ;QUK88Y $&Q&K95;&L Q3&
75;$ =+ &3V5=K =+ ;Y ?3YL5 8 LYLQ&9C 5;88Y# W& W588 ?K&L&;Q Q3& L QQ&K5;2 K&?K&L&;QQ5=; =+ ?=W&K ?=KQL ;$ Q3& =; &?Q =+ L QQ&K5;2 VK58&L# L&$
=; Q3& QK&Q9&;Q K&?=KQ&$ 5; T<<# Q3Q W588 & V&KY UL&+U8 W3&; $&85;2 W5Q3 =9?8&X 5;Q&K Q5;2 LYLQ&9L W5Q3 $&8YC
$&- /#' '! #' # " 2"!
2(+!(
15>51 .)@78 '@)07 . '@)07, 6?<)0.8
3 ?3&;=9&;=; ?K=$U &L 2EB2/= @&V&;QLA W35 3 Q7& V8U& 5; L&Q# 88&$ 0+F<=C LU88Y ;=Q 88 Q3& &8&9&;QL =+ Q3& U;5V&KL& K& ?=LL58&
=UQ =9&L +=K Q3& 25V&; ?3&;=9&;=;M Q= $&.;& 9=$&8 9&;L Q= $&Q&K95;&
W3&Q3&K &KQ5; =UQ =9&L K& ?=LL58& =K ;=QC 9=$&8# Q3&K&+=K&# L&8& QL &KQ5; LUL&Q # W35 3 K&?K&L&;QL Q3& ?=LL58& =UQ =9&L# =+ Q3& U;5V&KL& M 5L 88&$ Q3&)F+2< =+ Q3& 9Q3&9Q5 8 9=$&8T1RC
".)<)0. 151 3<'-<), 0,45 9Q3&9Q5 8 9=$&8 += 4+<
@&A7 += =B .. B) U;5V&KL& G)2= ./0B= < .. =UQ =9&L 0+= =E=B 2! .. B) &3V5=K7
H/4. 37D 5+../= 311367 Q 5L W&88 7;=W; Q3Q ; ??&K# $&?&;4
$5;2 =; Q3& Q&9?&KQUK&# L 5 &# 85EU5$ WQ&K =K LQ&9C 3& U;5V&KL& 5L 25V&;#
W5Q3 Q3& Q&9?&KQUK& &X?K&LL&$ 5; &8L5UL# Y Q3& L&Q )2%)& K!G)C& DG)!8 +*TNR&%A
;?L 0$ $0N2:D5 D"2/6 (:D :"$528/ Q8625 QEJ$6E K
;$ Q3& &3V5=K Y Q3& LUL&Q
) @@2%) +*TNR&[A3@K!G)C +[&>[[A3@DG)!8 +>[[&%AAA &KQ5; &3V5=K ; & L&8& Q&$ +K=9 U;5V&KL& 5; L&V&K8 WYL" Y L59?8&
&;U9&KQ5=; @L 5; X9?8& >CTA# Y Q3& + Q =+ 3V5;2 &KQ5; ?K=?&KQ5&L# &Q C V&KY &,& Q5V& WY Q= $&L K5& ?3&;=9&;=; 5L Y 9&;L =+ &EUQ5=;L" ;
=UQ =9& =+ Q3& U;5V&KL& 5L ?KQ =+ Q3& &3V5=K 5+ ;$ =;8Y 5+ 5Q LQ5L.&L &KQ5;
=;LQ5QUQ5V& &EUQ5=;LC
".)<)0. 15= 3'@)07, 6?<)0.845 B E0+F<= =B 0 -& -" BG2 /4=7 ) /B)/B+. /2.@&A G+B) )I! -@IA ) -@IA += =+ B2 =<+ I &3V5=K8 &EUQ5=;L0 += 02*
B I @&& -& -A7 ) =B += .. B) &EUQ5;2 L? &7 ) 9E<E4.
@&& -& -A += .=2 .. &3V5=K8 &EUQ5=; K&?K&L&;QQ5=;2! @&A7 H/4. 37'7=;L5$&K 85;&K K&L5LQ=KC Q 5L W&88 7;=W; Q3Q Q3& K&8Q5=;
&QW&&; Q3& UKK&;Q 0=W5;2 Q3K=U23 Q3& W5K& ;$ Q3& V=8Q2& K=LL Q3&
Q&K95;8L 5L $&Q&K95;&$ Y 39JL 8W"
)
3& LYLQ&9 ; & 9=$&8&$ Y =;L5$&K5;2 L U;5V&KL& )# L &EUQ5;2 L? &)C =;L5$&K"
-" @& A -" @& A Q3& &3V5=K =+ Q3& K&L5LQ=K ; & 25V&; L
)@& A! -@& A )-@& A W35 3 9&;L ;=Q35;2 &8L& Q3Q
)@& A! ) 15>5> .) 8< . <.< 7),8
5V&; &KQ5; ?3&;=9&;=; Q= $&L K5&# 9Q3&9Q5 8 9=$&8 ; & U58Q 5; QW= LQ&?L" .KLQ 5$&;Q5+Y Q3& VK58&L Q= 9=$&8 ;$ Q3&5K $=95; =+ &X5LQ&; &#
Q3& U;5V&KL&# L& =;$ 5$&;Q5+Y 88 Q3& ?=LL58& =UQ =9&L# Q3& &3V5=K 1 C 3& &3V5=K ; & L?& 5.&$ Y K&EU5K5;2 Q3Q L=9& &3V5=K8 &EUQ5=;L K& LQ5L.&$C ; =K$&K Q= &X?K&LL Q3& 9=$&8 5; =;V&;5&;Q WY# 5Q ; &
;& &LLKY Q= 5;QK=$U & L=9& UX585KY VK58&L 5; $$5Q5=; Q= Q3=L& Q3Q 3V&
Q= & 9=$&8&$C 3&L& &XQK VK58&L K& 88&$.B0B F<+.= ;$ 85V& 5;
&KQ5; $=95;' W358& Q3& VK58&L Q3Q 3V& Q= & &X?85 5Q8Y 9=$&8&$ K&
88&$/0+!=B F<+.= ;$ 85V& 5; Q3& U;5V&KL&C
. ; 0QE25 :"$528/ 8" :DJ1625J:828 QEJ$6E
%
E26<5$ D$E2EJ2N$ 8$JO:D4
H/4. 37%7=;L5$&K Q3& L59?8& K&L5LQ5V& ;&QW=K7 K&?K&L&;Q&$ 5; 52C >C>
;$ LLU9& Q3Q Q3& &3V5=KL =+ Q3& UKK&;Q ;$ =+ Q3& V=8Q2& Q Q3&
&XQ&K;8 ?=KQ 3V& Q= & 9=$&8&$C 3& ?3YL5 8 ?K5; 5?8&L Q= UL& Q= 9=$&8 Q3& ?=KQ &3V5=K K& 5K 33=,JL 8WL ;$ 39JL 8WC ;$ K& 9;5+&LQ VK58&L W358&##;$K& 8Q&;Q VK58&LC 3& &3V5=K8 &EUQ5=;L K&"
) ))
) D)
@>C>A
Q 5L ;=W ?=LL58& Q= 25V& Q3& +=88=W5;2"
".)<)0. 15: 3<'-<), -0, A)<' ,<.< @7),845 /*
B)/B+. /2. G+B) .B0B F<+.= += $0 = B<+4.@&'&!AG)<
+= B) E0+F<= 2! /0+!=B F<+.= ' += B) E0+F<= 2! .B0B F<+.=
0! 1 + '+= B) !E.. )F+2<7 ) /0+!=B /B)/B+. /2.@&A += B)0 $0 I
)I! #5! '=E) B)B@I& 5A! ! @>CTA += .. B) /0+!=B )F+2< 2< =+/4.I )F+2< 0 B) B<+4.@&'&!A += .. .B0B F<+. <4<=0BB+20 2! B) /0+!=B /B)/B+. /2.
@&A7
15>5= C.-), C8<-8
Y;95 8 LYLQ&9L K& 3K Q&K5Z&$ Y Q59& &V=8UQ5=; ;$ K& =+ KU 58 59?=KQ; & 5; =;QK=8 Q3&=KYC Q 5L ?=LL58& Q= $&L K5& Q3&L& LYLQ&9L 5; Q3&
=;Q&XQ =+ &+C >C>" Q3& VK58&L =+ 5;Q&K&LQL K& +U; Q5=; =+ Q59& ;$# Q3&K&4 +=K&# Q3& U;5V&KL& 5L +U; Q5=; L? &C
;?L 0$ $0N2:D5 D"2/6 (:D :"$528/ Q8625 QEJ$6E ,
".)<)0. 159 3C.-), 8C8<-45 I0/+. =I=B/ += $0 I B<+4.@&&AG)< += B) B+/ H+= += =B .. L52;8 L? & 0 1 += .. B) )F+2<7 < +0+B= B) =B 2! /4= !<2/
B27
3& Q59& X5L K&?K&L&;QL Q3& =K$&K&$ L&Q =+ Q59& 5;LQ;QL =+ 5;Q&K&LQ# Q3& L52;8 L? & K&?K&L&;QL Q3& L&Q W3&K& Q3& =UQ =9&L =+ Q3& LYLQ&9 &V=8V& ;$
K&?K&L&;QL Q3& U;5V&KL&# ;9&8Y Q3& L&Q =+ 88 QK6& Q=K5&L Q75;2 V8U& 5; Q3&
L52;8 L? &C ;8=2=UL8Y Q= 9Q3&9Q5 8 9=$&8L# Q3& &3V5=K5L ;=Q35;2
&8L& Q3; LUL&Q =+ Q3& U;5V&KL& W35 3 L&8& QL +958Y =+ Q59& QK6& Q=K5&L Q3Q K& =9?Q58& W5Q3 Q3& LYLQ&9C
".)<)0. 15 3)- ).@7).45 I0/+. =I=B/ ) @&&A+=
=+ B2 Q59& 5;VK5;Q +! E3 ) !2< .. G ! G)< E3 += B) Q4L35+Q
=?&KQ=K$0 =
@E3-A@HA )-@HDGA @>CRA
3& Q59& 5;VK5; & ?K=?&KQY LYL Q3Q Q3& &3V5=K =+ Q3& $Y;95 8 LYLQ&9
$=&L ;=Q $&?&;$ &X?85 5Q8Y Y Q3& Q59&# L W&88 7;=W; +K=9 LYLQ&9 Q3&=KY
>T'# T'1C
; Q35L 3?Q&K W& 59 Q 9=$&85;2 ?3YL5 8 LYLQ&9L ;$# Q3&K&+=K&# Q3&
&3V5=K8 +K9&W=K7 W588 & 588ULQKQ&$ +=K =;Q5;U=UL $Y;95 8 LYLQ&9L
;$ Q3UL ) C UKQ3&K9=K& W& W588 LLU9& Q3Q Q3& L52;8 L? & 5L
$5,&K&;Q58& 9;5+=8$ @Q35L 5L ;=Q K&LQK5 Q5V& +=K Q3& 9=$&85;2 ?UK?=L&L ;$
5Q 5L ; &LL&;Q58 Q& 3;5 8 LLU9?Q5=; +=K 9;Y $&.;5Q5=;LA ;$ W& W588 LLU9&
Q3Q Q3& $Y;95 8 LYLQ&9L U;$&K =;L5$&KQ5=; K& Q59& 5;VK5;QC 3& K&LU8QL 588ULQKQ&$ 5; Q35L L& Q5=; ; & &L58Y &XQ&;$&$ Q= $5L K&Q& Q59& $Y;95 8 LYLQ&9L# L L3=W; 5; RR[C
Q 5L ?=LL58& Q= $&L K5& Q3& &3V5=K =+ $Y;95 8 LYLQ&9 Y 9&;L
=+ $5,&K&;Q58 &EUQ5=;L ;$ Q35L ; & +=K985Z&$ Y UL5;2 Q3& =; &?Q =+
6&Q L? & TT>C =;L5$&K $5,&K&;Q58& 9;5+=8$ ;$ Q7& L Q59& X5LC
=;L5$&K LU- 5&;Q8Y L9==Q3 9?.@.A! # 5C&C LU 3 Q3Q 5QL:3#$&K5VQ5V&
W5Q3 K&L?& Q Q=G5L $&.;&$C &Q$ & Q3& L&Q =+ 88 ?=LL58& 5;LQ;Q;&=UL23#
Q59& $&K5VQ5V& +=K ;Y ?=LL58&.@.A! C Q 5L Q3&; ?=LL58& Q= $&.;& Q3& L&Q )) + + . . . + )M ?=5;QL 5;)K& 5;$5 Q&$ W5Q3.)C 3& 5;$U &$
9?.)@.A )=C).@GA# 88&$ Q3&:3#4<2.20(B+20 2! .@.A# 5L 25V&; Y"
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%
8 2DM2J
".)<)0. 15/ 3< 8245 ):3#2<< ,B =4 2!+ += $0 = B) =4 + )0 +B G+.. +0+B = )@+ A7
; &8&9&;Q 5; Q3& L52;8 L? & ; & =;L5$&K&$ L Q3& V8U& Q7&; Y 9? K! 5; &KQ5; ?=5;Q G !C 3UL# ; &8&9&;Q =+ )@+ A 5L 25V&; Y ; &8&9&;Q =+ Q3& L52;8 L? &K@GA! Q=2&Q3&K W5Q3 5QL $&K5VQ5V&L 8 U8Q&$ 5;GU? Q= =K$&K:C
".)<)0. 151E 3C.-), '@)07, 6?<)0.845 B +"*
<0B+. /0+!2. G)+) <4<=0B= B) =+(0. =4 B) B+/ H+= : 0200(B+F +0B(<5B) =K$&K 2! B) +"<0B+. 9EB+206 0 B)
&EUQ5;2 L? &7 20=+< BG2 /4=
-& -")@+ A @>COA ) I0/+. =I=B/) @&&AG+B)
)K" -@K@GA&'K
'G&. . . &')K
'G) A )-@K@GA&'K
'G&. . . &')K
'G) A @>CNA += =+ B2 =<+ I +"<0B+. 9EB+20= 0 += 02B I@&&& -& -A H/4. 37337=;L5$&K Q3& L59?8& 5K U5Q K&?K&L&;Q&$ 5; 52C >CTC U??=L&
Q3Q 9=$&8 =+ Q3& &3V5=K =+ Q3& ?=KQ VK58&L ;$ 5L ;&&$&$C ; Q35L L& Q3& Q59& X5L 5L ;$ Q3& L52;8 L? & 5L C K=9 Q3& =;LQ5QUQ5V&
&EUQ5=;L =+ Q3& 5;$U Q=K ;$ =+ Q3& ? 5Q=K ;$ +K=9 5K 33=,JL 8WL 5Q +=88=WL Q3Q"
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;?L 0$ $0N2:D5 D"2/6 (:D :"$528/ Q8625 QEJ$6E G
=;L5$&K ;=W Q3& +=88=W5;2 9?L"
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Y LQK523Q+=KWK$ 8 U8Q5=;L# 5Q +=88=WL Q3Q Q3& &3V5=K =+ Q3& LYLQ&9 5L 2=V&K;&$ Y Q3& $5,&K&;Q58 &EUQ5=;"
-@=C@& AA )-@=C@& AA @>C>[A
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Q 5L LQK523Q+=KWK$ Q= 2&;&K85Z& Q3& ;=Q5=; =+ 8Q&;Q ;$ 9;5+&LQ VK58&L +=K $Y;95 8 LYLQ&9LC
".)<)0. 151> 3C.-), 8C8<- A)<' ,<.< @7),845 I0/+*
. =I=B/ G+B) .B0B F<+.= += $0 = ) @&&&!A G)< +=
B) B+/ H+= += B) /0+!=B =+(0. =4 += B) .B0B F<+.= =4
0 ! 1 @ + A += B) !E.. )F+2<7 B $0= .B0B F<+. <4<*
=0BB+20 2! B) /0+!=B I0/+. =I=B/) @&&A G+B) B) !2..2G+0(
/0+!=B )F+2<
)K" #5" =E) B)B@K& 5A! ! @>C>TA Q&;Q VK58&L ; ??&K 5; 9=$&85;2 $Y;95 8 LYLQ&9L +=K VK5=UL K&4 L=;LC 5KLQ# Q3&Y ; & UL&$ L59?8Y +=K 9Q3&9Q5 8 K&L=;L# 5; =K$&K Q= =4 Q5; ?KQ5 U8K +=K9 =+ Q3& &3V5=K8 &EUQ5=;LC & =;$# Q3&Y ; & UL&$ Q=
&X?K&LL 5;Q&K;8 8WL 2=V&K;5;2 Q3& &3V5=K =+ Q3& LYLQ&9C +&W &X9?8&L K&
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