Simulation dynamique et applications robotiques

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(1)Simulation dynamique et applications robotiques Ammar Joukhadar. To cite this version: Ammar Joukhadar. Simulation dynamique et applications robotiques. RR-3072, INRIA. 1996. �inria00073620�. HAL Id: inria-00073620 https://hal.inria.fr/inria-00073620 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE.

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(4) !!" . Ammar Joukhadar. N ˚ 3072 decembre 1996 ` THEME 3. ISSN 0249-6399. apport de recherche.

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(367) + qGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq IqXdq}O G= '().2-7%<*,'(-k/%Y;dnmH<*,:;<G'.1H

(368) :\qqGqGqqGqGq#qGqGqqGq#qGqGqqGq IqXdq} ).*,-k'(2%';<H<)A'4n<)(R<*,'(-k/%

(369) :'.)(%

(370) : qGqGq#qGqGqqGq#qGqGqqGq IqXdqX *)(*6+'= )A-k:('.-0<n

(371) :H<)A-7%

(372) +-7H<*,jk:;<%

(373) /'?)J*H<H<)A/

(374) + qqGq#qGqGqqGq <q}| H>= )A-72%'?*,'(-k/%

(375) :\qGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq <q}V /%

(376) +j7n

(377) :(-k/% qGqqGqGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq ')(d_¦<àdc6_ *7ª (] Xdq7S $ %'4)A/;dn

(378) +'.-0/

(379) %qGqqGqGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq Xdq}O *2;= '(+'.-0/

(380) %T;dn\+/%'?*,+' q#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq Xq}O<q7S GG:(+)A-7H

(381) '(-k/%t9 = %>= )(*,jk ;<Gj

(382) }*H<H<)A/+ qGqqGqGq#qGqGqqGq#qGqGqqGq Xq}O<q}O ¶jk-72-7%<*,'(-k/%;<:&*,+'('(: qGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq Xq}O<q} G= '().2-7%<*,'(-k/%Y;<:!H<*).* '4)A:;dnt+/%'4*,+' q#qGqGqqGq#qGqGqqGq Xq}O<qX /

(383) +*,jk-0:4*,'(-k/%\;dnt+/%'?*,+'QqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq Xdq} /jkj0-k:(-k/% q#qGqGqqGqGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq Xq}<q7S *,jk+n

(384) j;<#jh*l/)J+G;<j7*2+/jkjk-k:(-k/%qqGqGqqGqGq#qGqGqqGq#qGqGqqGq Xq}<q}O *,jk+n

(385) j;<#jh*+/%'4)(*,-7%'.G;<%

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(387) :\qGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq Xdq}N /%

(388) +j7n

(389) :(-k/% qGqqGqGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq ¶a

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(394) %2;dnm2/

(395) n

(396) r2%' H<*)n<%

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(399) BA' *)A'(-k+n

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(402) : qGqGq#qGqGqqGq#qGqGqqGq |<qX *2:?*,-k:(-k1H<*)n<%

(403) 1*6-h%*)A'(-k+n

(404) j4= \qGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq OIq}O<q}O OIq}O<q} OIq}O<qX. X. X

(405) M X S X

(406)

(407) X |

(408) X N

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(410) |<q}| |<q}V |<q}N '¬¦ V<q7S V<q}O. %

(411) l*H<H

(412) j0-k+*,'.-0/

(413) %= ;<-k+*,jk n<%\jk-k9*%';dnt9%

(414) /n q#qGqGqqGq#qGqGqqGq %

(415) l*H<H

(416) j0-k+*,'.-0/

(417) %m9

(418) )(*H -kn

(419) j0:\O'(::?H>= +-7*n

(420) i:4n<)jk: -71*,9:1qGqGqqGq /%

(421) +j7n

(422) :(-k/% qGqqGqGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq + (d_* c6a<_ *7ª ( $ %'4)A/;dn

(423) +'.-0/

(424) %qGqqGqGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq *2+/%

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(426) H<)A-?= '<= : ;

(427) -7%

(428) )A'(-k qGqGqqGqGq#qGqGqqGq#qGqGqqGq VIq}O<q7S Rd/).ln

(429) j7*,'.-0/

(430) %T;dn\H<)A/R

(431) j 2 q#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq VIq}O<q}O C

(432) /j7n

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(434) : qGqGqqGqGq#qGqGqqGq#qGqGqqGq VIq}<q7S : *,jk9/

(435) )A-k' 2:9 = %>= '(-kn

(436) : ^H<)A-7%

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(438) jk-k+*,'(-k/%:?n<)j022/

(439) ; jkG; p %<*2-kn

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(441) % q#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq V<qX /%

(442) +j7n

(443) :(-k/% qGqqGqGqqGqGq#qGqqGqGq#qGqGqqGqGqqGqGq#qGqGqqGq#qGqGqqGq ª (c ] *¾ª ( . . |. SM,X SMU SSO ,, V. SS SS SS SSX SSN SS Q SSU SO SOU. , V E.

(444) . V. !

(445) &. . . !. * H<)A+H

(446) '(-k/%8j7*H

(447) j7*%

(448) -d+*,'(-k/%8'1jk:1/n

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(450) jh*6'(-k/%; p %<*2-k<n

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(452) R</'(-k<n

(453) ;

(454) -7%'()Jr%'.-0/

(455) %8,'(jkj0<n

(456) j

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(458) :Gn<%\%r

(459) -h)J/%<%

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(463) j

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(470) 8/n j

(471) <H

(472) jk/)(*,'(-k/%T;<%

(473) /

(474) n

(475) r*n

(476) 11H

(477) j7*,+%'(:2H<*)>YH

(478) j0G<H

(479) jk/)(*,'.-0/

(480) %T;< j

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(489) %';<:. -7%'()(*,+'(-k/%

(490) :Y%'?)Jijk\)A/R</'l'2:(/

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(498) r%'/)A'.2%'-h%"«n

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(501) R</'l'!H<*)+/%

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(506) /)(= 2%'>jk: + *%

(507) +:;<:?n

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(512) jk8n<*%

(513) ;/%Y*%

(514) -7H<n

(515) j0n<%/R

(516) BA' )A-k9-k;<2/nT;4= /).1*R

(517) jk8 *2 j

(518) }*,-k;<# ;

(519) }n<%

(520) l1*6-h%t;<'4)A1{}|N

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(524) :G;<:GR</

(525) n

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(528) /

(529) R

(530) B5' * :?*6-0:.-h)' *n

(531) 9

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(534) %'8

(535) jh*l/)J+G;<G&)A/'('(%''j7*1HI/:(:(-7R

(536) -kjk-0'<2= ;

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(539) j0qC<*%

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(546) ¶;<-oi+-kjk *G *6'('(-7%

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(551) %q *TH

(552) jh*%

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(554) r2%' ;

(555) }n<%Tr = -k+n

(556) j02'(/

(557) n

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(560) '(;<j7*G; p %<*2-kn

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(567) r%'G%

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(570) / %

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(573) +8^n<%+ 2-7%jk-7R<)Am%

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(575) '2r= )A-d)#:

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(579) + -k:(:?*R

(580) jkqG*%

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(586) n

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(588) r/%

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(590) }*n

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(597) n<)A:G;dn2/n

(598) r2%'GH<*,:(:(-;dn 9%

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(600) '(-kj;<Y:(-7ln

(601) j7*,'.-0/

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(603) 8+*)G+1jk-k9*2%':.'-7%r

(604) -k:(-7R

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(607) n

(608) r2%';dn\9%

(609) /

(610) nq $#%'&(*+) ,-+. :2/

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(617) 'jk#;</1*,-7%

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(619) -71*,98d%

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(623) :q >%2\O'8,jk R<n

(624) '¶; }

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(630) n<%\/

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(637) :G'/n

(638) r2%' ;

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(648) j 2:8^%= +:(:.-0'.1j

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(657) :%'?)JG/R

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(663) ->:('2jk\+*,:;d*%

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(674) 2j

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(682) :1:(-72n

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(687) :m/R

(688) BA'(: )A-k9-k;<: /n

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(691) :¶jk-72-k'= :8

(692) ' /)J+:+/%'(-7%n

(693) :{ QM<8V<Qb~ <n

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(695) %'¶B(n

(696) :('(-«*R

(697) jk:;d*%

(698) :+)A'4*,-7%

(699) : +*,:1*,-k: H<*,:;d*%

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(703) rTn<*%

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(705) jk: +/

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(707) j7n

(708) :8j0:G/

(709) R

(710) B5'.: 1*%

(711) -7H<n

(712) j?= :GH<*)j0:G)A/RI/'(: %

(713) :(/

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(715) : ;

(716) }n<%2/n

(717) r%' R<*6j0-k:('.-0<n

(718) 8'jh*Y+/%'(-3 %

(719) n

(720) -k'= ;<: /

(721) )A+:

(722) '<= )J-0n<)J::()Ar%' *# n

(723) '(-kj0-k:()>;<:>-h%'<= 9)(*,'(n<)J:%n<= )A-kn

(724) :>4oi+*,+:>' *Y /H

(725) '(-72-k:()j7*1;= '(+'(-k/%T;<j7*Y+/jkjk-0:.-0/

(726) %%'4)AGjk: ;<-SO!= )A%'(:/

(727) R

(728) B5'.:q0G*%

(729) :+)J'?*,-7%

(730) : +*6: +:)A:.'?)A-k+'(-k/%

(731) :%

(732) HIn

(733) r%'H<*6: '?)A¶:4*,'(-k:A&*,-k'(:8,+<n

(734) -:.'¶j0+*,:¶;<j7*/)A+;dn#+/%'4) / jk ;

(735) }n<%t/R

(736) BA'*nT+/n<)A: ;

(737) n<%

(738) G/H= )(*6'(-k/%1 ;

(739) *,:(:(2R

(740) j7*,98<<n

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(742) W/)J+G;<-0:.+/%'.-h%

(743) n

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(745) ;;dn\+/%'?*,+'<n

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(747) / %

(748) ;<-0:.+/%'.-h%

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(754) -7)A1n<%:(-72n

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(756) jk1: p :(' 2 uGv,wvbx5y {V

(757) 8d||

(758) 8dV<S,8d|U

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(760) j7n

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(763) : H<)

(764) = +«4= 3 ;<%'(:'(/n

(765) '%)A:('?*%' \ 8 ZZ 8 ^ 9 8<' \ F

(766) ^ *r+G;

(767) }*n

(768) '?)A:2/; jk: n

(769) '(-kjk-k:<= :;d*%

(770) :jk;</1*6-h%

(771) #;<Gj7*i)A/

(772) R</'(-k<n

(773) q. . # & !. / '?)A2/

(774) ; jk:.'mn<%

(775) -7%'<= 9)(*,'.-0/

(776) %;<;<n

(777) 2/

(778) ; jk:8j

(779) n<%z;4= /)(1*R

(780) j0jk: p :(' 2 1*6:(:()A:.:(/)A'SqO<q}| 'j

(781) }*n

(782) '4)Ai)A-k9-k;<£j7*m= +*%

(783) -k<n

(784) 1;

(785) /R

(786) BA'(:)A-k9-k;<:Sq}O<q7S q1j7* )A%

(787) ;Yj0:(-7ln

(788) j7*,'.n<)

(789) \\ ' Z q$¡j<:('

(790) \\ +*)¢/%2%

(791) }n

(792) '(-kjk-k:(!H<*6:n<%12/

(793) ; jk ;4= /).1*R

(794) jk +/

(795) 1H

(796) jkHI/n<)2/

(797) ;= jk-k:()n<%T/R

(798) BA';4= /).1*R

(799) jkq$j:(' \ F

(800) ^ *br+ jk: *n

(801) '4)A: *H<H<)A/

(802) + : <n<*%

(803) ;m-kj^:

(804) }*,9-0';

(805) }n<%\/RB5')A-k9-k;<2+*)-kj¶n

(806) '(-kj0-k:(Y;d*%

(807) :++*6:jk 2 2/

(808) ; jk#; p %<*-0<n

(809) q : +*)(*,+'<= )A-k:('(-kn

(810) :H<)A-7%

(811) +-7H<*,jk:;<2%

(812) /'?)AG2/

(813) ; jk:./%'jk::?n

(814) -krÆ*%'(:2

(815) }n

(816) '(-kjk-k:?*,'(-k/% ;<:mH</j p ;d)J:\+/%r:mHI/n<)m)AH<)

(817) = :(%'()Yjh* /)(9¶= /= '?)A-k<n

(818) ;

(819) /R

(820) BA'(:8)J%

(821) ;£%

(822) /'?)A12/

(823) ; jk \ F

(824) ^ *br+2jk:l*n

(825) '4)A:2 /

(826) ; jk:9¶= /= '?)A-kn

(827) : '!%

(828) /

(829) n

(830) :!HI)(2';<l%

(831) /n

(832) ::()Ar

(833) -7);

(834) }*6j09/)A-k' 2:4oi+*,+:;A= B *2;= rj0/

(835) H<H= : HI/n<)j7* ;= '(+'.-0/

(836) %T;dn\+/%'?*,+'G{}VU

(837) 8dU~Aq %

(838) *H<H<)A/

(839) + :.2-35*n

(840) '(/1*6'(-kn

(841) '*,;d*H

(842) '?*6'(-kr*m= '< = ;= rj0/

(843) H<H= H</n<)>H<*,:(:()^;< :?*T)AH<)

(844) = :(%'?*,'(-k/%H p :(-kn

(845) j7*Y/).29¶= /= '?)A-kn

(846) G ;

(847) n<%m/

(848) R

(849) B5''G;<2:?*\1*,:.:( *T '(/n

(850) '%+/%

(851) :()JrÆ*%'G:(:H<)A/H<)J-?= '<= :;

(852) -7%

(853) )A'(-k1*6'?)A-k+2'G+%'?)Jl;

(854) -h%

(855) )J'(-k ql+)A%

(856) ; j7*2/

(857) ;= jk-k:?*,'(-k/% '\/H

(858) '(-72-k:(j7*+/

(859) 1H

(860) jk-k'<= ;dn 2/; jk'./n

(861) 'i% )A:('?*%' \ ^ ^ *br+Gjkl/%

(862) ;<)

(863) = jq

(864) }n

(865) '(-kjk-k:?*,'(-k/%t ;

(866) }n<%Y/)(1*,jk-k:?2%

(867) n<= )A-kn

(868) G<H

(869) jk-0+-k'(1HI/n<))

(870) = :(/n

(871) ;d)Aj

(872) A= n<*6'(-k/%1;dn 2/n

(873) r%'8%

(874) /n

(875) :GH<)(' ;<1H<)A%

(876) ;d)A2%t+/1H

(877) '(#j0:G;<-k:(+/

(878) %'(-7%

(879) n

(880) -k'= :)

(881) = :?n

(882) jk'?*%'(: :(:(%'(-kjkj0%'2;<1j7*T/)A+2;<2j7*\+/jkjk-k:(-k/%8¶j7*Y/)A+2;dn&)A/'('(%'1H<*,:(:4*,9;dn N.

(883) . . . ' #. ¡)J/'('(2%'^:('?*,'(-k<n

(884) *nW&)A/'('(%'¶; p %<*2-k<n

(885) 8'>;<+)A'?*,-7%

(886) :>' p H<:¶;</)J+;< +/%'?) / jkq¶j7*1H<).2'*n

(887) :(:(-;<G'?)(*,-k'() j0G: p :(' 2+/

(888) 12Gn<%

(889) !RI/k'(%

(890) /-7)A8

(891) ;</%' j

(892) %'4)= G:('jh*/)A+G';</%'j0:p :(/)J '(-k: :(/

(893) %'jk22/n

(894) r2%''jk:G;4= /).1*,'(-k/%

(895) :q +-¶:(-71H

(896) jk-dij

(897) }n

(898) '.-0jk-k:?*,'.-0/

(899) %;dn: :.' 2#+*)8;d*%