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Visibility-based probabilistic roadmaps for motion planning

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(1)Visibility-based probabilistic roadmaps for motion planning Thierry Simeon, Jean-Paul Laumond, Carole Nissoux. To cite this version: Thierry Simeon, Jean-Paul Laumond, Carole Nissoux. Visibility-based probabilistic roadmaps for motion planning. Advanced Robotics, Taylor & Francis, 2012, 14 (6), pp.477-493. �10.1163/156855300741960�. �hal-01993321�. HAL Id: hal-01993321 https://hal.laas.fr/hal-01993321 Submitted on 24 Jan 2019. 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..

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(190) ’ s &* ¨‘s & $  ‘ s Žh’OVŽ s %‹Ž‘ s;"‡‘ ‹‘ * % >” &s3“ +  *{‘ ( &* ¨‘s > R Y7t I 5 I : b 5 I : v 25Rw > n3n1 @W3_!§!AD=W=@ 3>3_!§=§@W 1 . . +. . . . . . /. . . . . /. +. . . . . . . . _h§. . /.

(191) œ7_h`¡U? k1 R1FV :: J NUG <3J V 13R1k2 \3: nQn1Sn o 476G Y nFG oD\ N q{;=b G [ G bToD\ G o‡y=;5: N tF;@oD\q{;@bD„ G bOJ G <QJt G []©5„ G bDJ N!1 &% % & ‘  ’

(192) s & $ ‘ $/&

(193) *-,3Ž ( &* % ” >S_ ž5Ÿ v  w > n3n1 ^@ =WA¸^@§=^3>k_h§@§=` 1 œ7_=_¡ ? 1  ;5;5J 6G < G <3JL? 1 V ; I bO©=: 1 &s3“ ]‘h‘¤‘  7”%h’OŽ+*ŒŽ>&s3“  ‘ ( ;  * &

(194) * ¨‘s & $ Ž r ‘ ( Ž *{’  K V K9CbO: NDN >«_!§=§@W 1 œ7_h¡ Ee1 %G!X b G © 4G <3J?}K 13EHG oO; 6 tk: 1 CbO;=t G t 4 Y 47N o 4 [bO; G J 6GBnQN q{;=b bD;@tF;@o nFG oO\ n Y G <3< 4 <3y 1  < ‡’ &

(195) %* %'& $ $¢

(196) ‘ * ¨‘s $ &s!s s 2 s "‡‘ ]‘ * %” > %

(197) 1  I3n o GG <3J R1 JQ: YFCH;=t 4 Y vŒˆ J N]w > n3n1 ^=^A¸Ÿ@^3> z94 Y7: xCbD: NDN _h§@§=¦ 1 œ7_h^¡K 1BMT47NDN ; I3PS1 47ND4 t 4 Y 4 o :e8 : o 69: 8 oO\3;5J3: Nn bD;@t G t 4 Y 47N oO: Nen ; I bY GTn Y G < 4 |F[ G o 4 ;@<J3: 6 ; I3X :A 6 :<}oH: <bD;=tk;=o 4 5 I : 1 ‡“  ,3Ž” p” - s ’OVŽ s %4,43 s p!Žh’” *{ &  $ 88& '&

(198) * ¨Žh’ ‘  $ ‘  ” Ž ). . . . . .

(199). . . . -. 0 00. . -. /. . . -. . . . . . .

(200). œ7_ žr¡ M 15R6G oO;F>  ‡G x G  4 oh> Ee15šG Y7:=>5K 1 ?=;@<3: NG <QJ š1  G Y7Y7:0=]; 1S C Vu23G <;=t N o G [ Y7:]A t GrN : J C Vu q{;=b¢^ š „ ;=bO© NOnFG [: Nh1  < "‡‘ ]‘

(201) * % ” • ,3Ž +$ 2 ‘@’ *-, ( % ‡Ž!’]” ;±Ž'%* phŽ - / + , "0

(202) 3 >SC 15R y G bD„ G Y G <3J G Y€Y vŒˆ J N]w > nQn1 _!Ÿ=Ÿ!A _h @¦3> R% C:oD: b N _h§@§=¦ 1 œ7_hŸ¡ 1 ;};@bh> u£13TX : b 6G b N G <3J R1 aQb G <Q© X=G <J3: b 2 o GBnQn : < 10 \3: GrI3NDNO4¨G < N‹Gr6-n Y 4 <3y N oOb G oD: y@xq{;@b n bD;@t G t 4 Y 47N o 4 [‡bD; G J 6Grnn Y G <3<3: b Nh1  < ('')'  s *ŒŽh’

(203) s &

(204) * ¨‘s & $  ‘s Žh’OŽVs %]Ž ‘ s7"‡‘ ‹‘ * % ” &sQ“ +  *{‘ ( &* ‘ s > š :oDbD; 4 o v 2±RUw > n3n1 _!`3_h¦A_!`=@^3>k_h§=§@§ 1 œ7_h ¡ 01 ;=b N \> a 1e2 []\}„ G bOo  G <3J 1 ;@Y€Y7: 1 u ;=o 4 ;@< n Y G <3< 4 <QyLq{;@b 6G <5xLJ3:y=bD:: N ;rq q{bO: : J3; 6 A VG <3J3; 6 bD: F: P54 ;=< NG o K 25nkG [ :;=t N o G [ Y7: Nh1  < ( '')'  s *ŒŽh

(205) ’ s &

(206) * ¨‘s & $  ‘ s r. Ž!’DŽ s %]Ž‘ s"‡‘ ‹‘ * % ” &sQ“ +  *Œ‘ ( &

(207) * ¨‘s > 23G < šT4 : y=; v 25RUw > n3n1 ^=^Q_h¦!AD^=^@=^Q>3_h§@§Bž 1 œ7_hW¡ š1 TNDI > Ee1 %G!X b G © 4 > ?5K 1EHG oO; 6 tk:=> V 1hu ;@o~„ G < 43G <3J 21h2 ;@bD© 4 < 1} <|k<3J 4 <3y< G bDbO;B„ nFGrNDN‹G y=: N „ 4 oO\ n bD;@t G t 4 Y 47N o 4 [bO; G J 6Grn¤n Y G <3<3: b Nh/ 1  < "‡‘ ]

(208) ‘ * % ” • ,3Ž +$ 2 ‘=’ * , ( % ‡Ž!’]” ;±'Ž %* phŽ - / + , "0

(209) 3 >FC 15R y G bO„ G YS: o G Y v{ˆ J N]w > n3n1 _ žk_]A _hŸ@^3> R % CH: oO: b N _!§=§=¦ 1 œ7_h¦¡ u£1HES4 <> š1FuLG <3;5[‹\ G >S? 1 K ;@\3: < G <3J 2S1  ;@oDo N []\ G Y7© 1 K ;=Y7Y 47ND4 ;=<J3: oD:[ o 4 ;=< 2R Y7y=;rA b 4 oO\ 6-NG <3J GBn3n Y 4 [ G o 4 ;=< Nh1  < +$ 2 ‘=’ * , ( ” ‘=’ "‡‘ ]‘ * % $¢

(210) ‘ * ¨‘s&s3“ $/&s ;  $ &

(211) * ¨‘s - / + , "0 3 >‡?}C 1 EGrI36 ;@<3J G <3J u£1eTX : b 6G b NLv{ˆ J N‹w > n3n1 _!=§A_žF_=> ! R % C:oD: b N _h§@§=W 1 . . . . . . . . . . . . . . . . . . =`. /. . -. .

(212)

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