Visual Servoing from Lines
Transcription
Visual Servoing from Lines
Visual Servoing from Lines Nicolas Andreff, Bernard Espiau, Radu Horaud To cite this version: Nicolas Andreff, Bernard Espiau, Radu Horaud. Visual Servoing from Lines. [Research Report] RR-4226, INRIA. 2001. <inria-00072393> HAL Id: inria-00072393 https://hal.inria.fr/inria-00072393 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. INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE Nicolas Andreff, Bernard Espiau et Radu Horaud N° 4226 Juillet 2001 ISSN 0249-6399 ISRN INRIA/RR--4226--FR+ENG THÈME 3 apport de recherche "!$#&%('&)+*-,./10325476980$/1,'&/:.<;=):>"'&?@A03B-C-'D.?FE-#G/:'&?.H IKJMNL O+N=PAQSRUT$VWN1XZY3[\VW]_^T J ^O+O+N`(OaY[ J ]_TbN3c ]_O+YdlN:eXZcb^jfgmnN^3VZTbeKTKo5N1h N1R le1cgN[Vq^TipsTiYjr]ktqeWeZRYjTD[N1e u YvbvD^3XwVfgN=XZN1[ J NXx[ J NyT&z|{7}}j~Q3b]__NV }iQSP$}AvDYjdN:e Y3|ewN:1fb^3TYs V J RUNT^XZNV JVZ]_]k[1eYjJ K5Yj^TiXZGfc5d5N1N^O+vbNXZVZN1XWeW]kN[T$YV5YewVWDifgTifbl ^jYj O+V N1J T3NVxYjOa_Yj]_TTbN1]_TbNYvbXWvbN1vbXZ^3XZIKN1Y3JeW[ NJ T$VZVZYj^VW]_7^]_TieWeiY qJ ew]kN1[ XWJ 3^Y]_Tb_^d iN:f¡eW]TbideVZ]_^TbN1fbe1yN¢iTbR(VN£]kY e TbeWNN1XZ<^3XZ]NTbvidDXWN:ewRUN1TiT3fgVxNYN:VZfM]^3cT¤V c7J V N¡N YjeW^j_`U^[ªY_V N1J f N-fg]_TbN¢i^TbXZOa]VW]_Yj^_T]¥1N1^f qY£nivb¦ [xXZ^N1v&XNXA[^7]_^OaXxYjfgd3]_TiNYVZ]_N1Tbe1N Y]_dNTi-OYN1XWT$N§VviTbY^XwVZVW]_]_[^bT¤k YjXZIKaJ 5N«N[_^3¨T3eWVZbXW]©^3VZN19f-kY¬VW^a7 ]kJ ewD]_[ YjJ XZYN1TiYYj_]_$¥N:VW]ke|[eWYji[ ]_J T7YjNT+XxeWYj]^3_]_T£dTb^jO+9NV T$J V N+J OY3e^VWO]_^^3TsXWN1N1^°$iN1YX|VZeW]N^33TiNe§XxYjYj$TivbfXW^3dvD_^ N1 XwVZY]|N:eY3®¯ew7viO+YjXWvgVWVZ]kYj^jgVW]kfg[N:en[Vx^3Y b vb]__]]TbVnd [^3NTiVn5fg]NVWN1]_T^TiXZe1^j VxYIKVZ]J ^3]kTe=Yj[^3TDT3f VZVZXWXZ^3Y¯TikewY¬kyYVZ]K^3YT¤e c Yj_]kfbYVZN1f ^V J ]_TeW]_OAbkYVZ]^3T«YTifN±gvDN1XW]_O+NT$VZY_]_T-V J N eWvDN:[]¢D[=[Y3ewN²^jYjT«^XWV J ^3d^3TiYj&VWXZ] J N1fgXZ^T¨ ³£´$µG¶W·¸ ¹| 7]kewDYj¤eWNXZ^]_TbdDc$viXW^mnN1[\VZ]3N d3N^3ONVWXZc7_]TbN=XZNviXWN:ewN1T3VxYVZ]^3T¤c l ni¦ [xN1XK[^7^Xxfg]TDYVWN:e º ê »gÂG¼\Ów½¨ÎÊÆ¾|¼xÎ"¿§Ò3¾£å ë&È"ÀGì:Á¯Ëí¼xÂGÌjÃiç|Ä:ËÑÆ¬ÅÇÆ¬Î"ËíÈʼ ÉÊäË ìjÉ"Ì1ÓnÉ|ÈWå èÍÎ Î"¼xÆbÐ Ï ¼xËÑȯҬÓ9¿«Ó Ô Ð ¼xƬËÑÕ̬Ó9¾¯Öx¼xÆ Ð ÓwÔ Ó\ÄÂGÃ×\Ø:Äj×\Ù:ÚWÛxØK¾¯Ì¬Ü¬ËkÓnÝ Î"Ó9ÞGÓnÒ¬ÓUßAà_ÍÎ"¼xÆ Ð ÓZá(Äâ¯Ë Ðnã\ä ¼xÈwå ¾|ƬҬÎÊÓUæ7ç|Ë èé¼:å èÎ î ½¯¼xÒ¬Ì3å ï ã Î(¼xÌ:Òjç|ËÑÆ¬Î"Ëí¼ ä ìjÓnÈWå èÎ Unité de recherche INRIA Rhône-Alpes 655, avenue de l’Europe, 38330 Montbonnot-St-Martin (France) Téléphone : +33 4 76 61 52 00 — Télécopie +33 4 76 61 52 52 | |-||q q«q =£ £ ´ ´ YjTDe¯[N9VWXxY¬Yj]_Êc¬Tb^3ie¤viXbN:h ewN1T$VW^TDeMbTbNKYjvbviXW^g[ J N^3TifbYON1T$VZYj_NO+N1T3V¯Tb^b3N_N5fgN YeZewN1XW7]keWeWNO+NT$V¤7]kewbN1 vifgN:YeKX^fgXW^3eW]©NVZXZN1e Y°3VZ]i^3]&TTifg^Nie5fbXWY ^3]©v&VZNN1XZe1O+9]_eK__fgN5N²N:f enV Nh ¢D TbY]egX5Nh NKbTbewiN²X9Tbb^3TbbN-N1Nh VW_iNfgXZNKNvbV JXbN1N1h h eW^NXZT$]_°$VxYbVWN5]_^NTaV9dYNvbh ^3vDON1NNh h VWN XZ]k[°3^7i^N Xxfgfg^N:TbeTKvbNXWh N:]_Tie[fg]viN Yl N:nDe¦ [xXWN1NvbX XbN1h eW]_NTbT$^VZXZYjOVW]_N^h N:Tiee N:eA[^7^3XZfg^3TbTKN1h N1e=eW^T$VAviYXwVZ]_[b_] N1L XWN1O+NT$V ]_NTYfiYjvgVbNh N:e Y£ L Y3eWeWNXZ7]_eZewN1O+NT$V 7]_eWbN" 9T¡N &NV1cN1_N1eAvDN1XWO+NVWVWN1T3V+fgN f5YNh]_¢idTbTb]_N1XO+vbNXZT$^V«viY¡XWN1OvDYjN1X-T$VY]__Y¡_NbTiXx^jeVW]_^vbT_ieWf]N1 Yjb_Xx]_deTbvbN1XZO^N1vbT$XZV-]Nh VbfgN1h Nefg®¡XZ^f5]N:VWh N:[e^3bfbvbYkTiYjdeN£ vD]_OaYjXWYjVWd3]_NNqN1T$¨VWY¡XZN_^XW]q^fbVZYjNVW]_[^^3T ONOaV-YVWTiXxfgYjNTieW°$kYbVW] ]_^XbTiN:h O Yj_]_eW]_T7NbNTXxeW]VW^3N1T YYTiNh YjVb_N²h$VW]kYj°3_i]_f5N Nh fgN=N:Yje=iN:h eZ°$eWi] Y VZ]]N1^3T-Tie¨N1T£fgAew]_OOA^3bbkYVZN1]O+^3T«NT$°$V¯N VN±g[vK^NTih XZfg]O+]VW]_N^T$TDVxe¨Yjd3_NO+^ NYjT$_VN1e¯ewbfgXN ew_N VZY [ Y3]eK_]VbviN h YjY3XWVWew]k7[O+ivg]_NVZX ^jVWf]k°$ bbT«N VWXZ ] N1L NfgVWVWXZN5N ^3^3Xw]$V fgJ NK^d3[^^3TiO+YO+Ê YTifgN ¸ 1 ¶ " ! ´ « YeZewN1XW7]keWeWNO+N1T3VK7]_eWbN1ÊcgdNh ^3ONh VWXZ]_NqvbXZ^jmnN:[\VW]_N3c7XWN1vbXbN1h eWNT$VZYjVW]_^TfgN:efgXZ^]VWN:ecg[^7^3XZfg^3TbTKN1h N1e5fgN l ni¦ [x3NX ¯ ! ´ ¸ ¸ ¯´ P q | ¸ bg ʸ J 33 } ²N1 ^O+^NXWVZV XW-XWY]eVW]k[Y Y NT$]kVWenXxVZYj^MXZRneZ^jeWb|N§tq]]kTewitqY]keW7iN1YjXW37^N1]_TbXW3d ^]_Tb=d§====²²==§§==§§====§§==§§==²²====§§==§§==§§====§§==²²== P 3 P p^jVW]_YVZ]^3T-^¯V J ]_es^3XW=§=²=§==§=§=§==²=§=§==§=§=²==§=§=§==§=²= ~ ´ g ´ ´ " g ¸# $ |! }b o5}b]_3Tb^ XZOau Yj_N1]¥1[N1Yf keKl ^niT¦ [xlN1niXK¦ [x[3^7N^X Xxfg[^7]TD^3YXZVWfgN:]_eTiYj§VWN1=e =§§==§§==§§====²²==§§==§§====§§==§§==²²====§§==§§==§§====§§==²²== ~~ }b}b33 P} RUo5Oa]_TbY^dXZN=OaYjYj_]_d3]¥1TbN1O+f Nl T$nV i¦ ^j[xN1Y+X 'P [&s^7^Xx]_fgTb]_N TiYVZ=N1§e§==§§==§§====²²==§§==§§====§§==§§==²²====§§==§§==§§====§§==²²== %( J }b } }b}b ]k}b3eW[{ ieWeWRUp]_^T«TF^jV VWJ ]_=^N T=P §^ |=eWY+vi§_Y3]=Tb[N+§N§==ge1==§§O==^VW²²]_^==T«§§^j==|V==§§N ==[1Yj§§O+==N§§XxYª=====²²²===§§§===§§§======§§§===§§§===²²²======§§§===§§§===§§§======§§§===²²²=== 1 }b }b } RUT«V J N=]OaYdN §==§=²=§==§=§=§==²=§=§==§=§=²==§=§=§==§=²= :} )#¸ ¸ ! 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P c' d X X ^3TiewN:°$bNT$VW_cD]©95N d3]3N§V J NeWYON=^3XW]_NT$VxYVW]_^T«VZ^aV J N'P & _]TiN1eqYTif«VW^V J N1]X²vbXZ^jmnN1[VW]_^Tie1cb5N ^ VZYj]_TV J N=^_^ ]_Tbd eWgenVZNO® [^3e 1 ew]_T P ew]_T X X eW^J _gN1XWVWN²]_^VT«J ]kN=e b^jTb¯7V TbJ ^N§ ^3TiXWeKOY®XWN V J N YTbd_N1e X Pi IKJ ]_e eWgenVZNO ]ke eW]O+]__YXKVW^V J N§^3TbN§^ VxYj]_TbN1f-]?T 7 % (8¨YjTif-]©Vxe [^3e X " 1 " " " eW]T X " 1 " J N1XWN J X J §fbNv&J NTifg]_TbJ da^3T- J NV J N1XKV J N=7]kew] _N J YjJ |^¨V J N 'P &s_]TbN=v&^]_T$VZeK]_T75YJ XZfbe5^3X5^3gVnKR YjXxfbeRUT-V J N [1YJ eWN§ N fgeW]N:O+Yjvb¯_ ]]©V V cGJ N=TbN^jXZVxN=YVWV ]_^N T¨cgVWXZV ]J N=N1fg^3XZvD^N1T«XZYj VWY3]_[^N1Tie e YjXZN ^=vDYjYTD°$f bNciV §]keqXZNeWvb]_dXZT£N1eW]kNeqT$V5]kfgV NJ T$N VZ]_Y3[1Yjfb¤fg]VW^3]_X ^T£Y¨YjTDV f-NeWPa ew]_TbVWXxN:Ye[ VW]_^^jT«VW]kO[N ^gfg¢iiTiYj^a__Pb- V YVqVW^ 1 # C C C ; ?I [ P N EKI B`a ]T0[9PJEKT C J J J J J J J J ieWNN§^jviXWN:]_ewTbN1N:T3e V YjTiNfXZNV JeW^N O+fbNANvgeWV]_OAJ b[k^YT$VZVW]^3XZ^T" XWN:sewiN ©Vx[e^O+VZ^-vieYjXZ^N V J V N=eWN N1°$bN NT$Y¬VZ7]_]Y^3¤bYXq[\^VZ9]V YjVWN]_^T«[^3^jT$¨VWXZV ^J ¨N=kY¬[y^3T3VZ5XWNA^3Gvb]XZT^v&XZ^j^3VZeWYjN1VWf]_^ T«]VYjTif^V JV N1TV ]T N Å⯽¨ÅǾ ¯ ! ´ ¸ ¸ ¯´ }g Vitesses de rotation Vitesses lineaires deg/s cm/s 50 10 0 40 -10 30 -20 20 -30 10 -40 Nb iterations Nb iterations 0 -50 0 20 40 60 80 100 120 140 |]_dbXZN %i®GgN1°$bNT$VZ]_Y$Y3[\VW]_YVZ]^3T ^jgV J 160 180 200 0 20 40 60 80 100 120 140 160 180 200 N [^T$VWXZ^3]TXW^VZYVZ]^3T YjTif=V J N1TA]_T=VWXxYjTieWkYVW]_^T¨® u ^jVxYVW]_^T c _NÇVed¯YjTDf§VWXxYjTieWkYVW]_^T c XW]_d J VedK[^T$VWXZ^" Erreur 70 60 50 40 30 20 10 Nb iterations 0 0 20 40 60 80 100 120 140 160 180 200 |]_dbXZNR(b® gN1°$bNT$VZ]_Y¯Y[VW]_YVW]_^T^|V J J NT£]_TVWXxYjTDewkYVZ]^3T¤® 9J XZXZ^Xxe ]_T£^XZ]_NT$VZYjVW]_^T c We ^_]_f N A [ ^ $ T W V Z X ^ M _ ] £ T W X ^ Z V j Y W V _ ] ^ £ T j Y i T « f V J J _]TiN d\cD^T-V N=]_OaYjd3N²_]_TbN§vbXW^mnN1[VW]_^Tie cÊfgj^ VWVWN1f«_]TiN dKYjTDf-^3TV N=kYeWNX ewv&^jVv&^3eW]VW]_^T c fbY3e N:f«]_TbN d Position 3D 512 Z -0.344 ⊕ 410 307 -0.506 z y 205 -0.667 x -0.195 102 -0.040 -1.0082 Y -0.9741 0 0 51 102 154 205 256 307 358 410 461 512 0.114 -0.9400 X J J I J J _]|T«]_dV bJ XZN=N]_Oa:bYj®dN*7N:c °3NiÇVeNd T$YVW]kTiYjfGY]_T«[VWV]_¬J YjN VW]_P ^& Tew^vi¤Y3V [N*N²c[XZ^]_d T$J VWVeXZd^ &]T-XW^VZYjVW]_^TYjTDfaV NT]_TVZXZYTieW_YjVW]_^T¤® XxYmnN:[\VZ^XZ^¤V N VWXZ] N1fgXZ^T ½¯½ Æ6wKxoyry\× }3} sp k#l6n=m9mhnrk#s6n=l^pstiHmhq s l6itn sti l Vitesses lineaires Vitesses de rotation cm/s deg/s 20 50 10 40 0 30 -10 -20 20 -30 10 -40 Nb iterations Nb iterations 0 -50 0 20 40 60 80 100 120 140 160 180 |]_dbXZNs3®.7]_OAbVZYTbN^3ieY3[\VZ]YVZ]^3T^V J 200 0 20 40 60 80 100 120 140 160 180 200 N[^3T$VWXZ^ ]_TXZ^jVxYVZ]^3TYjTifV J N1T]_TVZXZYTiewkYVZ]^3T¤® u ^VZYVZ]^3TZc_NÇVrdYjTif VZXZYTiewkYVZ]^3T c XW]_d J Vrd [^T$VWXZ^" Erreur 70 60 50 40 30 20 10 Nb iterations 0 0 20 40 60 80 100 120 140 160 180 200 J N[^T$VZXW^3|]_TXW^VZYjVW]_^TJ YjTifsV J NT]T VZXZYTiewkYVZ]^3T¤® 9J XZXW^3XZe ]_T ^3XW]_NT$VxYVW]_^T j ^ 5 V J cÊew^3]kf«]_TbN dcb^T-V N=]OaYjd3N§]_TbN=vbXZ^jmnN:[\VW]_^TDe cÊfg^jVWVWN:f-_]_TbN d YTif-^T-V N=kYeWNXeWvD^V vD^$ew]VW]_^Tc fiYe N1f-]_TbNd\ |]_dbXZN£:}b®7]_OAbVZYTbN^3ie Y[VW]_YVW]_^T zxy Position 3D 512 Z -0.343 ⊕ 410 -0.507 307 z y 205 -0.671 x -0.202 102 -0.044 -0.9971 Y -0.9605 0 0 51 102 154 205 256 307 358 410 461 512 0.114 -0.9239 X J J I J ZV|XW]_] dJ bN1XZfbNXW^31T-Pi®]_T«V J 7N=]O]_OabYjVZdYjTiN*Nc ^NDÇeVed YY[TiVW]_fY]_VWT«]_^V T J N ^P=& V ewNviY3[[^3N*T3VZcXZXW]_^3d J Ve]_Td XW^VZYjVW]_^TYjTDfV N1T]TVWXxYjTieW_YjVW]_^T¤® XZYjmnN1[\VZ^XZ^j=V N Å⯽¨ÅǾ ¯ ! 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