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Submitted on 14 Nov 2009
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Fabrice Lamarche
To cite this version:
Fabrice Lamarche. Humanoïdes virtuels, réaction et cognition : une architecture pour leur autonomie..
Modélisation et simulation. Université Rennes 1, 2003. Français. �tel-00432175�
N Ordre : de la thèse
2966
THÈSE présentée
DEVANT L'UNIVERSITÉ DE RENNES 1
Mention : INFORMATIQUE pour obtenir
le grade de : DOCTEUR DE L'UNIVERSITÉ RENNES 1
PAR
LAMARCHE Fabrice Équipe d'accueil : SIAMES, IRISA, Rennes École doctorale : MATISSE
Composante universitaire : INSA de Rennes
TITRE DE LA THÈSE
Humanoïdes virtuels, réaction et cognition : une architecture pour leur autonomie
Soutenue le 19 décembre 2003 devant la commission d'Examen COMPOSITION DU JURY
M. : Daniel HERMAN Président du jury MM. : Marc CAVAZZA Rapporteurs
Ronan BOULIC
MM. : Jean Paul LAUMOND Examinateurs Stéphane DONIKIAN
Bruno ARNALDI
˚
✑ ✒ ✔ ✖ ✘ ✚ ✜ ✣ ✥ ✚ ✔ ★ ✪✥ ✭ ✣ ✔ ✘ ✪✯ ✔ ✣ ✖ ✘ ✘ ✱ ✣ ✥ ✳ ✖ ✥ ✥ ✱ ✣ ✥ ✶ ✸✺✼ ✾ ✼ ❁ ❂ ✣ ✚ ✳ ✸✒ ✥ ✳ ✖ ✔ ✚ ✪✜ ✒ ✸✪✯ ✔ ✣ ❇ ✣ ✘ ✚ ✭ ✖ ✘ ✥ ✸✣ ✳ ✔ ★ ❋ ✣ ✚
❁ ✼ ❂ ● ■ ❁ ❑ ❋ ✺✖ ✪ ✣ ✒ ✸ ✺★ ✜ ✜ ✖ ✥ ✪★ ✘ ✭ ✣ ✚ ✔ ✖ ❙ ✖ ✪✸✸✣ ✔ ❑ ✔ ✣ ✘ ✜ ★ ✘ ✚ ✔ ✣ ✔ ✣ ✚ ✭ ✪✥ ✜ ✒ ✚ ✣ ✔ ✖ ❙ ✣ ✜ ✭ ✣ ✘ ★ ❇ ❨ ✔ ✣ ✒ ✥ ✣ ✥ ✳ ✣ ✔ ✥ ★ ✘ ✘ ✣ ✥ ❭ ❪ ✣ ✥
✣ ❴ ✳ ✱ ✔ ✪✣ ✘ ✜ ✣ ✥ ✭ ✪❙ ✣ ✔ ✥ ✣ ✥ ✘ ✺★ ✘ ✚ ❜ ✖ ✪✚ ❞ ✒ ✣ ✔ ✣ ✘ ❜★ ✔ ✜ ✣ ✔ ❇ ★ ✘ ❢ ★ ❣ ✚ ✳ ★ ✒ ✔ ✸✖ ✔ ✣ ✜ ✐ ✣ ✔ ✜ ✐ ✣ ✣ ✚ ✸✺✪✘ ✚ ✱ ✔ ❦ ✚ ❞ ✒ ✣ ❋ ✣ ✳ ★ ✔ ✚ ✣ ✶
✸ ✺✖ ✘ ✪❇ ✖ ✚ ✪★ ✘ ✜ ★ ❇ ✳ ★ ✔ ✚ ✣ ❇ ✣ ✘ ✚ ✖ ✸✣ ✣ ✚ ✶ ✸✖ ✔ ✱ ✖ ✸✪✚ ✱ ❙ ✪✔ ✚ ✒ ✣ ✸✸✣ ✣ ✘ ❢ ✱ ✘ ✱ ✔ ✖ ✸ ❑ ❇ ❦ ❇ ✣ ✥ ✪ ❑ ❋ ✣ ✭ ★ ✪✥ ❨ ✪✣ ✘ ✸ ✺✖ ✭ ❇ ✣ ✚ ✚ ✔ ✣ ❑
❇ ✖ ✜ ✒ ✔ ✪★ ✥ ✪✚ ✱ ❇ ✣ ✳ ★ ✒ ✥ ✥ ✣ ❜✔ ✱ ❞ ✒ ✣ ❇ ❇ ✣ ✘ ✚ ✶ ✥ ★ ✔ ✚ ✪✔ ✭ ✣ ❇ ★ ✘ ✭ ★ ❇ ✖ ✪✘ ✣ ✭ ✣ ✔ ✣ ✜ ✐ ✣ ✔ ✜ ✐ ✣ ✳ ★ ✒ ✔ ✖ ✸✸✣ ✔ ❙ ★ ✪✔ ✜ ✣ ❞ ✒ ✪ ✥ ✣
✳ ✖ ✥ ✥ ✣ ✖ ✪✸✸✣ ✒ ✔ ✥ ❭
■ ✘ ✳ ✔ ✣ ❇ ✪✣ ✔ ✸✪✣ ✒ ❑ ❋ ✣ ✥ ★ ✒ ✐ ✖ ✪✚ ✣ ✔ ✖ ✪✥ ✔ ✣ ❇ ✣ ✔ ✜ ✪✣ ✔ ② ✔ ✒ ✘ ★ ❂ ✔ ✘ ✖ ✸✭ ✪ ✣ ✚ ❁ ✚ ✱ ✳ ✐ ✖ ✘ ✣ ✑ ★ ✘ ✪③ ✪✖ ✘ ✳ ★ ✒ ✔ ❇ ✺✖ ❙ ★ ✪✔
✣ ✘ ✜ ✖ ✭ ✔ ✱ ❑ ✜ ★ ✘ ✥ ✣ ✪✸✸✱ ✣ ✚ ✥ ★ ✒ ✚ ✣ ✘ ✒ ✭ ✒ ✔ ✖ ✘ ✚ ✜ ✣ ✥ ✚ ✔ ★ ✪✥ ✖ ✘ ✘ ✱ ✣ ✥ ✭ ✣ ✔ ✣ ✜ ✐ ✣ ✔ ✜ ✐ ✣ ✥ ✪✘ ✚ ✣ ✘ ✥ ✣ ✥ ✥ ✒ ✔ ✸ ✺✖ ✘ ✪❇ ✖ ✚ ✪★ ✘ ✜ ★ ❇ ✳ ★ ✔ ⑤
✚ ✣ ❇ ✣ ✘ ✚ ✖ ✸✣ ❭ ⑦ ✔ ⑧ ✜ ✣ ✶ ❙ ★ ✒ ✥ ❑ ❋ ✺✖ ✪ ✣ ✒ ✸ ✺★ ✜ ✜ ✖ ✥ ✪★ ✘ ✭ ✣ ✚ ✔ ✖ ❙ ✖ ✪✸✸✣ ✔ ✥ ✒ ✔ ✒ ✘ ✥ ✒ ❋ ✣ ✚ ❞ ✒ ✪ ❇ ✣ ✚ ✪✣ ✘ ✚ ✳ ✖ ✔ ✚ ✪✜ ✒ ✸✪✯ ✔ ✣ ❇ ✣ ✘ ✚ ✶
✜ ❷ ✒ ✔ ✭ ✣ ✳ ✒ ✪✥ ✭ ✣ ✘ ★ ❇ ❨ ✔ ✣ ✒ ✥ ✣ ✥ ✖ ✘ ✘ ✱ ✣ ✥ ❭ ❸ ★ ✒ ✥ ❇ ✺✖ ❙ ✣ ❺ ✳ ✣ ✔ ❇ ✪✥ ✭ ✣ ✔ ✱ ✖ ✸✪✥ ✣ ✔ ✒ ✘ ✔ ❦ ❙ ✣ ✭ ✺✣ ✘ ❜ ✖ ✘ ✚ ✖ ❻ ✖ ✘ ✚ ✭ ✱ ❨ ✒ ✚ ✱
✖ ❙ ✣ ✜ ✒ ✘ ❋ ✣ ✒ ✘ ★ ❇ ❇ ✱ ✸✺❂ ✔ ✜ ✐ ✣ ✭ ✒ ❪ ✖ ✳ ✪✚ ✖ ✪✘ ✣ ② ✸★ ★ ✭ ❼ ❽ ✐ ✪✸✪✳ ✳ ✣ ❾ ✸✔ ✪✜ ✐ ❿ ❞ ✒ ✪ ✖ ❜ ✖ ✪✚ ✳ ✖ ✔ ✚ ✪ ✭ ✣ ✥ ✳ ✔ ✣ ❇ ✪✣ ✔ ✥ ❋ ✣ ✒ ❴
❇ ✣ ✚ ✚ ✖ ✘ ✚ ✣ ✘ ✥ ✜ ✯ ✘ ✣ ✭ ✣ ✥ ➀ ✳ ✣ ✔ ✥ ★ ✘ ✘ ✖ ❢ ✣ ✥ ✪✘ ✚ ✣ ✸✸✪❢ ✣ ✘ ✚ ✥ ➀ ❼❋ ✣ ✘ ✣ ❇ ✺✣ ✘ ❙ ✖ ✘ ✚ ✣ ✳ ✖ ✥ ❑ ❇ ✖ ✪✥ ✜ ✺✣ ✥ ✚ ❙ ✔ ✖ ✪❿ ❭
➃ ✣ ❙ ★ ✒ ✭ ✔ ✖ ✪✥ ✖ ✒ ✥ ✥ ✪ ✔ ✣ ❇ ✣ ✔ ✜ ✪✣ ✔ ✾ ★ ✘ ✖ ✘ ② ★ ✒ ✸✪✜ ✣ ✚ ● ✖ ✔ ✜ ❪ ✖ ❙ ✖ ❺ ❺ ✖ ❞ ✒ ✪ ★ ✘ ✚ ✖ ✜ ✜ ✣ ✳ ✚ ✱ ✥ ✭ ✣ ✔ ✖ ✳ ✳ ★ ✔ ✚ ✣ ✔ ✜ ✣ ✚ ✚ ✣
✚ ✐ ✯ ✥ ✣ ✣ ✚ ✭ ★ ✘ ✜ ✭ ✣ ❇ ✺✖ ✜ ✜ ★ ✔ ✭ ✣ ✔ ✭ ✣ ✸✣ ✒ ✔ ✚ ✣ ❇ ✳ ✥ ➅ ❇ ✣ ✔ ✜ ✪ ✶ ➃ ✣ ✖ ✘ ❽ ✖ ✒ ✸ ➆ ✖ ✒ ❇ ★ ✘ ✭ ❞ ✒ ✪ ✖ ✖ ✜ ✜ ✣ ✳ ✚ ✱ ✭ ✣ ❜ ✖ ✪✔ ✣ ✳ ✖ ✔ ✚ ✪✣
✭ ✣ ❇ ★ ✘ ❋ ✒ ✔ ❻ ➅ ❇ ✣ ✔ ✜ ✪ ✶ ✑ ✖ ✘ ✪✣ ✸ ➈ ✣ ✔ ❇ ✖ ✘ ✭ ✺✖ ❙ ★ ✪✔ ✳ ✔ ✱ ✥ ✪✭ ✱ ❇ ★ ✘ ❋ ✒ ✔ ❻ ❑ ✜ ✣ ❜❣ ✚ ✒ ✘ ✔ ✱ ✣ ✸ ✳ ✸✖ ✪✥ ✪✔ ❭
➃ ✣ ✥ ★ ✒ ✐ ✖ ✪✚ ✣ ✔ ✣ ❇ ✣ ✔ ✜ ✪✣ ✔ ✸ ✺✣ ✘ ✥ ✣ ❇ ❨ ✸✣ ✭ ✣ ✥ ❇ ✣ ❇ ❨ ✔ ✣ ✥ ★ ✒ ✣ ❴ ⑤❇ ✣ ❇ ❨ ✔ ✣ ✥ ✭ ✒ ✳ ✔ ★ ❋ ✣ ✚ ❁ ✼ ❂ ● ■ ❁ ❞ ✒ ✣ ❋ ✺✖ ✪ ✣ ✒
❢ ✔ ✖ ✘ ✭ ✳ ✸✖ ✪✥ ✪✔ ✶ ✜ ➊ ✚ ★ ❻ ✣ ✔ ❭ ✼✸✥ ❇ ✺★ ✘ ✚ ✳ ✖ ✔ ✚ ✪✜ ✒ ✸✪✯ ✔ ✣ ❇ ✣ ✘ ✚ ✥ ★ ✒ ✚ ✣ ✘ ✒ ✭ ✒ ✔ ✖ ✘ ✚ ✸✖ ✔ ✱ ✭ ✖ ✜ ✚ ✪★ ✘ ✭ ✣ ✜ ✣ ✭ ★ ✜ ✒ ❇ ✣ ✘ ✚ ❞ ✒ ✪
❜❣ ✚ ✳ ✖ ✔ ❜★ ✪✥ ✭ ★ ✒ ✸★ ✒ ✔ ✣ ✒ ✥ ✣ ❭ ➆ ✣ ✒ ✔ ✖ ✜ ✜ ✒ ✣ ✪✸ ✖ ✒ ✥ ✣ ✪✘ ✭ ✒ ✳ ✔ ★ ❋ ✣ ✚ ✖ ✪✘ ✥ ✪ ❞ ✒ ✣ ✸✖ ❨ ★ ✘ ✘ ✣ ✐ ✒ ❇ ✣ ✒ ✔ ✔ ✱ ❢ ✘ ✖ ✘ ✚ ✭ ✖ ✘ ✥ ✸✣ ✥
✜ ★ ✒ ✸★ ✪✔ ✥ ❑ ❇ ✖ ✪✥ ✖ ✒ ✥ ✥ ✪ ✣ ✘ ✭ ✣ ✐ ★ ✔ ✥ ❑ ❇ ✺★ ✘ ✚ ★ ➍ ✣ ✔ ✚ ✒ ✘ ✜ ✖ ✭ ✔ ✣ ✭ ✣ ✚ ✔ ✖ ❙ ✖ ✪✸ ✪✭ ✱ ✖ ✸ ✭ ✒ ✔ ✖ ✘ ✚ ✜ ✣ ✥ ✭ ✣ ✔ ✘ ✪✯ ✔ ✣ ✥ ✖ ✘ ✘ ✱ ✣ ✥ ❭
② ✔ ✒ ✘ ★ ❑ ❁ ✚ ✱ ✳ ✐ ✖ ✘ ✣ ❑ ⑦ ✣ ★ ✔ ❢ ✣ ✥ ❑ ➎ ✐ ✪✣ ✔ ✔ ❻ ❑ ➏ ✖ ✭ ✪❑ ❂ ✸✖ ✪✘ ❑ ❂ ✘ ✖ ✚ ✐ ★ ✸✣ ❑ ❋ ✺✣ ✥ ✳ ✯ ✔ ✣ ✳ ★ ✒ ❙ ★ ✪✔ ✜ ★ ✘ ✚ ✪✘ ✒ ✣ ✔ ✶ ✚ ✔ ✖ ❙ ✖ ✪✸✸✣ ✔
✖ ❙ ✣ ✜ ❙ ★ ✒ ✥ ❭ ✼✸ ✣ ✥ ✚ ✒ ✘ ✣ ✳ ✣ ✔ ✥ ★ ✘ ✘ ✣ ❞ ✒ ✣ ✸✺★ ✘ ✘ ✣ ✜ ✪✚ ✣ ✳ ✖ ✥ ✖ ✥ ✥ ✣ ❺ ➐ ❁ ✚ ✱ ✳ ✐ ✖ ✘ ✣ ● ✱ ✘ ✖ ✔ ✭ ✖ ✪✥ ❭ ● ✣ ✔ ✜ ✪ ✶ ✚ ★ ✪ ✳ ★ ✒ ✔ ✚ ★ ✘
✚ ✔ ✖ ❙ ✖ ✪✸ ❜ ★ ✔ ❇ ✪✭ ✖ ❨ ✸✣ ❑ ✚ ✖ ✭ ✪✥ ✳ ★ ✘ ✪❨ ✪✸✪✚ ✱ ❑ ✚ ✖ ✔ ✱ ✖ ✜ ✚ ✪❙ ✪✚ ✱ ➅ ❋ ✣ ✜ ✔ ★ ✪✥ ❞ ✒ ✣ ❋ ✣ ❇ ✣ ✥ ★ ✒ ❙ ✪✣ ✘ ✭ ✔ ✖ ✪ ✸★ ✘ ❢ ✚ ✣ ❇ ✳ ✥ ✭ ✺✼ ❇ ✖ ❢ ✪✘ ✖
✣ ✚ ✭ ✣ ✜ ✣ ✥ ✘ ✒ ✪✚ ✥ ❨ ✸✖ ✘ ✜ ✐ ✣ ✥ ✳ ✖ ✥ ✥ ✱ ✣ ✥ ❭❭❭ ❂ ✔ ✔ ✪❙ ✣ ✸✖ ❇ ✣ ✘ ✚ ✪★ ✘ ✥ ✳ ✱ ✜ ✪✖ ✸✣ ✖ ✒ ❴ ✐ ✖ ❨ ✪✚ ✖ ✘ ✚ ✥ ✣ ✚ ✣ ❴ ⑤✐ ✖ ❨ ✪✚ ✖ ✘ ✚ ✥ ✭ ✒ ❨ ✒ ✔ ✣ ✖ ✒
✭ ✒ ❨ ★ ✘ ✐ ✣ ✒ ✔ ➐ ✾ ✪✜ ✐ ✖ ✔ ✭ ❑ ⑦ ➑ ✣ ✘ ★ ✸✖ ➎ ✒ ✔ ❨ ★ ❑ ➒ ✪✜ ★ ❨ ★ ✒ ✪✸✸✣ ❑ ✸✺✖ ❨ ❨ ✱ ✾ ★ ❇ ✣ ✚ ✸✣ ✳ ✣ ✚ ✪✚ ✘ ★ ✒ ❙ ✣ ✖ ✒ ❁ ✣ ❨ ❭ ➃ ✣ ✥ ★ ✒ ✐ ✖ ✪✚ ✣
❞ ✒ ✣ ✜ ✣ ❨ ✒ ✔ ✣ ✖ ✒ ❢ ✖ ✔ ✭ ✣ ✚ ★ ✒ ❋ ★ ✒ ✔ ✥ ✜ ✣ ✚ ✚ ✣ ✳ ✣ ✚ ✪✚ ✣ ✖ ❇ ❨ ✪✖ ✘ ✜ ✣ ❞ ✒ ✪ ❜ ✖ ✪✚ ✥ ★ ✘ ✜ ✐ ✖ ✔ ❇ ✣ ✣ ✚ ✥ ✖ ✔ ✱ ✳ ✒ ✚ ✖ ✚ ✪★ ✘ ❭ ● ★ ✘ ✥ ✪✣ ✒ ✔
➃ ✣ ➍ ❑ ✚ ★ ✘ ✜ ★ ✚ ✱ ❨ ✣ ✸✸✣ ✭ ✣ ✥ ✜ ✐ ✖ ❇ ✳ ✥ ❇ ✣ ❇ ✖ ✘ ❞ ✒ ✣ ✖ ✒ ✚ ✖ ✘ ✚ ❞ ✒ ✣ ✚ ✣ ✥ ✣ ❴ ✳ ✔ ✣ ✥ ✥ ✪★ ✘ ✥ ❨ ★ ✔ ✭ ✣ ✸✖ ✪✥ ✣ ✥ ➅ ✜ ✣ ❜❣ ✚ ✒ ✘ ✳ ✸✖ ✪✥ ✪✔
✭ ✣ ➀ ❨ ★ ✥ ✥ ✣ ✔ ➀ ✖ ❙ ✣ ✜ ✚ ★ ✪ ❭ ❾ ✘ ✣ ❇ ✣ ✘ ✚ ✪★ ✘ ✳ ★ ✒ ✔ ⑦ ✒ ✪✸✸✱ ✭ ★ ✘ ✚ ❋ ✺✖ ✭ ★ ✔ ✣ ✸✣ ✭ ✱ ❨ ★ ✔ ✭ ✣ ❇ ✣ ✘ ✚ ✭ ✺✪✭ ✱ ✣ ✥ ❼✸✣ ✚ ✣ ✔ ❇ ✣ ✘ ✺✣ ✥ ✚
✳ ✖ ✥ ✖ ✥ ✥ ✣ ❺ ❜★ ✔ ✚ ❿ ❑ ✳ ★ ✒ ✔ ⑦ ✸★ ✒ ❺ ✖ ✪✸✸✣ ✳ ★ ✒ ✔ ✜ ✣ ✥ ✥ ★ ✘ ✥ ❞ ✒ ✪ ★ ✘ ✚ ❜ ✖ ✪✚ ✥ ★ ✘ ✥ ✒ ✔ ✘ ★ ❇ ❑ ✳ ★ ✒ ✔ ● ✖ ✔ ✜ ★ ✭ ★ ✘ ✚ ✸✺✖ ✜ ✜ ✣ ✘ ✚
✪✚ ✖ ✸✪✣ ✘ ✔ ✱ ✜ ✐ ✖ ✒ ➍ ✣ ✸✣ ✜ ❷ ✒ ✔ ❑ ✳ ★ ✒ ✔ ● ✖ ✔ ➑ ✖ ✘ ❑ ✣ ✘ ✜ ★ ✔ ✣ ✒ ✘ ❜★ ✒ ✭ ✒ ✜ ★ ✭ ✣ ❑ ✳ ★ ✒ ✔ ● ✖ ✚ ✐ ✪✣ ✒ ❑ ✼ ✥ ✖ ✣ ✚ ✸✣ ✒ ✔ ✥ ✣ ✘ ❜ ✖ ✘ ✚ ✥ ❑
❞ ✒ ✣ ✸✸✣ ❨ ✣ ✸✸✣ ❜ ✖ ❇ ✪✸✸✣ ❑ ✳ ★ ✒ ✔ ❁ ✖ ❇ ❻ ③ ✣ ✣ ✳ ❺ ✣ ✘ ❑ ✳ ★ ✒ ✔ ❽ ✪✣ ✔ ✔ ✣ ❂ ✘ ✚ ★ ✪✘ ✣ ❑ ❋ ✖ ❇ ✖ ✪✥ ✶ ✜ ★ ✒ ✔ ✚ ✭ ✣ ❨ ✸✖ ❢ ✒ ✣ ✥ ❑ ✳ ★ ✒ ✔ ✸✣ ✥
➀ → ✸✸✣ ✥ ✭ ✣ ✸✖ ✜ ✖ ❜✣ ✚ ✺➀ ❑ ✭ ★ ✘ ✚ ✸✣ ✥ ❢ ✔ ✖ ✘ ✭ ✥ ✜ ✖ ❜✱ ✥ ❇ ✺★ ✘ ✚ ✥ ✖ ✒ ❙ ✱ ✥ ✘ ★ ❇ ❨ ✔ ✣ ✭ ✣ ❜ ★ ✪✥ ✭ ✒ ✥ ★ ❇ ❇ ✣ ✪✸ ❞ ✒ ✪ ❇ ✣ ❇ ✖ ✘ ❞ ✒ ✖ ✪✚ ❑
✳ ★ ✒ ✔ ❁ ★ ✳ ✐ ✪✣ ❑ ✭ ★ ✘ ✚ ✸✣ ✳ ✒ ✘ ✜ ✐ ❇ ★ ✚ ✪❙ ✣ ✸✣ ✥ ✚ ✔ ★ ✒ ✳ ✣ ✥ ❑ ✳ ★ ✒ ✔ ■ ❙ ✣ ✸❻ ✘ ✣ ✣ ✚ ❪ ✖ ✚ ✐ ✣ ✔ ✪✘ ✣ ❑ ✭ ✣ ✥ ✚ ★ ✳ ✥ ✭ ✣ ✥ ✣ ✜ ✔ ✱ ✚ ✖ ✪✔ ✣ ✥ ❑
✳ ★ ✒ ✔ ❽ ✖ ✥ ✜ ✖ ✸✣ ➆ ✖ ✒ ✔ ✣ ✘ ✚ ❑ ✒ ✘ ✣ ❨ ✪❨ ✸✪★ ✚ ✐ ✱ ✜ ✖ ✪✔ ✣ ✔ ✣ ❇ ✖ ✔ ❞ ✒ ✖ ❨ ✸✣ ✚ ✖ ✘ ✚ ✳ ✖ ✔ ✥ ★ ✘ ✚ ✔ ✖ ❙ ✖ ✪✸ ❞ ✒ ✣ ✳ ★ ✒ ✔ ✥ ✣ ✥ ❞ ✒ ✖ ✸✪✚ ✱ ✥
✐ ✒ ❇ ✖ ✪✘ ✣ ✥ ❑ ✳ ★ ✒ ✔ ➆ ★ ➣✜ ❑ ✚ ✒ ✖ ✥ ✥ ✖ ✒ ❙ ✱ ❇ ★ ✘ ✖ ↔ ✜ ✐ ✣ ✭ ✣ ✚ ✐ ✯ ✥ ✣ ❑ ✳ ★ ✒ ✔ ② ✖ ✸✭ ★ ✒ ❑ ❇ ★ ✘ ✥ ✪✣ ✒ ✔ ✪✭ ✱ ✣ ❑ ✳ ★ ✒ ✔ ⑦ ✔ ✪❺ ❺ ✸❻ ❑
✥ ✪ ✒ ✘ ❋ ★ ✒ ✔ ❋ ✺✖ ✪ ❨ ✣ ✥ ★ ✪✘ ✭ ✺✒ ✘ ❢ ✔ ✖ ✳ ✐ ✪✥ ✚ ✣ ❑ ✜ ✺✣ ✥ ✚ ✚ ★ ✪ ❞ ✒ ✣ ❋ ✣ ✭ ✱ ❨ ✖ ✒ ✜ ✐ ✣ ✔ ✖ ✪❑ ✳ ★ ✒ ✔ ➃ ✒ ✸✪✖ ✘ ❑ ❇ ★ ✘ ❨ ✪✘ ➊ ❇ ✣ ✱ ✚ ✣ ✔ ✘ ✣ ✸
✖ ❙ ✣ ✜ ❞ ✒ ✪ ❋ ✺✣ ✥ ✳ ✯ ✔ ✣ ✳ ★ ✒ ❙ ★ ✪✔ ✔ ✣ ✚ ✔ ✖ ❙ ✖ ✪✸✸✣ ✔ ✒ ✘ ❋ ★ ✒ ✔ ❑ ✘ ★ ✥ ✳ ✔ ✪✥ ✣ ✥ ✭ ✣ ❨ ✣ ✜ ❇ ✣ ❇ ✖ ✘ ❞ ✒ ✣ ✘ ✚ ❼✚ ★ ✘ ✜ ★ ✭ ✣ ✖ ✒ ✥ ✥ ✪❿ ❑ ✳ ★ ✒ ✔
❇ ★ ✘ ❇ ★ ✔ ✖ ✸ ❙ ★ ✒ ✥ ✣ ✘ ✔ ✣ ❇ ✣ ✔ ✜ ✪✣ ❑ ❇ ✖ ✚ ❦ ✚ ✣ ✖ ✒ ✥ ✥ ✪ ❼ ✜ ★ ❇ ❇ ✣ ❞ ✒ ★ ✪❑ ✪✸ ✘ ✺✣ ✥ ✚ ❋ ✖ ❇ ✖ ✪✥ ✚ ✔ ★ ✳ ✚ ✖ ✔ ✭ ❿ ❭ ❾ ✘ ✳ ✣ ✚ ✪✚ ❇ ★ ✚
✳ ★ ✒ ✔ ❇ ✣ ✥ ✳ ✖ ✔ ✣ ✘ ✚ ✥ ❑ ❙ ★ ✒ ✥ ✖ ❙ ✣ ❺ ✣ ✒ ✳ ✣ ✒ ✔ ✭ ✣ ❇ ★ ✘ ✭ ✱ ✳ ✖ ✔ ✚ ✳ ★ ✒ ✔ ✸✖ ❜✖ ✜ ✒ ✸✚ ✱ ❑ ✜ ✺✣ ✥ ✚ → ✘ ✪ ❑ ❋ ✣ ✥ ✒ ✪✥ ✭ ✪✳ ✸➊ ❇ ✱ ❑ ❙ ★ ✒ ✥
✳ ★ ✒ ❙ ✣ ❺ ❦ ✚ ✔ ✣ ✔ ✖ ✥ ✥ ✒ ✔ ✱ ✥ ❭ ➃ ✺✱ ✚ ✖ ✪✥ ✐ ✣ ✒ ✔ ✣ ✒ ❴ ✭ ✣ ❙ ★ ✚ ✔ ✣ ✥ ★ ✒ ✔ ✪✔ ✣ ✸✣ ❋ ★ ✒ ✔ ✭ ✣ ❇ ✖ ✥ ★ ✒ ✚ ✣ ✘ ✖ ✘ ✜ ✣ ❭ ■ ✘ → ✘ ❑ ✭ ✖ ✘ ✥ ❇ ★ ✘
✐ ✖ ❨ ✪✚ ✒ ✭ ✣ ✭ ✣ ❢ ✖ ✔ ✭ ✣ ✔ ✸✣ ❇ ✣ ✪✸✸✣ ✒ ✔ ✳ ★ ✒ ✔ ✸✖ → ✘ ❑ ❇ ✪✸✸✣ ❨ ✪✥ ★ ✒ ✥ ✶ ✼✥ ✖ ❨ ➆ ❑ ✸ ✺✒ ✘ ✣ ✭ ✣ ✥ ✥ ✣ ✒ ✸✣ ✥ ✳ ✣ ✔ ✥ ★ ✘ ✘ ✣ ✥ ❞ ✒ ✪ ✥ ★ ✪✚
✜ ✖ ✳ ✖ ❨ ✸✣ ✭ ✣ ❇ ✣ ✚ ✚ ✔ ✣ ✣ ✘ ✣ ❴ ✣ ✔ ❢ ✒ ✣ ✸✣ ✜ ★ ✚ ✱ ✜ ✔ ✱ ✖ ✚ ✪❜ ✭ ✺✒ ✘ ✚ ✔ ✖ ❙ ✖ ✪✸ ❞ ✒ ✪ ❇ ✣ ✳ ✔ ✣ ✘ ✭ ❨ ✣ ✖ ✒ ✜ ★ ✒ ✳ ❼✚ ✔ ★ ✳ ✂ ❿ ✭ ✣ ✚ ✣ ❇ ✳ ✥ ❭
