30.07.2013 Views

Randomized Kinodynamic Planning Steven M. LaValle James J ...

Randomized Kinodynamic Planning Steven M. LaValle James J ...

Randomized Kinodynamic Planning Steven M. LaValle James J ...

SHOW MORE
SHOW LESS

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

¢¡¤£¦¥¨§©¥£¦§¥¦£¦¡¤©¡¤£¨£¨£¦<br />

¨<br />

<br />

¤ <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¤¨¤<br />

¨<br />

¦¦¦<br />

¦¨¤<br />

¤<br />

<br />

<br />

¨¦¦¨<br />

<br />

¦¦¨<br />

¨¦¦<br />

¤¤<br />

¦¦¨<br />

<br />

<br />

¤


¡ ££¢¥¤§¥§¦¦¨¢§£<br />

£ <br />

©<br />

¦¦ <br />

<br />

¨¤ ¤ <br />

<br />

¤<br />

¤¦<br />

¤<br />

<br />

© ¨¨<br />

<br />

¥<br />

<br />

© ¨<br />

<br />

<br />

<br />

¨<br />

¤<br />

¥ <br />

¤<br />

¤ <br />

§<br />

£<br />

¤<br />

¤ <br />

<br />

£ <br />

<br />

<br />

<br />

© ¤ ¨ ¦<br />

£¤ <br />

<br />

© <br />

<br />

¥ <br />

<br />

<br />

<br />

¦ <br />

<br />

¤<br />

<br />

<br />

<br />

<br />

<br />

<br />

¦¨§¦<br />

<br />

¥<br />

<br />

<br />

<br />

<br />

¥ <br />

¥<br />

¥¥


¡ ¨ © <br />

<br />

¤ © ¦<br />

¤<br />

<br />

<br />

<br />

£¢ <br />

<br />

<br />

¥¦ ¥¤ ¤<br />

©<br />

¨ <br />

<br />

¤<br />

£<br />

¥ <br />

<br />

¦ ¦§¦¨ <br />

<br />

¦ £<br />

¨<br />

¨ ¦¦©¤ ¤<br />

<br />

¦£ <br />

<br />

<br />

¤<br />

¨ <br />

<br />

§<br />

<br />

¡¦<br />

<br />

¤ <br />

<br />

¦


¡ <br />

¥<br />

<br />

<br />

<br />

<br />

£ ¤<br />

¥<br />

¢£¢<br />

<br />

¨ ¤¦ <br />

¢<br />

¤ © © ¤¤¢ © <br />

<br />

¦¥¨§¤<br />

<br />

¦ <br />

©¥¨©¢<br />

£¢<br />

¢¨<br />

¢¦¤¢ ¢¡¢¥ ¢¡¤<br />

<br />

©¤¡¡<br />

¤<br />

<br />

¢ <br />

<br />

¦¨¤<br />

<br />

<br />

¨¨<br />

¤¦ £ ¤<br />

<br />

£ §¦ ¨<br />

<br />

© ¦ <br />

<br />

¤£<br />

<br />

¤ <br />

<br />

¦<br />

© ¦ ¤ © <br />

<br />

¤¨ <br />

<br />

¨ <br />

<br />

¨ <br />

<br />

<br />

<br />

¤¤ §<br />

¤<br />

<br />

<br />

¦


¦ © <br />

¡¦ ¢ ¦¥¡¦ ¦¥ <br />

<br />

¤ <br />

¡<br />

¡£¡ ¤£ © ¥<br />

¢<br />

¨ ¨ ¤ <br />

<br />

¦¥¨ ¨ <br />

<br />

¨ <br />

<br />

¤ <br />

¤<br />

£ <br />

<br />

¡ ¤ <br />

§©¨<br />

¨ ¢ ¨ ¨ ¤¨ <br />

<br />

<br />

<br />

¨ © <br />

<br />

¨£ ¦<br />

<br />

¤ <br />

<br />

© ¦ <br />

<br />

¡¤ £ ¤£ <br />

<br />

<br />

<br />

¤¤ ¨<br />

<br />

¦ <br />

<br />

£ ¤<br />

<br />

¤ ¨<br />

<br />

<br />

<br />

<br />

<br />

¤ § ¦ <br />

<br />

¤ ¤¥ <br />

<br />

¤¤¨ ¦ <br />

<br />

§<br />

<br />

¦


¤ ¡¡ £¢ ¨ ¥¤ <br />

©¨<br />

¥¨ <br />

<br />

© ¨ <br />

<br />

¨ <br />

<br />

© ¦¥ ¦ <br />

<br />

<br />

<br />

§ <br />

¦§<br />

<br />

<br />

<br />

¨<br />

<br />

<br />

¨ <br />

<br />

<br />

¨¤¤<br />

© £ <br />

<br />

¦¦<br />

¨<br />

£ <br />

¥<br />

© <br />

£<br />

££<br />

<br />

<br />

¤¨ <br />

¦<br />

¨ <br />

<br />

© <br />

¦<br />

¦<br />

¦<br />

<br />

<br />

<br />

©<br />

¤ <br />

<br />

§ ¦£¨§ <br />

<br />

¦ <br />

<br />

© £¤ <br />

<br />

£ © <br />

© ¦<br />

¢ © ¦ ¢ ¦<br />

<br />

¤¦ ¤


¢ ¢<br />

¤<br />

<br />

¨¤<br />

¡ £¢ £ ¨<br />

¦ ¨<br />

¤ ¨<br />

<br />

<br />

¤ ¤§¦¥¨© §¦§¤© ¦¨¡¢§£©¨ ¡¢¡¤£¨£¨£¦ £ ¢¦¢¡¢¦¡<br />

¨ ¦ £<br />

¦<br />

¤¤ <br />

<br />

¤¦¨ <br />

<br />

¤ ¦<br />

<br />

<br />

<br />

© <br />

<br />

<br />

£ <br />

<br />

<br />

<br />

¤ <br />

¤¦¥<br />

§¦<br />

¢<br />

<br />

<br />

¤ £ <br />

¤<br />

£ © ¢<br />

<br />

¤<br />

<br />

<br />

<br />

<br />

<br />

¤ ¤<br />

<br />

<br />

©<br />

© <br />

¤<br />

<br />

<br />

¦ <br />

<br />

<br />

¦


¦ ¡ <br />

<br />

<br />

¦<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¤ ¢ <br />

¤<br />

¤ © <br />

<br />

<br />

<br />

<br />

£ <br />

¢<br />

<br />

<br />

¨ ¦ <br />

<br />

¦ ¦ © ¨ <br />

<br />

¦ ¤£¦¥¨§¨©<br />

¦<br />

© <br />

<br />

£¥§© ¨ <br />

<br />

£¥¨§¨© ¦ £¥§© ¦ £¥¨§¨© <br />

¦<br />

<br />

¨<br />

¥¤<br />

<br />

¨¦ <br />

£<br />

£¦¥¨§¨© © £¥¨§¨© <br />

<br />

¤<br />

©<br />

<br />

<br />

© <br />

<br />

§¦ <br />

¨<br />

¦<br />

<br />

£¥¨§¨© <br />

<br />

<br />

<br />

£¥¨§¨©


50<br />

100<br />

150<br />

200<br />

250<br />

300<br />

350<br />

50<br />

100<br />

150<br />

200<br />

250<br />

300<br />

350<br />

50 100 150 200 250 300 350<br />

50 100 150 200 250 300 350<br />

50<br />

100<br />

150<br />

200<br />

250<br />

300<br />

350<br />

50<br />

100<br />

150<br />

200<br />

250<br />

300<br />

350<br />

50 100 150 200 250 300 350<br />

50 100 150 200 250 300 350<br />

¢ £ ¨<br />

<br />

£¦¥¨§¨© <br />

<br />

¢¡ ¡ © ¦ <br />

¡£<br />

© ¤¦¥ £¨§© ¥ £§© ¨¥<br />

¤£<br />

¡¨ § <br />

<br />

¦ £ <br />

<br />

¡ ¤£ ©<br />

<br />

¦¥ £¨§© ¥ £§© © ¤¡ ¡ ¨ <br />

<br />

¥ £§© <br />

¨<br />

¨ <br />

<br />

<br />

£ ££ © <br />

<br />

© ¦¦ <br />

<br />

¨<br />

<br />

¤ ¤


¤ © ¤ <br />

<br />

<br />

<br />

<br />

¤ <br />

<br />

¦ <br />

<br />

¢ ¦ <br />

<br />

© ¦ ¦ ¨<br />

<br />

© <br />

<br />

¤¥ <br />

<br />

£ <br />

<br />

¨ ¨ © <br />

<br />

£ <br />

<br />

<br />

© <br />

©<br />

¨ <br />

<br />

¦ <br />

<br />

§ ¤ ¤ <br />

¢ ¦ © <br />

<br />

<br />

<br />

© <br />

<br />

<br />

<br />

¨ £ <br />

<br />

© ¦ <br />

¢<br />

¨ ¨<br />

<br />

<br />

<br />

¡ ¡¤£¨£¦¤£¢ ¡¥§£ ¢¡ ¨¥¥¤§¦©¨¨§¤£¦ ¢¡¤£¦¥¨§© ¤ <br />

<br />

©<br />

<br />

<br />

£ ¤ ¤ <br />

<br />

¤<br />

<br />

¤


© © <br />

© © ¡


© ¤£ © <br />

<br />

£ © <br />

¡¢¡ ¤£ <br />

<br />

§ £¦¥¨§ ¤ ¥ ¢ © © <br />

<br />

© © § £¥ <br />

<br />

¦<br />

© <br />

©<br />

£ § ¨§ ¢ © ¤ <br />

<br />

¢ © © £ § £ £ <br />

<br />

£ <br />

<br />

£ § £ £ <br />

<br />

£ <br />

¦<br />

<br />

<br />

£ <br />

<br />

<br />

<br />

<br />

¦ © © ¦ <br />

¤ ¤£¨<br />

©<br />

© ¨ <br />

<br />

<br />

<br />

<br />

¦<br />

¤ ¦ £ <br />

<br />

¦ ¦ ¤ ¡ ¨ £<br />

<br />

© © <br />

<br />

¤ ¦<br />

<br />

¦<br />

¤ © <br />

<br />

© <br />

<br />

§ <br />

¤¢<br />

<br />

<br />

£ ¤ ¤ <br />

©<br />

<br />

<br />

<br />

<br />

<br />

¤<br />

© <br />

<br />

¦


x<br />

init<br />

ε<br />

x<br />

near<br />

x<br />

new<br />

© © © <br />

© © ¦¨ <br />

¨ © <br />

<br />

© © ¦ ¨ © <br />

©<br />

© ¤ ¡ © ¢ © © <br />

<br />

¦© ¤ ¦ § <br />

¨<br />

¦ <br />

<br />

£¢ §¥¤ © ¥ <br />

<br />

¤ <br />

<br />

¨ ¢ © © <br />

<br />

¨ ¦ <br />

<br />

¨ ¤ <br />

<br />

¡¦ <br />

<br />

© ¢ © © £ £ <br />

<br />

£ © ¤ <br />

§¦ £ ©¨ ¦ <br />

£ £ © ¢ © © <br />

<br />

<br />

£ ¤£ ¤¦<br />

<br />

<br />

£<br />

<br />

<br />

¦ <br />

<br />

<br />

<br />

<br />

©<br />

<br />

x


© ¨ © ¤ ¤£ © ¦¥ £§© <br />

<br />

§ ¤£ © ¥ ¥ £§© <br />

<br />

¡¢¡ ¤£ <br />

<br />

§ £¦¥ § ¤ ¥ ¢ © © <br />

<br />

© © § § £¥ ¨ <br />

<br />

© © ¥ £ ¨ <br />

¦<br />

¨ © § ¥<br />

<br />

¢ ¨ § ¥<br />

<br />

¡ <br />

© <br />

© ¤ <br />

<br />

© <br />

<br />

¨<br />

<br />

£<br />

<br />

© <br />

<br />

¦ ¤ <br />

<br />

¨ ¦¨ <br />

<br />

© <br />

<br />

£¢<br />

£¥¤¦£ £¡¡ © © ¦<br />

£¢<br />

<br />

<br />

£ ¦ © ¦ £ ©<br />

<br />

¤ ¥ £¨§© © £§ © <br />

<br />

§ ¤<br />

<br />

£<br />

<br />

© ¨£ <br />

£<br />

¤<br />

<br />

© ¨ © ¤ ¨ ©<br />

<br />

¦§ © ¨ © ¤ ¨ <br />

<br />

¤ © § ¥<br />

<br />

¤ <br />

<br />

¤ © <br />

¤¦<br />

¤ © £¦ <br />

<br />

¦ ¨ ¨ ©


¨<br />

<br />

<br />

<br />

¨¨ <br />

¤¦¨<br />

¤ ¤ ¤ <br />

<br />

<br />

<br />

¦ ¤<br />

<br />

<br />

<br />

¦<br />

¦¦§¨<br />

<br />

<br />

¨¤ £ © <br />

<br />

£ ©£ ¥ £¨§© <br />

<br />

¥ £§© ¡ ¤ ¥ £¨§© <br />

<br />

¨ © <br />

<br />

¤ <br />

<br />

¦¥ <br />

<br />

<br />

<br />

¢ ¦©¨¤© £¢¤£¢¦¥ §¨§¤¤¡©¢¢¡¤£¦¥ ¦¡¤¡©¢<br />

© <br />

¢<br />

¥ ¨ ¨ ¡¦ ¥ © <br />

<br />

¤<br />

<br />

§ <br />

<br />

£ ¦ <br />

©¤<br />

£ <br />

<br />

£<br />

¤<br />

¨¨<br />

¦<br />

¦


¡ <br />

¤ £¢ £¤¦¥ ¤<br />

¨§ ¤ ¢ ¤ ¦¥ © <br />

¤ ¢ ¤ ¥ ¢£ <br />

¢<br />

¤ ¢ ¤ ¦¥ <br />

© <br />

<br />

<br />

©<br />

§ £ <br />

<br />

¤ © ¤ ¤¦<br />

¥ ¨ <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¢ <br />

<br />

<br />

¨<br />

<br />

¢<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¢ <br />

<br />

§<br />

<br />

<br />

£ ¥ £<br />

£¨ ¤ ¢ ¤ ¦¥ © <br />

<br />

£ ¥ <br />

<br />

¤ £¨ <br />

<br />

<br />

<br />

<br />

<br />

¨¥<br />

<br />

© © <br />

§ <br />

<br />

<br />

§ ¤¨<br />

<br />

<br />

§ © <br />

<br />

¨ <br />

§<br />

§ ¡ ¨ <br />

<br />

<br />

§<br />

§ ¡ ¢<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨ ¢ § § <br />

<br />

¨ § §<br />

<br />

<br />

¤¨ <br />

<br />

¡ © <br />

§<br />

£<br />

<br />

¦


¢ © ¦ © © <br />

<br />

<br />

<br />

© ¦ §¦ ¦ ¦<br />

¨<br />

§¦ ¦ <br />

¨<br />

¦ ¦ <br />

©<br />

¢ ¦ ¦ ¡¦ ¦ <br />

<br />

¢ ¦ <br />

© ¡ ¨ ¨<br />

¨ § <br />

<br />

¦ ¤¦¨¦¦¨<br />

¦<br />

¢ ¢§<br />

£ ¢¡ £ ¨ ¤ <br />

<br />

¨¨¨ ¦ ¦¦ <br />

<br />

<br />

<br />

¥<br />

¢<br />

© <br />

<br />

<br />

¤<br />

¤§ © £ <br />

<br />

¡ © ¦<br />

¤£<br />

<br />

£ <br />

<br />

¥ £ <br />

<br />

© ¢£ ¥ © <br />

<br />

¡ © ¢ § ¡ §¦©¨<br />

<br />

§ ¦ £¦¨<br />

¤¦£ £ ¢ © ¨¦<br />

<br />

¡ £¡ <br />

<br />

¤<br />

¤<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨ <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨


¡¦<br />

<br />

<br />

<br />

¦¦ © © ¦ ¡ <br />

¤¦£ ¢ ¨ © ¡ ¦ ¦<br />

<br />

¨ ¤¦<br />

<br />

¡ ¤¦ <br />

<br />

© ¨¤ § §¤ <br />

<br />

© <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¢¡ <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨<br />

<br />

<br />

<br />

<br />

¡<br />

© <br />

<br />

¦ © ¡ ¦¡ ¦ ¡ <br />

¤<br />

¡ ¡ <br />

£ £ ¢ ¤ ¢¦ <br />

£<br />

© <br />

<br />

© <br />

§<br />

¡ ¡ ¤ <br />

<br />

¤ ¤<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨ <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¦ ¦ <br />

©<br />

© ¤<br />

<br />

© <br />

¨<br />

© ¡ ¡ <br />

<br />

¥£ ¢ ¨¦ ¨<br />

¤<br />

© <br />

¦£<br />

¤ © ¤<br />

©<br />

¦ <br />

<br />

<br />

<br />

<br />

<br />

¨<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨


¤¨ © ¨ © <br />

<br />

© ¦ <br />

¦<br />

¦


© ¨


© © <br />

<br />

<br />

¤ © <br />

<br />

<br />

<br />

¡ <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨ ¡ <br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¡<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¨<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¡<br />

<br />

<br />

<br />

¨<br />

<br />

<br />

<br />

<br />

<br />

¨<br />

© ¨¡ ¡ <br />

¤ <br />

£<br />

<br />

<br />

¤ © <br />

<br />

¡ ¦¡ ¡ ¡ ¡ ¡ ¦ © <br />

<br />

<br />

¤<br />

©


§ ¢¦ <br />

<br />

© <br />

<br />

¡ ¡¦ <br />

<br />

© © <br />

<br />

¦<br />

<br />

¢¡ <br />

<br />

<br />

<br />

<br />

<br />

<br />

¦ ¡<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¡§¦<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¡§¦ ¨<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

<br />

¡ ¨<br />

¨ © ¤<br />

¨<br />

¡ ¡¦¡ ¡ ¡ ¡ ¡ ¦ © £


© © ¦ <br />

<br />

¦¦


© ££ © <br />

<br />

¤ ¤


¦ © ¤ <br />

<br />

<br />

<br />

§¦


¢¡<br />

£ ¡¥¤§¦ £ ¡<br />

¦ © ¨©¨ <br />

<br />

¨ ¤¨ <br />

¨<br />

¡ £¦¡¤ <br />

£ © <br />

<br />

© ¤ <br />

<br />

¤<br />

<br />

¦¤ <br />

©<br />

<br />

¨<br />

<br />

¤<br />

¤¦ © <br />

<br />

¨ <br />

<br />

¨ © © ¨ <br />

<br />

© <br />

£<br />

£ § § £¥ <br />

¨¨<br />

¨ ¦ <br />

<br />

¤£ © © ¨ <br />

¨<br />

<br />

¨ <br />

¨ <br />

¤ § ¢ <br />

<br />

© ¤¨ <br />

©<br />

¨ ¥ £§©<br />

<br />

¦¦ ¨ <br />

<br />

¦ ¥ ¢¨


¨ § ¡ <br />

<br />

¦ ¨ ¨¦ ¤<br />

<br />

¨ <br />

<br />

<br />

<br />

¨ <br />

<br />

¤ ¦ <br />

¤<br />

¡ ¨ ¦¢ <br />

<br />

¨¨<br />

© <br />

¤£ ¨ ¡<br />

¤£ © ¥ £§© ¤¤ ¡ ¦ <br />

¤ © ¨ <br />

¨ © <br />

© ¦ <br />

<br />

¤ ¤ ¤ <br />

<br />

¨<br />

<br />

¨ §¨ <br />

<br />

© ¨ ¨ <br />

<br />

¨ <br />

¤<br />

¡ <br />

© ¨ ¨<br />

¦¥<br />

§¥ § §¥ £ £ <br />

<br />

© ¢¨¥ ©¥<br />

¥ § ¨ ¥ £ <br />

<br />

¥ ¥ <br />

¢<br />

<br />

¡<br />

<br />

<br />

¨ £ <br />

¡ ¨ © ¨ ¦ ¨ <br />

<br />

<br />

<br />

© ¤ <br />

<br />

£ ¡ <br />

£ § <br />

<br />

¤¤


© ¥ © ¥ <br />

¤<br />

¦<br />

<br />

¦¥ ¦ ¡ ¡ ¥ £¢ ¥ ¨ <br />

§ ¦ ¨ ¡ ¦ © ¨ <br />

<br />

£ § <br />

<br />

¥¤<br />

© §¦ <br />

§¦©¨<br />

§<br />

¡ ¨<br />

<br />

¢<br />

<br />

<br />

¥ ¦ © <br />

¢<br />

© © ¦¥<br />

<br />

¤ <br />

<br />

¤£ © ¥ £§© ¤<br />

¢<br />

¤ <br />

<br />

£ © £ © § <br />

<br />

¤ ¤¨ <br />

<br />

<br />

©<br />

<br />

£ <br />

§<br />

§ <br />

¦¥ £§© <br />

£ ¤¨ ¤£ © ¥ £§© ¨<br />

¤¤<br />

© ¨ © <br />

¤<br />

§ © © <br />

<br />

<br />

<br />

<br />

<br />

<br />

¥<br />

<br />

¦ ¨¦ © <br />

¢¤<br />

§ <br />

<br />

<br />

§ § ¦ <br />

<br />

¤ ¤ ¨ © <br />

<br />

¥ £¨§© <br />

<br />

<br />

§£¦¦ §£ <br />

¦ ¦ ¦ <br />

<br />

¦<br />

<br />

£ <br />

¤<br />

¢ ¤


¨ ¨ <br />

<br />

¦ ¦ <br />

<br />

¨ <br />

<br />

¤ ¦ © <br />

<br />

¦ <br />

<br />

¨ ¢<br />

<br />

§ <br />

<br />

¤<br />

<br />

¢¨ <br />

© £ © <br />

<br />

¨ ¢ ¦<br />

¨<br />

¦¥ £¤<br />

¨¤<br />

<br />

¤ © ¦ © <br />

<br />

¤¦ <br />

© <br />

<br />

¦ ¥¨ ¨¥§<br />

<br />

© <br />

<br />

§<br />

§<br />

¨¤<br />

¡<br />

¥<br />

£ <br />

£¢<br />

<br />

¢<br />

<br />

<br />

© ¦ <br />

<br />

<br />

¥¤<br />

©<br />

<br />

¨§<br />

¦<br />

¥<br />

£ <br />

¢ <br />

©<br />

¢<br />

¤ ¤ <br />

¦¨ <br />

<br />

¤¦ © <br />

¦<br />

<br />

<br />

¤ ¤ ¤ <br />

¨<br />

¤ ©


¤ ¤© ¤ <br />

¤§<br />

¨<br />

¤ <br />

<br />

¦ ¤<br />

¦¤¦<br />

© ¤<br />

<br />

¢ £¢ ¢ ¤ © <br />

¡<br />

© ¥ <br />

<br />

<br />

<br />

© <br />

<br />

<br />

¤<br />

¦<br />

¤ ¦¨<br />

<br />

© <br />

<br />

<br />

<br />

<br />

<br />

© ¤ § <br />

<br />

¤ ¢ <br />

<br />

<br />

£ ¢ ¤ © £<br />

¤<br />

¤ ¤ <br />

<br />

¨ <br />

<br />

<br />

<br />

¤ ¢¤ <br />

<br />

<br />

<br />

<br />

<br />

<br />

£<br />

© <br />

<br />

¢<br />

<br />

¤<br />

<br />

© ¦ ©


© £ <br />

<br />

¨§ © ¦<br />

<br />

¨ <br />

<br />

<br />

¡£ £¡ <br />

¡<br />

© <br />

<br />

¤<br />

<br />

¦ ¦ <br />

¨<br />

¦ £ ¤ <br />

¤ ¤¨ <br />

¤<br />

¨ <br />

¤<br />

¤ © <br />

<br />

¨ <br />

<br />

<br />

¡ £¢¥¤§¦©¨§¢<br />

¨ ¦ ¢¦ ¤<br />

¢<br />

¢ ¨ <br />

<br />

¦ <br />

<br />

¢ © ¤<br />

<br />

¨ © <br />

¨ ¥<br />

<br />

¢ ©¤£¦<br />

¤¥¥ ¥ ¤ <br />

£ £ <br />

¢ ¥ ¥ ¤¨¢ ¢ ¤ <br />

<br />

¦ <br />

<br />

© ¡ ¤ ¨ ¨ ¡


§¡ £ £¢¥¤ ¦¨§ <br />

¤ ¢ © ¥ ¢ ¨ <br />

¦ ¤ ¤¤ <br />

£ ¥ <br />

¨£ <br />

<br />

£ £ ¡¦ <br />

<br />

£ <br />

<br />

¢ ¨ ¨ ¨ ¥ ¦<br />

¨ ¦ £ <br />

¦ §¦<br />

¢ © £ <br />

¦<br />

¥ © ¨© ¢ <br />

<br />

£ ¡ ¦ <br />

¨ <br />

¦<br />

¥ © ¢ ¢¢ ¢ © <br />

£ ¡¦<br />

<br />

<br />

¦ ¥ ¨ <br />

¥ £ £ ¡¦<br />

¥ £ £ <br />

<br />

¤ ¢ ¢ <br />

<br />

£ £ ¦ £ ¦ ¡¦


¨ ¨ © ¨ ¨¦ ¨<br />

¨ ¦ ¦<br />

¨ © ¨ <br />

¡¦<br />

¨ © <br />

¦ <br />

¤ <br />

<br />

¦ ¡¦<br />

<br />

© ¢ £ ¤ ¨ <br />

¨ <br />

¢ © £ £ <br />

<br />

¨ ¤ £¡¢ <br />

<br />

£ § £ ¦¡ ¥¨ ¥ <br />

£<br />

<br />

§¦ ¥ ¨ ¥ ¨ £ <br />

<br />

¥¡ ¦ ¨<br />

<br />

© ¢ ¨ ©¢©¥ <br />

<br />

© <br />

§ £¢ <br />

¢ ¢© ¡¦ <br />

¨ ¨ © ¥<br />

<br />

¢ £ £ £ <br />

¨¨<br />

¦ ¦¡¦ ¤ <br />

¥¨ ¢¢ ¤ <br />

¨ ¥ ¥¤ ¢ <br />

<br />

¦¤ ¨ ¥§


¥ ¨ £ <br />

¡¦ ¦ <br />

¨ ¡¥¨ © <br />

<br />

¢ ¤¡ £¢ ¢ <br />

<br />

¨ ¢ ¥ ¤¤ ¨ <br />

£ ¦ ¦ <br />

<br />

<br />

¢ ¤<br />

£ £ <br />

©¢ ¥ © <br />

¢ £ £ <br />

¡¦ £¤ ¢¥¨ £ £ <br />

<br />

¨ ¡ ¤ ¨ £ £ <br />

<br />

£ £ <br />

<br />

¢ ¢ ¢ £ £ <br />

<br />

¡ ¢ ¨ ¥§ <br />

¨ ¦ ¢ <br />

£ £ <br />

¨ ¢¢ ¨<br />

<br />

¨ £ ¢ ¦ ¢ <br />

<br />

<br />

¢ ¥ ¥ ¢ ¨ <br />

¡¡ ¡¦


¢ ¥ <br />

<br />

¥ ¥ ¥¤ ¢ ¨ <br />

¨<br />

¥§ <br />

¢ ¥ © <br />

<br />

¤ <br />

¢¦¦¢<br />

¦ ¢¤¥ § ¢ £ £ <br />

<br />

¥ ¤ £ £ <br />

<br />

© ¨ ¢ £ ¤ <br />

<br />

¥ ¥ © ¥¢ ¥¨ £ <br />

¦ ¦ ¦¡¦ <br />

¤ ¥£ ¥ <br />

<br />

¦ ¥ ¥ ¨ ¡ © ¦ £ <br />

<br />

¡¦ <br />

¦ ¥¨ © © ¦ ¥¨<br />

<br />

¦¡¥¨ ¨ ¨ ¡¦<br />

¦¥ ¥¨¡¥ ¥ ¢ ¢ <br />

¢ £ ¡¦<br />

¦ ¥ ¥¨ ¢¢ ¤ ¢ <br />

¦ <br />

¦§¦ ¤ ¥¨£ ¦ <br />

¦ ¨ ¦ © ¡¢<br />

<br />

¡¦


¦ ¢¡ ¦ £ £ ¥<br />

<br />

¦ ¤ ¢ ¤ ¨ ¨ ¢ <br />

§ ¦ <br />

¦ <br />

<br />

¨ ¥ ¤ <br />

<br />

¨ ¡¥§ <br />

¤ ¢ £¢ ¢ £ <br />

<br />

¢ ¥ ¨ § £ <br />

¦ <br />

¢¢ ¡ ¨ ¤ ¥¨<br />

<br />

¢ £ £ ¦ <br />

<br />

<br />

¢¢ ¨ ¢ ¨ ¦¥ ¤ ¥¨ <br />

<br />

£ ¦ <br />

<br />

¢¢ ¢ ¤ <br />

<br />

£ <br />

<br />

¡¦ ¢ © ¨¨<br />

<br />

£ <br />

<br />

¢ ¤ ¤ ¢ £ ¢ ¤<br />

¤ ¦ ¡¦ ¥ ¢ ¨ ¦<br />

¨¢ ¦¥ ¨ <br />

¥ ¨ ¥ <br />

¢ ¢ ¢¢ ¤ <br />

£ ¡¦ <br />

¢ © ¢ £ ¢ ¨ <br />

<br />

© ¢ ¤ <br />

¤<br />

¥


¨ ¢ ¥ ¤ ¤¤<br />

<br />

¢ £ £ ¦<br />

¥<br />

© © ¥¨ <br />

<br />

¢ ¢<br />

¤ ¨<br />

<br />

¦¥ £ ¡ £ £ <br />

<br />

<br />

¥ ¢ ©¤ <br />

¢ £ £ ¤

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!