Practical Stabilization of Driftless Systems on Lie Groups

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HAL Id: inria-00072293

https://hal.inria.fr/inria-00072293

Submitted on 23 May 2006

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Practical Stabilization of Driftless Systems on Lie Groups

Pascal Morin, Claude Samson

To cite this version:

Pascal Morin, Claude Samson. Practical Stabilization of Driftless Systems on Lie Groups. RR-4294,

INRIA. 2001. �inria-00072293�

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ISRN INRIA/RR--4294--FR+ENG

a p p o r t

d e r e c h e r c h e

THÈME 4

INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE

Practical stabilization of driftless systems on Lie groups

Pascal Morin — Claude Samson

N° 4294

Octobre 2001

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(17)

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=>

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hkjVX[X9ckot_`bis»¡mXxg_i~X9oepSOcfe

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, H LQ

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H L ¼ )

! ! " M

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, H! L_òyhkjeph~¢mhmxGcmjs _`j¨c=j~X_`mS:OhkxpS~hh r hq7epSVX hmxg_ik_ij RTSVXxgXhkxpXk¢fepS~XxgX"Xvn_òtegoyc[l~xphmz{X9uég_ihkj

(18)

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H

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(19)

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¼ k½GeghHepSVXSVhkWYhmmX9jVXhka~oTuckotX

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=

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= H=

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H= L H()

$ = 2

! " ! !=

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cqj r 2 H ) ! " ! L

cmj

r ophmWYX-c

rVr

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r

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r

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r

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r P 2 2 L H

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( H

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k½

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cmxpXbiXet³¦_ij:¡fcqxg_`cmje £ x e c2mxghmaVlhklOX9xgcqep_`hmjhkj y =jVXHX9ckot_`bis¡kXxg_~X o"egS~cfe[epS~_`o

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= H

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L

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= ¼fZ½

(20)

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cqxgX

r

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r

s

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=

_ ) 3

= P

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H L '

= hqegSVXxg£"_`opX

¼ <m½

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¡

5r

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r

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¼ k½ThkxpW c»mxc r X r

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L_`jegSVXYotX9j~otXhq

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r

£X_`mSet³¦¡mX u´ephkx_doTm_`¡mX9j2:s

<

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) 3

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) L ¼

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