Plannification des prises pour la manipulation robotisée

HAL Id: tel-00629228

https://tel.archives-ouvertes.fr/tel-00629228

Submitted on 5 Oct 2011

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Plannification des prises pour la manipulation robotisée

Belkacem Bounab

To cite this version:

Belkacem Bounab. Plannification des prises pour la manipulation robotisée. Automatique / Robo-

tique. Université Paul Sabatier - Toulouse III, 2011. Français. �tel-00629228�

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Université Toulouse 3 Paul Sabatier (UT3 Paul Sabatier)

Systèmes (EDSYS)

Planification de prises pour la manipulation robotisée

mardi 7 juin 2011

Belkacem Bounab

Systèmes Automatiques

Veronique Perdereau - Professeur à l'Université Pierre et Marie Curie-ParisVI, France.

Belkacem Barkat - Professeur à l'Université de Batna, Algérie.

Daniel Sidobre - Maître de Conférences (HDR) à l'UPS, Toulouse, France.

Abdelouhab Zaatri - Professeur à l'Université de Constantine, Algérie.

LAAS-CNRS

Jean-Jaques Barrau - Professeur à l'UPS, Toulouse, France.

Taha Chittibi - Maître de conférences à l'École Militaire Polytechnique, Alger, Algérie.

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0.484

!2 !1 0 1 2

!2

!1.5

!1

!0.5 0 0.5 1 1.5 2

Y

X

c1

c2 o

g_c

Q^∗_G= 0.205

!2 !1 0 1 2

!2

!1.5

!1

!0.5 0 0.5 1 1.5 2

Y

X c1

c2 g_c o

Q^∗_G= 0.205

!2 !1 0 1 2

!2

!1.5

!1

!0.5 0 0.5 1 1.5 2

Y

X c3

c1

c2 g_c o

Q^∗_G= 0.432

!2 !1 0 1 2

!2

!1.5

!1

!0.5 0 0.5 1 1.5 2

Y

X c1

o

g_c c2

c3

Q^∗_G= 0.464

!2 !1 0 1 2

!2

!1.5

!1

!0.5 0 0.5 1 1.5 2

Y

X c1

c2 g_c

o

c3 c4

Q^∗_G= 0.748

!2 !1 0 1 2

!2

!1.5

!1

!0.5 0 0.5 1 1.5 2

Y

X g_c o

c1 c2

c3

c4 c5

Q^∗_G= 0.773

!2 !1 0 1 2

!2

!1.5

!1

!0.5 0 0.5 1 1.5 2

Y

X g_c o

c1 c2

c3

c4 c5

Q^∗_G= 0.773

0 20 40 60 80 100 120 140 160

−1

−0.5 0 0.5

!"

#$%&'$()*

!

Q

j

j =

1, . . . , N

s

∈ [0, 1]

i = 1, . . . , n

i

=

+ (s

− sp

)

−

sp

− sp

k (s

∈

[sp

, sp

]) sp

j = 1, . . . , N + 1 s

:

sp

= 0 , . . . , sp

= l

l

, . . . , sp

= 1

<

l

? l

= -

−

- , . . . , l

= l

+ -

−

- , . . . , l

= l

+ -

−

- @

!5 0 5

!5 0 5

X

Y

Q^∗_G= 0.586

!5 0 5

!5 0 5

X

Y

Q^∗_G= 0.657

!5 0 5

!5 0 5

X

Y

Q^∗_G= 0.768

!4 !2 0 2 4

!4

!3

!2

!1 0 1 2 3

X

Y

Q^∗_G= 0.464

!4 !2 0 2 4

!3

!2

!1 0 1 2 3

X

Y

Q^∗_G= 0.636

!4 !2 0 2 4

!3

!2

!1 0 1 2 3

X

Y

Q^∗_G= 0.754

∆

1

R

(

,

,

) R

(

,

,

)

1

: #

i=1

(a

+ a

) = −δ

#

i=2

(

−

) × (a

+ a

) =

(a

" 0, a

" 0, δ > 0)

!

!

!

"!

#_""

#

#

#

$

!

!

!!

"#

!

#_$$

#

#!

#

$

1

2 3 g 1

g 11

−

2

"

3

"

g 11 12

−

δ

g

r

: #

i=1

(x

+ x

) = −

#

i=2 i

× (x

+ x

) = (x

" 0, x

" 0)

i

=

−

r

x

= a

δ x

= a

δ

min

=(x¹¹,x¹²,···,···,xn1,xn2)^T

?

: = , " @

A (3 × 2n) (3 × 1)

A =





11 12 21 22

· · ·

0 0 t

t

· · · t

t



 , =





−

0





t

=

×

(i = 1, . . . , n ; j = 1, 2)

(

,

,

)

−

11 12

ij

(i .= 1 ; j = 1, 2)

11 12

n 1

T ∗

−

n

i

n

T ∗

r

r

0 5 10 15 20 25 30 35 0

0.1 0.2 0.3 0.4 0.5 0.6 0.7

f^Tx^∗ rball

T ∗

r

R

n

R

R

R

R

1 2

a b (a, b) " 0

1 2

1

, , ,

1 2 2 1 2

ψ

1

= a ;

= b [cos(ψ) − sin(ψ) ] ;

= l

1 2

a b ψ

!

!

!

"

"

"

#

%

&

#

'

"

$

(

ψ a b

= ×

- -

/1 1

2 1

= [a + b cos(ψ)] − b sin(ψ)

/¹

= l b [sin(ψ) + cos(ψ) ]

/

/

= a b l sin(ψ) a

+ b

+ 2 a b cos(ψ)

x

x =

· = l b [b + a cos(ψ)]

a

+ b

+ 2 a b cos(ψ)

ψ x

a b 0 ! cos(ψ) ! 1 x

lb²

a²+b²

! x !

2+ab)

(a+b)²

a b

&

&

&

&

&

&

−

! ψ !

2

1 2

0 ! x ! l

1 2

ψ ∈ =

−

, 0 >

−1 ! cos(ψ) ! 0

x A

lb

b−a

,

+b2

B x

l

ψ = −150

cos(ψ) = −1

1 2

x =

[0, l] a b

x β

1 2

1 2

β

ψ a b

tan(β) = b sin(ψ) a + b cos(ψ)

1

2

β ∈ [0, ψ]

x β

x = l(cot(β ) cot(ψ) + 1) 1 + cot

(β)

&!!"#$#%!"#$%

&

!

π

2

< ψ <

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170

−3

−2

−1 0 1 2 3 4

β

!

!"#"$%& !"#"'%& !"#"(%& !"#")%& !"#"*%& !"#"+%& !"#",%& !"#"-%& !"#".%& !"#"$%%& !"#"$$%& !"#"$'%& !"#"$(%& !"#"$)%& !"#"$*%& !"#"$+%& !"#"$,%&

x β

ψ l = 1

x β

ψ l = 1

ψ

< ψ < π x

l cot

(ψ) 2 A C

cot

(ψ) + 1 − 1 B ! x ! −l cot

(ψ) 2 A C

cot

(ψ) + 1 + 1 B

1 2

β

1 2

x β

i

R

1

= [2, 0, 0]

;

= [0, 1.5, 0]

;

= [0, 0, 2]

;

= [1.2, −2, 0]

1

= [1, 0, 0]

;

= [0, 1, 0]

;

= [0, 0, 1]

;

= [0, −1, 0]

µ ! 0.3

R

µ = 0.5

R

# ! & ' ( &

#

&

#

!

&

!

"

#

$

%

$

$

$

µ = 0.3

# ! & '

( &

#

&

#

!

&

!

"

#

$

"

"

"

µ = 0.5

m

n

i

g

=

n

"

i=1 m

"

j=1

a

;

= [

,

×

]

; a

" 0

ij

m

R

nm

g

=

D #

i=1

#

j=1

a

=

#

#

j=1 i

× a

= ; a

" 0

k

D #

i=1

#

j=1

a

= − #

j=1

a

#

#

j=1

(

−

) × a

=

; i .= k , a

" 0

g

∆

= #

j=1

a

k

∆

=

#

i=1

#

j=1

a

i .= k

k

∆

n

n n − 1

i*=k

∆

∆

R

R

R

R

k

k

−

R

1

k = 1 D #

i=1

#

j=1

a

= −

#

i=2

#

j=1

(

−

) × a

= ; a

" 0

i

2

1

1