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Fig. 3.12
Continuous photograph of tool manipulation [5]
ξ
x
,
ξ
y
]
T
The target position in the image plane is defined as
ξ
=[
and the 3D
z
]
T
position of the target is defined as
x
=[
x
,
y
,
. Using the perspective projection
function
f
, we can write
=
f
(
x
). From the kinematics of the hand and tweezers
structure, we can write the tip of tweezers point as
x
=
g
(
ξ
θ
). By differentiating this
relation we get
=
∂
x
∂
f
g
∂θ
w
˙
θ
w
=
J
˙
˙
ξ
θ
w
(3.17)
∂
where
J
is an image Jacobian. Using this relationship, the desired wrist joint angle
θ
dw
is computed as
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