Biomedical Engineering Reference
In-Depth Information
Fig. 6.11 Point-to-point Cartesian trajectories executed by the three controllers: the VITE-based
method produces on average the blue line, the minimum-jerk controller result is in green, and the
DLS system using Orocos in red. Bands containing all the measured paths within a confidential
interval of 95 % are drawn in corresponding colors. Controller settings are
T ﾼ
2.0 s for the
minimum-jerk system;
ʱ ﾼ
0.008,
ʲ ﾼ
0.002,
K
P
ﾼ
3 for the VITE (see Hersch and Billard
2008
)
for the meaning of the parameters); and
ʼ ﾼ
10
5
for the damping factor of the DLS algorithm
Table 6.5 Mean errors along with the confidence levels at 95 % computed when the target is
attained. An average measure of the variability of executed path is also given for the three
controllers
Controller
Position error
Orientation error
Mean radius of the trajectory band
10
3
mm 0.041
VITE
1.3
1.4
0.05 rad
10
10.8 mm
10
3
mm 0.048
Min-jerk
3.0
1.3
0.008 rad
2.5
1.5 mm
10
3
mm 0.016
DLS
1.3
1.4
0.028 rad
2.0
1.36 mm
both cameras, it can also reach it. Here we further simplified the problem (from the
visual point of view) and decided to learn only the position of the end-effector (
x, y, z
)
since the orientation of the hand in the image is difficult to detect reliably. For this
problem, the input space is defined by the position of the hand (or the target) in the two
cameras (
u
l
,
v
l
)and(
u
r
,
v
r
) with respect to the current head configuration.
To sum up, having defined the input and the output space, the map
M
that is to be
learned is
,
ð
x
;
y
;
z
Þ
H
ﾼ
Mu
l
;
v
l
;
u
r
;
v
r
;
T
;
V
s
;
V
g
ð
6
:
29
Þ
4
represent the visual input of the position of the hand in
the iCub cameras, whereas (
T
,
V
s
,
V
g
)
where (
u
l
,
v
l
,
u
r
,
v
r
)
∈
ℝ
3
accounts for the proprioceptive part
of the input designating the tilt, the pan, and the vergence of the eyes; finally,
(
x
,
y
,
z
)
H
∈
ℝ
∈
ℝ
3
is the Cartesian position of the hand expressed in the head-centered
frame.
This map can be learned by a regression method if enough training samples are
available and these can be in turn collected if we can measure (
u
l
,
v
l
,
u
r
,
v
r
)by
Search WWH ::
Custom Search