Biomedical Engineering Reference
In-Depth Information
This is obtained through a least-square fitting on each point's neighborhood (Radu
2009
). Given a point
p
an
d
its neighborhood
P
k
, the plane tang
en
t to the surface can
be defined as a couple
x
, where
x
is a point of the plane and
n
is the normal to the
plane. We define the neighborhood
P
k
of a point
p
as the set of points that lies within
a circular area having radius equal to the radius of the robotic palm. The distance
between a point
p
i
∈
ðÞ
;
n
P
k
and the fitting plane can be expressed as
dist
i
ﾼ
ð
p
i
x
Þ
n
:
ð
6
:
30
Þ
In order to compute the plane parameters, we need to minimize the distance dist
i
for each point. If we impose that
x
is the centroid of the neighborhood (i.e.,
x
ﾼ
1
k
X
k
iﾼ
1
p
i
), then the solution for
n
can be calculated by analyzing the eigenvectors
and eigenvalues of the covariance matrix:
k
X
k
1
T
C
ﾼ
ð
x
p
i
Þ
ð
x
p
i
Þ
ð
6
:
31
Þ
iﾼ
1
Once the normals of all points have been computed, a seed point
p
is chosen and
every point
p
i
∈
P
k
is evaluated;
p
i
will be added to the current cluster only if it is
locally connected to the seed
p
and if the angle between the normals of
p
and
p
i
is
smaller than a specified threshold; otherwise it is added to the list of potential seeds.
The point cloud is thus subdivided into several regions having similar curvatures.
Later in order to assure grasp stability, we select only the regions that contain a
sufficient number of points. We effectively impose the condition that the hand is
placed on a smooth and large enough surface of the object.
6.6.2 Points Evaluation
Appropriate end-effector positions are ranked by means of a score function which
biases those with specific characteristics. We choose the
N
points with the highest
score as returned by a function that weighs the object shape and dimension:
sp
ðÞﾼ
w
1
vp
ðÞþ
w
2
mp
ðÞ
ð
6
:
32
Þ
where
v
(
p
) is an auto-adaptive function representing the evaluation of visual
properties at the point
p
and
m
(
p
) is a fixed component that depends on the object
dimension.
m
(
p
) can integrate a user-defined task component.
w
1
and
w
2
are
relative weights which can be chosen empirically to balance the contribution of
the two components:
1.
Visual component
: The first part of the score function takes into account the
shape of the object. In particular, we would like to grasp the object on a point
Search WWH ::
Custom Search