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Transactions on Industrial Electronics
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
3
III. L
OCALIZATION IN GLASS-WALLED ENVIRONMENTS
A. Case classification by reflective characteristics
Suppose that
,
is a scalar range measured by the ith scan of
the LRF at time . Our approach assumes that
,
is measured
as a consequence of one out of the five cases shown in Fig. 2.
Case 1 and Case 2 are defined as diffuse reflection and specular
reflection, respectively. Meanwhile,
,
may include the range
measurements under multiple penetrations. Case 3 and Case 4
are the first and second penetration, respectively. In this paper,
it is assumed that the maximum number of penetrations is two
for simplicity. The number of penetrations is dependent on the
number of glass walls. Case 0 indicates the uncertain reflection.
Case 0 can be caused by unknown obstacles or unpredictable
reflections. Therefore, five cases can be defined as shown in
Fig. 2. Let
,
be the case which is causative of
,
.
,
is
defined as the following equation:
,
∈
1,2,3,4,0
(1)
In the proposed method,
,
is estimated by comparing
,
to the reference distances corresponding to four cases except
for Case 0. The reference distances imply expected range
measurements at a potential pose of a robot. Let
be the
predicted robot pose from the odometry. The reference
distances are calculated on the basis of robot pose
and
occupancy grid map .
,
,
is given by the
following equations:
∆
cos
,
∆
sin
, (2)
∆
∆
,
∆
,
, ∆
tan
∆
,
∆
,
, (3)
∆
(4)
where ∆
,
and ∆
,
correspond to the incremental linear
displacement of the left and right wheel, respectively; is the
wheelbase; and
,
,
is the estimated robot
pose at time 1. In (2)–(4), it is assumed that the robot is a
two-wheeled differential drive mobile robot.
In grid map , glass walls are represented as occupied
regions. In other words, the glass wall and the opaque obstacle
are not distinguished as shown in Fig. 3. This is natural because
multiple diffuse reflections take place on glass surfaces when
the robot moves around the glass-walled environment. This fact
implies that the user does not have to make an effort in order to
specify glass wall regions in the grid map. The users are
required to modify the grid map only when the glass walls are
modeled as the empty space. In such a case, the corresponding
cells should be replaced by occupied cells.
The proposed localization scheme is carefully designed by
adding the case estimation of the range measurements. The
following two assumptions are made in order to overcome
difficulties caused by a glass wall.
(i) The local tracking localization is successfully carried out
with low uncertainties.
(ii) For localization purposes, it is sufficient enough to exploit
only a part of the range measurements.
Assumption (i) is required because simultaneous
consideration of high pose uncertainty and estimation of
reflective characteristics is extremely difficult. Assumption (ii)
is commonly accepted because noisy or occluded
measurements will not be considered for localization in
general.
In order to observe environmental geometries around
predicted robot pose
with low uncertainty, preliminary
samples are extracted through systematic sampling. In our
approach, preliminary samples correspond to the voters for the
estimation of
,
. Predicted robot pose
is not an accurate
robot pose. Thus, if
,
is estimated on the basis of
only, the
incorrect case estimation may occur. For this reason,
preliminary samples are extracted around
. Voting is then
carried out by each preliminary sample. The case of the highest
vote will be considered as
,
for each range measurement. A
more detailed scheme can be explained by the following four
steps.
1) Extraction of preliminary samples: Let be the number
of preliminary samples. In order to extract preliminary
samples, we use systematic sampling at regular angular
intervals around
. The pose
,
,
of the nth
preliminary sample is extracted by the following equations:
,
,
(5)
Fig. 2. Five cases by reflective characteristics. The thick light blue lines
represent the glass wall. The thin red lines represent the LRF measurements.
The black blocks represent opaque obstacles.
Fig. 3. Illustration of grid mapping. In grid map , opaque obstacles are
represented as occupied regions. Similarly, glass walls are represented as
occupied regions.