IEEE Robotics & Automation Magazine - March 2023 - 42

DY ,Y
N
H = R 1 5=
i
a
i
b
i
where
YY ,a
i
b
i
YY ,
:
1 N
a
1:N
b
represents the time series of two different
map points clusters;
represents
"
the ith state of the time series; and 5
represents the exclusive or. DE represents
the Euclidean distance of two clusters. If
DH and DE are both lower than the
threshold, which means that the distance
in temporal and spatial of the two clusters
are close enough, then the two clusters
will be merged. Otherwise, the two
clusters will not be merged. After that,
we find the minimal Hamming distance
with respect to all other map points in
the cluster and use this map point to represent the cluster.
TO REDUCE THE TIME AND
MEMORY CONSUMPTION
OF GMP, TIME-SERIESBASED
MAP POINT
CLUSTERING IS
PERFORMED FIRST.
„
GMP
After that, with BPF and survival analysis, we can obtain an
accurate persistence probability of map points clusters and
model the survival function of the clusters.
Then, persistence probability is used to predict the state
of map points clusters for a given time. We introduce a long
short-term exponential model [9], [10] to fuse the last observation
and the persistence of clusters and predict the state.
We define the threshold of map points cluster's survival time
c as
yt
cc ;;++ ---11
l
! 11
(/())( ()/(
mm yy ttl)), where
tt
represents the state of map points cluster at time t, which
is the same as in the " BPF " section; and m represents the
number of observations.
ptl () is the prediction of the state
pt ye
l ()
=+ -cc
-tt
tt t)/
ll )/
Pt 1 e
l
(( )(()
()(),
where P(t) is the persistence probability
of map points cluster, the same as in
the " BPF " section. t represents the current
time, and tl represents the time of
last observation. When
;;l % c
-
expression e
tt/
l ctt
,
the
is close to one, which
means that the expected occupancy would
be the same as the one recently observed.
And when
e((tt)/ )
;;l & c
-
l - c
tt ,
the expression
is close to zero, which weakens
the effect of the latest observation.
The performance of our semistatic
map point cluster prediction is presented
in Figure 5. The first seven days are the data collection session.
We use the data of the first seven days to model the time series
of map points clusters, then predict the future states of map
points clusters in the last several days. If the prediction value
is higher than the threshold (0.5) we set, it is set to one, which
means that it survives at the current time; otherwise, it is set to
zero, which means that it is no longer alive at the current time.
SIMULATION AND REAL-WORLD EXPERIMENTS
Map Point Cluster Observation
Map Point Cluster Persistence
Map Point Cluster Presence Prediction
1
1
1
1
234 5
Days
Modeling
Prediction
67 89 10
FIGURE 5. The survival analysis and prediction of a map point cluster. The observations of map
point cluster yt during the data collection session (blue) are sent to the persistence filter and
survival analysis part. Then we can obtain the persistence probability P(t) of the map point
cluster (green) and predict the state ()
ptl of the map point cluster for a given time (red).
42 IEEE ROBOTICS & AUTOMATION MAGAZINE MARCH 2023
SIMULATION
The simulation scene and the model of our intelligent wheelchair
are shown in Figure 6. The model of our intelligent
wheelchair is equipment with 3D lidar and a RealSense camera
(stereo). The simulations are done in Gazebo using an
indoor museum environment. In this
environment, there are periodic and
gradual, incremental changes, such as
lighting conditions and periodically
placed boards. We operate the intelligent
wheelchair in the simulation scene
across days (where the interval is 3 h)
and collect the temporal maps of the
environments. The previous seven days
are used as training datasets, and the
next several days are the testing datasets.
For comparison, our results contain
the following state-of-the-art
methods: VINS-Fusion [19] [without
an inertial measurement unit (IMU)],
ORB-SLAM2 [14], ORB-SLAM3 [15]
(without an IMU), LTVS with the FreMen
map prediction method [9], and
LTVS with the auto regressive moving
average (ARMA) map prediction
method [8]. The localization results of
our method are listed in Table 1, with
the best results for each sequence in
bold. The sequence we used is 12 h
after the training datasets. Compared
with other static visual SLAM methods,
our GMP method can predict the
p (t) P(t)
yt
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