![](bg2.png)
points along the images allows computing the image
Jacobian, that relates the change of the coordinates
in the image with the changes in motion in the
ground plane. Then, using the principles of visual
servoing, the second robot can follow the route, as in
(Burschka, 2001). Also, in the behaviour-based
control (Balch, 1998), some features of the images
are extracted to carry out the localization and
navigation of the members of a team in a formation
problem. However, other approaches suggest that
these processes could be achieved just comparing
the general visual information on the images,
without necessity of extracting any feature. These
appearance-based approaches are specially useful for
complicated scenes in unstructured environments
where appropriate models for recognition are
difficult to create. As an example, (Matsumoto,
1999) addresses a method consisting on the direct
comparison of low-resolution images. This method
may lead to errors when the size of the route is quite
long so other features must be added to make the
method more robust, such as histogram, texture and
density of edges, (Zhou, 2003). However, these
features contain no geometric information so they
are useful just for localization but not for navigation.
When working with the whole images, the
complexity of the problem can be reduced by means
of the PCA (Principal Components Analysis)
subspace as in (Kröse, 2004) or (Maeda, 1997),
where through PCA techniques a database is created
using a set of views with a probabilistic approach for
the localization. In classical PCA approaches, all the
views along the route must be available before the
compression can be done so the navigation of the
second robot cannot begin until the leader has
finished learning the route. Actually, a new model
must be built from the scratch when we want to
include information about new locations in the map.
These problems can be overcome using an
incremental PCA method, as shown in (Payá, 2007).
In this paper, we present an appearance-based
method for route following where incremental PCA
has been used to build the database, and a
probabilistic Markov process has been implemented
for robot localization during the navigation. First,
the representation of the environment along the route
is detailed. Then, in section 3, the basics of
localization and control in route following are
outlined. In the 4th section, the probabilistic
approach to make navigation more robust is
presented and to finish, the results and conclusions
of the work are shown.
2 REPRESENTATION OF THE
ENVIRONMENT
The philosophy of the appearance-based methods
consists in working with the general visual
information of the images, without extracting any
interesting point. Thus, this family of methods
presents the disadvantages of the size of the database
necessary to retain all the information of the
environment and the computational cost of the
comparisons between the whole images.
When working with 64x64 images, the data
vectors fall in a 4096 dimensional space. However,
all these data are generated from a process with just
three degrees of freedom (position and orientation of
the robot). This way, before storing the images, a
reduction of the dimensionality of the data can be
performed with the goal of retaining the most
relevant information of each scene. Since pixels tend
to be very correlated data, a natural reduction step
consists on performing Principal Components
Analysis (PCA), as in (Kirby, 2001).
Each image
j
x
j
K
1;
1
=
, being M the
number of pixels and N the number of images, can
be transformed in a feature vector (also named
projection of the image)
j
x
j
K
1;
1
=ℜ
, being K
the PCA features containing the most relevant
information of the image,
.
≤
In traditional PCA,
first of all, the data matrix is built using the images
of the environment. The PCA transformation is
computed from the covariance of the data matrix
using SVD and the Turk and Pentland’s method
(Turk, 1991). After the process, a new data matrix
with the most relevant information is obtained.
In classical PCA approaches, all the images
along the environment must be available before
carrying out the compression. This way, the robots
that follow the route should wait the leader one to
run till the end. However, in collaborative tasks, it is
usual that some robots follow the first one while it is
still recording the information. Then, with this
approach, the robot that is building the database
should do it from the scratch when a new image
along the route is captured, what is computationally
very expensive. To overcome this disadvantage, a
progressive construction of the database can be
implemented, using the incremental PCA algorithm
exposed in (Artac, 2002). When the leader captures
a new image, it is added to the database, updating all
the projections that were previously stored.
As can be proved, when having a set of
eigenvectors from a set of views, when a new image
is added to the database, these eigenvectors and the
VISAPP 2008 - International Conference on Computer Vision Theory and Applications
392