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238 J. Gaspar et al.
system by displacing all incoming rays, each having a unique Euler angle, so
as they converged at a single point. Thus, their method produced a camera
with a single centre of projection, imaging a distorted scene. Since they did
not derive an analytical expression for the distortion, it was measured as a
change in the height of a small object, given a change in its elevation angle
and remained less than 2.5%.
Concluding, many omnidirectional vision systems, despite not having a
single projection centre, are well approximated by a single projection centre
model. In this way models based on the single projection centre property may
become the most common, in the same way as the pin-hole model is used for
standard cameras even when it is just an approximation valid for the tasks at
hand.

3 Environmental Perception for Navigation

Traditionally, localisation has been identified as a principal perceptual com-
ponent of the navigation system of a mobile robot [53]. This has driven
continuous research and development on sensors providing direct localisation
measurements.
There is a large variety of self-localisation solutions available [5] in the
literature. However, in general they are characterised by a hard and limiting
tradeoff between robustness and cost. As paradigmatic and extreme examples
we can refer to solutions based on artificial landmarks (beacons) and those
based on odometry. Solutions based on beacons are robust but expensive
in terms of the materials, installation, maintenance or configuration to fit
a specific new purpose. The solutions based on odometry are inexpensive, but
since they rely on the integration of the robot’s internal measurements, i.e.
not grounded to the world, errors accumulate over time.
We use vision to sense the environment as it allows navigation to be regu-
lated by the world. In particular, we have noted the advantages of omnidirec-
tional vision for navigation, including its flexibility for building environmental
representations. Our robot combines two main navigation modalities: Visual
Path Following and Topological Navigation. In Visual Path Following, the
short-distance / high-accuracy navigation modality, the orthographic view of
the ground plane is a convenient world model as it makes simple represent-
ing / tracking ground plane features and computing the pose of the robot.
Panoramic views are a complementary representation, which are useful in the
identification and extraction of vertical line features. These types of views are
easily obtained from omnidirectional cameras using image dewarpings.
In Topological Navigation, the large-distance low-precision navigation
modality, omnidirectional images are used in their raw format to characterise
the environment by its appearance. Omnidirectional images are advantageous
as they are more robust to occlusions created e.g. by humans. Visual servoing
is included in topological navigation as the means of providing local control.