Page 28 - Autonomous Mobile Robots

12 Autonomous Mobile Robots

In summary, ladar offers considerable advantages over passive imaging but
there remain many technical difficulties to be overcome before they can meet
the tough requirements for vehicle guidance. The advantages are:

• Unambiguous 3D measurement over wide FOV and distances
• Undiminished night-time performance and tolerance to adverse
weather conditions

The limitations are:

• Relatively high cost, bulky, and heavy systems
• Limited spatial resolution and low frame rates
• Acquisition of phantom points or multiple points at edges or
permeable surfaces
• Active systems may be unacceptable in certain applications

The important characteristics to consider, when selecting a ladar for a guid-
ance application, are: angular resolution, range accuracy, frame rate, and cost.
An excellent review of ladar technology and next generation requirements is
provided by Stone at NIST [12].

1.2.2 Modeling of Image Formation and Calibration
1.2.2.1 The ideal pinhole model

It is worthwhile to introduce the concept of projection and geometry and some
notation as this is used extensively in visual sensing techniques such as stereo
and structure from motion. Detail is kept to a minimum and the reader is referred
to standard texts on computer vision for more information [13–15]. The stand-
ard pinhole camera model is adopted, while keeping in mind the underlying
3
assumptions and that it is an ideal model. A point in 3D space {X ∈ R } pro-
˜
2
jects to a point on the 2D image plane {˜x ∈ R } according to the following
equation:
x = PX: P ∈ R 3×4 (1.1)

This equation is linear because we use homogeneous coordinates by aug-
˜ T
T
4
menting the position vectors with a scalar (X =[X 1] ∈ R ) and likewise
3
T
the image point (x =[xy w] ∈ R : ˜x = x/w). A powerful and more natural
way of treating image formation is to consider the ray model as an example
of projective space. P is the projection matrix and encodes the position of the

© 2006 by Taylor & Francis Group, LLC

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