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Chapter 2
Related Work
This chapter presents work related to this thesis. At first, general applications where coordinate frame
transformations are used will be presented. Afterwards component-based robotic middlewares which
partly support transformations are discussed. These middlewares and how coordinate frame transformations
are used in different applications are of interest for this work, because they show what already
exists in this area and which topics still must be addressed.
2.1 Coordinate Frame Transformations
Coordinate frames and the transformation of data between different coordinate frames are widely used
in many applications. Coordinate frame transformation provide the mathematic foundation to solve
the problems which occur in these applications. Being a basic mathematic tool coordinate systems and
their transformation are described in many math books like [17][20]. In the following, examples of
areas where transformations are used are given. Further the way how coordinate frame transformations
are managed in these applications is judged in terms of the use in robotic systems.
An application where transformations are used for a long time is celestial mechanics [14]. There
they are used to transform observational quantities from one coordinate frame to another. These
could for example be two observatories on the earth exchanging data of some observation. Celestial
mechanics are a difficult and complex topic, that also deals with uncertain observations. In most
cases not the Cartesian coordinate systems is used, but Geodetic or Geocentric coordinate systems
are used. In general some methods like the use of uncertainties can also be applied in robotics, but
celestial mechanics provide far more methods like the determination of orbits which are not needed
in robotics.
Another application where coordinate systems are widely used is aerospace [19]. There the position
of an airplane is normally given relative to the coordinate system of the earth. However if a
spacecraft is sent into deep space a heliocentric system is preferred. Further there are additional coordinate
systems like Body Coordinates or Wind Coordinates and there is also an coordinate system
for navigation. Altogether aerospace is a complex application where coordinate systems are used.
Aerospace has to deal with other problems like wind which does not occur in service robotics. Thus
the way how coordinate systems are used in aerospace can not be directly applied in robotics.
Further CAD systems like AutoCAD [2] or 3D modelling suits like Blender [3] use coordinate
systems. There the position of bodies in relation to each other are described. The transformations have
precise values which means that there is no uncertainty included. In contrast thereto robotic systems
include sensors and actuators which introduce uncertainty. Further in robotics the transformation is
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