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check whether the provided inputs and outputs are as
expected during integration.
Common Errors in Geometric Rigid-Body
Relations Calculations in Robotics
In [3], we identified five common errors that could be
prevented by making the semantics underlying the geometric rigid-body relations explicit. In addition to teaser
presented at the beginning of the tutorial (see "Common
Error 1"), "Common Error 2" through "Common Error 5"
show how the other four common errors can be prevented
using the software presented in this tutorial.
Extending Geometry Library
withSemantic Checking
If a programmer wants to perform actual geometric relation
calculations using his own geometry library that does not offer
semantic support, he can easily build semantic support on top
of this library. Due to the software design (see the "General
Software Design" section), which is based on composition,
extending a geometry
library with semantic support boils down to impleThe actual numerical
menting a limited number
of functions, which make
calculations with the
the connection between
semantic operations (e.g.,
particular coordinate
composition) and actual
coordinate representation
representation are
calculations (e.g., multiplication of homogeneous
performed on top of the
transformation matrices).
Due to the compositionsemantic checks.
based design, there is no
need to change the original class libraries. A tutorial explaining how to extend your
geometry library with semantic checking is available [2].
Conclusion
This tutorial presented a software design founded on the
semantics underlying the rigid-body geometric relations of
position, orientation, pose, linear velocity, angular velocity, and
twist (presented in [3]), and shows how this software prevents
common errors, and hence reduces application (and, especially, system integration) development time considerably.
This tutorial is supplementary to the software Web
page [2], containing a more detailed explanation on the
C++ libraries implementing the geometric semantics for
rigid-body calculations. This software is publicly and freely

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IEEE ROBOTICS & AUTOMATION MAGAZINE

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available under the dual LGPLv2.1/BSD open-source license.
The design explained in this tutorial is, however, more generally applicable and can be used as a basis for libraries in other
languages. Furthermore, we believe it is particularly suitable
as a programming language-independent domain-specific
language (DSL) for geometric relations. Therefore, future
work aims at developing a DSL founded on the semantics
proposed in [3] and the software design presented in this
tutorial along with tools to do the actual checking, generate
verified code (model-to-text conversion), and transform
between different coordinate representations (model-tomodel conversion).
Acknowledgments
The authors would like to acknowledge the financial support by KU Leuven's Concerted Research Action
G0A/2010/011 Global realtime optimal control of autonomous robots and mechatronic systems, the FWO Project
G040410N Autonomous manipulation using a flying robot,
the KU Leuven-BOF PFV/10/002 Center-of- Excellence
Optimization in Engineering (OPTEC), and the European
FP7 projects 2008-ICT-230902-ROSETTA 2008-ICT231940-BRICS and FP7-ICT-288533 RoboHow.Cog.
References
[1] (2011). Robotics Library. [Online]. Available: http://sourceforge.net/apps/
mediawiki/roblib
[2] T. De Laet and S. Bellens. (2012, May). Geometric Semantics Software. [Online].
Avaliable: http://www.orocos.org/wiki/geometric-relations-semantics-wiki
[3] T. De Laet, S. Bellens, R. Smits, E. Aertbelien, H. Bruyninckx, and J. De
Schutter, "Geometric relations between rigid bodies: Semantics for standardization," IEEE Robot. Autom. Mag., vol. 20, no. 1, pp. 84-93.
[4] T. Foote. (2012). Robot Operating System (ROS) Geometry Stack. [Online].
Avaliable: http://ros.org/wiki/geometry
[5] R. Smits. (2011). KDL: Kinematics and Dynamics Library. [Online]. Avaliable: http://www.orocos.org/kdl
[6] K. Waldron and J. Schmiedler. "Kinematics," in Handbook of Robotics. Berlin, Germany: Springer-Verlag, 2008, pp. 9-33.

Tinne De Laet, KU Leuven, Belgium. E-mail: Tinne.DeLaet@
mech.kuleuven.be.
Steven Bellens, KU Leuven Leuven, Belgium. E-mail: Steven.
Bellens@mech.kuleuven.be.
Herman Bruyninckx, KU Leuven Leuven, Belgium. E-mail:
Herman.Bruyninckx@mech.kuleuven.be.
Joris De Schutter, KU Leuven Leuven, Belgium. E-mail: Joris.
DeSchutter@mech.kuleuven.be.

http://www.sourceforge.net/apps/ http://www.orocos.org/wiki/geometric-relations-semantics-wiki http://www.ros.org/wiki/geometry http://www.orocos.org/kdl

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