IEEE Robotics & Automation Magazine - June 2013 - 91
© digital vision
tutorial
Geometric Relations Between
Rigid Bodies (Par t 2)
From Semantics to Software
By Tinne De Laet, Steven Bellens, Herman Bruyninckx, and Joris De Schutter
R
igid bodies are essential primitives in the modeling
of robotic devices, tasks, and perception. Basic
geometric relations between rigid bodies include
relative position, orientation, pose, linear velocity,
angular velocity, twist, force, torque, and wrench. In
Part 1 of this tutorial [3], we explicitly stated the semantics of
all coordinate-invariant properties and operations, and, more
importantly, all the choices that are made in coordinate
representations of these geometric relations. This resulted in a
set of concrete suggestions for standardizing terminology
and notation.
In this tutorial, we show how the proposed semantics
allow us to write fully unambiguous software interfaces,
including automatic checks for semantic correctness of all
geometric operations on rigid-body coordinate representations. As a teaser, "Common Error 1: Logic Errors in Geomet-
Digital Object Identifier 10.1109/MRA.2012.2230501
Date of publication: 6 June 2013
1070-9932/13/$31.00©2013IEEE
ric Relation Calculations" shows how one of the common
errors listed in [3] can be prevented using the software presented in this tutorial.
This tutorial is supplementary to the software Web page
[2], containing a more detailed explanation on the C++
libraries implementing the geometric semantics for rigidbody calculations.
Following the same pattern as [3] this tutorial uses a running example to explain the different aspects. First, four use
cases involving manipulations of the geometric relations
between rigid bodies are proposed. Each of the use cases is
illustrated using the running example. Next, a software
design implementing the semantics for the geometric
relations between rigid bodies and inspired by the different
use cases is proposed. Using the running example, a particular C++ implementation of this design, referred to as "geometric_relations_semantics" [2], is demonstrated on the
running example for all four use cases. The geometric_relations_semantics library provides the semantic checking for
jUNE 2013
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IEEE ROBOTICS & AUTOMATION MAGAZINE
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