Second Scandinavian Workshop on
Interval Methods and Their Applications
TheSecond Scandinavian Workshop on Interval Methods and Their Applications
was hosted by the institute Informatics and Mathematical Modelling of the Tech-
nical University of Denmark, August 25–27, 2005 . The workshop attracted 44
participants from 11 countries.
Theworkshop provided a forum to review and discuss the state-of-the-art in
interval methods and their applications. Probably half the participants would iden-
tify themselves with engineering or scientiﬁc disciplines considered as “applications
areas” by the interval community. The workshop was preceded by a one day tutorial
given by George Corliss.
What was most striking was variety of engineering applications on which sig-
niﬁcant progress was reported. Whether we call them “interval,” “validated,” or
“reliable,” techniques, there is a feeling that such techniques may be turning a
corner from being of academic interest only toward the (yet very long) path toward
becoming the usual way engineers solve their problems.
Robotics: Jean-Pierre Merlet presented an illustrative example in kinematics,
workspace analysis, singularity avoidance, motion planning, and optimal design
of a six-legged platform. Interval analysis helps manage inevitable uncertainties in
the robot, and it has been able to provide solutions to problems for which no other
solutions are known.
Structures: George Corliss, Raﬁ Muhanna, and Arnold Neumaier described inter-
valﬁnite element methods for structures with large uncertain material properties
or loads. Neumaier achieved quite small overestimation for large, uncertain truss
structures leading to linear systems with over 5000 variables and over 10000 interval
Control: William Edmonson, Luc Jaulin, Martin Berz, and Dennis Bonn
interval techniques to control problems. Edmonson proposed validated techniques
from signal processing for a system of micro-robots for space applications includ-
ing craft location, collision avoidance, communications, rendezvous, and docking.
Jaulin demonstrated sailboat control and a wheeled stair-climbing robot by apply-
ing constraint propagation techniques to linear differential equations. Berz’s COSY
software package is used to control the operation of most of the world’s particle
accelerators. He showed how the use of Poincar
e sections signiﬁcantly reduces