Current research topics of Leo Dorst
My research is generally in the area of
principles of autonomous
systems, for which I am responsible within our group
Intelligent Autonomous Systems.
Specific subjects that involve my personal research are:
Abstracts and publications on these subjects may be found here.
Applications of Geometric (Clifford) Algebra
Recently (from September 1997) I have become very enamored of Geometric Algebra, and am
studying it diligently to use it in geometric problems in robotics.
I have done a sabbatical with Hestenes' group at Arizona State University
from November 98 to April 99, and have applied it towards a solution of
the collision detection problem (see below).
More information here.
Objects in Contact
The generation of collision-free paths for a robot is commonly
represented in the parameter space of the robot, better known as
configuration space. Obstacles are represented as sets of forbidden
states. It is an essential but unsolved problem to calculate these sets
for arbitrary robots and environments. With Rein
van den Boomgaard, I have developed an analytical
framework for computations of objects in contact, which has now been
connected to the mathematical theory of contact transformations. Using
homogeneous coordinates in projective space, we expect to convert the
theory into a practical computational method.
Here is an overview talk in ps or
But using geometric algebra, one can address the issues in n-dimensional
space, see here!
There is a dichotomy in robot behavior, between reactive behavior
and planned behavior. In an exploration task, both meet. With
Ben Kröse, I try to characterize the
geometry of the sensor motor configuration spaces in which the reactive
behavior resides, in order to obtain a better formal understanding and
characterization of this transition in behavior in exploration tasks.
Reasoning with uncertainty in robotics
With people from the
ILLC, I am trying to get a better hold on
the proper uncertainty reasoning mechanisms in robotics, notably
in representations of uncertain geometry. We organized a
Abstraction in path planning
The robot path planning problem is well-understood on the lowest level,
that of configuration spaces, and optimal paths may be computed using
a method like wave-propagation (A*). It is an open problem how to abstract
from paths generated and represented in this way to more abstract path
descriptions, and corresponding planning algorithms. I am trying to approach
this using geometric/topological methods (with a pinch of homology).
Digitized straight lines
A very long time ago, for my Ph.D. thesis, I worked on the estimation of
properties of digitized straight boundaries. I solved the problem by finding
a characterization of those boundaries, and the set of continuous lines
that could have generated them. The transform that made the problem
tractable is actually a precursor of the slope transform.
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