Universität Salzburg

Conference EUROCAST-2005

10th International Conference On Computer Aided Systems Theory

February 7-11, 2005, Las Palmas de Gran Canaria



Workshop Session:     "ROBOTICS   and   CONTROL"

co-organized by Jochen Pfalzgraf

NOTE:   This session includes the originally planned separate session     "Symbolic, Numeric and Connectionist Methods in ROBOTICS" .


Advisory Board:

Bruno Buchberger   (Linz),     Jacques Calmet   (Karlsruhe),     John A. Campbell  (London)

Among others,   welcome are all contributions dealing with
symbolic, numeric, connectionist methods in ROBOTICS including hybrid symbolic and numerical and neural network techniques and, more general, soft computing approaches. Work dealing with (scenario) SIMULATION is also of interest.

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Please send your submission (extended abstract, including references) to the organizer of this session.

******     DEADLINE for Extended Abstracts:   October 31, 2004   ( +   epsilon)     ******

EUROCAST-2005 web page     (http://www.ciber.ulpgc.es)

Important Information

Originally planned:     Opening Talk

Jochen Pfalzgraf:   "On a Hybrid Symbolic, Connectionist Approach for Modeling Robot Arm Kinematics"

The kinematics model of a robot arm (we are considering open kinematic chains) is described by a corresponding robot map having the configuration space as its domain and the workspace as codomain. In other words, the robot map asssigns to every configuration of the joint parameters a point of the workspace of the robot arm. Standard problems arising are the direct kinematics problem, the inverse kinematics problem and the singularity problem. A classical method to establish the robot map is the approach by Denavit-Hartenberg. It leads to a completely symbolic description of the direct kinematics model of an arm and forms the basis for solving the inverse kinematics problem. In order to represent an entire robot arm class it is of basic interest to find a completely symbolic closed form solution of the inverse kinematics problem. Using a two joint robot arm, B.Buchberger demonstrated the principle to achieve this task with the help of a computer algebra system applying his Gröbner bases method. Later we made own investigations, among others, constructing a more complex test example. It turned out that this task leads to very hard performance problems when the degree of freedom of a robot arm increases. An interesting sideeffect is that these investigations showed a natural way to construct benchmarks for computer algebra.
A completely different way to represent the kinematic model of a robot arm is to learn the corresponding robot map with the help of a suitably chosen connectionist network using a powerful artificial neural network simulator. This approach also reaches soon its limits when the number of joints increases.
These experiences formed the basis of the idea to combine both approaches with the hope to cope with the increasing complexity. The simple idea is to devide the joints of a robot arm into two sets, then model one set of consecutive joints symbolically, the other set with the connectionist method and finally to combine both parts to represent the complete robot map. In a diploma thesis a student in our group worked on this idea using selected robot arm types and he could demonstrate that it is worthwhile considering this approach for use in concrete applications.
In our working group a new connectionist simulator (FlexSimTool) which will provide a flexible tool for simulation of a large class of neural network types that have neurophysiological roots has been developed and implemented (work is in progress). An own novel mathematical approach for modeling network structures that uses methods from category theory and geometry provides a precise guideline for the generic implementation of networks in the new simulation tool. It can be shown theoretically with an argument form category theory that the mathematical model helps to reduce complexity of learning in concrete simulations this new simulator. Topics of intended future work deal with the extension of the FlexSimTool including modules or interfaces concerning robot simulation, computer algebra, fuzzy reasoning, multiagent systems techniques, a logic module (especially based on the concept of logical fiberings - an approach dealing with distributed logics). Work is in progress.
The flexible simulation tool will be well suited for the treatment of industrial application problems.

Of further and related interest on ROBOTICS:   Math in ROBOTICS