On Robotics Scenarios and Modeling with Fibered Structures

Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)


The field of robotics has been one of the main working areas of the RISC-Linz group in the MEDLAR project. In the first project year of BRA 3125 (subsequently referred to as MEDLAR I) we started with case studies (Pfalzgraf and Stokkermans 1992) in order to get an overview of material which we considered to be relevant as support and motivation of future project work. These future aspects are especially seen with regard to the applications of methods developed by the other project partners. Therefore it became more and more clear that one of the main objectives of our work on robotics has to do with the construction of “scenarios” where various reasoning methods can be applied and tested and extended. That means that we thought of providing testbeds where each partner should be able to identify a problem suitable for application of her/his corresponding methods, respectively. This would describe the ideal case. Subsequently, in the next section, we will go into more details. Actually, the development of these ideas started in the course of MEDLAR I and they found enough interest as to be continued in the first year of MEDLAR II (BRP 6471), the project successor of MEDLAR I. The existing material is intended to serve as a basis for work on parts of a MEDLAR practical reasoner (in the third year). In our case this refers to a reasoning module for specific robotics problems which corresponds to our special fields of interest namely algebraic approaches to geometric reasoning problems with emphasis on robot kinematics and singularity problems.


Base Space Autonomous Agent Fibered Structure Activation Truth Inverse Kinematic Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Caferra, R., Zabel, N. (1992): A method for simultaneous search for refutations and models by equational constraint solving. J. Symb. Comput. 13: 613–641.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Cunningham, J. (1993): Concurrent deduction: classical and modal. In: Working Notes of 1993 AAAI Fall Symposium on Automated Deduction in Non-Standard Logics. AAAI, Menlo Park, CA.Google Scholar
  3. Gabbay, D. (1990): Labelled deductive systems, part I. CIS, University of Munich, CIS-Bericht 90-22.Google Scholar
  4. Goldblatt, R. (1984): Topoi. The categorial analysis of logic. North-Holland, Amsterdam (Studies in logic and the foundations of mathematics, vol. 98).zbMATHGoogle Scholar
  5. Große, G., Hölldobler, S., Schneeberger, J., Sigmund, U., Thielscher, M. (1992): Equational logic programming, actions, and change. In: Proceedings of the Joint International Conference and Symposium on Logic Programming’ 92. MIT Press, Cambridge, MA, pp. 177–191.Google Scholar
  6. Hörmann, K., Hübner, T., Spreng, M. (1993): Contact analysis and verification in a 2D environment with uncertainties. J. Intell. Robotic Syst. 7: 175–193.CrossRefGoogle Scholar
  7. Lambek, J., Scott, P. (1986): Introduction to higher-order categorical logic. Cambridge University Press, Cambridge (Studies in advanced mathematics, vol. 7).zbMATHGoogle Scholar
  8. Letz, R., Schumann, J., Bayerl, S., Bibel, W. (1992): SETHEO: a high-performance theorem prover. J. Autom. Reason. 8: 183–212.MathSciNetzbMATHCrossRefGoogle Scholar
  9. MacLane, S. (1971): Categories for the working mathematician. Springer, Berlin Heidelberg New York Tokyo (Graduate texts in mathematics, vol. 5).Google Scholar
  10. Pfalzgraf, J. (1991): Logical fiberings and polycontextural systems. In: Jorrand, P., Kelemen, J. (eds.): Fundamentals of artificial intelligence research. Springer, Berlin Heidelberg New York Tokyo, pp. 170–184 (Lecture notes in computer science, vol. 535).CrossRefGoogle Scholar
  11. Pfalzgraf, J. (1995): On geometric and topological reasoning in robotics. Ann. Math. Artif. Intell. (to appear).Google Scholar
  12. Pfalzgraf, J., Stokkermans, K. (1992): Scenario construction continued and extended with a view to test and enhancement of reasoning methods. Tech. Rep. RISC Linz 92-27.Google Scholar
  13. Sigmund, U. (1992): LLP — Lineare logische Programmierung. Master’s thesis, Technische Hochschule Darmstadt, Darmstadt, Federal Republic of Germany.Google Scholar
  14. Wang, D. (1991a): Reasoning about geometric problems using algebraic methods. In: Medlar Milestone II Deliverable, Grenoble, November 1991.Google Scholar
  15. Wang, D. (1991b): On Wu’s method for solving systems of algebraic equations. Tech. Rep. RISC Linz 91-52.Google Scholar

Copyright information

© Springer-Verlag Wien 1995

Authors and Affiliations

There are no affiliations available

Personalised recommendations