Abstract
Some selected applications of mathematical modeling methods in the AI field robotics are presented in survey style by examples of geometric reasoning, topological reasoning and so-called fibered logical spaces for logical reasoning in robotics. The main perspective is on interaction and combination of different fields and methods from symbolic mathematical computation and AI and the mutual stimulation given by the various disciplines.
sponsored by the Austrian Ministry of Science and Research (BMWF), ESPRIT BRA 3125 ”MEDLAR”
The selected information material we presented here should illustrate the above mentioned aspects and, hopefully, contains some suggestions valuable for the reader.
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References
J. Angeles. Rational Kinematics. Springer, New York-Berlin, 1988.
D.R. Baker. Some topological problems in robotics. Mathematical Intelligencer, 12:66–76, 1990.
J. Bochnak, M. Coste, and M-F. Roy. Géometrie algébrique réelle. Springer Verlag, 1987.
J.-D. Boissonat and J.-P. Laumond (eds.). Geometry and Robotics. Springer Verlag, 1989. Lecture Notes in Computer Science 391.
B. Buchberger. Gröbner bases: An algorithmic method in polynomial ideal theory. In Multidimensional Systems Theory (N.K.Bose, ed.), pages 184–232. D.Reidel Publ. Comp., Dordrecht-Boston-Lancaster, 1985.
B. Buchberger. Applications of Gröbner bases in non-linear computational geometry. Mathematical Aspects of Scientific Software (J.R.Rice, ed.), 14:59–87, 1987.
B. Buchberger, G. Collins, and B. Kutzler. Algebraic methods for geometric reasoning. Ann. Rev. Comput. Sci., 3:85–119, 1988.
J.W. Burdick. On the inverse kinematics of redundant manipulators: Characterization of the self-motion manifolds. IEEE, pages 264–270, 1989.
J.F. Canny. The Complexity of Robot Motion Planning. MIT Press, Cambridge Massachusetts and London, 1988.
G.E. Collins: Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. Lecture Notes In Computer Science, 33:134–183, 1975.
J.J. Craig. Introduction to Robotics. Addison-Wesley Publ. Co., 1986.
F. Dargam, J. Pfalzgraf, V. Stahl, and K. Stokkermans. Towards a toolkit for benchmark scenarios in robot multi-tasking. Technical Report 91-45.0, RISC-Linz, J. Kepler University, Linz, Austria, 1991.
R. Eckmiller. Concerning the emerging role of geometry in neuroinformatics. In Parallel Processing in Neural Systems and Computers, Eckmiller, Hartmann, Hauske (eds.). Proceedings, Elsevier Sc. Publ (North-Holland), 1990.
H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer Verlag, 1987.
D. Gabbay. Labelled Deductive Systems, Part I. CIS, University of Munich, 1990. CIS-Bericht-90-22.
D.H. Gottlieb. Robots and fibre bundles. Bulletin de la Société Mathématique de Belgique, 38:219–223, 1987.
D.H. Gottlieb. Topology and the robot arm. Acta Applicandae Mathematicae, 10:1–5, 1987.
J. Heinzelreiter and H. Mayr. Machining simulation and verification by efficient dynamic modeling. In 23rd ISATA, Int. Symp. on Automotive Technology and Automation, Dec. 3–7, Vienna, Austria, 1990.
P. Hintenaus. The inverse kinematics system — installation guide, user's manual, program documentation. RISC-Linz Report no 87-18.0, RISC-Linz, J. Kepler University, Linz, Austria, 1987.
H. Hong. Improvements in CAD-based quantifier elimination. PhD Thesis, Ohio State University, 1990.
J.E. Hopcroft. The impact of robotics on computer science. Communications of the ACM, 29:486–498, 1986.
D. Kapur and J.L. Mundy. Geometric Reasoning. MIT Press, Cambridge Massachusetts and London, 1989. Special Issue of AI.
A. Karger and J. Novák. Space Kinematics and Lie Groups Gordon and Breach Science Publishers, New York-London-Paris-Montreux, 1985.
U. Karras. On mathematics in robotics. Lecture Notes (in German), DMV Seminar on Mathematics in Robotics; held in Blaubeuren, November, 1988.
O. Khatib. Real-time obstacle avoidance for manipulators and mobile robots. Internat. J. of Robotics Research, 5:90–98, 1986.
D.E. Koditschek. Exact robot navigation by means of potential functions: Some topological considerations. In Proceed. IEEE Int. Conf. on Robotics and Automation, 1987.
H. Mayr, M. Held, and H. Öllinger. SMART-A Universal System for the Simulation of Robot and Machining Tasks. In CAPE'89, Tokyo, Japan, 1989.
J.M. McCarthy. An Introduction to Theoretical Kinematics. MIT Press, Cambridge Massachusetts and London, 1990.
K. Mehlhorn. Data Structures and Algorithms, Vol. 1–3. Springer Verlag, 1984.
R.P. Paul. Robot Manipulators. MIT Press, Cambridge Massachusetts and London, 1982.
J. Pfalzgraf. Logical fiberings and polycontextural systems. In Fundamentals of Artificial Intelligence Research, Ph. Jorrand, J.Kelemen (eds.). Lecture Notes in Computer Science 535, Subseries in AI, Springer Verlag, 1991.
J. Pfalzgraf. Neural Networks in Robotics Simulation. In: Symbolic Computation Tools for Technological Applications, J. Heinzelreiter et.al. In Proceedings IFAC Symposium on Robotics Control (SYROCO'91), Vienna, Austria, 1991.
J. Pfalzgraf. On geometric and topological reasoning in robotics to be submitted to Annals of Math and AI, 1992.
J. Pfalzgraf, K. Stokkermans, and D. Wang. The robotics benchmark. Proc. 12-month MEDLAR Workshop (Weinberg Castle, Austria, November 4–7), 1990.
F.P. Preparata and M.I. Shamos. Computational Geometry. Springer Verlag, 1985.
J.H. Reif and J.A. Storer. 3-dimensional shortest paths in the presence of polyhedral obstacles. In Mathematical Foundations of Computer Science 1988. Proceedings. Lecture Notes in Computer Science 324, 1988.
J.T. Schwartz, M. Sharir, and J. Hopcroft. Planning, Geometry, and Complexity of Robot Motion. Ablex Publishing, Norwood New Jersey, 1987.
S. Stifter. An axiomatic approach to voronoi-diagrams in 3D. J. of Computer and System Sciences, 43:361–379, 1991.
D.M. Wang. Reasoning about geometric problems using algebraic methods. proc. medlar 24-month review workshop, grenoble, december 1991. Technical Report 91-51.0, RISC-Linz, J. Kepler University, Linz, Austria, 1991.
W.T. Wu. Basic principles of mechanical theorem proving in elementary geometries. J. Automated Reasoning, 2:221–252, 1986.
C-K. Yap. An O(n log n) algorithm for the voronoi diagram of a set of simple curve segments. Discrete Comput. Geom., 2:365–393, 1987.
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Pfalzgraf, J. (1993). On mathematical modeling in robotics. In: Calmet, J., Campbell, J.A. (eds) Artificial Intelligence and Symbolic Mathematical Computing. AISMC 1992. Lecture Notes in Computer Science, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57322-4_8
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DOI: https://doi.org/10.1007/3-540-57322-4_8
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