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The International Journal of Robotics Research
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A Catastrophe Theory Model of Planar Orientation

Mark W. Wright

Edinburgh Virtual Environment Centre, King's Buildings, University of Edinburgh, Edinburgh, Midlothian EH9 3JZ, UK

Graham E. Deacon

Mechatronic Systems and Robotics Research Group, School of Mechanical and Materials Engineering, University of Surrey, Guildford, Surrey, GU2 5XH, UK

The manipulation of planar objects using linear fences is of interest in robotics and parts feeding applications. The global behavior of such systems can be characterized graphically using Brost's push stability diagram (PSD). Previously, we have shown specifically under what conditions this representation undergoes qualitative, topological transitions corresponding to globally distinct behavioral regimes. In this paper, we show that these insights form a united Whole when viewed from the perspective of catastrophe theory. The key result is that a planar object being pushed by a fence under the assumption of Coulomb friction is functionally equivalent to a gravitational catastrophe mnachine. Qualitative changes in global behavior are thus explained as catastrophes as singularities are encountered on a discriminant surface due to smooth changes in parameters. Catastrophe theory thus forms part of a computational theory of planar orientation, the aim of which is to understand such systems and make predictions about their behavior.

Key Words: catastrophe theory • singularity theory • planar orientation • rotational stability • behavioral equivalence

The International Journal of Robotics Research, Vol. 19, No. 6, 531-565 (2000)
DOI: 10.1177/027836490001900601
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