# A catastrophe theory model of planar orientation

## Abstract

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, the authors have shown specifically under what conditions this representation undergoes qualitative, topological transitions corresponding to globally distinct behavioral regimes. In this paper, they 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 machine. 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.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Edinburgh (GB)

- OSTI Identifier:
- 20067738

- Resource Type:
- Journal Article

- Journal Name:
- International Journal of Robotics Research

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 6; Other Information: PBD: Jun 2000; Journal ID: ISSN 0278-3649

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; MATHEMATICAL MODELS; ORIENTATION; ROBOTS; AUTOMATION; INDUSTRIAL PLANTS

### Citation Formats

```
Wright, M.W., and Deacon, G.E.
```*A catastrophe theory model of planar orientation*. United States: N. p., 2000.
Web. doi:10.1177/02783640022067012.

```
Wright, M.W., & Deacon, G.E.
```*A catastrophe theory model of planar orientation*. United States. doi:10.1177/02783640022067012.

```
Wright, M.W., and Deacon, G.E. Thu .
"A catastrophe theory model of planar orientation". United States. doi:10.1177/02783640022067012.
```

```
@article{osti_20067738,
```

title = {A catastrophe theory model of planar orientation},

author = {Wright, M.W. and Deacon, G.E.},

abstractNote = {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, the authors have shown specifically under what conditions this representation undergoes qualitative, topological transitions corresponding to globally distinct behavioral regimes. In this paper, they 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 machine. 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.},

doi = {10.1177/02783640022067012},

journal = {International Journal of Robotics Research},

issn = {0278-3649},

number = 6,

volume = 19,

place = {United States},

year = {2000},

month = {6}

}