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The Mathematics of Collision Avoidance in Two Dimensions

Published online by Cambridge University Press:  18 January 2010

S. H. Hollingdale
S. H. Hollingdale
Affiliation:
(Royal Aircraft Establishment)
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Extract

The geometry of collision at sea has been dealt with in a series of papers published in the Journal, notably by Sadler (10, 306), Calvert (13, 127), Garcia-Frias (13, 316) and Morell (14, 163); and a further contribution from Calvert (to which reference is made in this paper) will be published in the next number.

The object of the present paper is to examine whether anti-collision manœuvres, here considered for the case of two craft moving in a plane, can be formulated on a rigorous logical basis. If they can, then clearly a proper appreciation of the geometry of collision is a prerequisite to the formulation of any rules and regulations. In this important paper the author gives a precise and complete answer to the basic problem, and he proves mathematically that it is the only answer. As Dr. Hollingdale freely acknowledges, however, this can only be a contribution to the study of the collision problem, which involves innumerable operational factors in addition to the geometry of the situation.

The convention adopted in the present paper is that each craft shall manœuvre so that if the other craft stands on, the sight line always rotates in the anti-clockwise direction. The analysis shows that a simple set of manœuvres can in fact be developed on this basis and that such manœuvres are the only ones that, geometrically, meet all the specified requirements. In all cases the combined manœuvre converts a collision situation into a ‘miss’ of at least a specified magnitude.

Type
Research Article
Information
The Journal of Navigation , Volume 14 , Issue 3 , July 1961 , pp. 243 - 261
Copyright
Copyright © The Royal Institute of Navigation 1961

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References

REFERENCES

1Calvert, E. S. (1960). Manœuvres to ensure the avoidance of collision. This Journal, 13, 127.Google Scholar
2Calvert, E. S. (1961). A comparison of two systems for avoiding collision. To be published in this Journal, 14, No. 4.Google Scholar
3Wylie, F. J. and Planty, . (1960). Forum on the Calvert methods of manœuvring to avoid collision at sea and of radar display. This Journal, 13, 455.Google Scholar
4Gaudillère, P. (1958). The avoidance of collision in the air. This Journal, 11, 40.Google Scholar
5Wylie, F. J. (1960). Fifteen years of marine radar. This Journal, 13, 419.Google Scholar