Representing Simple Trajectories as Oriented Curves

Carola Eschenbach, Christopher Habel and Lars Kulik, University of Hamburg

We present a formal framework for the description of ordering information on directed linear structures like trajectories of moving objects. The foundation of this approach is an axiomatic characterization of oriented curves. They provide a generalized notion of direction. The proposed geometric framework allows a qualitative characterization of oriented curves without commitment to concepts of measurement. The geometry of oriented curves is applied to reasoning about the possibility of meeting of objects that move along intersecting trajectories. To determine the possibility of meeting is part of planning and scheduling tasks, e.g. concerning systems of transport vehicles, as well as in the task of avoiding collision. We show that the reasoning system proposed here needs only one purely temporal notion, namely that of simultaneity.

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