A Relative Orientation Algebra with Adjustable Granularity

The granularity of spatial calculi and the resulting mathematical properties have always been a major question in solving spatial tasks qualitatively. In this paper we present the Oriented Point Relation Algebra (OPRAm), a new orientation calculus with adjustable granularity. Since our calculus is a relation algebra in the sense of Tarski, fast standard inference methods can be applied. One of the major problems—depending on the environment, the robots’ capabilities and the tasks to be solved—is the choice of the granularity of an applied calculus. To present, granularity had to be chosen at the start and could not be changed on the fly. In a dynamically changing environment under real time conditions it is necessary to choose a coarse but still adequate granularity of the spatial representation: only in that case irrelevant feature changes fail to trigger unnecessary inference steps. A qualitative, coarse abstraction suppresses tiny changes in the environment and leads to fast computation.