Fine-grained Qualitative Spatial Reasoning about Point Positions

TL;DR

This paper introduces a new qualitative spatial calculus that allows for fine-grained reasoning about point orientations and distances, enhancing spatial cognition models and robotic applications.

Contribution

It presents a novel calculus supporting arbitrary granularity in ternary relations, improving reasoning complexity and demonstrating its capabilities through implementation.

Findings

New calculus supports arbitrary granularity in spatial relations

Improved reasoning complexity over existing calculi

Implementation validates the calculus's effectiveness

Abstract

The ability to persist in the spacial environment is, not only in the robotic context, an essential feature. Positional knowledge is one of the most important aspects of space and a number of methods to represent these information have been developed in the in the research area of spatial cognition. The basic qualitative spatial representation and reasoning techniques are presented in this thesis and several calculi are briefly reviewed. Features and applications of qualitative calculi are summarized. A new calculus for representing and reasoning about qualitative spatial orientation and distances is being designed. It supports an arbitrary level of granularity over ternary relations of points. Ways of improving the complexity of the composition are shown and an implementation of the calculus demonstrates its capabilities. Existing qualitative spatial calculi of positional information are compared to the new approach and possibilities for future research are outlined.