A framework for robust cognitive spatial mapping

Spatial knowledge constitutes a fundamental component of the knowledge base of a cognitive, mobile agent. This paper introduces a rigorously defined framework for building a cognitive spatial map that permits high level reasoning about space along with robust navigation and localization. Our framework builds on the concepts of places and scenes expressed in terms of arbitrary, possibly complex features as well as local spatial relations. The resulting map is topological and discrete, robocentric and specific to the agent's perception. We analyze spatial mapping design mechanics in order to obtain rules for how to define the map components and attempt to prove that if certain design rules are obeyed then certain map properties are guaranteed to be realized. The idea of this paper is to take a step back from existing algorithms and literature and see how a rigorous formal treatment can lead the way towards a powerful spatial representation for localization and navigation. We illustrate the power of our analysis and motivate our cognitive mapping characteristics with some illustrative examples.