Merging probabilistic models of navigation:: the Bayesian Map and the Superposition operator

This paper deals with the probabilistic modeling of space, in the context of mobile robot navigation. We define a formalism called the Bayesian Map, which allows incremental building of models, thanks to the Superposition operator, which is a formally well-defined operator. Firstly, we present a syntactic version of this operator, and secondly, a version where the previously obtained model is enriched by experimental learning. In the resulting map, locations are the conjunction of underlying possible locations, which allows for more precise localization and more complex tasks. A theoretical example validates the concept, and hints at its usefulness for realistic robotic scenarios.