This paper concerns the incremental learning of hierarchies of representations of space in artificial or natural cognitive systems. We propose a mathematical formalism for defining space representations (Bayesian Maps) and modelling their interaction in hierarchies of representations (sensorimotor interaction operator). We illustrate our formalism with a robotic experiment. Starting from a model based on the proximity to obstacles, we learn a new one related to the direction of the light source. It provides new behaviours, like phototaxis and photophobia. We then combine these two maps so as to identify parts of the environment where the way the two modalities interact is recognisable. This classification is a basis for learning a higher level of abstraction map that describes the large-scale structure of the environment. In the final model, the perception–action cycle is modelled by a hierarchy of sensorimotor models of increasing time and space scales, which provide navigation strategies of increasing complexities.