Despite its omnipresence in robotics application, the nature of spatial knowledge and the mechanisms that underlie its emergence in autonomous agents are still poorly understood. Recent theoretical works suggest that the Euclidean structure of space induces invariants in an agent’s raw sensorimotor experience. We hypothesize that capturing these invariants is beneficial for sensorimotor prediction and that, under certain exploratory conditions, a motor representation capturing the structure of the external space should emerge as a byproduct of learning to predict future sensory experiences. We propose a simple sensorimotor predictive scheme, apply it to different agents and types of exploration, and evaluate the pertinence of these hypotheses. We show that a naive agent can capture the topology and metric regularity of its sensor’s position in an egocentric spatial frame without any a priori knowledge, nor extraneous supervision.