We propose an architecture for self-motivated agents allowing them to construct their own knowledge of objects and of geometrical properties of space through interaction with their environment. Self-motivation is defined here as a tendency to experiment and to respond to behavioral opportunities afforded by the environment. Interactions have predefined valences that specify inborn behavioral preferences. The long-term goal is to design agents that construct their own knowledge of their environment through experience, rather than exploiting pre-coded knowledge. Over time, the agent learns relations between elements of the environment that afford its interactions, and its perception of these elements, in the form of data structures called signatures of interactions. These signatures allow the agent to attribute a low level semantics to elements that constitute its environment based on valences of interactions, without predefined knowledge about these elements and regardless of the number of element types. Signatures of interaction are then used to localize elements in space and to construct data structures that characterize spatial properties of space, called signatures of places and signatures of presence. Signatures of place and of presence characterize space using interactions rather than geometrical or topological properties. The agent uses these structures to maintain an egocentric representation of affordances of the surrounding environment, without any preconception about the elements that compose the environment, and without using notions of geometrical space. Experiments with simulated agents show that they learn to behave in their environment, taking into account multiple surrounding objects, reaching or avoiding objects according to the valence of the interactions that they afford.