We present an architecture for self-motivated agents to organize their behaviors in space according to possibilities of interactions afforded by initially unknown objects. The long-term goal is to design agents that construct their own knowledge of objects through experience, rather than exploiting precoded knowledge. Self-motivation is defined here as a tendency to experiment and to respond to behavioral opportunities afforded by the environment. Some interactions have predefined valences that specify inborn behavioral preferences. Over time, the agent learns the relation between its perception of objects and the interactions that they afford, in the form of data structures, called signatures of interaction, which encode the minimal spatial configurations that afford an interaction. The agent keeps track of enacted interactions in a topological spatial memory, to recognize and localize subsequent possibilities of interaction (through their signatures) afforded by surrounding objects. Experiments with a simulated agent and a robot show that they learn to navigate in their environment, taking into account multiple surrounding objects, reaching or avoiding objects according to the valence of the interactions that they afford.