We present an architecture for self-motivated agents to organize their behaviors according to possibilities of interactions proposed by the environment, and to modify the environment to construct new possibilities of interactions. The long-term goal is to design agents that construct their own knowledge of objects through experience, rather than exploiting pre-coded knowledge, and exploit this knowledge to generate complex behaviors that satisfy their intrinsic motivation principles. Self-motivation is defined here as a tendency, based on inborn behavioral preferences, to experiment and to respond to behavioral opportunities afforded by the environment. Over time, the agent integrates, through its experience, relations between interactions and object affording them in the form of data structures, called signatures of interaction, which encode the minimal spatial configurations affording an interaction. The agent then exploits these signatures to recognize distant possibilities of interactions (or affordances), but also incomplete affordances. These structures help the agent defining behaviors that can construct affordances from separated elements. Experiments with a simulated agent show that they learn to navigate in their environment, reaching, avoiding and constructing objects according to the valence of the interactions that they afford.