Perceiving the topological structure of space through sensorimotor interaction

This paper deals with the perception of mobile robotic systems within the framework of interactive perception, and inspired by the sensorimotor contingencies theory. These approaches state that perception is an ability built from the motor and sensory data that an agent/robot experiences through its environment exploration. In a recent article, the authors have shown that the perception of space, provided it is limited to the agent’s own body, finds a solid mathematical basis in the SMC theory. An extension of these results to the agent working space is proposed in this paper. More precisely, it is demonstrated that a specific motor quotient space constitutes one possible support for a good representation of space. By defining a partial order relation over all the set of partitions of the motor space, a refinement process is defined on the basis on the sensorimotor invariants. The finest motor partition, obtained after having experienced all environment states, is then shown to be homeomorphic to the robot working space. A very simple algorithm implementing these ideas is proposed together with mathematical proofs establishing its convergence. Simulations show the properties of the obtained spatial representation for different scenarios.