Toward a memory model for autonomous topological mapping and navigation: The case of binary sensors and discrete actions

We propose a self-organizing database for perceptual experience capable of supporting autonomous goal-directed planning. The main contributions are: (i) a formal demonstration that the database is complex enough in principle to represent the homotopy type of the sensed environment; (ii) some initial steps toward a formal demonstration that the database offers a computationally effective, contractible approximation suitable for motion planning that can be accumulated purely from autonomous sensory experience. The provable properties of an effectively trained data-base exploit certain notions of convexity that have been recently generalized for application to a symbolic (discrete) representation of subset nesting relations. We conclude by introducing a learning scheme that we conjecture (but cannot yet prove) will be capable of achieving the required training, assuming a rich enough exposure to the environment.