  The design of robotic systems is largely dictated by our purely human
intuition about how we perceive the world. This intuition has been proven
incorrect with regard to a number of critical issues, such as visual change
blindness. In order to develop truly autonomous robots, we must step away from
this intuition and let robotic agents develop their own way of perceiving. The
robot should start from scratch and gradually develop perceptual notions, under
no prior assumptions, exclusively by looking into its sensorimotor experience
and identifying repetitive patterns and invariants. One of the most fundamental
perceptual notions, space, cannot be an exception to this requirement. In this
paper we look into the prerequisites for the emergence of simplified spatial
notions on the basis of a robot's sensorimotor flow. We show that the notion of
space as environment-independent cannot be deduced solely from exteroceptive
information, which is highly variable and is mainly determined by the contents
of the environment. The environment-independent definition of space can be
approached by looking into the functions that link the motor commands to
changes in exteroceptive inputs. In a sufficiently rich environment, the
kernels of these functions correspond uniquely to the spatial configuration of
the agent's exteroceptors. We simulate a redundant robotic arm with a retina
installed at its end-point and show how this agent can learn the configuration
space of its retina. The resulting manifold has the topology of the Cartesian
product of a plane and a circle, and corresponds to the planar position and
orientation of the retina.
