More and more researcher in artificial intelligence are concerned with perception of the environment. Ahead of consideration about objects or task spaces common in developmental robotics, this research is interested in the birth of the principle of space by a naive agent. It is only after having acquired this principle that it is possible to build the higher level paradigms such as the existence of objects or grasping tasks, etc. Indeed space existence is most of the time an a priori knowledge about the world which is brought by the engineer with the definition of models such as kinematics models or spatial state parameters. This work is based on the analysis of the so-called sensorimotor flow, particularly on the study of correlation and invariance in exteroceptive and proprioceptive signals, i.e. sensorimotor contingencies. Such contingencies carry fundamental structural information on the world. Poincaré suggested that information about dimension of the space in which the agent movements are embedded, such as the 3D euclidean space of translation or possibly more complex spaces, can be extracted from the study of sensorimotor manifold. Later, studies have been proposed by Philipona et. al then by Laflaquière et. al to extract this specific dimension. More recently, Laflaquière et. al have shown that it was also possible to obtain an internal representation of the agent’s movements in a simple environment by the construction of specific motor partitions. The approach is an extension of the work from Laflaquière et. al with a focus on self-interaction by the agent. Indeed, as pointed out by Frolov, self-interaction allows the agent not to make any prior hypothesis on environment stability as any sensation would be caused by the agent itself. From the use of sensory invariance and the construction of kernel sets, an internal, i.e. proprioceptive, representation of the self-touching interaction can be built. A first but incomplete solution have already been proposed which is completed in the present work. In the former, the internal representation is built to geometrically characterize the shape of the body, based on this, some contributions prove that it is also possible to use it as an internal representation of movements in space and as a basis for motor planning and particularly sensation reaching. This will allow a totally naive agent, with no knowledge on its structure or on the dimension of the space it is embedded in, to successfully predict self-interaction.