Geometric Design Principles for Brains of Embodied Agents

I propose a formal model of the sensorimotor loop and discuss its extrinsic embodiment constraints in relation to intrinsic degrees of freedom. These degrees form the basis of adaptation in terms of learning and should therefore be coupled with the embodiment constraints. Notions of sufficiency and embodied universal approximation allow us to formulate principles for such a coupling. This provides a geometric approach to the design of control architectures for embodied agents.