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The proposed architecture applies the principle of predictive coding and deep learning in a brain-inspired approach to robotic sensorimotor control. It is composed of many layers each of which is a recurrent network. The component networks can be spontaneously active due to the homeokinetic learning rule, a principle that has been studied previously for the purpose of self-organized generation of behavior. We present robotic simulations that illustrate the function of the network and show evidence that deeper networks enable more complex exploratory behavior.