Infants learn to speak rapidly during their first years of life, gradually improving from simple vowel-like sounds to larger consonant-vowel complexes. Learning to control their vocal tract in order to produce meaningful speech sounds is a complex process which requires to learn the relationship between motor and sensory processes. In this paper, a computational framework is proposed that models the problem of learning articulatory control for a physiologically plausible 3-D vocal tract model using a developmentally-inspired approach. The system babbles and explores efficiently in a low-dimensional space of goals that are relevant to the learner in its synthetic environment. The learning process is goal-directed and self-organized, and yields an inverse model of the mapping between sensory space and motor commands. This study provides a unified framework that can be used for learning static as well as dynamic motor representations. The successful learning of vowel and syllable sounds as well as the benefit of active and adaptive learning strategies are demonstrated. Categorical perception is found in the acquired models, suggesting that the framework has the potential to replicate phenomena of human speech acquisition.