In this paper, a new machine-learning method, called Dual-Schemata model, is presented. Dual-Schemata model is a kind of self-organizational machine learning methods for an autonomous robot interacting with an unknown dynamical environment. This is based on Piaget's Schema model, that is a classical psychological model to explain memory and cognitive development of human beings. Our Dual-Schemata model is developed as a computational model of Piaget's Schema model, especially focusing on sensori-motor developing period. This developmental process is characterized by a couple of two mutually-interacting dynamics; one is a dynamics formed by assimilation and accommodation, and the other dynamics is formed by equilibration and differentiation. By these dynamics schema system enables an agent to act well in a real world. This schema's differentiation process corresponds to a symbol formation process occurring within an autonomous agent when it interacts with an unknown, dynamically changing environment. Experiment results obtained from an autonomous facial robot in which our model is embedded are presented; an autonomous facial robot becomes able to chase a ball moving in various ways without any rewards nor teaching signals from outside. Moreover, emergence of concepts on the target movements within a robot is shown and discussed in terms of fuzzy logics on set-subset inclusive relationships.