Proto Symbol Development and Manipulation in the Geometry of Stochastic Model for Motion Generation and Recognition

Humans primitive skill of imitative learning is regarded as an origin of human intelligence because it is said that imitation is fundamental function for communication and symbol manipulation He have proposed mimesis model in order to approach to a symbol emergence framework from behavior recogni tion generation for humanoid robots This mimesis model is able to abstract observed others behaviors into proto symbols to recognize others behavior us ing the proto symbols and to generate motion patterns using the proto symbols based on a stochastic model In this paper we extend the mimesis model to ge ometric proto symbol space which contains relative distance information among proto symbols We also discuss how to generate complex behavior by geometric proto symbol manipulation and how to recognize novel behavior using combina tion of the proto symbols Introduction Recently the human behavioral science and the human intelligence have be come conspicuous as a real research issue of robotics Although the moti vation of the arti cial intelligence originated there the physical limitations have forced or justi ed the researchers to carry on their research in a limited scope and scale of complexity It ought to be the major challenge of contem porary robotics to study robotic behaviors and intelligence in the full scale of complexity mutually sharing research outcomes and hypotheses with the human behavioral science and human intelligence The discovery of mirror neurons have been a notable topic of brain sci ence which have been found in primates brain and humans brain re when the subject observes a speci c behavior and also re when the subject start to act the same behavior Furthermore it is located on Broka s area which has close relationship between language management The fact suggests that the behavior recognition process and behavior generation process are combined as the same information processing scheme and the scheme is nothing but a core engine of symbol manipulation ability Indeed in Donald s Mime sis Theory it is said that symbol manipulation and communication ability are founded on the behavior imitation that is integration of behav ior recognition and generation We believe that a paradigm can be proposed T Inamura H Tanie and Y Nakamura taking advantage of the mirror neurons with considerations of Deacon s con tention that the language and brain had evolved each other So far we have proposed a mathematical model that abstracts the whole body motions as symbols generates motion patterns from the symbols and distinguishes motion patterns based on the symbols In other words it is a functional realization of the mirror neurons and the mimesis theory For the integration of abstract recognition and generation the hidden Markov model HMM is used One as observer would view a motion pattern of the other as the performer the observer acquires a symbol of the motion pat tern He recognizes similar motion patterns and even generates it by himself One HMM is assigned for a kind of behavior We call the HMM as symbol representation Symbols are required to represent similarity or distance between each symbol An example application is symbol manipulation based on the sim ilarity or distance information However our conventional method have no way to represent similarity of relationship between each behavior Therefore in this paper we extend the mimesis model to geometric symbol space which contains relative distance information among symbols We also discuss how to generate complex behavior by geometric symbol manipulation in the sym bol space and how to recognize novel behavior using combination of symbols by known symbols Hierarchical Mimesis Model Usual mimesis models and its defects Figure shows the con guration of usual mimesis models The model consists of three processing perception part generation part and develop ment part In the perception part observed motion patterns are analyzed into basic motion elements Motion elements are low level physical parameter for short period of time like joint angle angular velocity or torque Others motion are represented by the sequence of the element then the dynamics in the motion is abstracted as symbol representations namely HMMs We have call such symbol representation as proto symbols Here one defect arises that the relationship between two similar behavior have been lost when the behavior transfered into proto symbols An aspect of the symbol is that semantic relation exists among symbols contrary to the icons and labels which have no relation representation between each elements To solve this defect a hierarchy structure is needed in which the relation in the lower motion pattern layer will be kept in the higher symbol layer We call such structure as Hierarchical Mimesis Model In following sections we introduce an mathematical framework for the Hierarchical Mimesis Model Proto Symbol Development and Manipulation in the Geometry of Stochastic Model Observation Proto-symbols Communication Concept Formation