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To realize the natural symbiosis of human and robots, we need to clarify multi-aspect model structure of their interaction through physical, mental, social interfaces. Here, we notice the dual interaction model which is composed of intention adjustment process in social interaction and entrainment adjustment process under common intention. The former should be designed on the assumption that human behavior and dialogue would have an uncertainty. The latter needs to have the function to entrain human and robot mutually through audio and visual information. In our approach, the former is realized by making a stochastic inference based on dynamic Bayesian network (DBN) model, and making human and robot interact by social communication protocol. The latter is described by nonlinear oscillator to realize entrainment. We adopt a navigation problem and cooperative walking problem to verify the fundamental effectiveness of the duality interaction model. Finally, using this duality model, we discuss how to design walking instructor robots.