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In a situation where a robot initiates conversation with a person, when is the appropriate timing and where is an appropriate position from which to say the first greeting word? In this study, we analyze human interaction and establish a model for a natural way of initiating conversation. The model mainly concerns the participation state  and spatial formation . When a person is going to participate in a conversation, at a moment when a particular spatial formation occurs, she would feel that she is participating in the conversation; once she perceived her participation she would try to maintain particular spatial formations. There are theories in human communication for these concepts [1, 2], but they only cover the situation after people have started to talk. We build a model that precisely describes the constraints and expected behaviors for the phase of initiating conversation. The proposed model is implemented in a humanoid robot, and it is confirmed as effective in an evaluation experiment based on a shopkeeper scenario.