# Coordinating Entrainment Phenomena: Robot Conversation Strategy for Object Recognition
## 4 System Design
### Conversation Strategy Selection Function
#### 4.3.1 Implicit Entrainment Generation Module  
When the robot uses the implicit entrainment strategy, the robot does not explicitly request how to refer to an object in the _Ask_ part. The implicit entrainment generation module generates a speech that asks an interlocutor to start referring to an object. In the _Confirm_ part, the robot in this module chooses the confirmation behavior and adopts the implicit entrainment strategy, and the robot confirms the indicated object with minimum information for distinguishing among objects based on the proposed design described in Section 2.4. The procedure comprises two steps: (1) Deciding whether to use a pointing gesture, and (2) deciding which object attributes to use in the confirmation speech. Deciding whether to Use a Pointing Gesture  
Whether a pointing gesture is used depends on the extent to which how the pointing gesture narrows down the candidates for the indicated object. For example, if there are many objects around the indicated object adjacently and a pointing gesture does not narrow the candidates for the indicated object, pointing gestures are not useful for identifying one object out of many, and the robot does not use them in such cases. The procedure of deciding whether to use a pointing gesture is as follows. First, we define the pointing and facing direction area centered on the indicated object, which is the area where the objects can be narrowed down by the robot's pointing gesture and face direction, and the system calculates the number of objects existing in each range. As the definition of the pointing and facing direction area, we use the limit distance model proposed by [PERSON] et al. [39] In the limit distance model, people cannot distinguish the indicated object if the edge of another object is in the area of \(\theta_{\text{L}}\) from the indicated direction. In other words, the limit distance includes area \(\theta_{\text{L}}\) and the distance from the center of another object to its edge. They reported that the limit angle of pointing gesture is \(\pi/18\) rad through their experiment [39]. Accordingly, in this study, we decide the pointing direction area using the limit distance model and the limit angle. To determine the facing direction area, we used the limit distance using the limit angle as \(\pi/9\) rad because the useful field of view, which is the visual area over which information can be extracted at a brief glance without eye or head movements [40; 41], is a maximum of \(\pi/9\) rad [42]. If only one object is situated within the facing direction area, a pointing gesture can identify it. Thus, the robot confirms the indicated object with a pointing gesture. Even if other objects exist in the facing direction area, a pointing gesture can identify the object if it is alone within the pointing direction area. In this case, the robot confirms the indicated object with a pointing gesture as well. If there are other objects in the pointing gesture's area, the decision of whether to point depends on the ratio \(x\) between the number of objects in the facing direction area and in the pointing direction area. In our study, the robot uses a pointing gesture in cases where \(x<0.5\). In other words, if the pointing gestures narrow down the candidates for the indicated object by 50%, the robot confirms the indicated object using a pointing gesture. Figure 7 shows an example of how to decide whether to use a pointing gesture. In Figure 7a, there are two objects in the pointing direction area and five in the facing direction area, and the ratio \(x=0.4\). In such a case, pointing gestures are useful to narrow down the candidates for the indicated object, and the robot use a pointing gesture. In Figure 7b, there are three objects in the pointing direction area and three in the facing direction area, and the ratio \(x=1\). In such a case, pointing gestures do not narrow down the number of objects compared to the case inwhich the indicated object is pointed out only be the face direction, and the robot does not use a pointing gesture.