# Modeling a Pre-Touch Reaction Distance around Socially Touchable Upper Body Parts of a Robot
## 4 Results and Implementation
### Implementation  
The next step is to implement the obtained pre-touch reaction distances on a robotic agent. We used an android robot with a masculine appearance [49] and an OptiTrack system that resembles our data collection to capture the body parts' positions in real-time. The robot reacted to the interaction when the hand approached the threshold distance using the markers' position information, based on the data collection results.  
In the implementation of the pre-touch reactions for the robot, we prepared three boundaries for the shoulder, elbow, and hand and another for the face, based on a past study [16], to achieve pre-touch reaction behaviors for typical upper body parts. The boundary thresholds are defined as T\({}_{\text{face}}\), T\({}_{\text{shoulder}}\), T\({}_{\text{elbow}}\), and T\({}_{\text{hand}}\) from the positions of each body part of the robot, i.e., P\({}_{\text{face}}\), P\({}_{\text{Rshoulder}}\), P\({}_{\text{Relbow}}\), and P\({}_{\text{Rhand}}\). The distances between the participant's hand (P\({}_{\text{Phand}}\)) and each body part of the robot were calculated by the Optitrack system's outputs (D\({}_{\text{face}}\), D\({}_{\text{shoulder}}\), D\({}_{\text{elbow}}\), and D\({}_{\text{hand}}\)). When this distance was equal to or less than a threshold (e.g., D\({}_{\text{elbow}}\) <= T\({}_{\text{elbow}}\)), the robot reacted and looked at the person, using as a reference the marker on the participant's head. We implemented this looking behavior because, in previous works, this reaction was adequate to obtain a more accurate distance [16]. In this implementation, we simply used the average values as the pre-touch reaction distance threshold for defining the model based on these analyses (Figure 4, shoulder = 24.8 cm, elbow = 24.1 cm, hand = 21.5 cm). Note that we can change the system's thresholds by considering the angle and gender of interacting partners.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Acclination**} \\ \cline{2-3}  & **First Half** & **Last Half** \\ \hline Shoulder & 23.9 (1.7) & 25.0 (1.9) \\ Elbow & 22.9 (1.5) & 24.5 (1.8) \\ Hand & 20.8 (1.7) & 21.4 (1.6) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average (S.E.) minimum comfortable distance in centimeters, considering acclimation.  
Finally, we tested our developed system. The touches wore a marker on their right hand (fingers) and their head, as shown in Figure 5a, and were standing approximately 1.0 m from the robot's position, as shown in Figure 5b. Then, the touches slowly moved their hands while approaching the robot's body part to check the robot's reaction. We designed the robot to react by looking at the touches' face and confirmed that it autonomously reacted to the pre-touch behaviors (Figure 6) by testing with multiple different touches.  
Figure 4: Visualizations of pre-touch reaction distance in proposed condition. (**a**) show the frontal view of the boundaries and (**b**) shows the lateral view of the boundaries. For readability, figure only shows boundaries for left body part (blue: Tface, yellow: Tshoulder, red: Telbow, green: Thand).  
Figure 5: Implementation setup: (**a**) markers’ positions on the participant: hand for computing distance and head as reference for android’s reaction; (**b**) implementation setup using an OptiTrack system and three approaching angles: front, left, and right.