# Fall Recognition System to Determine the Point of No Return in Real-Time
## 2 Materials and Methods
### COM-Based Labeling  
The COM is an indicator for evaluating the walking and postural stability of the human body; it provides significantly intuitive and crucial information. Walking and posture become increasingly stable as the COM becomes closer to the BOS. This concept has been actively applied to not only analyze the posture of the human body but also to develop algorithms for controlling the posture of legged robots, especially bipedal robots, such as the zero-moment point control algorithm [18]. Thus, in this study, the labeling technique for classifying the postural stability of the human body was based on the COM, which is calculated based on the following equation:  
\[x_{com}=\frac{\sum_{i=1}^{n}M_{x,i}}{\sum_{i=1}^{n}F_{x,i}}=\frac{\sum_{i=1}^{ n}m_{i}\cdot x_{c,i}}{\sum_{i=1}^{n}m_{i}} \tag{1}\]  
Here, \(M_{x,i}\) and \(F_{x,i}\) refer to the moment and force applied to the \(i\)th part of the human body, respectively. \(m_{i}\) is the weight of the \(i\)th part of the human body and \(x_{c,i}\) is the location of the COM for the \(i\)th part of the human body. Parts of the human body refer to sections of the human body that are distinguished according to joints (e.g., the brachium and antebrachium of arms, thighs, and calves). The equation for calculating the COM in the \(x\)-direction is consistent with Equation (1) and can be applied in the same way as for calculating the COM in the \(y\)- and \(z\)-directions.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Fall Phases** & **Sub-Division of the Critical Phase** & **Classification of Behaviors** \\ \hline Pre-fall phase & \
\begin{tabular}{c} Standing (S) \\ Walking (W) \\ \end{tabular} & Daily activities \\ \hline Critical phase &
\begin{tabular}{c} Imbalance (I) \\ Falling down (F) \\ \end{tabular} & Fall in progress \\ \hline Post fall phase & Post Fall (P) & After falling down \\ \hline Recovery phase & Recovery (R) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Sub-division of the critical phase among the entire phases of the fall progress.  
Figure 1: Phases of fall progress process and sub-division of the critical phase.  
Theoretically, at least 17 IMU sensors should be installed to calculate the COM of the human body in consideration of all parts of the human body. However, as it was necessary to analyze only the postural changes according to the movement of the lower body, only five IMU sensors attached to the lower body and waist of a person were utilized to estimate the COM in this study.  
The fall data were labeled based on the norm information on the COM estimated by the five IMU sensors. Figure 2 shows the cases of labeling forward and backward fall data. In this figure, the black dotted line indicates the standing phase among the activities of daily living (ADL) and is labeled as S. The yellow dotted line refers to the walking phase among the ADLs and is labeled as W. The blue dotted line refers to the imbalance phase and is labeled as I. The red dotted line refers to the falling down phase and is labeled as F. Index 1 refers to units of 10 ms. COM(x, y) represents the COM based on the moving coordinates on a flat surface using the label values of the fall data. Figure 2b refers to a backward fall caused by a person standing and falling backward. The COM(x, y) analysis revealed that the internal area of a circle forming the BOS boundary was divided into two sections, although the person was not walking. The COM(x, y) analysis in Figure 2a revealed that the black dots in the standing phase were concentrated at one dot. These dots were not clearly distinguished because they were covered by yellow dots during the walking phase. The end of the red dotted line (i.e., the falling down phase) indicates the point where the human body collides with the ground.