# The Exoskeleton Balance Assistance Control Strategy Based on Single Step Balance Assessment
## 2 Single Step Balance Assessment Method  
### The Concept of Single Step Balance  
In this paper, single step balance is defined as a state in which a human is able to regain balance in one step. It is important for humans, especially for elderly and disabled people, to regain balance within a minimum number of steps when suffering from an unexpected disturbance. To quantitatively evaluate whether a human is in a single step balance state, the CP concept [14] is utilized in this paper. \[x_{CP}=x+\dot{x}\sqrt{l/g} \tag{1}\]where \(x_{CP}\) is the position of CP, \(l\) is the distance between the center of mass (CoM) of the human and ankle, \(g\) is gravitational acceleration. On the basis of the CP concept, as shown in Figure 1, a single step balance state is defined as a state that when the swing foot is touching the ground and the CP is within the base of support (BoS). Conversely, if CP is outside of the BoS when the swing foot touches down, the human is in a single step unbalance state. Based on this definition of single step balance and (1), it is obvious that the degree of single step balance is determined by the state of CoM (\([x,\dot{x}]\)). To investigate the relationship between a single step balance state and the velocity of CoM, 30 groups of \"walk-stop\" experiments for every 5 healthy young male adults (Mean age: 23.5 (1.3), mean weight: 58.7 (5.1) kg, mean trunk length: 0.432 (0.025) m, mean leg length: 0.815 (0.05) m, mean length between ankle and toe: 0.168 (0.06) m) were carried out. All subjects gave their informed consent before participating in the experiment. The experiment was approved by the Harbin Institute of Technology ethical committee. The kinematics data of the human walking are measured by Raptor-4 Digital Realtime System of Motion Analysis corp. 12 Raptor-4 digital cameras send the trails of markers on the human body to the Cortex software for data acquisition at 120 Hz. A 22-markers Helen-Hayes model was adopted in this experiment. During the \"walk-stop\" experiment, all subjects were required to walk at a given speed and tried to stop in one step when hearing the unexpected stopping command. If the subject can stop walking in only one step, the subject is considered as in the single step balance state, otherwise the subject is in the single step unbalance state. The results of \"walk-stop\" experiment are shown in Table 1.  
The experiment results in Table 1 show that the success rates of stopping walking in one step at low and medium walking speed are 100% and 99%, respectively. However, the success rate drops to 2.7% when walking speed is high. Therefore, the human is able to keep single step balance at low and medium walking speed, and is almost in a single step unbalance state at a high walking speed. To investigate the relationship between the swing foot and CP, another 10 groups of experiments were carried out. Each subject walked at three different speeds (low, medium, and high) and suffered from an unexpected forward disturbance during walking. Figure 2 shows the results of one subject (Age: 24, weight: 55 kg, leg length: 0.802 m). As shown in Figure 2, the time of the swing foot touching down before disturbance is \(t_{A}\), and the time of the swing foot touching down after disturbance is \(t_{B}\) \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Walking Speed**} & \multicolumn{2}{c}{**Average Groups**} & \multicolumn{2}{c}{\(\boldsymbol{d_{SC}(m)}\)} \\ \cline{2-5}  & **Success** & **Fail** & \(\boldsymbol{d_{SC}(t_{A})}\) & \(\boldsymbol{d_{SC}(t_{B})}\) \\ \hline Low (0.8 m/s) & 30 & 0 & 0.115 & 0.307 \\ Medium (1.3 m/s) & 29.7 & 0.3 & 0.124 & 0.401 \\ High (1.8 m/s) & 0.8 & 29.2 & 0.293 & 0.538 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The results of “walk-stop” experiment. Figure 1: Single step balance and unbalance state.