# System for Evaluation and Compensation of Leg Length Discrepancy for Human Body Balancing
## 5. Mechatronic System Design
### Experimental Results
#### 5.4.3 Experiment 3: A Healthy Volunteer with a Simulated LLD  
The goal of Experiment 3 was to test the HBBA algorithm on a volunteer with a simulated LLD. The mass and height of the volunteer in Experiment 3 are 81.14 kg and 179 cm. As can be seen in Figure 18e and Table 4, Volunteer 3 has approximately equal loads on both legs, as well as the same positions of the LASIS and RASIS markers. The placement of Volunteer 3 on the force plates and the conducting of the LLD evaluation and compensation with a simulated LLD is shown in Figure 20. When Volunteer 3 stood still and had a static posture on the force plates, the height of which was 425 mm (Figure 20c), the system evaluated that Volunteer 3 is balanced. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Subject**} & \multicolumn{2}{c}{\(CoM_{x}\)} & **Mass** & \(m_{L}\) & \(m_{R}\) & **Height** & **LASIS** & **RASIS** \\ \cline{2-9}  & **Mean [mm]** & **SD [mm]** & **[kg]** & **[kg]** & **[kg]** & **[cm]** & **[cm]** & **[cm]** \\ \hline Volunteer 1 & 13.25 & 0.798 & 91.15 & 40.29 & 50.86 & 178 & 104 & 104 \\ Volunteer 2 & \(-\)9.80 & 0.490 & 55.34 & 29.44 & 25.90 & 157 & 96 & 96 \\ Volunteer 3 & \(-\)0.21 & 0.861 & 81.14 & 40.65 & 40.49 & 179 & 106 & 106 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measurement results of the CoM along the \(x\)-axis (\(CoM_{x}\)), mass, loads on the left (\(m_{L}\)) and right (\(m_{R}\)) legs, the positions of the LASIS and RASIS anatomical points for three chosen volunteers. Figure 19: Experiment 2: Shift of the CoM along the \(x\)-axis (\(CoM_{x}\)) depending on a force plate height difference \(\Delta z\). The simulation of shortening the right leg was done by reducing the height of the right force plate \(z_{R}\) from 425 mm to 410 mm (Figure 20d). This simulated length difference between the left and right legs equal to \(\Delta l=-15\) mm. The HBBA had the task of balancing Volunteer 3. The HBBA parameters were \(\varepsilon=1\) mm and \(\gamma=0.5\). In the initial state (\(k=0\)), the \(CoM_{x}\) equaled 26.5 mm, which was the result of a higher load on the right force plate (\(m_{R}=48.98\) kg) than on the left force plate (\(m_{L}=32.16\) kg). Considering that \(|CoM_{x}|\geq\varepsilon\), according to the algorithm in Figure 8 and Equation (18), the right platform was lifted by 13.2 mm. The response of the variables observed while running the HBBA is shown in Figure 21.  
The values of these variables at the end of each iteration are shown in Table 5. The first HBBA iteration was started at \(t=6.7\) s after the subject was maintaining a static and calm posture. After the first iteration, the load difference between the left and right leg was reduced. It is interesting to notice that at the time \(t=25\) s (Figure 21c), the subject lost their focus just as the new iteration of the HBBA was about to be run. The balancing trigger was not issued and the HBBA waited for the subject to once again maintain a static posture so that a new iteration was started at \(t=43\) s.  
The HBBA stopped when in the last iteration (\(k=2\)) the \(CoM_{x}\) equaled \(-0.6\) mm. The height of the left force plate \(z_{L}\) was 425.0 mm, and the height of the right force plate \(z_{R}\) was 425.4 mm. The loads on the left and right legs were \(m_{L}=40.73\) kg and \(m_{R}=40.46\) kg, which shows that Volunteer 3 was balanced. The LLD was evaluated to \(-15.4\) mm in this case, while the simulated LLD equaled to \(15\) mm. The HBBA successfully conducted an evaluation and compensation of simulated LLD for Volunteer 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Iteration**} & \(CoM_{x}\) & \(z_{L}\) & \(z_{R}\) & \(\Delta z\) & \(m_{L}\) & \(m_{R}\) \\  & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[kg]** & **[kg]** \\ \hline \(k=0\) & 26.4 & 425.0 & 410.0 & 15.0 & 32.16 & 48.98 \\ \(k=1\) & 4.4 & 425.0 & 423.2 & 1.8 & 39.21 & 41.94 \\ \(k=2\) & \(-0.6\) & 425.0 & 425.4 & \(-0.4\) & 40.73 & 40.46 \\ \hline \hline \end{tabular}
\end{table}