## 3 Results  
Table 1 shows the medians of the stride time and walking speed for all the subjects under the three conditions. A Kruskal-Wallis ANOVA showed that there was no statistical difference in stride time among these conditions (\(p=0.964\)). However, the Kruskal-Wallis ANOVA rejected the null hypothesis that the walking speeds under all three conditions came from the same distribution (\(p=0.018\)). Furthermore, the results of the multiple comparison tests exhibited a significant difference between conditions 1 and 2 (\(p=0.016\)). The time lag \(\tau\) was calculated to be 10 s for all the subjects, as in [12]. Figure 4a shows the LSEs for the acceleration data of one subject in the AP direction during NW (condition 1). From the figure, it can be seen that the macroscopic regime (approximately \(\log\epsilon\geq-0.6\) for \(m=5\)), the LSEs increase as the length scale \(\epsilon\) decreases. In the scaling range (approximately \(-1.8<\log\epsilon<-0.6\) for \(m=5\)), the LSEs first increase and then decrease. The curves vary slowly around 2 and reach a plateau below 2. For all embedding dimensions, the values of the LSEs related to the plateau remain approximately constant, while the corresponding scale region shifts with the embedding dimensions. In the noise regime (approximately \(\log\epsilon<-1.8\) for \(m=5\)), the LSEs increase as \(\epsilon\) increases and reach the embedding dimension at the noise level. This phenomenon was also observed in a previous study [12]. Figure 4b shows the LSE curves for the acceleration data of the same subject in the AP direction during RWW (condition 3). It can be seen that, In the macroscopic regime, the curves are similar to the ones in Figure 4a. Significant differences between the two figures can be observed in the scaling range and noise regime. The value of LSE for the plateau becomes larger than 2, and increases slightly with the embedding dimension. In the noise regime, the increment rate of the LSE is larger than that in Figure 4a. The LSEs for all of the subjects in the AP direction during NW indicated the existence of a plateau in the scaling range; the curves for only two subject were different from those of the others. As shown in Figure 4c, the value of the LSE related to the plateau for one of the two subjects with different LSE increased with the embedding dimension. During assisted walking (conditions 2 and 3), the LSEs for this subject and the plateau vanished (Figure 4d). For the other nine subjects during assisted walking (conditions 2 and 3), individual differences were apparent. The correlation dimensions for seven of them increased with the intervention of the robotic walker, while those for the remaining two subjects were the same as during NW. Unlike those in the AP direction, the LSEs for the acceleration data of all the subjects in the ML direction are separated from each other, similar to the ones in Figure 4d. The LSEs in the V direction of all the subjects are similar to those in Figure 4a, and the platea \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Condition 1 NW** & **Condition 2 RW** & **Condition 3 RWW** \\ \hline Stride time s & 1.15 \(\pm\) 0.02 & 1.15 \(\pm\) 0.03 & 1.16 \(\pm\) 0.02 \\ Walking speed m\(\cdot\)s\({}^{-1}\) & 1.18 \(\pm\) 0.04 \({}^{\star}\) & 1.13 \(\pm\) 0.06 \({}^{\star}\) & 1.16 \(\pm\) 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured gait parameters. The values are reported as median \(\pm\) median absolute deviation; \({}^{\star}\) indicates a statistically significant difference in walking speed between conditions 1 and 2.  
all the conditions. This confirms that it is possible to obtain the correlation dimensions. However, the Kruskal-Wallis ANOVA indicates that there is no statistically significant difference in the obtained correlation dimensions along the V direction under all three conditions (\(p=0.61\)). In addition, the values of the LSEs for the plateau in the AP and V directions in condition 2 were slightly higher than those in condition 1.