## 4 Discussion  
### Gait Alternation with the Intervention of Robotic Walker  
The human gait can be described by a deterministic chaotic system [36; 37]. However, diseases such as [PERSON]'s disease and diabetic peripheral neuropathy result in gait impairments and affect the dynamics of the gait. The results in [38] showed the chaotic nature of the gain of healthy people and the stochastic walking behavior of patients with [PERSON]'s disease, implying that the chaotic nature was disturbed by the [PERSON]'s disease. Healthy subjects have been shown to have better local dynamic stability than diabetic neuropathic patients [12]. Similarly, we hypothesized that the gait dynamics would be affected by the movement of the walker. The determinism in gait, as one of the chaotic properties, would change with the intervention of the walkers, including the robotic walker. We examined the changes in the gait parameters, i.e., the LSE and %DET, with and without the robotic walker. While no statistical difference was found in the stride time among the three conditions, significant differences were observed in the walking speed between conditions 1 and 2. In condition 2, the walker acts like a payload to push, and its movements slow down the subjects. The value of the plateau in the scaling range of the LSE can be used to determine the local geometrical structure [33]; if the value remains approximately constant with the increase in the embedding dimension, it could be considered an estimate of the correlation dimension. In general, the existence of the correlation dimension, which is a non-integer, indicates that the intrinsic dynamics are governed by a strange attractor [17; 39]. As described in Section 3, even though the plateau in the scaling range exists for the acceleration data (AP direction) of all the subjects during NW, the LSE value related to the plateau for two of them increases with the increase in the embedding dimension (Figure 4c). Thus, the corresponding correlation dimensions for these two subjects in the AP direction could not be estimated using this approach. The totally separated LSEs with different embedding dimensions and vanished plateau (Figure 4d) in the two subjects, indicate that the corresponding behavior related to walker-assisted walking is similar to the noisy one shown in Figure 3a, rather than a pure chaotic one. Thus, the acceleration data during assisted walking seem to be noisier. Moreover, during walker-assisted walking, the shapes of the LSEs of nine subjects in the AP direction remained almost unchanged, while changes in the LSE for the other two subjects were apparent. Consequently, the change in the shape of the LSE of each subject revealed the influence of the walker at an individual level. In the ML direction, because the plateaus were not observed, unlike in the V direction, it is extremely hard to find the deterministic patterns. As shown in Figure 3b, the noise influences the shape of the LSEs. From the change in the shape of the LSE, we noted that the use of the walker results in disturbances to the gait dynamics in the AP direction, which acts like noise. More robust analysis methods are required to obtain the correlation dimensions for all the subjects and conditions cannot be obtained using the current approach. The %DET is the proportion of recurrent points forming diagonal line structures parallel to the main diagonal in the recurrence plot. The %DET would be very small for purely random processes and equal 100% for a periodic curve. While the analysis of the LSEs in the AP direction did not exhibit clear, the %DET in the AP direction were significantly different between NW and RWW. The decrease in %DET indicated a decrease in the predictability of the gait dynamics in the AP direction. Therefore, the change in %DET also reflects the influence of the robotic walker in the AP direction. The influence of the rollator was not evident because no significant differences was found between condition 2 and the other conditions.