## 5 Discussion
### Comparison between Stability Indices and CP
#### 5.2.3 Comparison between Indices by SD and RMSE  
An additional experiment is implemented in this section to observe the difference values of C-Z, CP-C, and CP-Z in a restricted environment and to determine which values reflect environmental factors. To analyze values on the \(x\)-axis and \(y\)-axis, 180 test cases were carried out using the same assumptions; C-Z, CP-C, and CP-Z correspond to COG-ZOP, CP-COG, and CP-ZMP, respectively. Moreover, a hurdle that differed in height as a percentage of lower limb's height was set up intentionally to vary the movement of the hip joint. Thirty cases of walking were performed over the hurdle, the height of which was determined as a percentage of the lower limb's height (84 cm). The hurdle heights corresponded to 0%, 10%, 20%, 30%, 40%, and 50% of limb height, and were named Case 1, Case 2, Case 3, Case 4, Case 5, and Case 6, respectively. The height of 0% in Case 1 corresponds to natural walking, with a concentration on maintaining balance. The results of this group are discussed in terms of the SD and the RMSE of C-Z, CP-C, and CP-Z. We expected that the values, including the CP, would display proportional features, depending on the changeable height of the disturbance before the implementation of experiment. However, the experimental results were a little different from our intuition, as shown in Figures 11 and 12. Figure 11: _Cont._  
Figure 11: SD results of difference values of C-Z, CP-C and CP-Z according to the height percentage of lower limb (0%: Case 1; 10%: Case 2; 20%: Case 3; 30%: Case 4; 40%: Case 5; 50%: Case 6): (a) \(x_{\text{COG}}\)—\(x_{\text{ZMP}}\); (b) \(y_{\text{COG}}\)—\(y_{\text{ZMP}}\); (c) \(x_{\text{CP}}\)—\(x_{\text{COG}}\); (d) \(y_{\text{CP}}\)—\(y_{\text{COG}}\); (e) \(x_{\text{CP}}\)—\(x_{\text{ZMP}}\); (f) \(y_{\text{CP}}\)—\(y_{\text{ZMP}}\). Figure 11 displays the SD results of the C-Z, CP-C, and CP-Z, depending on the height of the hurdle. When comparing the SD values with respect to the \(x\) value, as shown by Figure 11a,c,e, it can be seen that the SD distribution generally decreases with increasing height of the hurdle from 0 to 50%. On the other hand, in the SD results for the \(y\) values, as given in Figure 11b,d,f, the SD distribution in Figure 11b increases slowly, while most of the SD distribution in Figure 11d and in Figure 11f converge, with the exception of the values in Case 1. In particular, the SD distribution in Case 2 in Figure 11d,f is wider than others, because the 10% height in Case 2 causes human motion to take on a wide range of joint rotations, and there are many ways of maintaining forward kinematics. Additionally, the SD distributions in Case 5 and Case 6 are narrower than in the other cases, since the movement of the limbs is more restricted when the height of hurdle increases. In summary, the SD results on the \(x\)-axis are in proportion, depending on the increased movement in the lower limb's joint, for all indices. The SD outcomes on the \(y\)-axis have a similar tendency, but only in cases with the CP. Figure 12 shows the difference between two values among the COG, ZMP, and CP by using RMSE. As the result, the distribution values between COG and ZMP as shown in Figure 12a,b do not have a marked tendency; however, the RMSE distribution including the CP decreases with increasing height of the hurdle, as shown in Figure 12c-f. Among them, the RMSE distribution in Figure 12d,f is the largest in Case 2, for the same reason as in the SD discussion, i.e., that the walking body can be moved around more freely at 10% of the height of the limb than at other percentages of height. In summary, with respect to the results of SD and RMSE, it can be noticed that walking in environments that cause more movement of joints can be classified based on the difference values between the COG, ZMP, and CP. This shows the potential of using CP, which is able to assist in classifying the relationship between environment and the motion of the limbs.