## 5 Discussion
### Comparison between Stability Indices and CP
#### 5.2.1 Classification of Walking State  
The difference values between the COG, ZMP and CP are estimated as given in Figure 8 based on the experimental data. On the \(x\)-axis, the difference values between the COG ZMP, and CP are calculated as shown in Figure 8a. Significantly, C-Z and CP-C form a cyclic triangular wave, and CP-Z is almost constant, with the exception of some points. Two footsteps, left and right, can be interpreted as follows:  
* \(t_{0}\)-\(t_{1}\) (SS\({}_{\text{L}}\)): the single stance by the left limb is from \(t_{0}\) of the lowest value of C-Z until \(t_{1}\), where C-Z is the same as CP-C.
* \(t_{1}\)-\(t_{2}\) (DS): the double stance is from \(t_{1}\) until \(t_{2}\), where C-Z or CP-Z is inverted. * \(t_{2}\)-\(t_{3}\) (SS\({}_{\text{R}}\)): the single stance by the right limb is from \(t_{2}\) until \(t_{3}\), where C-Z is the same as CP-C.
* \(t_{3}\)-\(t_{4}\) (DS): the double stance is from \(t_{3}\) until \(t_{4}\), where C-Z or CP-Z is inverted. Figure 7: Results of stability indices and CP which are detected from the human walking (red line: COG, blue line: ZMP, and black line: CP): (**a**) Traces of stability indices and the CP in the \(xy\)-axis; (**b**) results of stability indices in \(x\)-axis (walking forward); (**c**) results of stability indices and the CP in \(y\)-axis (toward left and right). On the \(y\)-axis, the difference values are estimated as given in Figure 8b. Here, the points \(t_{LC}\) and \(t_{RC}\) denote the transition state of the swing limb from back to forward. In the left and right single stance, the load point changes on the foot as follows:  
* \(t_{0}\)-\(t_{LC}\) (HP\({}_{\rm L}\)): the load point is on the heel in SS\({}_{\rm L}\) from \(t_{0}\) until \(t_{LC}\), where the values of CP-C and CP-Z go down sharply. * \(T_{LC}\)-\(t_{1}\) (TP\({}_{\rm L}\)): the load point is on the toe in SS\({}_{\rm L}\) from \(t_{LC}\) until \(t_{1}\). * \(t_{2}\)-\(t_{RC}\) (HP\({}_{\rm R}\)): the load point is on the heel in SS\({}_{\rm R}\) from \(t_{2}\) until \(t_{RC}\), where the values of CP-C and CP-Z increase dramatically. * \(t_{RC}\)-\(t_{3}\) (TP\({}_{\rm R}\)): the load point is on the toe in SS\({}_{\rm R}\) from \(t_{RC}\) until \(t_{3}\). Figure 9 summarizes the above results for two steps from the SS\({}_{\rm L}\) and the SS\({}_{\rm R}\) to the DS. HS and the HO refer to a heel-strike and a heel-off with a prefix R(right) or L(left), respectively. Furthermore, TS and the TO denote the toe-strike and toe-off, respectively, with the prefixes R and L corresponding to right and left, respectively. One step from a side-SS to the DS is defined as being from 0 to 100%. A point of note is the T state, where the force position is inverted from the HP\({}_{\rm L(R)}\) (period of pressure on heel) to the TP\({}_{\rm L(R)}\) (period of pressure on toe) in walking. The T state clearly indicates a change in the incline value of CP, since T indicates the moment in which the swing limb passes the stance limb, as shown in Figure 7c. Moreover, this significance is reflected in the difference value with the conventional indices, as given in Figure 8b. In summary, the walking state described using the difference values of COG, ZMP and CP is more sementalized than using the difference values between COG and ZMP only. With respect to specific categories, the difference values in the \(x\)-axis with regard to walking direction clarify the SS\({}_{\rm L}\), SS\({}_{\rm R}\), and DS; on the other hand, the difference values in the \(y\)-axis for left and right indicate the instant of HP\({}_{\rm L}\), TP\({}_{\rm L}\), HP\({}_{\rm R}\), and TP\({}_{\rm R}\) through to \(t_{LC}\) and \(t_{RC}\).