## 4 Results and Discussions
### Optimization of Leg Mass Ratio  
Based on the parameters of the human body structure, the mechanism parameters of the bipedal robot are configured as \(l_{bper}=0.2\) and \(l_{hipper}=0.4\) as the ratio of the robot rod length, the optimal mass ratio of leg to body and hip, \(m_{per}\), is analyzed.  
Figure 4 shows the variation in the full-range energy consumption \(COT_{ave}\) when \(m_{per}\) varies in the range of [0, 0.6]. The \(COT_{ave}\) first decreases and then increases with an increase in \(m_{per}\). The minimum value, \(COT_{min}\) of 0.042322, is observed at \(m_{per}=0.08\). When \(m_{per}\) varies in the range of [0, 0.15], \(COT_{ave}\) consistently remains at a low level.  
When the leg mass of the robot constitutes a small proportion of the total body mass, achieving optimal full-range energy consumption becomes more feasible.  
Figure 5 shows that when \(V=\) {0.3, 0.4, 0.5, 0.6}, the \(COT\) corresponding to the different step lengths changes with \(m_{per}\). For large values, i.e., \(V=\) {0.4, 0.5, 0.6}, the \(COT\) increases with an increase in \(m_{per}\) when the step length is short. For example, as shown in Figure 5d, when \(V=\) 0.6 and \(D=\) 0.3, \(COT\) is 0.119031 for \(m_{per}=0.5\). At longer step length, \(m_{per}\) does  
Figure 4: The variation in \(COT\) when \(m_{per}\) varies in the range of [0, 0.6].  
Figure 3: The variations in the \(COT\) under different walking speeds and step lengths. (**a**) The variation in \(COT\) under different speeds and step lengths; (**b**) the variation in \(COT\) under different walking speeds; (**c**) the variation in \(COT\) under different step lengths.  
not considerably affect the \(COT\). For example, in Figure 5d, when \(V=0.6\) and \(D=0.9\), the \(COT\) remains nearly unchanged.  
For small values, i.e., \(V=0.3\), the \(COT\) increases with an increase in \(m_{per}\) when the step length is short. For example, as shown in Figure 5a, when \(V=0.3\) and \(D=0.3\), \(COT\) is \(0.023598\) for \(m_{per}=0.4\). At longer step lengths, the \(COT\) first decreases and then increases with an increase in \(m_{per}\). For example, in Figure 5a, when \(V=0.3\) and \(D=0.9\), \(COT\) is \(0.033129\) for \(m_{per}=0.15\).  
When \(m_{per}\) is small, such as \(m_{per}=0.1\) in Figure 5b, the \(COT\) is small when the step length is short (\(D=0.3\)) and increases with a long step length, i.e., \(D=0.9\). With an increase in \(m_{per}\), \(COT\) significantly increases for shorter step lengths. However, the energy consumption of long step length walking remains nearly unchanged with an increase in \(m_{per}\).  
Figure 5a shows that a smaller \(m_{per}\) does not always correspond to a lower full-range energy consumption. For example, as shown in Figure 4, the optimal full-range energy consumption, the minimal \(COT\), appears at \(m_{per}=0.08\).  
Figure 6 shows the variation in the optimal step length with the walking speed when \(m_{per}=0.08\) and the \(COT\) values correspond to the optimal step length. The optimal step length increases with an increase in the walking speed. For example, in Figure 6, when \(V=0.5\), the optimal step length \(D=0.44\), and the corresponding \(COT\) is \(0.034425\).  
Figure 5: \(COT\) versus \(m_{per}\) with different walking speeds (\(V\)) and step lengths (\(D\)): (**a**) \(V=0.3\); (**b**) \(V=0.4\); (**c**) \(V=0.5\); (**d**) \(V=0.6\).