## 4 Simulation and Analysis
### Simulation Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Description** & **First (0.15 s)** & **Second (0.47 s)** & **Third (1.15 s)** & **Fourth (1.47 s)** & **Total (2 s)** \\ \hline original actuator & 34.04 J & 182.1 J & 302 J & 450 J & 535.8 J \\
2 Mpa & 34.5 J & 160.4 J & 279.7 J & 405.7 J & 490.5 J \\
4 Mpa & 34.7 J & 156.7 J & 275.9 J & 398 J & 482.6 J \\
6 Mpa & 34.7 J & 155.8 J & 274.8 J & 395.9 J & 480.3 J \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy consumption of the hip actuator at left-front leg. Figure 9: Performance of HPCA with different initial inflation pressure of the accumulator. Numbers 1 and 2 represent the swing and supporting phase, respectively. The above results prove that the HPCA does not play a role in energy conservation in the supporting phase, and in the swing phase, the energy efficiency of the actuator is not greatly affected by the initial inflation pressure and working volume of the accumulator. The explanation for this phenomenon can be summarized as follows:  
1. In the supporting phase, the piston chamber of the actuator at left-front leg is connected to the oil return circuit, and the flow required for the piston movement is mainly supplied by the servo valve. Thus, the energy supplied by the power source is the same whether it is the original actuator or the HPCA. But, for the actuator at rear-right leg, the piston is in the extension stage and sustains compression, and the ring chamber of the actuator is connected to the oil return circuit. Because of the unequal area of the piston, a large flow required causes the opening of the valve core to increase, and then there is a large pressure drop in the ring chamber (as shown in Figure 11). Therefore, a smaller pressure fluctuation in the piston chamber can be enough to adjust actuator output to balance the load. 2. In the swing phase, due to the small fluctuation of the loads, the pressure difference between the piston and ring chambers of the two actuators remains relatively stable, as can be seen from \begin{table}
\begin{tabular}{c c c c} \hline
**Description** & \(\Delta J_{1,2}\) & \(\Delta J_{2,3}\) & \(\Delta J_{total,3}\) \\ \hline original actuator & 149 & 130.2 & 149 \\ \(2\times 10^{-5}\) m\({}^{3}\) & 132.5 J & 125.8 J & 133.6 J \\ \(4\times 10^{-5}\) m\({}^{3}\) & 132.7 J & 125.8 J & 133.6 J \\ \(6\times 10^{-5}\) m\({}^{3}\) & 132.3 J & 126.1 J & 133.9 J \\ \hline \end{tabular}
\end{table} 
Table 6: Energy consumption of the hip actuator at rear-right leg. Figure 10: Performance of HPCA with different working volume of accumulator. \begin{table}
\begin{tabular}{c c c c} \hline
**Description** & \(\Delta J_{1,2}\) & \(\Delta J_{2,3}\) & \(\Delta J_{3,4}\) & \(\Delta J_{total,4}\) \\ \hline original actuator & 147 J & 119 J & 148 J & 84.5 J \\ \(2\times 10^{-5}\) m\({}^{3}\) & 120.8 J & 119 J & 119.4 J & 84.6 J \\ \(4\times 10^{-5}\) m\({}^{3}\) & 120.6 J & 119 J & 120 J & 84.8 J \\ \(6\times 10^{-5}\) m\({}^{3}\) & 121.5 J & 119.1 J & 119.6 J & 85.1 J \\ \hline \end{tabular}
\end{table} 
Table 5: Energy consumption of the hip actuator at left-front leg. Figure 11. Therefore, the oil supplied by the power source for the piston movement seldom flows into the accumulator. The steps to improve the energy efficiency by changing the inflation pressure and working volume of the HPCA will have little effect.