## 4 Simulation and Analysis
### Simulation Results  
Because with better representative, the simulation results of the hip actuator (hip F/E) at the left-rear and right-front legs are only shown in Figure 9. The desired trajectories (\(x_{p}\) in legend) of the actuators magnified by a corresponding multiple are used as a reference in some pictures. It can be seen from the results that, for the hip actuator at the left-front leg, the first abrupt point of the piston chamber pressure (\(P_{pis}\)) always occurs in 0.15 s during the swing phase, and the second appears at the transition from the swing phase to the supporting phase, while for the actuator at the right-rear leg, the first abrupt point of the piston chamber pressure (\(P_{pis}\)) always occurs in 0.35 s during the swing phase, and the second abrupt point appears at the transition from the supporting phase to the swing phase of the next cycle. As can be seen from the flow curves (\(Q_{accu}\)), the positive parts indicate that the accumulator, as a flow source, always supplies fluid for the piston extension, while the negative parts indicate that the accumulator, as an energy-storage unit, has been absorbing the oil released by the piston retraction. The energy consumption curves shown in the Figure 9 can be obtained by integrating the power(\(Q_{S}\times P_{S}\)). The energy consumption values at each point of the piston reversal are shown in Tables 3 and 4. It is can be seen that, for the actuator at left-front leg, the energy consumption of the original actuator increases by 148.6 J, 119 J, 148 J, and 85 J between the reversal points. But, for the HPCA, such data is around 122 J, 119 J, 122 J, and 84 J, respectively. This is consistent with the law described in Section 3.2.3, which indicates that the process of the piston from shortening to elongation can release energy. For the actuator at rear-right leg, such values are 149 J, 130J, and 149 J for the original actuator and are around 134 J, 128 J, and 134 J for the HPCA. This is also consistent with the law described in Section 3.2.3. It is worth adding that the energy released is caused by the pressure transition of the piston from extension to retraction. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Description** & **Symbol** & **Value** \\ \hline input pressure & \(P_{S}\) & 20 Mpa \\ torso mass & & 110 kg \\ gait length & \(L\) & 0.236 m \\ gait height & \(H\) & 0.1 m \\ gait cycle & \(T\) & 1 s \\ stiffness in \(x\)-axis & \(k_{x}\) & 5000 N/m \\ stiffness in \(z\)-axis & \(k_{z}\) & 8000 N/m \\ damping in \(x\)-axis & \(b_{x}\) & 10 N/m/s \\ damping in \(z\)-axis & \(b_{z}\) & 15 N/m/s \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of simulation. The simulation results of group 2 are displayed in Figure 10 in the same way as for group 1, and the incremental energy consumption between the reversal point is shown in Tables 5 and 6. It can be seen that the influence of the working volume change of the accumulator on the energy efficiency of the actuator is the same as caused by the change of the initial inflation pressure detailed above, and the increase in the working volume of the accumulator does not significantly improve the energy efficiency of the HPCA during the reversal of the piston from contraction to extension. This is also consistent with the law described in Section 3.2.3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Description** & **First (0.35 s)** & **Second (1 s)** & **Third (1.35 s)** & **Total (2 s)** \\ \hline original actuator & 130.2 J & 279.2 J & 409.4 J & 558.4 J \\
2 Mpa & 128 J & 264.2 J & 392.5 J & 528.8 J \\
4 Mpa & 128 J & 262.7 J & 390.7 & 525.4 J \\
6 Mpa & 128 J & 260.4 J & 387.9 J & 520.8 J \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Energy consumption of the hip actuator at rear-front leg.