## 5 Experimental Verification  
### Experimental Setup  
Due to limitations of devices, it is currently not possible to test the HPCA on a robot platform. Therefore, a single-leg test bench was designed to verify the simulation results. As can be seen from Figure 12, the test bench is mainly composed of beam I and II connected by slider in horizontal direction. The slider in vertical direction is mounted on the beam II and connects to the counterweight, so that the counterweight can only move in the vertical direction along beam II. The counterweight and hip are connected by bolts so that the leg can only swing in the x-z plane relative to the counterweight. According to the experimental setting, the lateral movement of beam II is limited. The total mass of the leg prototype is 45.3 kg.  
The experiment was divided into two groups with aims to test the energy efficiency characteristics of the HPCA with different loads and foot trajectories. In group 1, the leg prototype was mounted on the hanging bracket and could not touch the ground during the experiment. The foot trajectory described in Section 3.1 was used. In group 2, the foot remained in contact with the ground at all times and the initial standing height of the robot is set to 0.65 m. The sinusoidal signal with frequency of 1 Hz and amplitude of 0.05 m was used as the foot trajectory in the \(z\)-axis and the desired trajectory was set to zero along the \(x\)-axis. A large hydraulic station ensured a constant supply pressure for the experiment (200 bar).  
A flow sensor cannot be installed between the accumulator and cylinder, so the flow data \(Q_{accu}\) can be calculated by Equation (10). The pressure in the piston chamber \(P_{accu}\) can be measured by the miniature pressure sensor (Model: TE/EB1 UM- 00000P- 350 BA) mounted on the actuator, and then the change of the pressure \(\dot{P}_{accu}\) can be obtained through deriving \(P_{accu}\). The energy consumption of the leg prototype can be calculated as follows:  
\[E=\int W_{hip}dt+\int W_{free}dt \tag{19}\]  
with  
\[W_{hip}(W_{knee})=\left\{\begin{array}{cc}(A_{pis}\hat{x}_{p}-Q_{accu})P_{S}&( \hat{x}_{p}>0)\\ A_{r}P_{S}|\hat{x}_{p}|&(\hat{x}_{p}<0),\end{array}\right. \tag{20}\]  
where the displacement of the piston \(x_{p}\) can be measured by the linear transducer (model: VISHAY/REC 38L 03C 502 B) mounted on the actuator, and then the velocity \(\hat{x}_{p}\) can be obtained through deriving \(x_{p}\).  
The stiffness and damping of the virtual model were set to 3500 N/m and 0 N/m/s on the \(x\)-axis and 5300 N/m and 0 N/m/s on the \(z\)-axis; the experimental process is shown in Figure 13. The accumulator models and the parameters used in the two groups are shown in Table 7.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Accumulator** & **Initial Pressure** & **Working Volume** \\ \hline different inflation pressure & HAWE AC-13-1/4 & 2 and 4 Mpa & \(1.3\times 10^{-5}\) m\({}^{3}\) \\ different working volume & HAWE AC-13-1/4, AC-40-1/4 & 3 Mpa & \(1.3\times 10^{-5}\) and \(4\times 10^{-5}\) m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Experimental grouping.  
Figure 12: Test bench.  
Figure 13: Trajectory tracing test. **(A)** Group 1; **(B)** group 2.