*5.1. Validation of the Energy Model*

In order to verify the energy model proposed in this paper, some experiments are carried out. Different from the electrical actuated robots [21,22], the energy consumption of a hydraulic actuated robot is obtained by the data of joint sensors. For SCalf, the position and force sensors mounted on the actuator (Figure 4) are used to measure the cylinder lengths *ci* and joint forces *τ<sup>i</sup>* (*i* = 1, 2). Here, the equations of the RF leg are used. The mechanical parameters can be found in Table 2.

The joint angular velocities in Equation (34) can be obtained by the following equations.

$$\begin{cases} \theta\_1 = \frac{\pi}{2} - \arccos(\frac{a\_1^2 + b\_1^2 - c\_1^2}{2a\_1b\_1}) - e\_1 - e\_2\\ \theta\_2 = \pi - \arccos(\frac{a\_2^2 + b\_2^2 - c\_2^2}{2a\_2b\_2}) - e\_3 + e\_4 \end{cases} \tag{42}$$

$$\dot{\theta}\_i = \frac{d\theta}{dt}, \quad i = 1, 2 \tag{43}$$

The torques in Equation (34) are equal to the forces multiplied by their force arms, where *i* = 1, 2.

$$\tau\_i = f\_i \cdot a\_i \sqrt{1 - \cos(\frac{a\_i^2 + c\_i^2 - b\_1^2}{2a\_i c\_i})} \tag{44}$$

In the experiment, the gait parameters are chosen from Table 4. The sensor data are recorded with a frequency of 80 Hz. In this work, data of 5 gait cycles are recorded. The curves of joint positions, joint torques, and the leg power of the RF leg are illustrated in Figures 10–12.

From the above experiment results, the joint positions, joint torque, and leg power have the same trends in the experiment and simulation. The energy consumptions during 5 cycles are 393.69 J and 421.80 J for the experiment and simulation, respectively. The mean powers of the RF leg in the experiment and simulation can be calculated as 157.48 W and 168.72 W respectively. The differences between the data are mainly caused by the foot force distribution. Based on the energy consumptions and average power, the proposed energy model is verified.

**Figure 10.** The joint positions of the RF leg.

**Figure 11.** The joint torques of the RF leg.

**Figure 12.** A comparison of the power variation between the experiment and simulation.

#### *5.2. Simulation Results*

#### 5.2.1. Step Length

In this part, the step lengths are set as different values while the other gait parameters use default values. The step lengths ranges from 0.15 m to 0.5 m with an interval of 0.05 m. The energy consumption conditions and the *Ecost* are shown in Figure 13.

From Figure 13, we can know that with the increasement of the step length, the energy consumption during different phases and *Ecost* are both increasing but that the growth rate of *Ecost* is slower than the energy consumption.

**Figure 13.** The energy consumptions with different step lengths.
