## 4 Discussion  
In experiment 2, we could not perform a running experiment with the humanoid developed in this study because more work is required to develop methods for stabilization in the pitch and roll directions. During running, the vertical component of the ground reaction force can be up to 1800 N, which is much larger than the horizontal component of approximately 180 N [37]. Therefore, the ground reaction force influences stabilization in the pitch and roll directions but not in the yaw direction. When the ground reaction force does not act in alignment with the COM of the humanoid, angular momentum is generated and the robot falls. To prevent this situation, some researchers have  
Figure 6: Experimental results for angular momentum compensation. Figure 7: Experiment with a real robot. Upper row shows the experiment without angular momentum control. Lower row shows the experiment with angular momentum control. The humanoid was suspended with orange cables connected to a hanger, which could rotate passively in the yaw direction, and did not contact with the ground. focused on stabilization in the pitch and roll directions by controlling the ground reaction force [38; 39]. In contrast, in this study, we focused on yaw stabilization using the upper body, because the ground reaction force does not have a large influence on stabilization in the yaw direction. In this study, we designed an upper-body mechanism that has human-like link length and mass properties to achieve angular momentum compensation in the yaw direction during running. In experiment 1, we confirmed that the upper body could generate almost the same angular momentum as a human's upper body during running. In addition, we calculated the angular momentum in the yaw direction with the 300 g lighter forearm. These results indicate that mass parameters have a large influence on the angular momentum generated during running. To achieve angular momentum compensation during running, it is important to incorporate the capacity of generating angular momentum in designing a humanoid robot. The upper body developed in this study was found to be able to perform fast movement as well as a human. This upper body will be useful in future research on effective sports movements such as ball throwing. We propose in this paper an angular momentum compensation method using a humanoid upper body. This method can be used with other humanoid robots that do not have human-like mass properties. The reason for this is that the robot can calculate the angular momentum required using its mass property data and the control method developed. In addition, the control method can be applied to active turning by changing the angular momentum reference of the waist. In experiment 2, which involved running on a straight course, the angular momentum reference of the waist was set to zero. In addition, we assume that the proposed method for stabilization in the yaw direction can be applied to stabilization in the pitch and roll directions with a change in the ground reaction force. In general, the upper body has a large mass and moment of inertia, and it can thus generate large angular momentum in the pitch, roll and yaw directions. The angular momentum generated by the ground reaction force can be compensated for by the upper-body motion. When the humanoid cannot effectively use its upper body, the humanoid should generate motion within a range that maintains the stabilization with only its legs and torso. By integrating these methods, the humanoid can perform faster and wider-ranging motions. In future work, we intend to apply the proposed method for stabilization to the pitch and roll directions. In addition, we will utilize the robot in the place of human subjects to confirm various running characteristics. In summary, we found that the angular momentum compensation in the yaw direction using the upper body during the flight phase can improve the capability of humanoid hopping and running performance.