## 7 Experiment
### Real-Time Whole-Body Imitation of Singly and Doubly Supported Motions
#### 7.1.4 Similarity Evaluation  
The similarity indexes of the WBF method and the LLF method were applied to evaluate our imitation system in real time. The trajectories of both indexes are shown in Figure 13. In the double-support phase, the WBF similarity index is above 0.94, and the LLF index is above 0.98. The variation trends of the two curves are similar, and the value of the LLF index is higher than that of the WBF index. From the 55 th motion loop to the 70 th motion loop, the similarity index curves show obvious fluctuations because of the slight delay in the movements of the robot's right arm. This slight delay can be observed from the RShoulderPitch angle trajectories (Figure 12a). During the mode-switch phase, both similarity index curves dip down and form troughs. However, the index values remain above 0.93. In the single-support phase, the WBF similarity index shows a decline compared with that in the double-support phase, whereas the LLF index returns to a high level. GA-LVVJ considers the local geometrical relations between articulated links and obtains the joint angles of the imitated  
Figure 11: Left key joint angle trajectories of the human and the robot in the first experiment. (a)–(f) depict the joint angle trajectories of LShoulderPitch, LShoulderRoll, LElbowRoll, LHipRoll, LHipPitch and LKneePitch, respectively.  
Figure 12: Right key joint angle trajectories of the human and the robot in the first experiment. (a)–(f) depict the joint angle trajectories of RShoulderPitch, RShoulderRoll, RElbowRoll, RHipPoll, RHipPitch and RKneePitch, respectively.  
posture directly and accurately, thereby contributing to the excellent observed performance in terms of local posture similarity.  
In the WBF method, in which the ground is regarded as the reference, if the robot is standing on its right foot, then the right tibia is the mother link of the right thigh and the right thigh is the mother link of the torso. In turn, the torso is the mother link of the upper links of the other limbs, which are the mother links of their respective lower links. Thus, the deviations of the mother links will accumulate and affect the positions of their child links in the world frame, even if their local similarity is high. This phenomenon will be more evident during the single-support phase because the links of the supporting leg, which serve as the mother links of the other parts, may deviate considerably to maintain balance. As shown in Figures 14 and 15, in the right-support phase, because the right leg angles are considerably modified to maintain balance, the left-thigh WBF similarity index shows an evident decline in the single-support phase compared with the double-support phase. Because the left tibia is the child link of the left thigh, the left-tibia WBF similarity index shows a sharper decline than that of the left thigh. Furthermore, the decline will be more evident when the single-support posture is more challenging. However, with a lowest value above 0.94, the WBF similarity index still indicates good performance in terms of the imitation similarity as seen from the perspective of the world frame.  
In short, this experiment verifies that the joint angle consistency between the human demonstrator and the robot is high and that our system performs well in terms of both the local similarity and the whole-body similarity.