## 1 Introduction
In [40], a humanoid robot was made to imitate human upper-limb motions and was issued walking, hand closing and opening, and mode switch instructions via speech signals to complete a pen shopping task. [PERSON] et al. used additional postures to switch on/off the locomotion function and successfully directed a robot to pick up a ball using upper-limb imitation [29; 41]. The system had only one static reference position for locomotion, and the additional postures were not spontaneous human motions; consequently, the operation was relatively time-consuming and inconvenient. In [25], an imitation system was used to issue walking instructions by means of upper-limb postures. The volunteers participating in this research verified the difficulty of this method. Some imitation systems involving dynamic balance have been proposed and developed in recent years. The work presented in [42] focused on controlling the legs of the humanoid robot by a master-slave approach to realize dynamic biped walking. In [43], the authors improved their system by proposing a set of safety limitations to meet the dynamics of Linear Inverse Pendulum at any time. Furthermore, they calculated additional reference ZMP informations without the foot force sensor devices they had used before, which relieved operation stress of the operator. In [44; 45], the authors proposed, designed and developed a whole-body human-in-loop teleoperation control system with balance feedback, which enabled the operator to control the robot to perform powerful manipulation tasks. Their works are impressive and enlightening to our work. On the other hand, while their works focused on humanoid robot's capability and stability of dynamic biped locomotion and performing tasks, the whole-body imitation similarity might be limited. In the work presented in [42; 43], the authors only used the information of the human's end effector and center of mass to generate reference joint angles, and the foot height was also restricted. In [44; 45], only upper limbs and hips were considered in the motion mapping, and the motions of the lower limbs subjected to the torso orientation of the operator. The single-support motions were also not mentioned in this work. Our focus is quite different. We mainly focus on generating comprehensive stable whole-body imitation motions of the humanoid robot with high similarity. Other than the positions of the end effectors, the positions of the joints are fully considered in our motion mapping methods, to endow the robot with the ability of generating more similar human behaviors. In terms of user friendliness,our system only employs a RGB-D camera (the camera which provides color information and estimated depth information) to obtain the human body information, and does not need any wearable devices used in the above work. The evaluation of the motion similarity between a human demonstrator and a humanoid robot is another critical issue for both the optimization of multiple solutions and the assessment of the effectiveness of an imitation system. For solution optimization, in [23], the imitation similarity was measured by calculating the distance between the normalized vectors representing the human and the robot, and the corresponding error function was applied in the IK optimization problem. [PERSON] et al. presented state, action and effect metrics for different correspondence mappings associated with various imitators and imitation tasks [46]. For assessing the effectiveness of an imitation system, [PERSON] et al. used an evaluation metric called the Mean Opinion Score to quantify the imitation quality [25]. However, this approach was subjective and not sufficiently accurate. In [16; 17; 21; 24], the researchers evaluated the imitation similarity by determining the position errors of the end effectors between the scaled human model and the robot; however, this approach could not completely reflect the similarity of the postures because the end effectors represent only a few points on the entire body.