## 1 Introduction
For fast and stable running, various characteristics of human running have been identified in studies on human sciences and sport sciences, including the following:  
* The stance leg acts like a linear spring. A human leg can be modeled as a SLIP model. * The knee and ankle joints in the stance leg serve as torsion springs that provide leg elasticity and the ability to kick the ground strongly [21; 22]. * The leg and joint stiffness change depending on the running speed [23]. * Rapid knee bending occurs in the swing phase to avoid contact of the foot with the ground [24]. * The pelvis rotates in the frontal plane to increase the jumping force [25]. * Moment compensation is accomplished using torso and arm swinging in yaw direction [26; 27]. We are working to develop a robot that can run like a human by mimicking the above characteristics. Previously, we developed a lower-body robot that mimics human characteristics,such as leg joint stiffness and pelvic rotations in the frontal plane and can hop with a large joint output of approximately 1000 W by not dissipating the energy at landing but storing the energy in its elastic parts [25; 28; 29]. In addition, the lower-body robot has the human link length and mass properties, such as the mass, center-of-mass (COM) position in the link, and inertial matrix of each link. The reason for this is that link length and mass properties would result in angular momentum. The currently available humanoid robots do not have human like link lengths or mass properties. These humanoid robots are presumed to have been developed with a focus on walking, which is a movement slower than running. When the angular velocities of joints are not very large, the angular momentum generated is not large and has little influence on the whole-body motion. Some researchers are interested in methods of generating stable motion during the stance phase. [PERSON] et al. are developing stable control based on the momentum as a norm during walking exercises [30]. [PERSON] et al. investigated a back-handspring motion with a multi-link robot and proposed motion planning considering global physical quantities such as the center of mass or angular momentum during the stance phase [31]. On the other hand, during the flight phase, the angular momentum of the whole body of the robot cannot be modified. The upper body and legs are connected to the waist, where the movement of legs and an upper body are generated. It means that when the robot swings only its legs without active moving of the upper body joints during the flight phase, the waist and upper body rotate in yaw direction due to the angular momentum generated by the legs movement. As a result, when the direction of the waist deviates from the traveling direction, the robot cannot perform straight running. To solve it, humans move their upper body actively including arms for generating the angular momentum in opposite direction from that generated by the legs movement [26; 27]. In this study, our focus is on the flight phase that occurs during the hopping or running motion of a robot, and we aimed to prevent rotation of the waist by aggressively generating angular momentum with the upper body equivalent to that generated by the legs during the flight phase. To this end, we propose an angular momentum compensation control method that uses the arms and torso inspired by the mechanisms of human running. Moreover, to realize the proposed method with a real humanoid, we developed an upper-body mechanism to mimic human link lengths and mass properties. We performed experiments with the robot that we developed to evaluate the proposed methods. We confirmed that the humanoid robot could compensate for the angular momentum in the yaw direction that is generated by lower-body movement in midair. The remainder of this paper is organized as follows. In Section 2, we describe the proposed method for compensating for angular momentum in the yaw direction and the design of the upper-body mechanism that mimics the human mass properties.