# Effects of Torso Pitch Motion on Energy Efficiency of Biped Robot Walking
## 1 Introduction  
Compared with other types of robots, humanoid robots have good adaptability to the environment, strong obstacle avoidance ability, small moving blind area, and good quality in line with human habits. These have attracted great attention and in-depth research of scholars, such as dynamics analysis [1, 2, 3], stability criteria [4, 5, 6], trajectory planning [7, 8, 9, 10], etc. Because the development of humanoid robots is restricted by the development of mechanism, materials, computer technology, control technology, microelectronics technology, communication technology, sensor technology, artificial intelligence, mathematical methods, bionics, etc., humanoid robots cannot yet achieve real anthropomorphism. There are still many problems to be solved in this field, such as walking stability, high-speed walking, reducing energy consumption, etc. Gait is a type of coordination relationship between joints in time and/or space when a robot is walking. Gait planning of biped robots depends on the ground conditions, lower limb structure, and the control difficulty, and it must meet the requirements of motion stability, walking speed, mobility, etc. For this reason, a variety of methods for gait planning have been adopted. Gait planning methods based on a simplified model are commonly used methods, such as an inverted pendulum or linear inverted pendulum [11, 12]. The simplified model brings a lot of convenience to robot research. The state of the system is only the position and velocity of the center of mass (CoM) of the robot. The gait is generated by the motion of CoM and the design of the landing point, and the trajectory of each join is obtained byinverse kinematics. The disadvantage is that the simplified model is an approximation of the robot and it is not accurate enough. When studying the energy efficiency of biped walking, this in-accurate model is difficult to work on. The method based on the zero-moment point (ZMP) stability criterion is another common method of gait planning. This type of method designed the reference ZMP trajectory first and then determined the motion of each joint that can realize the reference ZMP trajectory. [PERSON] et al. (2013) and [PERSON] et al. (2014) used ZMP based stability criteria to generate gait patterns. The advantage of this method is that if the reference ZMP is designed near the center of the stable region, the stability margin can be large. However, due to the limited changes of ZMP caused by hip motion, not all the expected ZMP trajectories can be achieved. In addition, in order to obtain the desired ZMP trajectory, the hip joint acceleration may need to be very large. In this case, due to the relatively large torso, energy consumption increases, and it is difficult to control the upper body. There are also some methods based on the multi-link model. [PERSON] et al. (2015), [PERSON] et al. (2016), and [PERSON] et al. (2017) designed the gait pattern of a five-link biped robot, and [PERSON] et al. (2019) and [PERSON] et al. (2018) designed the gait pattern of a seven-link biped robot. In their methods, the trajectories of hip and feet were defined in different ways first, then joint angles were obtained by inverse kinematics. In addition, torso angle was designed vertical during walking in their methods. This may make the design of the torso angle simple. However, torso keeping vertical may not be the best energy-efficient method for biped walking. This paper presents a gait generation method for biped robots with torso pitch motion (TPM). We also provide a common gait pattern with torso keeping vertical (TKV) to study the effects of TPM on the energy efficiency of biped robots. Based on the model of a planar five-link robot, the gait of the biped robot is generated by optimization. Firstly, the trajectories of hip position, torso angle, swing ankle position are designed as polynomials with some gait parameters.