# Effects of Torso Pitch Motion on Energy Efficiency of Biped Robot Walking
## 6 Conclusions  
In this paper, a gait pattern generation method of biped robots with torso pitch motion is proposed to study the influence of torso motion on the walking efficiency of biped robots.  
Figure 14: Energy consumption of each joint when gait period is 1.0 s and step length is 0.3 m.  
Figure 15: Ground reaction force on trailing leg during DSP when gait period is 1.0 s and step length is 0.3 m.  
The cyclic gait of a five-link biped robot is designed. The trajectories of the hip joint and swing ankle are defined as polynomials. The trajectory of torso angle is also defined as polynomials. The total energy consumption of all joint actuators per unit distance of the robot is chosen as the optimization objective. In addition, a genetic algorithm is used to optimize the gait parameters.  
Firstly, a valid walking gait with torso pitch motion can be generated according to our proposed method. As shown in Section 5.1, walking stability is satisfied and ground reaction forces satisfy the unilateral constraints and no-sliding constraints. Secondly, to compare the walking efficiency of TPM and TKV, we generate the optimal gaits with various gait periods and step lengths. According to the optimization results shown in Section 5.2, TPM saves more than 12% energy on average compared with TKV. Thirdly, torso angle parameters are also studied according to optimal gait in Section 5.3. Although the parameters related to the torso motion with different gait periods and step lengths are various, the overall trend is that torso leans forward during DSP and leans backward during SSP. Lastly, in order to analyze the reason that TPM saves energy than TKV, we compare the energy consumption of each joint of TPM and TKV in Section 5.4. It is observed that the main factor of energy-saving in TPM compared with TKV is the reduction of energy consumption of the swing knee during DSP. This is because TPM can reduce the push force of the trailing leg during DSP.  
In this research, we designed a gait generation method with TPM that can save more energy than TKV. However, the trajectory of the torso angle we designed is only one of all possible trajectories. There may be a better trajectory for torso angle. This will be the content of our future research.  
Conceptualization, L.L. and X.L.; methodology, L.L. and J.L.; software, L.L.; validation, Z.X. and J.L.; formal analysis, L.L. and Z.X.; investigation, L.L.; writing--original draft preparation, L.L.; writing--review and editing, Z.X. and J.L.; supervision, X.L.; project administration, X.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51375085.  
Not applicable.  
No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
[PERSON] would gratefully thank [PERSON] at the School of Mechatronics Engineering, Beijing Institute of Technology, for his careful editing of the manuscript and for providing constructive suggestions.  
The authors declare no conflict of interest.