# Energy-Efficient Hip Joint Offsets in Humanoid Robot via Taguchi Method and Bio-inspired Analysis
## 6 Discussion  
We investigated the optimization for reducing power consumption at the hip of a humanoid robot via the Taguchi method. The two-stage optimization achieved a larger reduction in consumption than that obtained using only one stage. Power consumption at the hip was mainly influenced by the \(Y\) axis offset. Therefore, the closer the sides of the hip joint, the lower the energy consumption. The sum of RMS power consumption from the right hip joint (\(Pow_{\text{rms}}\)) over time during the motions is shown in Figure 11 and supplementary materials. Humanoid robots implement zero-moment point walking to keep the point position inside the supporting polygon and thus stabilize the robot's walking. The supporting polygon is a convex hull containing the contact points between the feet and ground. If both feet are close due to the hip joints being close, the supporting polygon becomes narrower. During single-leg support, the robot sways its upper body from side to side to place the zero-moment point inside the supporting polygon. Consequently, placing the hip joints closer reduces the area to move the zero-moment point to keep it within the supporting polygon while switching from double- to single-leg support. Then, the moment acting on the roll joint is decreased by the smaller moment arm of the upper body, related to the roll joint. Therefore, joint offsets along the \(Y\) axis are advantageous to improving energy efficiency by reducing power consumption in the roll joint, as both hip joints are close. We explored the reason for the reduction of power consumption through bio-inspired analysis from human gait mechanics. The finding in this study is similar to the influence of the body's center of gravity (COG) pathway on human walking efficiency. Minimizing the body's COG, displaced from a level line of progression, is considered to be a major mechanism for reducing the muscular effort of walking and, consequently, for saving energy. The least energy would be used if the weight being carried remained at a constant height and followed a single central path. No additional lifting effort would then be needed to recover from the intermittent falls downward or laterally [11]. As an additional analysis, we compared the maximum required torque at the joint after optimization. The reduction of actuating torque is an important issue for reducing the weight of the actuators. Except for the pitch joint during the turning motion, all maximum torques generated at each joint were reduced by a minimum of 0.95% and a maximum of 44.67%. Before the optimization, the maximum torque of all joints was generated at a value of 70.91 Nm at the roll joint during the sideways walking motion. Through the optimization, this value was reduced to 59.15 Nm, which was also the maximum torque for the optimized model. Although we obtained valuable insights on offset design, some limitations of this study remain to be addressed. We considered only mechanical power to represent power consumption, because it is impossible to calculate the electrical power dissipated in the actuator before selecting the motor and other electronic components. In addition, although the negative mechanical power can be restored using a regeneration system, we neglected this aspect because humanoid robots typically do not implement a regeneration system. We expect to use the findings in this study to design an improved humanoid robot. By improving energy efficiency, the operating time of humanoid robots can be extended. As for future work, we plan to verify energy efficiency optimization while a humanoid robot performs various tasks. Moreover, we intend to extend joint offset optimization to include knee and ankle joints. The following are available online at [[http://www.mdpi.com/2076-3417/10/20/7287/s1](http://www.mdpi.com/2076-3417/10/20/7287/s1)]([http://www.mdpi.com/2076-3417/10/20/7287/s1](http://www.mdpi.com/2076-3417/10/20/7287/s1)).