# Energy-Efficient Hip Joint Offsets in Humanoid Robot via Taguchi Method and Bio-inspired Analysis
## 1 Introduction  
As quality of life improves, the demand for humanoid robots to help or replace humans in various activities is increasing. However, the mobility of humanoid robots is limited by their main power source, batteries, which have limited available power. To improve the performance of humanoid robots, energy efficiency must be increased to provide longer operation periods or enable the use of lighter and smaller batteries.  
Several studies have aimed to improve energy efficiency by reducing power consumption in the actuators of humanoid robots. [PERSON] et al. [1] observed that the rotation of the hip joint from its original orientation improves energy efficiency by reducing and distributing the joint's mechanical power in the hip joints. [PERSON] et al. [2] proposed a biarticular design for humanoid robot legs using a redundantly actuated parallel mechanism to improve energy efficiency. [PERSON] et al. [3] designed a four-bar linkage for knee and ankle joints, thus decreasing the mass and moment of inertia of the lower body to enhance energy efficiency. [PERSON] et al. [4] studied an asymmetric compliant antagonistic joint design to improve performance mobility, which is closely related to energy efficiency.  
Although previous research has improved the energy efficiency of humanoid robots, no study has considered the offset between hip joints to this end. This offset is the gap between adjacent joints along a coordinate axis (e.g., a roll-yaw-pitch hip joint, where the offset is represented by each gap between the roll and yaw joint and between the yaw and pitch joint along the \(X\), \(Y\), and \(Z\) axes). Mechanically, it is difficult to overlap multiple joints at a single intersection point and, therefore, the effect of joint offset on the humanoid robot should be investigated.  
In this study, we optimized the hip joint offset in a humanoid robot to improve energy efficiency by reducing consumption at the actuating joints. Optimization considered bipedal locomotion, which is representative of humanoid robots, by including turning, forward, backward, and sideways walking motions. We analyzed the mechanical power consumption of the actuated hip joints using a humanoid model, implemented in physics simulation software (MuJoCo, Roboti, Seattle, DC, USA) for energy optimization. Specifically, the objective function was the root-mean-square (RMS) mechanical power consumption from the actuated hip joints.  
The complex dynamics of multi-joint humanoid robot legs hinder the ability of investigations of the joint offset effect to obtain, for instance, an analytical solution. Therefore, it is more appropriate to use numerical optimization for this study. However, it becomes impractical, given the time-consuming generation of many complex simulation models of humanoid robot legs with different joint offset configurations.  
To minimize the time-consuming efforts of numerical optimization, we implemented the Taguchi method, which is an experimental approach for the robust, optimal design of products under various conditions. As the method conducts optimization based on an orthogonal array, it can minimize the number of simulation models required, thus reducing the optimization execution time. For the Taguchi method, we set the joint offsets as control factors and the four abovementioned types of motions as noise factors.