# Gait Planning Research for an Electrically Driven Large-Load-Ratio Six-Legged Robot
## 2 Configuration and Walking Gait of the Large-Load-Ratio Six-Legged Robot  
### Configuration of the Large-Load-Ratio Six-Legged Robot  
To conveniently carry out the analysis of the gait planning, the electrically driven large-load-ratio six-legged robot is called the large-load-ratio six-legged robot for short. The leg of the robot is designed based on the walking leg of a hexapod. Each leg has three joints, including an abductor joint, hip joint, and knee joint. The abductor joint, hip joint, and knee joint are respectively defined as \(A_{i}\), \(H_{i}\), and \(K_{i}\) (\(i\) = 1-6). Each leg is made up of three linkages: a coxa, thigh, and shin. The axis of the abductor joint runs parallel to the \(Z\)-axis. The axes of the hip joint and knee joint follow the direction of the \(Y\)-axis. To maintain the characteristics of universal walking, the configuration of the robot body is designed as a regular polygon. The mechanism of the robot and structure of the leg are respectively shown in Figures 1 and 2.  
In Figure 1, the body coordinate system of the robot is set as \(\sum_{\text{B}}\) located at the center of the body. The ground coordinate system is defined as \(\sum_{\text{G}}\). The abductor joint coordinate system of leg \(i\) is regarded as \(\sum_{A_{i}}\), including the \(z_{1}^{(i)}\)-axis, \(x_{1}^{(i)}\)-axis, and \(y_{1}^{(i)}\)-axis. The \(z_{1}^{(i)}\)-axis is parallel to the \(Z_{\text{B}}\)-axis of the body coordinate system. The \(x_{1}^{(i)}\)-axis is kept parallel with the coxa of leg \(i\). The leg \(i\) lies in the plane \(z_{1}^{(i)}x_{1}^{(i)}\). The foot coordinate system \(\sum_{o_{i}}\) of leg \(i\) is parallel to the body coordinate system \(\sum_{\text{B}}\). The foot coordinate system \(\sum_{f_{i}}\) of leg \(i\) is parallel to the abductor joint coordinate system \(\sum_{A_{i}}\) of leg \(i\). The foot position matrix of leg \(s_{k}\) is set as \({}^{\text{B}}\text{P}_{\text{F}}^{(s_{k})}\) in the body coordinate system. The coordinate system, which is located at the body and connects the body to the leg \(i\), is regarded as \(\sum_{0_{i}}\). The coordinate system \(\sum_{0_{i}}\) and the coordinate system \(\sum_{A_{i}}\) are coincident with each other, when the rotating angle \(\theta_{i}\) of the abductor joint of leg \(i\) is zero degrees.  
Figure 1: Electrically driven large-load-ratio six-legged robot: (**a**) schematic diagram of the mechanism; and (**b**) top view of the mechanism.  
In Figure 1, the \(0^{\circ}\) lines are kept parallel with the \(X_{\rm B}\)-axis of the \(\sum_{\rm B}\) and pass through the origins of the coordinate systems of the abductor joints. The included angle \(\Delta\theta_{i}\) between the \(0^{\circ}\) line and leg \(i\) is defined as the initial angle of the abductor joint. The initial angle \(\Delta\theta_{i}\) can be used to set the initial position of the abductor joint when the robot begins to walk. The range of \(\Delta\theta_{i}\) is limited from \(0^{\circ}\) to \(60^{\circ}\). \(\theta_{i}\) is the rotation angle of the abductor joint based on the initial angle \(\Delta\theta_{i}\). The initial angles \(\Delta\theta_{2}\) and \(\Delta\theta_{5}\) are always zero degrees for legs 2 and 5. The initial angles \(\Delta\theta_{1}\), \(\Delta\theta_{3}\), \(\Delta\theta_{4}\), and \(\Delta\theta_{6}\) can vary within their range, and they are equal to each other when the robot begins to walk. In Figure 2, the lengths of the coxa, thigh, and shin are set as \(l_{\rm c}\), \(l_{\rm t}\), and \(l_{\rm s}\). The rotation angle of the abductor joint is set as \(\theta_{i}\). \(\beta_{i}\) (\(i\) = 1-6) is regarded as the included angle between the coxa of leg \(i\) and the thigh of leg \(i\). \  
\({}^{0}_{\rm A}\mathbf{R}^{(i)}\) is the rotation matrix from the abductor joint coordinate system \(\sum_{A_{i}}\) to the coordinate system \(\sum_{0,t^{\prime}_{\rm A}\mathbf{R}^{(i)}}\in\mathbf{R}^{3\times 3}\).