## 3 Dynamic Balance Control Method  
The diagonal gait can be equivalent to a virtual leg. Ideally, the diagonal legs soar and land at the same time. However, in fact, during the trot process of the quadruped robot, one leg always lands first in the falling process. As shown in Figure 4, the leg that lands first will be impacted by the ground, causing body shake and affecting the stability of the robot's movement. According to the above problems, a method is proposed to use flight rate as a stability index to describe the landing condition of the diagonal leg, and the value range of flight rate \(\lambda\) is 0-1. \[\lambda=\frac{t_{s}}{t} \tag{6}\]  
where, \(t_{s}\) is the flighting time and \(t\) is half cycle. In order to keep the quadruped robot moving stably during diagonal walking, the diagonal legs need to land at the same time to improve the flight rate. The landing attitude of the swing leg is controlled through attitude feedback, as shown in Figure 5:  
Figure 4: The soar period of the actual diagonal gait. In Figure 5, 1 and 4 represent the left-front leg and right-rear leg of the quadruped robot. During the walking process, the trunk roll angle is \(\theta_{roll}\) and the pitch angle is \(\theta_{pitch}\). The robot length is \(L_{b}=2L^{\prime}\) and width is \(W_{b}=2W^{\prime}\), \(H\) is the height of the robot centroid, \(h^{\prime}\) represents the height of the 1 leg and \(h^{\prime\prime}\) represents the height of the 4 leg. \(l^{\prime}\) and \(l^{\prime\prime}\) represent the front-back moving distance of 1 and 4 legs, respectively. It can be concluded that:  
\[\left\{ \begin{array}{l}l^{\prime}=x_{01}-h^{\prime}\tan\left(\theta_{pitch} \right)\\ h^{\prime}=z_{01}+W^{\prime}\sin(\theta_{roll})+L^{\prime}\sin\left(\theta_{ pitch}\right)\\ l^{\prime\prime}=x_{04}-h^{\prime\prime}\tan\left(\theta_{pitch}\right)\\ h^{\prime\prime}=z_{04}-W^{\prime}\sin(\theta_{roll})-L^{\prime}\sin\left( \theta_{pitch}\right)\\ \end{array} \right. \tag{7}\]  
The quadruped robot can predict the best landing point through formulas (7), and the prediction results are shown in Table 1 below:  
\(x_{i},y_{i},z_{i}\) represent the \(x,y,z\) coordinate axes at the end of the leg \(i\), \(x_{0i},y_{0i},z_{0i}\) represent the starting \(x,y,z\) coordinate axes at the end of the leg \(i\). \(i\) take \(1,\ 2,\ 3,\ 4\) to represent the left-front leg, the right-front leg, the left-rear leg, and the right-rear leg, respectively. \(\delta\) and \(\gamma\) are coefficients, as follows:  
\[\delta =\left\{ \begin{array}{ll}0&i=2.3\\ 1&i=1.4\\ \end{array} \right. \tag{8}\] \[\gamma =\left\{ \begin{array}{ll}0&i=1.4\\ 1&i=2.3\\ \end{array} \right.\]  
The stable condition of the body in diagonal gait is that the diagonal legs are raised and landed at the same time, that is, the flight rate \(\lambda\) is equal to 1 as far as possible. In other words, the projection of the body's gravity center on the support plane should be close to the diagonal line. Therefore, the robot's gravity center is self-balanced by adjusting the time difference of the robot's diagonal legs. The four cases of gravity center distribution are shown in Figure 6: \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(x_{i}\) & \(y_{i}\) & \(z_{i}\) \\ \hline \(Left\)\(fore\) & \(x_{01}-\delta z_{01}\tan(\theta_{pitch})\) & \(y_{01}\) & \(z_{01}+\delta(W^{\prime}\sin(\theta_{roll})+L^{\prime}\sin(\theta_{pitch}))\) \\ \(Right\)\(fore\) & \(x_{02}-\gamma z_{02}\tan(\theta_{pitch})\) & \(y_{02}\) & \(z_{02}+\gamma(W^{\prime}\sin(\theta_{roll})+L^{\prime}\sin(\theta_{pitch}))\) \\ \(Left\)\(bind\) & \(x_{03}-\gamma z_{03}\tan(\theta_{pitch})\) & \(y_{03}\) & \(z_{03}-\gamma(W^{\prime}\sin(\theta_{roll})+L^{\prime}\sin(\theta_{pitch}))\) \\ \(Right\)\(bind\) & \(x_{04}-\delta z_{04}\tan(\theta_{pitch})\) & \(y_{04}\) & \(z_{04}-\delta(W^{\prime}\sin(\theta_{roll})+L^{\prime}\sin(\theta_{pitch}))\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The landing points. Figure 5: The robot attitude feedback is displayed from different perspectives.