# A Bio-Inspired Control Strategy for Locomotion of a Quadruped Robot
## 5 Results and Discussion
### Virtual Prototype Simulation  
Webots is a development environment used to model, program and simulate mobile robots. First of all, a quadruple robot virtual prototype is created in the Webots simulation platform, as shown in Figure 14, where its components and configurations are the same as described in Figure 1. In addition, in order to facilitate the observation of locomotion performance and foot trajectory of the robot, the CPS sensors (used to obtain the location of GPS points in the world coordinate system of the simulation platform) are added in its body geometric center and foot point respectively. Meanwhile, the touch sensors were added at its foot, which were used to measure the force of the foot in the vertical direction. Figure 14: The quadruped robot virtual prototype. Figure 13: The CPG-NN-WT outputs. The basic parameters of the robot virtual prototype are shown in Table 3.  
The simulation results with the representative trot and walk gaits and their mutual transitions are shown in Figures 15-18, where the parameters of the CPG-NN-WT control model are the same as in Figure 13.  
The upper part of Figure 15 is the robot centroid displacement (geometric center of the robot body), and the lower part is the foot force bearing status of the left front leg. As shown in the upper part of Figure 15, during the trot, walk gaits and their mutual transition process, the centroid displacement curves in the forward direction \(x_{c}\) is smooth and coherent without large fluctuations. In its vertical direction \(y_{c}\), the curve is smooth and has almost no fluctuation. Further, the slope of the forward direction curve \(x_{c}\) of centroid displacement is large in the trot gait but small in the walk gait due to the different duty factors of the two gaits. In addition, since the yaw control is not taken into account, the lateral displacement curve \(z_{c}\) of centroid is shifted during gait transition. As shown in the lower part of Figure 15, during the trot, walk gaits or their mutual transition process, the force of the foot is balanced and has small mechanical impact without sharp mutation relatively. (In order to more intuitively reflect the stress state, there is no filtering processing). Figure 16 shows the comparison of the preplanned WT (desired trajectory) with real trajectory of the left front leg when robot is traveling. As shown in Figure 16, there are left or right shifts between the real trajectory curves and the preplanned WT curve due to the yaw angle, which is generated during the gait transition but which is not taken into account while processing data. However, the real trajectories are still in accordance with the preplanned WT if the effect of yaw angle is not taken into account, e.g., the real trajectory of which the yaw angle is 0 during the first gait period is in accordance with the preplanned WT well, and its maximum absolute error in \(x\) is under 0.4 mm, which is about \(2\times 10^{-3}\)\(S\) and its maximum absolute error in \(y\) is under 0.2 mm, which is about \(6.7\times 10^{-3}\)\(H\), as shown in Figures 17 and 18. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline size: \(L\times W\times H\) (mm) & 500 \(\times\) 200 \(\times\) 405 \\ mass (kg) & 4 \\ \(l_{1}\) (mm) & 150 \\ \(l_{2}\) (mm) & 150 \\ hip joint range & \((-\pi,\pi)\) \\ knee joint range & \((-\pi,\pi)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The robot virtual prototype parameters. Figure 15: Centroid displacement and the foot force bearing status of the robot virtual prototype. Figure 19 shows the simulation video captures of the virtual prototype in the Webots platform. Throughout the whole simulation process, the locomotion of the quadruped robot is smooth and fluent. Referring to Figure 13, it can be seen that during the whole simulation process, the \"CPG part\" has played its advantages in gait planning and controlling well, while the \"NN part\" has the ability to adjust the foot positions according to the preplanned WT.