## 5 Experiment and Analysis  
(1) Quadruped robot prototype  
The experimental platform of the quadruped robot is shown in Figure 13. There are three joints on each leg: the hip joint \(\alpha\), knee joint \(\beta\) and ankle joint \(\theta\). The size of the platform is 1.2 m \(\times\) 0.5 m \(\times\) 1.4 m, and the weight is 150 kg. Figure 13a is the simulation prototype of the quadruped robot, and Figure 13b is the experiment of the quadruped robot. Figure 12: Output signal of the local CPG network. Figure 13: Quadruped robot. (**a**) Simulation prototype of quadruped robot. (**b**) Experimental prototype of quadruped robot. (2) Foot trajectory and joint trajectory planning  
Since the ideal angular displacement of the hip joint can be approximated as a cosine function [14], we assume that the control signal of the hip joint is \(\alpha=3\cos(2\pi t/T)\). The trajectory of the foot is a cycloid, as shown in Figure 14b. The height of the robot's hip joint is \(h=100\) cm from the ground, and the step length of each stride is 30 cm. The former leg is taken as an example to calculate the joint angular displacement and that of the knee and ankle joints, as shown in Figure 14a; thus, we obtain the following formula:  
\[\left. \begin{array}{l}l_{1}\cos\alpha-l_{2}\cos(\beta-\alpha)+l_{3}\cos[ \theta-(\beta-\alpha)]=x\\ l_{1}\sin\alpha+l_{2}\sin(\beta-\alpha)+l_{3}\sin[\theta-(\beta-\alpha)]=h-y \end{array} \right\} \tag{30}\]  
where \(l_{1}=45\) cm, \(l_{2}=60\) cm and \(l_{3}=50\) are the lengths of the robot's thigh, middle leg and calf; \(x\) and \(y\) are the analytic coordinates of the foot trajectory, as shown in Figure 14c, where \(\alpha\) and \(h\) are known. Thus, Equation (30) is a system of two equations with two unknowns, \(\beta\) and \(\theta\), whose solution is unique. The calculated relationship between \(\beta\), \(\theta\) and \(\alpha\) is shown in Figure 15. \(\alpha\) ranges from \(30^{\circ}\) to \(50^{\circ}\), which can be seen from the solid blue line in Figure 15, in order to make sure that the quadruped robot has a large stability margin when walking. The joint trajectory planning process of the hind leg of the robot is the same as that of the foreleg except for the different range of joint angles and the different shape of the curve. Thus, the experimental prototype of the quadruped robot used for local CPG network gait control has been completed. It is only necessary to input periodic control signals corresponding to the angular displacements of the four hip joints into the prototype, and then the control signals of the knee and ankle joints of each leg will be obtained according to the corresponding relations in Figure 15; thus, we can drive the robot prototype to walk. (3) Experiment on simulation prototype and experimental prototype  
The random selected parameters \(a\in[1,\,2]\) of the self-growing network are shown in Table 3. The time constant \(Tr\) is shown in Table 1. After calculating the output of the network and cosine to  
Figure 14: Foot trajectory of robot. (**a**) Structure diagram of one leg. (**b**) Experimental prototype of quadruped robot. (**c**) The analytic coordinates of foot trajectory. Figure 15: Trajectory planning of the knee and ankle joints. fit the output signal according to Equation (29), the result is shown in Figure 16. We can see that the output of the network is definitely the interaction oscillations between N1, N3, N2, and N4. N1 and N3 are input to the left front and the right hind hip joint of the simulation prototype, while N2 and N4 are input to the right front and the left hind hip joint of simulation prototype; then, the trot gait of the robot is implemented, and the simulation decompositions are shown in Figure 17a. As can be seen from Figure 17a, from \(t=0.2\) s to \(t=1.7\) s, the left front leg and the right hind leg are in the swing phase and swing forward; from \(t=1.9\) s to \(t=3.4\) s, the right front leg and the left hind leg are in the swing phase and swing forward.