## 4 Structure of Local CPG Network
Since there are 24 axons in the network, there are 48 parameters with 24 time constants and 24 connection weights in the network. Such a large number of parameters in the network is not conducive to the study of the rule between the output and growth results of the network. In order to facilitate the analysis, the axons in the network are divided into two categories: in the first category are the axons that inhibit the connection between the output neurons, with a total of 12; the second category are the axons connected with the peripheral neuron (the input neuron and the Renshaw Cell) between the output neuron, with a total of 12. For the first type of axons, only the connection weights in the growth results are used, and the time constants are all set to 0. For the second type of axon, only the time constant in the growth result is used, and the connection weights are all fixed values. This halves the network's parameter variables. The time constants of the axons of each neuron after a certain growing process are shown in Figure 10.0  
According to Equation (25), the connection weight \(a\in(1,2)\) can be obtained. In order to simplify the calculation, a random number between (1, 2) is taken as the value of \(a\). The connection weights obtained are shown in Table 2, and the connection weights between the output neuron and the peripheral neuron are set to 1 and 2, which meet \(a\in[1,2]\). The output result of the entire network is calculated according to Equation (29), as shown in Figure 10.1 \begin{table}
\begin{tabular}{c c c} \hline
**Time Constant** & **Length of Corresponding Axon** & **Value** \\ \hline \(T_{r1}\) & Length of axon between output neuron N1 and Renshaw Cell N6 & 2.1801 \\ \(T_{r2}\) & Length of axon between output neuron N2 and Renshaw Cell N5 & 2.5868 \\ \(T_{r3}\) & Length of axon between output neuron N3 and Renshaw Cell N8 & 1.1984 \\ \(T_{r4}\) & Length of axon between output neuron N4 and Renshaw Cell N11 & 1.9691 \\ \(T_{r5}\) & Length of axon of Renshaw Cell N5 & 2.8071 \\ \(T_{r6}\) & Length of axon of Renshaw Cell N6 & 2.2821 \\ \(T_{r7}\) & Length of axon of input neuron N7 & 3.7401 \\ \(T_{r8}\) & Length of axon of Renshaw Cell N8 & 1.2096 \\ \(T_{r9}\) & Length of axon of input neuron N9 & 5.4620 \\ \(T_{r10}\) & Length of axon of input neuron N10 & 4.8037 \\ \(T_{r11}\) & Length of axon of Renshaw Cell N11 & 1.8388 \\ \(T_{r12}\) & Length of axon of input neuron N12 & 4.6752 \\ \(T_{r13}\)–\(T_{r24}\) & Length of interactional axon between N1, N2, N3 and N4 & 0 \\ \hline \end{tabular}
\end{table} 
Table 1: The time constant of the axon in the network. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(a_{10,1}\) & \(a_{7,2}\) & \(a_{9,3}\) & \(a_{12,4}\) & \(a_{1,6}\) & \(a_{2,5}\) & \(a_{3,8}\) & \(a_{4,11}\) & \(a_{6,1}\) & \(a_{5,2}\) & \(a_{8,3}\) & \(a_{11,4}\) \\ \hline \(1\) & \(1\)As can be seen from Figure 12, the output signals of the four output neurons have the same period and phase difference and a similar range of amplitude after a period of stability. Furthermore, it is verified that the self-growing network model established in this paper can obtain a local CPG network which can satisfy the biological CPG network input and output characteristics, and the output of the network can be used for the control of the hip joint of quadruped robot. If the output signal of neuron N1 is used as the basis to calculate the phase difference, it can be determined that the output phase difference between N2 and N1 is 168.0\({}^{\circ}\), the output phase difference between N3 and N1 is 33.6\({}^{\circ}\) and the output phase difference between N4 and N1 is 264.0\({}^{\circ}\). The ideal phase differences of the corresponding hip joints of the quadruped robot at the walk gait are 180\({}^{\circ}\), 90\({}^{\circ}\) and 270\({}^{\circ}\).