# Study on Head Stabilization Control Strategy of Non-Wheeled Snake Robot Based on Inertial Sensor
## 6 Discussion  
The simulation and experimental data are analyzed in the following. Figure 17 is the comparison of the head pitch angle with and without the stable algorithm in the simulation and experimental environments. By calculating the peaks and troughs of the curve, the average value of the peaks without the stable algorithm under  
Figure 16: Head stabilization experimental data. Figure 15: Head stabilization experiment with stabilization algorithm. (**a**) Phase is 0; (**b**) phase is \(\pi/2\), (**c**) phase is \(\pi\); (**d**) phase is \(3\pi/2\). the simulation is shown to be \(6.74^{\circ}\), and the average value of the troughs is \(-7.98^{\circ}\). The average value of the peaks with the stable algorithm under the simulation is \(2.86^{\circ}\), and the average value of the troughs is \(-0.30^{\circ}\). By calculation, the reduction ratio of the head stabilization amplitude in the simulation environment is shown to be \(21.47\%\). The average value of the peaks without the stable algorithm under the experiment is \(6.13^{\circ}\), the average value of the troughs is \(-1.57^{\circ}\), the average value of the peaks with the stable algorithm under the experiment is \(1.77^{\circ}\), and the average value of the troughs is \(0.08^{\circ}\). By calculation, the reduction ratio of the head stabilization amplitude in the experimental environment is shown to be \(22.08\%\). In Figure 17a, the Root Mean Square Error (RMSE) of the simulation without the stability algorithm is \(5.10\), and the RMSE of the simulation with the stability algorithm is \(1.57\); the RMSE between the simulations with and without the stable algorithm is \(4.42\). In Figure 17b, the RMSE of the experiment without the stability algorithm is \(3.23\), and the RMSE of the experiment with the stability algorithm is \(0.94\); the RMSE between the simulations with and without the stable algorithm is \(2.68\). According to the calculation results, the head stabilization efficiency of the snake robot in this scheme is high, which can effectively restrain the head fluctuation and ensure the stabilization of its head. As can be seen from Figure 18, the stabilized joint angle under the simulation is approximately \(0^{\circ}\) to \(3^{\circ}\), and the stabilized joint angle under the experiment is approximately \(0^{\circ}\) to \(2^{\circ}\); this is because the head of the snake robot is affected by its own gravity. When the head of the snake robot bobs upwards, due to the influence of gravity and the compensation algorithm, the upward swing of the head is very small, almost zero. Therefore, in the simulation and the experiment with the stable algorithm, the joint angle is basically above \(0^{\circ}\). In Figure 18a, the RMSE between the simulations and experiments without the stable algorithm is \(13.57\), while the RMSE between the simulations and experiments with the stable algorithm is \(2.07\) as shown in Figure 18b. It can be seen that after adding the stability algorithm, the simulation and experimental data are significantly closer, both converging towards \(0^{\circ}\). In Figure 18, the pitch angle of the head module under the experiment is smaller than that of the simulation. This is due to the limitation of the material of the head module of the snake robot. When the snake robot performs an inchworm gait movement, the head module is affected by other joints to swing up and down, and due to the low rigidity of the head module material, it is difficult to achieve the predetermined joint angle, so the overall pitch angle of the head module under the experiment is smaller than the simulation data, especially when the head of the snake robot bobs upwards. Since the snake is affected by the gravity of its head and its own material, it is difficult for the head of the snake robot to bob upwards, so the head direction angle under the experiment is basically above \(0^{\circ}\). Figure 17: Comparing with and without stable algorithm under simulation and experiment.