## 5 Numerical Simulation Results
### Verification on the Simulator  
Once the neural network converged, the decision model of the mobile robot was determined, which will not change with respect to propagation of scene and time. To validate its actual performance, the trained neural network model was applied to the autonomous mobile robot navigation task in the simulator. The simulator randomly generated a 2D plane with obstacles and selected the start and destination positions, which are marked as red and green dots in Figure 8. At each sample time index \(t\), the measured obstacle distance \(d_{i}(t)\), \(i=1,\ldots,17\) and heading direction bias \(\phi^{i}\) were sent to the trained model to generate the probabilities of each motion type \(\mathcal{M}_{i}\) at \(t\), which was exactly the output of the model. Based on the obtained probabilities, the decision of the motion type was computed and the mobile robot changed its state according to (18) in the simulator test environment. To evaluate the real-time performance of the neural network model, it was loaded onto a laptop with \"AMD Ryzen7 5800H\" CPU and \"NVIDIA GeForce RTX 3060\" GPU to obtain the time consumed by each decision as shown in Table 1. Note that the total time was consumed by the process of the model outputting an executed action based on the input information obtained. In Table 1, a total number of 5 navigation tasks were considered, where the time consumed by the model at 6 moments was randomly selected to compute the average time spent on executing an action. The neural network model took only approximately 1 millisecond to make a decision. In the simulator, the mobile robot's state was represented by its pose \((x(t),\ y(t),\ \theta(t))\). Hence, the neural network performed real-time computation to choose a motion type based on acquired data, and a new state was obtained after executing an action. Connecting the coordinates of all occasions, a path from the starting point to the destination point was formed. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{5}{c}{**Consumed Time (s)**} \\  & \(a_{1}\) & \(a_{2}\) & \(a_{3}\) & \(a_{4}\) & \(a_{5}\) & \(a_{6}\) & \(Average\) \\ \hline
1 & 0.00123 & 0.00100 & 0.00100 & 0.00100  
The paths of the mobile robot in some exemplary cases are shown in Figure 8. The results demonstrate the appealing properties of the neural network based navigation method proposed in this paper, in that the mobile robot could arrive at the destination without colliding with any obstacles. The navigation performance in other cases was similar to those in Figure 8. Note that all the robot knows at a certain position is sensor information, so that it has no ability to make the optimal decision as in other global planning methods. However, compared with other approaches, the proposed method did not consume high computing resources to obtain the global environment information and was capable of responding to dynamic changes in time. As shown in Figure 8a,c,d, although the path is not the shortest, the robot safely moved from the starting point to the destination position through its own adjustment ability. The neural network was employed to replicate human behavior, but the planned paths shown in Figure 8 seemed not to conform to human thinking in theory. This is mainly due to two reasons: on the one hand, people usually combine the entire scene map to judge the integral path from a global perspective. However, when the information available to humans is reduced to a local area, the decision made is similar to the neural network. On the other hand, humans utilize the brain's memory to assist in decision making, which is unavailable to the neural network proposed in this paper. This limitation may cause the robot to spin around in a certain area. Note that the spinning of the robot as shown in Figure 8c is a local optimum caused by the proposed method.