## 3 Experimental Results
### Convolutional Neural Network Algorithm Using the Collision Grid Map  
A non-collision situation is defined when there is a fence only without any cow and in the case of the collision situation when cows stick their head out of the fence. A Convolutional Neural Network architecture using a Collision Grid Map consists of a convolutional layer, a pooling layer, and a fully connected layer. Figure 8 shows a block diagram of the network architecture. The convolutional layer is 3 * 3 in size and uses a Rectified Linear Unit (ReLu) activation function. The pooling layer is 2 * 2 in size and uses a _max_ function. A dully connected layer has 1024 neurons. Then the Adam optimizer [29] is used for optimization.  
Figure 9 shows visualization of the convolutional layer that is learned as a Collision Grid Map. The first convolutional layer is 3 * 3 in size and has 20 filters. In addition, the second convolutional layer is 3 * 3 in size and has 20 * 40 filters.  
\begin{table}
\begin{tabular}{c c} \hline
**Data** & **Size (KB)** \\ \hline Raw point cloud & 4508.9 \\ Vox grid data & 8.0 \\ Collision Grid Map & 5.7 \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of data size by types.  
Figure 8: Block diagram of the network architecture.  
Figure 9: Visualization of the convolutional layer that is a learned Collision Grid Map.  
The learned filter is able to detect the local features, when the Collision Grid Map is put in the neural network. The appearance of the filtered Collision Grid Map is shown in Figures 10 and 11. Figure 10 is an example of the collision situation. Similarly, Figure 11 is an example of the non-collision situation. The Collision Grid Map that is filtered by the first convolutional layer is shown in a filtered Collision Grid Map1. In addition, the Collision Grid Map that is filtered by a second convolutional layer is shown in a filtered Collision Grid Map2. The first convolutional layer is applied to the Collision Grid Map and the reacted edges are extracted from filtered collision grid map1. In the second convolutional layer, the network reacts as the distance, according to depth data as well as edges.  
The graph for comparison of accuracy for VoxNet and Convolutional Neural Network using Collision Grid Map is shown in Figure 12 and Table 2. The accuracy is measured with a test set of collision and non-collision situations. Accuracy for Convolutional Neural Network using the Collision Grid Map is measured 19.2% higher than VoxNet.  
Figure 11: Appearance of the Filtered Collision Grid Map about the non-collision situation.  
Figure 10: Appearance of the Filtered Collision Grid Map about the collision situation.  
Figure 13 shows the accuracy of detecting each situation according to the method. The accuracy of each situation is the failure that the end effector may collide with a cow when the cow sticks its head out and collides with the robot. When the cow actually sticks its head out, the Convolutional Neural Network using the Collision Grid Map is measured 92.7% whether or not the robot can classify the situation that the cow really sticks its head out. Voxnet is measured 5.4% less accurately than the Convolutional Neural Network using a Collision Grid Map method.