## 1 Introduction  
Many studies [1; 2; 3; 4] are proposed where the robot is suitable for feeding and monitoring livestock in the barn environment. When a mobile robot feeds the cattle, there is a problem with the cow sticking their head out of the fence for eating and colliding with the end effector of the manipulator. In order to solve the collision problem, the K-Nearest Neighbor method [5] was used to cluster point cloud data to detect obstacles. The depth space method [6; 7] was defined to find the obstacle in depth space and cartesian space. Obstacles were constructed with octree structures [8] to find a safe space. The ANN method [9; 10] was modeled as an adaptive neural network for predicting penetration rate and rock tensile strength. Recently, a Convolutional Neural Network (CNN) algorithm [11; 12; 13; 14; 15; 16] using image data for object classification was proposed. In the proposed method [11], the neural network shows the feature of image data using gradient descent for optimizing. As one of the deep neural network models, Alex Net [12] is a network that is deeply constructed and extracts not only simple features but also high-level features to enhance the performance of the object classification. In the VGG Net [13], it uses a filter size that is smaller than Alex Net and an increased depth layer to enhance the performance. When deeper networks are optimized, there is a degradation problem that the neural network is not efficiently learned by training data. ResNet [14] addresses the degradation problem used for the residual learning method. A pheromone convolutional method [15] is used as discrete gaussian distribution to generate the efficient network path in a topological network. In PSI-CNN [16], it extractsan untrained feature map from various image resolutions. The untrained feature map is used to fuse the original feature map. PSI-CNN shows stable performance when tested on low-resolution images acquired from CCTV cameras. Unlike images that are regularized pixel, the 3D point cloud is unordered data. These characteristics occur as invariant permutation problems when point cloud data is applied to the Convolutional Neural Network. Some references [17; 18; 19; 20] were proposed for the Convolutional Neural Network (CNN) using a 3d point cloud. In PointNet [21], an invariant problem is solved by a symmetric function formulated multi-layer perceptron (MLP) and a max pooling function. As the end-to-end deep neural network, PointNet is directly learned by point cloud, which segmented the features of 3d objects and demonstrated high performance in classifications. PointNet++ [22] is able to learn hierarchical features with increasing scales of contexts. The network of PointNet++ deals with non-uniform densities by using density adaptive strategy. In Reference [23], sparsity of point cloud was utilized by using sliding window detection with linear classifiers and a feature-centric voting method. Vote3 deep [24] is able to efficiently learn a 3d feature by a sparse convolutional layer, which is based on the voting scheme. VoxNet [25] is learned by three types of the occupancy grid maps [26; 27]. Learned network shows robust performance by a grid map, which is modeled by binary, hit, and density grid maps used for 3d point cloud from lidar or the RGBD camera. As the end-to-end learning network, proposed VoxelNet [28] extracts the 3D bounding box using 4-dimensional tensor and RGB data. It is based on a Region Proposal Network, a Convolutional Middle Layer, a Feature Learning Network, and a Voxel Feature Encoding (VFE) scheme. In this paper, the Collision Grid Map (CGM) method is proposed by using 3D data to predict collision between the cow and the end effector of the manipulator in a barn environment. In a conventional method [25], the network is learned by three types of voxel mentioned above. However, in this paper, the Collision Grid Map is used and composed of a two-channel without any voxel. Each cell in the first channel is computed by distribution of location data in the x-y plane.